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Title:
METHOD AND DEVICE FOR DETERMINING ADJUSTMENTS TO SENSITIVITY PARAMETERS
Document Type and Number:
WIPO Patent Application WO/2019/129485
Kind Code:
A1
Abstract:
A method is described herein including applying, by a metrology apparatus, an incident radiation beam to a substrate including first features on a first layer and second features on a second layer, a relationship between the first and second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting; receiving intensity data representing intensity of a portion of the incident radiation beam scattered by the first and second features; determining, based on the intensity data, a second value of the parameter of interest; and applying one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a difference between the first value and the second value.

Inventors:
KICKEN, Harm, Hubertus, Joseph, Elizabeth (P.O. BOX 324, 5500AH Veldhoven, 5500AH, NL)
ZAAL, Martijn, Maria (P.O. Box 324, 5500 AH Veldhoven, 5500 AH, NL)
Application Number:
EP2018/084345
Publication Date:
July 04, 2019
Filing Date:
December 11, 2018
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
ASML NETHERLANDS B.V. (P.O. Box 324, 5500 AH Veldhoven, 5500 AH, NL)
International Classes:
G03F7/20; G01N21/47
Domestic Patent References:
WO2009078708A12009-06-25
WO2009106279A12009-09-03
Foreign References:
US20170017162A12017-01-19
US20120242970A12012-09-27
US20030187840A12003-10-02
US20110027704A12011-02-03
US20110043791A12011-02-24
US20120242970A12012-09-27
US20060066855A12006-03-30
US20060033921A12006-02-16
US20100201963A12010-08-12
Attorney, Agent or Firm:
BROEKEN, Petrus (P.O. Box 324, 5500 AH Veldhoven, 5500 AH, NL)
Download PDF:
Claims:
CLAIMS 1. A method, comprising:

applying, by a metrology apparatus, an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting;

receiving first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features;

determining, based on the first intensity data, a second value of the parameter of interest for the first substrate; and

applying one or more adjustments to the at least one characteristic such that the at least one characteristic has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

2. The method of claim 1, further comprising:

applying the incident radiation beam to a second substrate comprising third features on a third layer and fourth features on a fourth layer, a second relationship between the third features and the fourth features being characterized by the parameter of interest having a third value, wherein the metrology apparatus is operated in accordance with the at least one characteristic having the second setting;

receiving second intensity data representing second intensity of a second portion of the incident radiation beam scattered by the third features and the fourth features;

determining, based on the second intensity data, a fourth value of the parameter of interest for the second substrate; and

determining a second difference between the third value of the parameter of interest and the fourth value of the parameter of interest.

3. The method of claim 2, further comprising:

determining, based on the second difference being less than a threshold value, that the metrology apparatus is calibrated for the at least characteristic having the second setting.

4. The method of claim 2, further comprising:

performing an additional calibration for the metrology apparatus by modifying the second setting at least one characteristic in response to determining that the second difference is equal to or greater than a threshold value.

5. The method of claim 1, wherein determining the second value of the parameter of interest comprises:

obtaining an intensity model that indicates an expected intensity distribution for the metrology apparatus for the at least one characteristic having the first setting;

identifying one or more components of the intensity model associated with the first features of the first layer and the second features of the second layer; and

determining the second value of the parameter of interest by calculating a second difference between the expected intensity distribution and the first intensity data based on the one or more components.

6. The method of claim 5, wherein the one or more components of the intensity model relate to a pupil point of the metrology apparatus and a feature position.

7. The method of claim 1, further comprising:

updating an intensity model indicating an expected intensity distribution for the metrology apparatus such that the intensity model reflects the at least one characteristic having the second setting.

8. A metrology apparatus, comprising:

memory; and

at least one processor operable to:

apply an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting;

receive first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features;

determine, based on the first intensity data, a second value of the parameter of interest for the first substrate; and

apply one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

9. The metrology apparatus of claim 8, wherein the at least one processor is further operable to:

apply the incident radiation beam to a second substrate comprising third features on a third layer and fourth features on a fourth layer, a second relationship between the third features and the fourth features being characterized by the parameter of interest having a third value, wherein the metrology apparatus is operated in accordance with the at least one characteristic having the second setting;

receive second intensity data representing second intensity of a second portion of the incident radiation beam scattered by the third features and the fourth features;

determine, based on the second intensity data, a fourth value of the parameter of interest for the second substrate; and

determine a second difference between the third value of the parameter of interest and the fourth value of the parameter of interest.

10. The metrology apparatus of claim 9, wherein the at least one processor is further operable to:

determine, based on the second difference being less than a threshold value, that the metrology apparatus is calibrated for the at least characteristic having the second setting.

11. The metrology apparatus of claim 9, wherein the at least one processor is further operable to:

perform an additional calibration for the metrology apparatus by modifying the second setting at least one characteristic in response to determining that the second difference is equal to or greater than a threshold value.

12. The metrology apparatus of claim 8, wherein the second value of the parameter of interest being determined corresponds to the at least one processor being operable to:

obtain an intensity model that indicates an expected intensity distribution for the metrology apparatus for the at least one characteristic having the first setting;

identify one or more components of the intensity model associated with the first features of the first layer and the second features of the second layer; and

determine the second value of the parameter of interest by calculating a second difference between the expected intensity distribution and the first intensity data based on the one or more components.

13. The metrology apparatus of claim 12, wherein the one or more components of the intensity model relate to a pupil point of the metrology apparatus and a feature position.

14. The metrology apparatus of claim 8, wherein the at least one processor is further operable to:

update, stored in the memory, an intensity model indicating an expected intensity distribution for the metrology apparatus such that the intensity model reflects the at least one characteristic having the second setting.

15. A non-transitory computer readable medium comprising instructions that, when executed by at least one processor of a computing device, causes the computing device to:

apply, by a metrology apparatus, an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting;

receive first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features;

determine, based on the first intensity data, a second value of the parameter of interest for the first substrate; and

apply one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

Description:
METHOD AND DEVICE FOR DETERMINING ADJUSTMENTS TO SENSITIVITY

PARAMETERS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 62/612,058 which was filed on December 29, 2017 and which is incorporated herein in its entirety by reference. FIELD

[0002] The present description relates to a method and apparatus to determine adjustments to characteristics of a metrology apparatus based on a parameter (such as overlay) of a process. BACKGROUND

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs) or other devices designed to be functional. In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the device designed to be functional. This pattern can be transferred onto a target portion (e.g., including part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the“scanning”-direction) while synchronously scanning the substrate parallel or anti parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate. SUMMARY

[0004] Manufacturing devices, such as semiconductor devices, typically involves processing a substrate (e.g., a semiconductor wafer) using a number of fabrication processes to form various features and often multiple layers of the devices. Such layers and/or features are typically manufactured and processed using, e.g., deposition, lithography, etch, chemical-mechanical polishing, and ion implantation. Multiple devices may be fabricated on a plurality of dies on a substrate and then separated into individual devices. This device manufacturing process may be considered a patterning process. A patterning process involves a pattern transfer step, such as optical and/or nanoimprint lithography using a lithographic apparatus, to provide a pattern on a substrate and typically, but optionally, involves one or more related pattern processing steps, such as resist development by a development apparatus, baking of the substrate using a bake tool, etching the pattern by an etch apparatus, etc., Further, one or more metrology processes are involved in the patterning process.

[0005] Metrology processes are used at various steps during a patterning process to monitor and/or control the process. For example, metrology processes are used to measure one or more characteristics of a substrate, such as a relative location (e.g., registration, overlay, alignment, etc.) or dimension (e.g., line width, critical dimension (CD), thickness, etc.) of features formed on the substrate during the patterning process, such that, for example, the performance of the patterning process can be determined from the one or more characteristics. If the one or more characteristics are unacceptable (e.g., out of a predetermined range for the characteristic(s)), one or more variables of the patterning process may be designed or altered, e.g., based on the measurements of the one or more characteristics, such that substrates manufactured by the patterning process have an acceptable characteristic(s).

[0006] With the advancement of lithography and other patterning process technologies, the dimensions of functional elements have continually been reduced while the amount of the functional elements, such as transistors, per device has been steadily increased over decades. In the meanwhile, the requirement of accuracy in terms of overlay, critical dimension (CD), etc., has become more and more stringent. Error, such as error in overlay, error in CD, etc., will inevitably be produced in the patterning process. For example, imaging error may be produced from optical aberration, patterning device heating, patterning device error, and/or substrate heating and can be characterized in terms of, e.g., overlay, CD, etc., Additionally or alternatively, error may be introduced in other parts of the patterning process, such as in etch, development, bake, etc., and similarly can be characterized in terms of, e.g., overlay, CD, etc., The error may cause a problem in terms of the functioning of the device, including failure of the device to function or one or more electrical problems of the functioning device. Accordingly, it is desirable to be able to characterize one or more these errors and take steps to design, modify, control, etc., a patterning process to reduce or minimize one or more of these errors.

[0007] In an embodiment, there is provided a method including: applying, by a metrology apparatus, an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting; receiving first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features; determining, based on the first intensity data, a second value of the parameter of interest for the first substrate; and applying one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

[0008] In an embodiment, there is provided a metrology apparatus including: memory and at least one processor. The at least one processor is operable to: apply an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting; receive first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features; determine, based on the first intensity data, a second value of the parameter of interest for the first substrate; and apply one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

[0009] In an embodiment, there is provided a non-transitory computer readable medium including instructions that, when executed by at least one processor of a computing device, causes the computing device to: apply, by a metrology apparatus, an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting; receive first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features; determine, based on the first intensity data, a second value of the parameter of interest for the first substrate; and apply one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Embodiments will now be described, by way of example only, with reference to the accompanying drawings in which: [0011] Figure 1 schematically depicts an embodiment of a lithographic apparatus;

[0012] Figure 2 schematically depicts an embodiment of a lithographic cell or cluster;

[0013] Figure 3A is schematic diagram of a measurement apparatus for use in measuring targets according to an embodiment using a first pair of illumination apertures providing certain illumination modes;

[0014] Figure 3B is a schematic detail of a diffraction spectrum of a target for a given direction of illumination;

[0015] Figure 3C is a schematic illustration of a second pair of illumination apertures providing further illumination modes in using a measurement apparatus for diffraction based overlay measurements;

[0016] Figure 3D is a schematic illustration of a third pair of illumination apertures combining the first and second pairs of apertures providing further illumination modes in using a measurement apparatus for diffraction based overlay measurements;

[0017] Figure 4 schematically depicts a form of multiple periodic structure (e.g., multiple grating) target and an outline of a measurement spot on a substrate;

[0018] Figure 5 schematically depicts an image of the target of Figure 4 obtained in the apparatus of Figure 3;

[0019] Figure 6 schematically depicts an example metrology apparatus and metrology technique;

[0020] Figure 7 schematically depicts an example metrology apparatus;

[0021] Figure 8 illustrates the relationship between an illumination spot of a metrology apparatus and a metrology target;

[0022] Figure 9 schematically depicts a process of deriving one or more variables of interest based on measurement data;

[0023] Figure 10A schematically depicts an example unit cell, an associated pupil representation, and an associated derived pupil representation;

[0024] Figure 10B schematically depicts an example unit cell, an associated pupil representation, and an associated derived pupil representation;

[0025] Figure 10C schematically depicts an example target comprising one or more physical instances of a unit cell;

[0026] Figure 11 depicts a high-level flow of obtaining weightings for determining a patterning process parameter from measured radiation;

[0027] Figure 12 depicts a high-level flow of determining a patterning process parameter from measured radiation; [0028] Figure 13 depicts a high-level flow of an embodiment of a data driven technique;

[0029] Figure 14 depicts a high-level flow of an embodiment of a data driven technique in combination with a physical geometric model;

[0030] Figure 15 depicts a high-level flow of an embodiment of a data driven technique in combination with a physical geometric model;

[0031] Figure 16 depicts a high-level flow of an embodiment of a data driven technique in combination with a physical geometric model;

[0032] Figure 17 depicts a high-level flow of an embodiment of a data driven technique in combination with a physical geometric model;

[0033] Figure 18 schematically depicts an embodiment of a multiple overlay unit cell of a target;

[0034] Figure 19 schematically depicts an embodiment of a multiple overlay unit cell of a target;

[0035] Figure 20 depicts an example graph of two vectors corresponding to two different overlays;

[0036] Figure 21 is an illustrative diagram of an overlay between two layers of a substrate, in accordance with various embodiments;

[0037] Figure 22 is an illustrative diagram of an exemplary substrate include a predicted amount of overlay between layers of the substrate, in accordance with various embodiments;

[0038] Figure 23 is an illustrative flow chart of an exemplary process for determining an adjustment to one or more characteristics of a metrology apparatus, in accordance with various embodiments; and

[0039] Figure 24 schematically depicts a computer system that may implement embodiments of this disclosure. DETAILED DESCRIPTION

[0040] Before describing embodiments in detail, it is instructive to present an example environment in which embodiments may be implemented.

[0041] Figure 1 schematically depicts a lithographic apparatus LA. The apparatus comprises:

- an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or DUV radiation);

- a support structure (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters;

- a substrate table (e.g., a wafer table) WT constructed to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate in accordance with certain parameters; and

- a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W, the projection system supported on a reference frame (RF).

[0042] The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation.

[0043] The support structure supports the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be a frame or a table, for example, which may be fixed or movable as required. The support structure may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms“reticle” or“mask” herein may be considered synonymous with the more general term“patterning device.”

[0044] The term“patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a pattern in a target portion of the substrate. In an embodiment, a patterning device is any device that can be used to impart a radiation beam with a pattern in its cross-section to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

[0045] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in a radiation beam, which is reflected by the mirror matrix.

[0046] The term“projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the more general term“projection system”.

[0047] The projection system PS has an optical transfer function that may be non-uniform, which can affect the pattern imaged on the substrate W. For unpolarized radiation, such effects can be fairly well described by two scalar maps, which describe the transmission (apodization) and relative phase (aberration) of radiation exiting the projection system PS as a function of position in a pupil plane thereof. These scalar maps, which may be referred to as the transmission map and the relative phase map, may be expressed as a linear combination of a complete set of basis functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials defined on a unit circle. A determination of each scalar map may involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients may be determined by calculating the inner product of a measured scalar map with each Zernike polynomial in turn and dividing this by the square of the norm of that Zernike polynomial.

[0048] The transmission map and the relative phase map are field and system dependent. That is, in general, each projection system PS will have a different Zernike expansion for each field point (i.e., for each spatial location in its image plane). The relative phase of the projection system PS in its pupil plane may be determined by projecting radiation, for example from a point-like source in an object plane of the projection system PS (i.e., the plane of the patterning device MA), through the projection system PS and using a shearing interferometer to measure a wavefront (i.e., a locus of points with the same phase). A shearing interferometer is a common path interferometer and therefore, advantageously, no secondary reference beam is required to measure the wavefront. The shearing interferometer may comprise a diffraction grating, for example a two dimensional grid, in an image plane of the projection system (i.e., the substrate table WT) and a detector arranged to detect an interference pattern in a plane that is conjugate to a pupil plane of the projection system PS. The interference pattern is related to the derivative of the phase of the radiation with respect to a coordinate in the pupil plane in the shearing direction. The detector may comprise an array of sensing elements such as, for example, charge coupled devices (CCDs).

[0049] The projection system PS of a lithography apparatus may not produce visible fringes and therefore the accuracy of the determination of the wavefront can be enhanced using phase stepping techniques such as, for example, moving the diffraction grating. Stepping may be performed in the plane of the diffraction grating and in a direction perpendicular to the scanning direction of the measurement. The stepping range may be one grating period, and at least three (uniformly distributed) phase steps may be used. Thus, for example, three scanning measurements may be performed in the y-direction, each scanning measurement being performed for a different position in the x-direction. This stepping of the diffraction grating effectively transforms phase variations into intensity variations, allowing phase information to be determined. The grating may be stepped in a direction perpendicular to the diffraction grating (z direction) to calibrate the detector.

[0050] The transmission (apodization) of the projection system PS in its pupil plane may be determined by projecting radiation, for example from a point-like source in an object plane of the projection system PS (i.e., the plane of the patterning device MA), through the projection system PS and measuring the intensity of radiation in a plane that is conjugate to a pupil plane of the projection system PS, using a detector. The same detector as is used to measure the wavefront to determine aberrations may be used.

[0051] The projection system PS may comprise a plurality of optical (e.g., lens) elements and may further comprise an adjustment mechanism AM configured to adjust one or more of the optical elements to correct for aberrations (phase variations across the pupil plane throughout the field). To achieve this, the adjustment mechanism may be operable to manipulate one or more optical (e.g., lens) elements within the projection system PS in one or more different ways. The projection system may have a co-ordinate system wherein its optical axis extends in the z direction. The adjustment mechanism may be operable to do any combination of the following: displace one or more optical elements; tilt one or more optical elements; and/or deform one or more optical elements. Displacement of an optical element may be in any direction (x, y, z or a combination thereof). Tilting of an optical element is typically out of a plane perpendicular to the optical axis, by rotating about an axis in the x and/or y directions although a rotation about the z-axis may be used for a non-rotationally symmetric aspherical optical element. Deformation of an optical element may include a low frequency shape (e.g., astigmatic) and/or a high frequency shape (e.g., free form aspheres). Deformation of an optical element may be performed for example by using one or more actuators to exert force on one or more sides of the optical element and/or by using one or more heating elements to heat one or more selected regions of the optical element. In general, it may not be possible to adjust the projection system PS to correct for apodization (transmission variation across the pupil plane). The transmission map of a projection system PS may be used when designing a patterning device (e.g., mask) MA for the lithography apparatus LA. Using a computational lithography technique, the patterning device MA may be designed to at least partially correct for apodization.

[0052] As here depicted, the apparatus is of a transmissive type (e.g., employing a transmissive mask). Alternatively, the apparatus may be of a reflective type (e.g., employing a programmable mirror array of a type as referred to above, or employing a reflective mask).

[0053] The lithographic apparatus may be of a type having two (dual stage) or more tables (e.g., two or more substrate tables WTa, WTb, two or more patterning device tables, a substrate table WTa and a table WTb below the projection system without a substrate that is dedicated to, for example, facilitating measurement, and/or cleaning, etc.). In such“multiple stage” machines, the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure. For example, alignment measurements using an alignment sensor AS and/or level (height, tilt, etc.) measurements using a level sensor LS may be made.

[0054] The lithographic apparatus may also be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g., water, to fill a space between the projection system and the substrate. An immersion liquid may also be applied to other spaces in the lithographic apparatus, for example, between the patterning device and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. The term “immersion” as used herein does not mean that a structure, such as a substrate, must be submerged in liquid, but rather only means that liquid is located between the projection system and the substrate during exposure.

[0055] Referring to Figure 1, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD comprising, for example, suitable directing mirrors and/or a beam expander. In other cases the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[0056] The illuminator IL may comprise an adjuster AD configured to adjust the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as s-outer and s-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as an integrator IN and a condenser CO. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross-section.

[0057] The radiation beam B is incident on the patterning device (e.g., mask) MA, which is held on the support structure (e.g., mask table) MT, and is patterned by the patterning device. Having traversed the patterning device MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor IF (e.g., an interferometric device, linear encoder, 2-D encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor (which is not explicitly depicted in Figure 1) can be used to accurately position the patterning device MA with respect to the path of the radiation beam B, e.g., after mechanical retrieval from a mask library, or during a scan. In general, movement of the support structure MT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT may be realized using a long-stroke module and a short- stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner), the support structure MT may be connected to a short-stroke actuator only, or may be fixed. Patterning device MA and substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe- lane alignment marks). Similarly, in situations in which more than one die is provided on the patterning device MA, the patterning device alignment marks may be located between the dies.

[0058] The depicted apparatus could be used in at least one of the following modes:

1. In step mode, the support structure MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e., a single static exposure). The substrate table WT is then shifted in the X and/or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

2. In scan mode, the support structure MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e., a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non- scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion.

3. In another mode, the support structure MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally, a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above.

[0059] Combinations and/or variations on the above-described modes of use or entirely different modes of use may also be employed.

[0060] As shown in Figure 2, the lithographic apparatus LA may form part of a lithographic cell LC, also sometimes referred to a lithocell or cluster, which also includes apparatuses to perform pre- and post- exposure processes on a substrate. Conventionally these include one or more spin coaters SC to deposit one or more resist layers, one or more developers DE to develop exposed resist, one or more chill plates CH and/or one or more bake plates BK. A substrate handler, or robot, RO picks up one or more substrates from input/output port I/O1, I/O2, moves them between the different process apparatuses and delivers them to the loading bay LB of the lithographic apparatus. These apparatuses, which are often collectively referred to as the track, are under the control of a track control unit TCU which is itself controlled by the supervisory control system SCS, which also controls the lithographic apparatus via lithography control unit LACU. Thus, the different apparatuses can be operated to maximize throughput and processing efficiency.

[0061] In order that a substrate that is exposed by the lithographic apparatus is exposed correctly and consistently, it is desirable to inspect an exposed substrate to measure or determine one or more properties such as overlay (which can be, for example, between structures in overlying layers or between structures in a same layer that have been provided separately to the layer by, for example, a double patterning process), line thickness, critical dimension (CD), focus offset, a material property, etc., Accordingly a manufacturing facility in which lithocell LC is located also typically includes a metrology system MET which receives some or all of the substrates W that have been processed in the lithocell. The metrology system MET may be part of the lithocell LC, for example it may be part of the lithographic apparatus LA.

[0062] Metrology results may be provided directly or indirectly to the supervisory control system SCS. If an error is detected, an adjustment may be made to exposure of a subsequent substrate (especially if the inspection can be done soon and fast enough that one or more other substrates of the batch are still to be exposed) and/or to subsequent exposure of the exposed substrate. Also, an already exposed substrate may be stripped and reworked to improve yield, or discarded, thereby avoiding performing further processing on a substrate known to be faulty. In a case where only some target portions of a substrate are faulty, further exposures may be performed only on those target portions that are good.

[0063] Within a metrology system MET, a metrology apparatus is used to determine one or more properties of the substrate, and in particular, how one or more properties of different substrates vary or different layers of the same substrate vary from layer to layer. The metrology apparatus may be integrated into the lithographic apparatus LA or the lithocell LC or may be a stand-alone device. To enable rapid measurement, it is desirable that the metrology apparatus measure one or more properties in the exposed resist layer immediately after the exposure. However, the latent image in the resist has a low contrast– there is only a very small difference in refractive index between the parts of the resist that have been exposed to radiation and those that have not– and not all metrology apparatus have sufficient sensitivity to make useful measurements of the latent image. Therefore measurements may be taken after the post-exposure bake step (PEB) which is customarily the first step carried out on an exposed substrate and increases the contrast between exposed and unexposed parts of the resist. At this stage, the image in the resist may be referred to as semi-latent. It is also possible to make measurements of the developed resist image– at which point either the exposed or unexposed parts of the resist have been removed– or after a pattern transfer step such as etching. The latter possibility limits the possibilities for rework of a faulty substrate but may still provide useful information.

[0064] To enable the metrology, one or more targets can be provided on the substrate. In an embodiment, the target is specially designed and may comprise a periodic structure. In an embodiment, the target is a part of a device pattern, e.g., a periodic structure of the device pattern. In an embodiment, the device pattern is a periodic structure of a memory device (e.g., a Bipolar Transistor (BPT), a Bit Line Contact (BLC), etc., structure).

[0065] In an embodiment, the target on a substrate may comprise one or more 1-D periodic structures (e.g., gratings), which are printed such that after development, the periodic structural features are formed of solid resist lines. In an embodiment, the target may comprise one or more 2-D periodic structures (e.g., gratings), which are printed such that after development, the one or more periodic structures are formed of solid resist pillars or vias in the resist. The bars, pillars or vias may alternatively be etched into the substrate (e.g., into one or more layers on the substrate).

[0066] In an embodiment, one of the parameters of interest of a patterning process is overlay. Overlay can be measured using dark field scatterometry in which the zeroth order of diffraction (corresponding to a specular reflection) is blocked, and only higher orders processed. Examples of dark field metrology can be found in PCT patent application publication nos. WO 2009/078708 and WO 2009/106279, which are hereby incorporated in their entirety by reference. Further developments of the technique have been described in U.S. patent application publications US2011-0027704, US2011-0043791 and US2012- 0242970, which are hereby incorporated in their entirety by reference. Diffraction-based overlay using dark-field detection of the diffraction orders enables overlay measurements on smaller targets. These targets can be smaller than the illumination spot and may be surrounded by device product structures on a substrate. In an embodiment, multiple targets can be measured in one radiation capture.

[0067] A metrology apparatus suitable for use in embodiments to measure, e.g., overlay is schematically shown in Figure 3A. A target T (comprising a periodic structure such as a grating) and diffracted rays are illustrated in more detail in Figure 3B. The metrology apparatus may be a stand-alone device or incorporated in either the lithographic apparatus LA, e.g., at the measurement station, or the lithographic cell LC. An optical axis, which has several branches throughout the apparatus, is represented by a dotted line O. In this apparatus, radiation emitted by an output 11 (e.g., a source such as a laser or a xenon lamp or an opening connected to a source) is directed onto substrate W via a prism 15 by an optical system comprising lenses 12, 14 and objective lens 16. These lenses are arranged in a double sequence of a 4F arrangement. A different lens arrangement can be used, provided that it still provides a substrate image onto a detector.

[0068] In an embodiment, the lens arrangement allows for access of an intermediate pupil-plane for spatial-frequency filtering. Therefore, the angular range at which the radiation is incident on the substrate can be selected by defining a spatial intensity distribution in a plane that presents the spatial spectrum of the substrate plane, here referred to as a (conjugate) pupil plane. In particular, this can be done, for example, by inserting an aperture plate 13 of suitable form between lenses 12 and 14, in a plane, which is a back- projected image of the objective lens pupil plane. In the example illustrated, aperture plate 13 has different forms, labeled 13N and 13S, allowing different illumination modes to be selected. The illumination system in the present examples forms an off-axis illumination mode. In the first illumination mode, aperture plate 13N provides off-axis illumination from a direction designated, for the sake of description only, as‘north’. In a second illumination mode, aperture plate 13S is used to provide similar illumination, but from an opposite direction, labeled‘south’. Other modes of illumination are possible by using different apertures. The rest of the pupil plane is desirably dark as any unnecessary radiation outside the desired illumination mode may interfere with the desired measurement signals.

[0069] As shown in Figure 3B, target T is placed with substrate W substantially normal to the optical axis O of objective lens 16. A ray of illumination I impinging on target T from an angle off the axis O gives rise to a zeroth order ray (solid line 0) and two first order rays (dot-chain line +1 and double dot-chain line -1). With an overfilled small target T, these rays are just one of many parallel rays covering the area of the substrate including metrology target T and other features. Since the aperture in plate 13 has a finite width (necessary to admit a useful quantity of radiation), the incident rays I will in fact occupy a range of angles, and the diffracted rays 0 and +1/-1 will be spread out somewhat. According to the point spread function of a small target, each order +1 and -1 will be further spread over a range of angles, not a single ideal ray as shown. Note that the periodic structure pitch and illumination angle can be designed or adjusted so that the first order rays entering the objective lens are closely aligned with the central optical axis. The rays illustrated in Figures 3A and 3B are shown somewhat off axis, purely to enable them to be more easily distinguished in the diagram. At least the 0 and +1 orders diffracted by the target on substrate W are collected by objective lens 16 and directed back through prism 15.

[0070] Returning to Figure 3A, both the first and second illumination modes are illustrated, by designating diametrically opposite apertures labeled as north (N) and south (S). When the incident ray I is from the north side of the optical axis, that is when the first illumination mode is applied using aperture plate 13N, the +1 diffracted rays, which are labeled +1(N), enter the objective lens 16. In contrast, when the second illumination mode is applied using aperture plate 13S the -1 diffracted rays (labeled -1(S)) are the ones that enter the lens 16. Thus, in an embodiment, measurement results are obtained by measuring the target twice under certain conditions, e.g., after rotating the target or changing the illumination mode or changing the imaging mode to obtain separately the -1st and the +1st diffraction order intensities. Comparing these intensities for a given target provides a measurement of asymmetry in the target, and asymmetry in the target can be used as an indicator of a parameter of a lithography process, e.g., overlay. In the situation described above, the illumination mode is changed.

[0071] A beam splitter 17 divides the diffracted beams into two measurement branches. In a first measurement branch, optical system 18 forms a diffraction spectrum (pupil plane image) of the target on first sensor 19 (e.g., a CCD or CMOS sensor) using the zeroth and first order diffractive beams. Each diffraction order hits a different point on the sensor, so that image processing can compare and contrast orders. The pupil plane image captured by sensor 19 can be used for focusing the metrology apparatus and/or normalizing intensity measurements. The pupil plane image can also be used for other measurement purposes such as reconstruction, as described further hereafter.

[0072] In the second measurement branch, optical system 20, 22 forms an image of the target on the substrate W on sensor 23 (e.g., a CCD or CMOS sensor). In the second measurement branch, an aperture stop 21 is provided in a plane that is conjugate to the pupil-plane of the objective lens 16. Aperture stop 21 functions to block the zeroth order diffracted beam so that the image of the target formed on sensor 23 is formed from the -1 or +1 first order beam. Data regarding the images measured by sensors 19 and 23 are output to processor and controller PU, the function of which will depend on the particular type of measurements being performed. Note that the term‘image’ is used in a broad sense. An image of the periodic structure features (e.g., grating lines) as such will not be formed, if only one of the -1 and +1 orders is present.

[0073] The particular forms of aperture plate 13 and stop 21 shown in Figure 3 are purely examples. In another embodiment, on-axis illumination of the targets is used and an aperture stop with an off-axis aperture is used to pass substantially only one first order of diffracted radiation to the sensor. In yet other embodiments, 2nd, 3rd and higher order beams (not shown in Figure 3) can be used in measurements, instead of or in addition to the first order beams.

[0074] In order to make the illumination adaptable to these different types of measurement, the aperture plate 13 may comprise a number of aperture patterns formed around a disc, which rotates to bring a desired pattern into place. Note that aperture plate 13N or 13S are used to measure a periodic structure of a target oriented in one direction (X or Y depending on the set-up). For measurement of an orthogonal periodic structure, rotation of the target through 90° and 270° might be implemented. Different aperture plates are shown in Figures 3C and D. Figure 3C illustrates two further types of off-axis illumination mode. In a first illumination mode of Figure 3C, aperture plate 13E provides off-axis illumination from a direction designated, for the sake of description only, as‘east’ relative to the‘north’ previously described. In a second illumination mode of Figure 3C, aperture plate 13W is used to provide similar illumination, but from an opposite direction, labeled‘west’. Figure 3D illustrates two further types of off-axis illumination mode. In a first illumination mode of Figure 3D, aperture plate 13NW provides off-axis illumination from the directions designated‘north’ and‘west’ as previously described. In a second illumination mode, aperture plate 13SE is used to provide similar illumination, but from an opposite direction, labeled‘south’ and‘east’ as previously described. The use of these, and numerous other variations and applications of the apparatus are described in, for example, the prior published patent application publications mentioned above.

[0075] Figure 4 depicts an example composite metrology target T formed on a substrate. The composite target comprises four periodic structures (in this case, gratings) 32, 33, 34, 35 positioned closely together. In an embodiment, the periodic structure layout may be made smaller than the measurement spot (i.e., the periodic structure layout is overfilled). Thus, in an embodiment, the periodic structures are positioned closely together enough so that they all are within a measurement spot 31 formed by the illumination beam of the metrology apparatus. In that case, the four periodic structures thus are all simultaneously illuminated and simultaneously imaged on sensors 19 and 23. In an example dedicated to overlay measurement, periodic structures 32, 33, 34, 35 are themselves composite periodic structures (e.g., composite gratings) formed by overlying periodic structures, i.e., periodic structures are patterned in different layers of the device formed on substrate W and such that at least one periodic structure in one layer overlays at least one periodic structure in a different layer. Such a target may have outer dimensions within 20 µm x 20 µm or within 16 µm x 16 µm. Further, all the periodic structures are used to measure overlay between a particular pair of layers. To facilitate a target being able to measure more than a single pair of layers, periodic structures 32, 33, 34, 35 may have differently biased overlay offsets in order to facilitate measurement of overlay between different layers in which the different parts of the composite periodic structures are formed. Thus, all the periodic structures for the target on the substrate would be used to measure one pair of layers and all the periodic structures for another same target on the substrate would be used to measure another pair of layers, wherein the different bias facilitates distinguishing between the layer pairs. [0076] Returning to Figure 4, periodic structures 32, 33, 34, 35 may also differ in their orientation, as shown, so as to diffract incoming radiation in X and Y directions. In one example, periodic structures 32 and 34 are X-direction periodic structures with biases of +d, -d, respectively. Periodic structures 33 and 35 may be Y-direction periodic structures with offsets +d and–d respectively. While four periodic structures are illustrated, another embodiment may include a larger matrix to obtain desired accuracy. For example, a 3 x 3 array of nine composite periodic structures may have biases -4d, -3d, -2d, -d, 0, +d, +2d, +3d, +4d. Separate images of these periodic structures can be identified in an image captured by sensor 23.

[0077] Figure 5 shows an example of an image that may be formed on and detected by the sensor 23, using the target of Figure 4 in the apparatus of Figure 3, using the aperture plates 13NW or 13SE from Figure 3D. While the sensor 19 cannot resolve the different individual periodic structures 32 to 35, the sensor 23 can do so. The dark rectangle represents the field of the image on the sensor, within which the illuminated spot 31 on the substrate is imaged into a corresponding circular area 41. Within this, rectangular areas 42-45 represent the images of the periodic structures 32 to 35. The target can be positioned in among device product features, rather than or in addition to in a scribe lane. If the periodic structures are located in device product areas, device features may also be visible in the periphery of this image field. Processor and controller PU processes these images using pattern recognition to identify the separate images 42 to 45 of periodic structures 32 to 35. In this way, the images do not have to be aligned very precisely at a specific location within the sensor frame, which greatly improves throughput of the measuring apparatus as a whole.

[0078] Once the separate images of the periodic structures have been identified, the intensities of those individual images can be measured, e.g., by averaging or summing selected pixel intensity values within the identified areas. Intensities and/or other properties of the images can be compared with one another. These results can be combined to measure different parameters of the lithographic process. Overlay performance is an example of such a parameter.

[0079] In an embodiment, one of the parameters of interest of a patterning process is feature width (e.g., CD). Figure 6 depicts a highly schematic example metrology apparatus (e.g., a scatterometer) that can enable feature width determination. It comprises a broadband (white light) radiation projector 2 which projects radiation onto a substrate W. The redirected radiation is passed to a spectrometer detector 4, which measures a spectrum 10 (intensity as a function of wavelength) of the specular reflected radiation, as shown, e.g., in the graph in the lower left. From this data, the structure or profile giving rise to the detected spectrum may be reconstructed by processor PU, e.g., by Rigorous Coupled Wave Analysis and non-linear regression or by comparison with a library of simulated spectra as shown at the bottom right of Figure 6. In general, for the reconstruction, the general form of the structure is known and some variables are assumed from knowledge of the process by which the structure was made, leaving only a few variables of the structure to be determined from the measured data. Such a metrology apparatus may be configured as a normal- incidence metrology apparatus or an oblique-incidence metrology apparatus. Moreover, in addition to measurement of a parameter by reconstruction, angle resolved scatterometry is useful in the measurement of asymmetry of features in product and/or resist patterns. A particular application of asymmetry measurement is for the measurement of overlay, where the target comprises one set of periodic features superimposed on another. The concepts of asymmetry measurement in this manner are described, for example, in U.S. patent application publication US2006-066855, which is incorporated herein in its entirety.

[0080] Figure 7 illustrates an example of a metrology apparatus 100 suitable for use in embodiments of the invention disclosed herein. The principles of operation of this type of metrology apparatus are explained in more detail in the U.S. Patent Application Nos. US 2006-033921 and US 2010-201963, which are incorporated herein in their entireties by reference. An optical axis, which has several branches throughout the apparatus, is represented by a dotted line O. In this apparatus, radiation emitted by source 110 (e.g., a xenon lamp) is directed onto substrate W via by an optical system comprising: lens system 120, aperture plate 130, lens system 140, a partially reflecting surface 150 and objective lens 160. In an embodiment, these lens systems 120, 140, 160 are arranged in a double sequence of a 4F arrangement. In an embodiment, the radiation emitted by radiation source 110 is collimated using lens system 120. A different lens arrangement can be used, if desired. The angular range at which the radiation is incident on the substrate can be selected by defining a spatial intensity distribution in a plane that presents the spatial spectrum of the substrate plane. In particular, this can be done by inserting an aperture plate 130 of suitable form between lenses 120 and 140, in a plane, which is a back-projected image of the objective lens pupil plane. Different intensity distributions (e.g., annular, dipole, etc.) are possible by using different apertures. The angular distribution of illumination in radial and peripheral directions, as well as properties such as wavelength, polarization and/or coherency of the radiation, can all be adjusted to obtain desired results. For example, one or more interference filters 130 (see Figure 9) can be provided between source 110 and partially reflecting surface 150 to select a wavelength of interest in the range of, say, 400 - 900 nm or even lower, such as 200 - 300 nm. The interference filter may be tunable rather than comprising a set of different filters. A grating could be used instead of an interference filter. In an embodiment, one or more polarizers 170 (see Figure 9) can be provided between source 110 and partially reflecting surface 150 to select a polarization of interest. The polarizer may be tunable rather than comprising a set of different polarizers.

[0081] As shown in Figure 7, the target T is placed with substrate W normal to the optical axis O of objective lens 160. Thus, radiation from source 110 is reflected by partially reflecting surface 150 and focused into an illumination spot S (see Figure 8) on target T on substrate W via objective lens 160. In an embodiment, objective lens 160 has a high numerical aperture (NA), desirably at least 0.9 or at least 0.95. An immersion metrology apparatus (using a relatively high refractive index fluid such as water) may even have a numerical aperture over 1.

[0082] Rays of illumination 170, 172 focused to the illumination spot from angles off the axis O gives rise to diffracted rays 174, 176. It should be remembered that these rays are just one of many parallel rays covering an area of the substrate including target T. Each element within the illumination spot is within the field of view of the metrology apparatus. Since the aperture in plate 130 has a finite width (necessary to admit a useful quantity of radiation), the incident rays 170, 172 will in fact occupy a range of angles, and the diffracted rays 174, 176 will be spread out somewhat. According to the point spread function of a small target, each diffraction order will be further spread over a range of angles, not a single ideal ray as shown.

[0083] At least the 0 th order diffracted by the target on substrate W is collected by objective lens 160 and directed back through partially reflecting surface 150. An optical element 180 provides at least part of the diffracted beams to optical system 182 which forms a diffraction spectrum (pupil plane image) of the target T on sensor 190 (e.g., a CCD or CMOS sensor) using the zeroth and/or first order diffractive beams. In an embodiment, an aperture 186 is provided to filter out certain diffraction orders so that a particular diffraction order is provided to the sensor 190. In an embodiment, the aperture 186 allows substantially or primarily only zeroth order radiation to reach the sensor 190. In an embodiment, aperture 186 allows substantially or primarily zeroth order radiation as well as some or all of the first order radiation (+/- 1) to reach sensor 190. In an embodiment, the sensor 190 may be a two-dimensional detector so that a two- dimensional angular scatter spectrum of a substrate target T can be measured. The sensor 190 may be, for example, an array of CCD or CMOS sensors, and may use an integration time of, for example, 40 milliseconds per frame. The sensor 190 may be used to measure the intensity of redirected radiation at a single wavelength (or narrow wavelength range), the intensity separately at multiple wavelengths or integrated over a wavelength range. Furthermore, the sensor may be used to separately measure the intensity of radiation with transverse magnetic- and/or transverse electric-polarization and/or the phase difference between transverse magnetic- and transverse electric-polarized radiation.

[0084] Optionally, optical element 180 provides at least part of the diffracted beams to measurement branch 200 to form an image of the target on the substrate W on a sensor 230 (e.g., a CCD or CMOS sensor). The measurement branch 200 can be used for various auxiliary functions such as focusing the metrology apparatus (i.e., enabling the substrate W to be in focus with the objective 160), and/or for dark field imaging of the type mentioned in the introduction.

[0085] In order to provide a customized field of view for different sizes and shapes of grating, an adjustable field stop 300 is provided within the lens system 140 on the path from source 110 to the objective lens 160. The field stop 300 contains an aperture 302 and is located in a plane conjugate with the plane of the target T, so that the illumination spot becomes an image of the aperture 302. The image may be scaled according to a magnification factor, or the aperture and illumination spot may be in 1:1 size relation. In order to make the illumination adaptable to different types of measurement, the aperture plate 300 may comprise a number of aperture patterns formed around a disc, which rotates to bring a desired pattern into place. Alternatively or in addition, a set of plates 300 could be provided and swapped, to achieve the same effect. Additionally or alternatively, a programmable aperture device such as a deformable mirror array or transmissive spatial light modulator can be used also.

[0086] Typically, a target will be aligned with its periodic structure features running either parallel to the Y-axis or parallel to the X-axis. With regard to its diffractive behavior, a periodic structure with features extending in a direction parallel to the Y axis has periodicity in the X direction, while the a periodic structure with features extending in a direction parallel to the X axis has periodicity in the Y direction. In order to measure the performance in both directions, both types of features are generally provided. While for simplicity there will be reference to lines and spaces, the periodic structure need not be formed of lines and space. Moreover, each line and/or space between lines may be a structure formed of smaller sub-structures. Further, the periodic structure may be formed with periodicity in two dimensions at once, for example where the periodic structure comprises posts and/or via holes.

[0087] Figure 8 illustrates a plan view of a typical target T, and the extent of illumination spot S in the apparatus of Figure 7. To obtain a diffraction spectrum that is free of interference from surrounding structures, the target T, in an embodiment, is a periodic structure (e.g., grating) larger than the width (e.g., diameter) of the illumination spot S. The width of spot S may be smaller than the width and length of the target. The target in other words is‘underfilled’ by the illumination, and the diffraction signal is essentially free from any signals from product features and the like outside the target itself. This simplifies mathematical reconstruction of the target as it can be regarded as infinite.

[0088] Figure 9 schematically depicts an example process of the determination of the value of one or more variables of interest of a target pattern 30’ based on measurement data obtained using metrology. Radiation detected by the detector 190 provides a measured radiation distribution 108 for target 30’.

[0089] For the given target 30’, a radiation distribution 208 can be computed / simulated from a parameterized mathematical model 206 using, for example, a numerical Maxwell solver 210. The parameterized mathematical model 206 shows example layers of various materials making up, and associated with, the target. The parameterized mathematical model 206 may include one or more of variables for the features and layers of the portion of the target under consideration, which may be varied and derived. As shown in Figure 9, the one or more of the variables may include the thickness t of one or more layers, a width w (e.g., CD) of one or more features, a height h of one or more features, a sidewall angle a of one or more features, and/or relative position between features (herein considered overlay). Although not shown, the one or more of the variables may further include, but is not limited to, the refractive index (e.g., a real or complex refractive index, refractive index tensor, etc.) of one or more of the layers, the extinction coefficient of one or more layers, the absorption of one or more layers, resist loss during development, a footing of one or more features, and/or line edge roughness of one or more features. One or more values of one or more parameters of a 1-D periodic structure or a 2-D periodic structure, such as a value of width, length, shape or a 3-D profile characteristic, may be input to the reconstruction process from knowledge of the patterning process and/or other measurement processes. For example, the initial values of the variables may be those expected values of one or more parameters, such as a value of CD, pitch, etc., for the target being measured.

[0090] In some cases, a target can be divided into a plurality of instances of a unit cell. To help ease computation of the radiation distribution of a target in that case, the model 206 can be designed to compute / simulate using the unit cell of the structure of the target, where the unit cell is repeated as instances across the full target. Thus, the model 206 can compute using one unit cell and copy the results to fit a whole target using appropriate boundary conditions in order to determine the radiation distribution of the target.

[0091] Additionally or alternatively to computing the radiation distribution 208 at the time of reconstruction, a plurality of radiation distributions 208 can be pre-computed for a plurality of variations of variables of the target portion under consideration to create a library of radiation distributions for use at the time of reconstruction.

[0092] The measured radiation distribution 108 is then compared at 212 to the computed radiation distribution 208 (e.g., computed near that time or obtained from a library) to determine the difference between the two. If there is a difference, the values of one or more of the variables of the parameterized mathematical model 206 may be varied, a new computed radiation distribution 208 obtained (e.g., calculated or obtained from a library) and compared against the measured radiation distribution 108 until there is sufficient match between the measured radiation distribution 108 and the radiation distribution 208. At that point, the values of the variables of the parameterized mathematical model 206 provide a good or best match of the geometry of the actual target 30’. In an embodiment, there is sufficient match when a difference between the measured radiation distribution 108 and the computed radiation distribution 208 is within a tolerance threshold. The tolerance threshold may, in one embodiment, be pre-set, however the tolerance threshold may additionally or alternatively be configurable.

[0093] In these metrology apparatuses, a substrate support may be provided to hold the substrate W during measurement operations. The substrate support may be similar or identical in form to the substrate table WT of Figure 1. In an example where the metrology apparatus is integrated with the lithographic apparatus, it may even be the same substrate table. Coarse and fine positioners may be provided to accurately position the substrate in relation to a measurement optical system. Various sensors and actuators are provided for example to acquire the position of a target of interest, and to bring it into position under the objective lens. Typically, many measurements will be made on targets at different locations across the substrate W. The substrate support can be moved in X and Y directions to acquire different targets, and in the Z direction to obtain a desired location of the target relative to the focus of the optical system. It is convenient to think and describe operations as if the objective lens is being brought to different locations relative to the substrate, when, for example, in practice the optical system may remain substantially stationary (typically in the X and Y directions, but perhaps also in the Z direction) and only the substrate moves. Provided the relative position of the substrate and the optical system is correct, it does not matter in principle which one of those is moving in the real world, or if both are moving, or a combination of a part of the optical system is moving (e.g., in the Z and/or tilt direction) with the remainder of the optical system being stationary and the substrate is moving (e.g., in the X and Y directions, but also optionally in the Z and/or tilt direction).

[0094] In an embodiment, the measurement accuracy and/or sensitivity of a target may vary with respect to one or more attributes of the beam of radiation provided onto the target, for example, the wavelength of the radiation beam, the polarization of the radiation beam, the intensity distribution (i.e., angular or spatial intensity distribution) of the radiation beam, etc., Thus, a particular measurement strategy can be selected that desirably obtains, e.g., good measurement accuracy and/or sensitivity of the target.

[0095] In order to monitor the patterning process (e.g., a device manufacturing process) that includes at least one pattern transfer step (e.g., an optical lithography step), the patterned substrate is inspected and one or more parameters of the patterned substrate are measured / determined. The one or more parameters may include, for example, overlay between successive layers formed in or on the patterned substrate, critical dimension (CD) (e.g., critical linewidth) of, for example, features formed in or on the patterned substrate, focus or focus error of an optical lithography step, dose or dose error of an optical lithography step, optical aberrations of an optical lithography step, placement error (e.g., edge placement error), etc., This measurement may be performed on a target of the product substrate itself and/or on a dedicated metrology target provided on the substrate. The measurement can be performed after-development of a resist but before etching or can be performed after-etch.

[0096] In an embodiment, a parameter obtained from a measurement process is a parameter derived from a parameter determined directly from the measurement process. As an example, a derived parameter obtained from a measurement parameter is edge placement error for the patterning process. The edge placement error provides a variation in the location of an edge of a structure created by the patterning process. In an embodiment, the edge placement error is derived from an overlay value. In an embodiment, the edge placement error is derived from a combination of an overlay value and CD value. In an embodiment, the edge placement is derived from a combination of an overlay value, a CD value and a value corresponding to a local variation (e.g., edge roughness, shape asymmetry, etc., of the individual structures). In an embodiment, the edge placement error comprises an extreme value (e.g., 3 standard deviation, i.e., 3s) of overlay and CD errors combined. In an embodiment, in a multi-patterning process involving creating structures and involving“cutting” structures by removing a portion of structure through etching of a pattern provided by the patterning process in relation to the structure, the edge placement error has the following form (or comprises one or more of the following terms):

herein s is standard

deviation, corresponds to the standard deviation of overlay, corresponds to the

standard deviation of the critical dimension uniformity (CDU) of structures created in the patterning process, corresponds to the standard deviation of the critical dimension uniformity (CDU) of cuts, if any, created in the patterning process, corresponds to the standard deviation of optical proximity effects (OPE) and/or proximity bias average (PBA) which is a difference between CD at pitch to a reference CD, and corresponds to the standard deviation of line edge roughness (LER) and/or local

placement error (LPE). While formulation above is in relation standard deviation, it can be formulated in a different comparable statistical manner, such as variance.

[0097] There are various techniques for making measurements of the structures formed in the patterning process, including the use of a scanning electron microscope, an image-based measurement tool and/or various specialized tools. As discussed above, a fast and non-invasive form of specialized metrology tool is one in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered (diffracted/reflected) beam are measured. By evaluating one or more properties of the radiation scattered by the substrate, one or more properties of the substrate can be determined. This may be termed diffraction-based metrology. One such application of this diffraction-based metrology is in the measurement of feature asymmetry within a target. This can be used as a measure of overlay, for example, but other applications are also known. For example, asymmetry can be measured by comparing opposite parts of the diffraction spectrum (for example, comparing the -1st and +1 st orders in the diffraction spectrum of a periodic grating). This can be done as described above and as described, for example, in U.S. patent application publication US2006-066855, which is incorporated herein in its entirety by reference. Another application of diffraction-based metrology is in the measurement of feature width (CD) within a target. Such techniques can use the apparatus and methods described above in respect of Figures 6-9. [0098] Now, while these techniques are effective, it is desirable to provide a new measurement technique that derives feature asymmetry within a target (such as overlay, CD asymmetry, sidewall angle asymmetry, etc.). This technique can be effective for specially designed metrology targets or perhaps more significantly, for determining feature asymmetry directly on a device pattern.

[0099] Referring to Figures 10A-C, principles of this measurement technique are described in the context of an overlay embodiment. In Figure 10A, a geometrically symmetric unit cell of a target T is shown. The target T can comprise just a single physical instance of a unit cell or can comprise a plurality of physical instances of the unit cell as shown in Figure 10C.

[0100] The target T can be a specially designed target. In an embodiment, the target is for a scribe lane. In an embodiment, the target can be an in-die target, i.e., the target is among the device pattern (and thus between the scribe lanes). In an embodiment, the target can have a feature width or pitch comparable to device pattern features. For example, the target feature width or pitches can be less than or equal to 300% of the smallest feature size or pitch of the device pattern, be less than or equal to 200% of the smallest feature size or pitch of the device pattern, be less than or equal to 150% of the smallest feature size or pitch of the device pattern, or be less than or equal to 100% of the smallest feature size or pitch of the device pattern.

[0101] The target T can be a device structure. For example, the target T can be a portion of a memory device (which often has one or more structures that are, or can be, geometrically symmetric as discussed further below).

[0102] In an embodiment, the target T or a physical instance of the unit cell can have an area of less than or equal to 2400 square microns, an area of less than or equal to 2000 square microns, an area of less than or equal to 1500 square microns, an area of less than or equal to 1000 square microns, an area of less than or equal to 400 square microns, less than or equal to 200 square microns, less than or equal to 100 square microns, less than or equal to 50 square microns, less than or equal to 25 square microns, less than or equal to 10 square microns, less than or equal to 5 square microns, less than or equal to 1 square micron, less than or equal to 0.5 square microns, or less than or equal to 0.1 square microns. In an embodiment, the target T or a physical instance of the unit cell has a cross-sectional dimension parallel to the plane of the substrate of less than or equal to 50 microns, less than or equal to 30 microns, less than or equal to 20 microns, less than or equal to 15 microns, less than or equal to 10 microns, less than or equal to 5 microns, less than or equal to 3 microns, less than or equal to 1 micron, less than or equal to 0.5 microns, less than or equal to 0.2 microns, or less than or equal to 0.1 microns.

[0103] In an embodiment, the target T or a physical instance of the unit cell has a pitch of structures of less than or equal to less than or equal to 5 microns, less than or equal to 2 microns, less than or equal to 1 micron, less than or equal to 500 nm, less than or equal to 400 nm, less than or equal to 300 nm, less than or equal to 200 nm, less than or equal to 150 nm, less than or equal to 100 nm, less than or equal to 75 nm, less than or equal to 50 nm, less than or equal to 32 nm, less than or equal to 22 nm, less than or equal to 16 nm, less than or equal to 10 nm, less than or equal to 7 nm or less than or equal to 5 nm.

[0104] In an embodiment, the target T has a plurality of physical instances of the unit cell. Thus, a target T could typically have the higher dimensions listed here, while the physical instances of the unit cell will have the lower dimensions listed here. In an embodiment, the target T comprises 50,000 or more physical instances of the unit cell, 25,000 or more physical instances of the unit cell, 15,000 or more physical instances of the unit cell, 10,000 or more physical instances of the unit cell, 5,000 or more physical instances of the unit cell, 1000 or more physical instances of the unit cell, 500 or more physical instances of the unit cell, 200 or more physical instances of the unit cell, 100 or more physical instances of the unit cell, 50 or more physical instances of the unit cell, or 10 or more physical instances of the unit cell.

[0105] Desirably, the physical instance of the unit cell or the plurality of physical instances of the unit cell collectively fills a beam spot of the metrology apparatus. In that case, the measured results comprise essentially only information from the physical instance of the unit cell (or its plurality of instances). In an embodiment, the beam spot has a cross-sectional width of 50 microns or less, 40 microns or less, 30 microns or less, 20 microns or less, 15 microns or less, 10 microns or less, 5 microns or less, or 2 microns or less.

[0106] The unit cell in Figure 10A comprises at least two structures that are, or will be, physically instantiated on the substrate. A first structure 1000 comprises lines and a second structure 1005 comprises an oval-type shape. Of course, the first and second structures 1000, 1005 can be different structures than depicted.

[0107] Further, in this example, there can be a relative shift between the first and second structures 1000, 1005 from their expected position due to their separate transfer onto the substrate to have an error in overlay. In this example, the first structure 1000 is located in a higher layer on a substrate than the second structure 1005. Thus, in an embodiment, the second structure 1005 can be produced in a first lower layer in a first execution of a patterning process and the first structure 1000 can be produced in a second higher layer than the first lower layer in a second execution of the patterning process. Now, it is not necessary that the first and second structures 1000, 1005 be located in different layers. For example, in a double patterning process (including, for example, an etching process as part thereof), the first and second structures 1000, 1005 could be produced in a same layer to form essentially a single pattern but there could still be an“overlay” concern in terms of their relative placement within the same layer. In this single layer example, both the first and second structures 1000, 1005 could have, for example, the form of lines like shown in Figure 10A for the first structure 1000 but the lines of the second structure 1005, already provided on the substrate by a first pattern transfer process, could be interleaved with the lines of the structure 1000 provided in a second pattern transfer process.

[0108] Significantly, the unit cell has, or is capable of having, a geometric symmetry with respect to an axis or point. For example, the unit cell in Figure 10A has reflection symmetry with respect to, for example, axis 1010 and point / rotational symmetry with respect to, for example, point 1015. Similarly, it can be seen that a physical instance of the unit cell (and thus a combination of physical instances of the unit cell) in Figure 10C has a geometric symmetry.

[0109] In an embodiment, the unit cell has a geometric symmetry for a certain feature (such as overlay). Embodiments herein focus on the unit cell having zero overlay when it is geometrically symmetric. However, instead, the unit cell can have zero overlay for a certain geometric asymmetry. Appropriate offsets and calculations would then be used to account for the unit cell having a zero overlay when it has a certain geometric asymmetry. Pertinently, the unit cell should be capable of change in symmetry (e.g., become asymmetry, or become further asymmetric, or become symmetric from an asymmetric situation) depending on the certain feature value.

[0110] In the example of Figure 10A, the unit cell has a geometric symmetry for a zero overlay (although it need not be zero overlay). This is represented by the arrows 1020 and 1025 which shows that the lines of the first structure 1000 are evenly aligned with respect to the oval-type shape of the second structure 1005 (and which even alignment at least in part enables the unit cell to have geometric symmetry as shown in Figure 10A). Therefore, in this example, when the unit cell has geometric symmetry, there is zero overlay. However, when there is an error in overlay (e.g., a non-zero overlay), the unit cell is no longer geometrically symmetric and by definition the target is no longer geometrically symmetric.

[0111] Further, where a target comprises a plurality of physical instances of the unit, the instances of the unit cell are arranged periodically. In an embodiment, the instances of the unit cell are arranged in a lattice. In an embodiment, the periodic arrangement has a geometric symmetry within the target.

[0112] So, in this technique, as discussed further hereafter, advantage is taken of the change in geometric symmetry (e.g., a change to a geometric asymmetry, or change to a further geometric asymmetry, or a change from geometric asymmetry to geometric symmetry) related to a feature asymmetry of interest (e.g., non-zero overlay) to be able to determine the feature asymmetry (e.g., non-zero overlay).

[0113] A target comprising a physical instance of the unit cell of Figure 10A can be illuminated with radiation using, for example, the metrology apparatus of Figure 7. The radiation redirected by the target can be measured, e.g., by detector 190. In an embodiment, a pupil of the redirected radiation is measured, i.e., a Fourier transform plane. An example measurement of such a pupil is depicted as pupil image 1030. While the pupil image 1030 has a diamond-type shape, it need not have such a shape. The term pupil and pupil plane herein includes any conjugates thereof unless the context otherwise requires (for example, where a pupil plane of a particular optical system is being identified). The pupil image 1030 is effectively an image, specified in terms of an optical characteristic (in this case intensity), of a pupil of the redirected radiation.

[0114] For convenience, the discussion herein will focus on intensity as an optical characteristic of interest. But, the techniques herein may be used with one or more alternative or additional optical characteristics, such as phase and/or reflectivity.

[0115] Further, for convenience, the discussion herein focuses on detecting and processing images of redirected radiation and in particular pupil images. However, the optical properties of the redirected radiation can be measured and represented in different manners than images. For example, the redirected radiation can be processed in terms of one or more spectrums (e.g., intensity as a function of wavelength). Thus, a detected image of redirected radiation can be considered as an example of an optical representation of the redirected radiation. Therefore, in the case of a pupil plane image, a pupil image is an example of a pupil representation.

[0116] Further, the redirected radiation can be polarized or non-polarized. In an embodiment, the measurement beam radiation is polarized radiation. In an embodiment, the measurement beam radiation is linearly polarized.

[0117] In an embodiment, a pupil representation is of primarily, or substantially, one diffraction order of redirected radiation from the target. For example, the radiation can be 80% or more, 85% or more, 90% or more, 95% or more, 98% or more or 99% or more, of a particular order of the radiation. In an embodiment, the pupil representation is of primarily, or substantially, zeroth order redirected radiation. This can occur, for example, when the pitch of the target, the wavelength of the measurement radiation, and optionally one or more other conditions cause the target to redirect primarily zeroth order (although there can be radiation of one or more higher orders). In an embodiment, a majority of the pupil representation is zeroth order redirected radiation. In an embodiment, the pupil representation is of zeroth radiation and separately of 1 st order radiation, which can then be linearly combined (superposition). The aperture 186 in Figure 7 can be used to select a particular order, e.g., the zeroth order, of radiation.

[0118] Having regard to pupil image 1030 corresponding to the geometrically symmetric unit cell of the first and second structures 1000, 1005, it can be seen that the intensity distribution is essentially symmetric within the pupil image (e.g., with the same symmetry type as of the geometric structure). This is further confirmed by removing the symmetric intensity distribution portion from the pupil image 1030, which results in the derived pupil image 1035. To remove the symmetric intensity distribution portion, a particular pupil image pixel (e.g., a pixel) can have the symmetric intensity distribution portion removed by subtracting from the intensity at that particular pupil image pixel the intensity of a symmetrically located pupil image pixel, and vice versa. In an embodiment, the pixel can correspond to the pixels of the detector (e.g., detector 190), but it need not; for example, a pupil image pixel could be a plurality of the pixels of the detector. In an embodiment, the point or axis of symmetry across which pixel intensities are subtracted corresponds with a point or axis of symmetry of the unit cell. So, for example, considering pupil image 1030, the symmetry intensity distribution portion can be removed by, for example, subtracting from the intensity Ii at that particular pixel shown the intensity Ii’ from a symmetrically located pixel, i.e., symmetrically located with respect to axis 1032. Thus, the intensity at a particular pixel with the symmetrical intensity portion removed, S i , is then S i = I i - I i ’. This can be repeated for a plurality of pixels of the pupil image, e.g., all the pixels in the pupil image. As seen in the derived pupil image 1035, the intensity distribution corresponding to the symmetric unit cell is essentially completely symmetric. Thus, a symmetric target with a symmetric unit cell geometry (and if applicable, a certain periodicity of instances of the unit cell) results in a symmetric pupil response as measured by a metrology apparatus.

[0119] Referring now to Figure 10B, an example of an error in overlay is depicted with respect to the unit cell depicted in Figure 10A. In this case, the first structure 1000 is shifted in the X-direction with respect to the second structure 1005. In particular, the axis 1010 centered on the lines of the first structure 1000 has shifted to the right in Figure 10B to axis 1045. Thus, there is an error in the overlay 1040 in the X-direction; that is, an X direction overlay error. Of course, the second structure 1005 could be shifted relative to the first structure 1000 or both could be shifted relative to each other. In any event, the result is an X direction overlay error. However, as should be appreciated from this unit cell arrangement, a purely relative shift in the Y-direction between the first structure 1000 and the second structure 1005 would not change the geometric symmetry of this unit cell. However, with an appropriate geometric arrangement, overlay in two directions or between different combinations of parts of the unit cell can change symmetry and could also be determined, as further discussed below.

[0120] As a consequence of the change in the physical configuration of the unit cell from the nominal physical configuration of the unit cell in Figure 10A and represented by the error in overlay 1040, the result is that the unit cell has become geometrically asymmetric. This can be seen by the arrows 1050 and 1055 of different length, which show that the oval-type shape of the second structure 1005 is unevenly located relative to the lines of the first structure 1000. The symmetry is examined with respect to the point or axis of symmetry of the pupil image 1030, i.e., in that case, axis 1032 which is now shown axis 1034.

[0121] The physical instance of the unit cell of Figure 10B can be illuminated with radiation using, for example, the metrology apparatus of Figure 7. A pupil image of the redirected radiation can be recorded, e.g., by detector 190. An example of such a pupil image is depicted as pupil image 1060. The pupil image 1060 is effectively an image of the intensity. While the pupil image 1060 has a diamond-type shape, it need not have such a shape; it can be a circular shape or any other shape. Moreover, the pupil image 1060 is of a substantially same axis or coordinate location as pupil image 1030. That is, in this embodiment, an axis of symmetry 1010 in the unit cell of Figure 10A and the same axis in the unit cell of Figure 10B align with an axis of symmetry 1032 of the pupil images 1030, 1060.

[0122] Having regard to pupil image 1060 corresponding to the geometrically asymmetric unit cell of the first and second structures 1000, 1005, it visually seems like the intensity distribution is essentially symmetric within the pupil image. However, there is an asymmetric intensity distribution portion within the pupil image. This asymmetric intensity distribution portion is due to the asymmetry in the unit cell. Moreover, the asymmetric intensity distribution is significantly lower in magnitude than a symmetric intensity distribution portion in the pupil image.

[0123] Therefore, in an embodiment, to more effectively isolate the asymmetric intensity distribution portion, the symmetric intensity distribution portion can be removed from the pupil image 1060, which results in the derived pupil image 1065. Like with obtaining derived pupil image 1035, a particular pupil image pixel (e.g., a pixel) can have the symmetric intensity distribution portion removed by subtracting from the intensity at that particular pupil image pixel the intensity of a symmetrically located pupil image pixel, and vice versa, as discussed above. So, for example, considering pupil image 1060, the symmetry intensity distribution portion can be removed by, for example, subtracting from the intensity Ii at that particular pixel shown the intensity I i ’ from a symmetrically located pixel, i.e., symmetrically located with respect to axis 1032 to yield S i . This can be repeated for a plurality of pixels of the pupil image, e.g., all the pixels in the pupil image. In Figures 10A and 10B, the full derived pupil images of Si are depicted for explanation purposes. As will be appreciated, half of a derived pupil image of Figure 10A or 10B is the same as the other half thereof. So, in an embodiment, the values from only half of the pupil image can be used for further processing discussed herein and so a derived image pupil used in further processing herein can be only half of the Si values for a pupil.

[0124] As seen in the derived pupil image 1065, the intensity distribution measured using a physical instance of an asymmetric unit cell is not symmetric. As seen in regions 1075 and 1080, there is an asymmetric intensity distribution portion visible once the symmetric intensity distribution portion is removed. As noted above, the full derived pupil image 1065 is shown and so the asymmetric intensity distribution portion is shown on both halves (even though they are equal to each other in terms of magnitude and distribution in their respective halves).

[0125] Thus, an asymmetry in the geometrical domain corresponds to an asymmetry in the pupil. So, in an embodiment, a method is provided that uses the optical response of a periodic target that possesses, or is capable of, inherent geometric symmetry in its physical instance of a unit cell to determine a parameter corresponding to a physical configuration change that causes a change in geometric symmetry (e.g., cause an asymmetry, or cause a further asymmetry, or cause an asymmetric unit cell to become symmetric) of the physical instance of the unit cell. In particular, in an embodiment, an overlay induced asymmetry (or lack thereof) in the pupil as measured by a metrology apparatus can be exploited to determine the overlay. That is, the pupil asymmetry is used to measure the overlay within the physical instance of the unit cell and thus within the target.

[0126] To consider how to determine the parameter corresponding to a physical configuration change that causes a geometric asymmetry in a unit cell, the intensity of a pixel in the pupil image can be considered in terms of the physical characteristics of the target that impact that pixel. To do so, an overlay example will be considered but the techniques and principles can be extended to another parameter corresponding to a physical configuration change that causes a geometric asymmetry in a unit cell (e.g., asymmetric sidewall angle, asymmetric bottom wall tilt, ellipticity in contact holes, etc.).

[0127] Referring back to the unit cells of Figures 10A and 10B, the intensity of a pixel ! , ¢ ! in the pupil image 1060 can be evaluated analytically as a combination of intensity components attributable to different physical characteristics of the unit cell. In particular, the physical configuration changes from the symmetric unit cell to the asymmetric unit cell can be evaluated to determine in what manner the intensity distribution changes and specifically within a pupil image.

[0128] So, in a very simple example to illustrate the principles, several changes in physical configuration of the unit cell profile can be evaluated (but of course more or different physical configuration changes can occur). One of the physical configuration changes that will be considered is the change in height of the structure 1000 in the Z direction, which is designated as∆$ % . However, significantly, this change in height will generally be uniform across the physical instance of the unit cell. That is, the∆$ % will result in a same changed physical configuration of the unit cell at one side of an axis or point of symmetry as at another side of the axis or point of symmetry. Similarly, other physical configuration changes, such as CD, sidewall angle, etc., changes, will also be generally uniform across the physical instance of the unit cell and thus yield a same changed physical configuration of the unit cell at one side of an axis or point of symmetry as at another side of the axis or point of symmetry. So, for convenience, only ∆$ % will be considered, but is representative of numerous other physical configuration changes that are uniform across the unit cell.

[0129] Another one of the physical configuration changes of the unit cell of interest is the relative shift between structure 1000 and structure 1005, namely the change in overlay 1040. This overlay shift will be referred to as∆$ &' . Of course, the overlay can be considered in a different or additional direction. Significantly, the∆$ &' will result in a different physical configuration of the unit cell at one side of an axis or point of symmetry than at another side of the axis or point of symmetry; each pair of symmetric pixels has information about overlay. Significantly, while change in most target profile parameters (CD, height, etc.) induce symmetric changes in the pupil (and thus can be considered symmetric parameters), change in overlay results in an asymmetric change in the measured pupil. Thus, a change in overlay gives an asymmetric pupil response. Further, most, if not all, other unit cell profile parameters do not create asymmetry of the unit cell or the pupil response. However, they can have an effect on the measured overlay value. As discussed below, to the first order, other unit cell profile parameters may have no effect. In an embodiment, to a second or higher order, other unit cell profile parameters have an effect on determination of the overlay value. Hence, as discussed in more detail below, by measuring the pupil asymmetry, overlay can be determined therefrom.

[0130] Specifically, to evaluate how overlay can be determined from a measured pupil asymmetry, the intensity ! of a pixel i in the pupil image 1060 can be defined as:

where ) is a base intensity attributable to the illumination radiation and a, e, f and g are coefficients. So, similarly, the intensity of the complementary symmetric pixel ¢ ! in the pupil image 1060 can be defined as:

where coefficients a’, b’, c’, d’, e’ and f’ are specific to the intensity of the complementary symmetric pixel ¢ ! and are comparable to the coefficients a, b, c, d, e and f for the intensity of a pixel ! in the pupil image 1060.

[0131] The difference of the intensity between the symmetric pixels in the pupil

image 1060 can then be evaluated as:

It has been discovered that due to, e.g., symmetry, all the terms that can contain only symmetric parameters, such as 7∆$ % , drop out as seen in equation (3). Further, due to, e.g., symmetry, the terms with an even power of overlay have been discovered to be equal for symmetrically positioned pixels and so terms such ∆$ & . ' likewise drop out. That leaves, terms that have a combination of overlay with a symmetric parameter and terms that have only overlay to an odd power (e.g., to the power of 1, 3, 5, 7, etc.).

[ 0132] In equation (3) above, it has been discovered that the difference of the intensity 5 ! is primarily dependent on That is, the difference of the intensity 5 ! is in great part linearly dependent on overlay

or more significantly, overlay is in great part linearly dependent on the intensity, specifically the difference of the intensity 5 ! . Thus, a combination of the intensities of the pixels can yield a good estimated value of the overlay when linearly combined with an appropriate conversion factor.

[0133] So, in an embodiment, it has been discovered that an overlay can be determined from a combination of intensities of the pixels that are appropriately weighted (wherein the weighting themselves acts a conversion factor of intensity to overlay or that can be combined with a conversion factor from intensity to overlay). In an embodiment, an overlay signal can be described as:

wherein the overlay signal M is the weighted combination of the signal components Si in the measured pupil and : ! are the respective weights for each of the signal components Si (and the weights act as a conversion factor between the signal component and overlay; as noted above, instead, a conversion factor could be used in combination with weights that do not act to convert the signal component to overlay). In an embodiment, the weights are a vector whose magnitude is related to the overlay. As noted above, the signal components S i can be determined for half of the measured pupil. In an embodiment, if the signal components S i have a substantially same magnitude for all pairs (N/2) of symmetric pixels (N), then the signal components S i can be averaged and combined with a conversion factor C from the total of the signal components Si to overlay according to the following formula to yield a total overlay: 8 So,

in an embodiment, the weights can have two roles– one is as a trust per pair of pixels in respect of its measurement of overlay and the other role is to convert a value of the optical characteristic of the signal component (e.g., intensity level, e.g., gray level) to an overlay value (in terms of, e.g., nanometers), As discussed above, the second role can be delegated to a conversion factor.

[0134] However, where, e.g., the signal components Si do not have a substantially same magnitude for all pairs of symmetric pixels, weighting all pixels in the measured pupil equally could result in a low signal- to-noise ratio (poor precision). Therefore, it is desirable to weight those pixels that are sensitive to overlay to have a greater contribution to the calculation of the overlay. So, in an embodiment, pixels sensitive to overlay get different (e.g., higher) weights than those pixels that have low sensitivity to overlay (effectively inactive pixels). As noted above, the pixels in regions 1075 and 1080 of the derived pupil 1065 have relatively higher sensitivity to overlay while the remaining pixels in the derived pupil 1065, which have low to no intensity relative to the pixels in regions 1075 and 1080, have low sensitivity to overlay (and accordingly should be weighted to have lower contribution to the overlay determination).

[ 0135] In an embodiment, the weights are effectively determined for the erm of equation (3). In an embodiment, the weights can be extended to be determined for the term as well as the ,∆$&'∆$%(and typically other comparable terms for other parameters, such as CD, sidewall angle, etc.). However, this calculation can be more complex than determining the weights effectively only for the

term of equation (3). Moreover, there is a tradeoff between robustness to non-linear processes (for symmetric parameters) and precision of determining overlay (i.e., in terms of how close the determined values are for each determination of the same actual overlay). So, there can be a sacrifice of precision for enhanced robustness using this calculation. Accordingly, an optimization can be performed to enhance precision (e.g., maximizing the influence of the linear terms and suppressing the non-linear terms), enhance robustness (e.g., maximizing the non-linear terms) or find a balance of both. Nevertheless, in any event, the use of a combination of intensities linearly combined with associated weightings can lead to a quick determination of overlay, as it requires merely a pupil acquisition and simple calculation of equation (4).

[0136] In an embodiment, where higher order terms become significant, a non-linear solution technique can be adopted to solve equation (3) having the and/or other higher order terms. As will

be appreciated, a non-linear solution technique can be more complex than simply multiplying each signal components Si in the measured pupil with a respective weight : for each signal components Si and then

adding all of them up. Moreover, there is again tradeoff between robustness to non-linear processes and precision of determining overlay (i.e., in terms of how close the determined values are for each determination of the same actual overlay). So, there can be a sacrifice of precision for enhanced robustness using this calculation. Accordingly, an optimization can be performed to enhance precision and/or enhance robustness.

[0137] So, with the realization of an asymmetric intensity distribution arising from a geometric asymmetry of a unit cell caused by overlay, the error in overlay can be determined through an analysis that has a focus on this asymmetric intensity distribution. Thus, a technique for determining overlay from the asymmetric intensity distribution arising due to the change in physical configuration of a target associated with overlay will now be discussed.

[0138] Referring to Figure 11, a method of determining the weights is schematically depicted. To enable the weight determination, the reconstruction techniques described above with respect to Figure 9 will be used to advantage. That is, in an embodiment, CD reconstruction is used to isolate an overlay signal from a pupil image of a physical instance of an asymmetric unit cell. [0139] The method of Figure 11 involves two processes. A first process 1100 involves using reconstruction techniques for CD and/or one or more other profile parameters of a target to derive a nominal profile of the target (and thus of the one or more physical instances of the unit cell therein) as exposed on a substrate as part of a patterning process. With the nominal profile of the target, the basic engine of the reconstruction technique is used in process 1110 to derive the weightings. The weightings can then be used to derive overlay from a measured pupil as described further in relation to Figure 12.

[0140] So, at process 1100, measurements 1130 of a substrate having one or more physical instances of a unit cell of interest provided thereon as a target, are obtained. In an embodiment, the measurements are of the target after etch. In an embodiment, the measurements are of the target after development but before etch. In an embodiment, the target is a device structure. In an embodiment, the measurements can be made, or have been made, using a metrology apparatus such as the metrology apparatus of Figure 7. For example, the target can comprise a physical instance of the unit cell of Figure 10A or Figure 10B, e.g., a single instance or a plurality of adjacent instance as shown in Figure 10C. In an embodiment, measurements of a plurality of targets (and thus of a plurality of physical instances of the unit cell) are obtained. In an embodiment, the measurements are of targets that are distributed across the substrate. In an embodiment, a plurality of substrates, each with one or more targets (each having one or more physical instances of the unit cell), is measured. So, in an embodiment, a radiation distribution 108 is obtained for each measured target.

[0141] Then, a reconstruction process at 1100, such as the reconstruction process described in and with respect to Figure 9, is used to derive a nominal profile of the physical instance of the unit cell, comparable to the profile 206 of Figure 9. The reconstruction process obtains an expected profile 1120 of the physical instance of the unit cell to start and facilitate the reconstruction process. In an embodiment, the derived nominal profile is obtained from an average of the profile of targets across one or more substrates. For example, the radiation distribution 108 for each target can be processed to derive a particular profile of that instance of the target and then the profiles for the plurality of instances of the target can be averaged together to derive the nominal profile. In an embodiment, the nominal profile comprises at least a geometric profile of the target. In an embodiment, the geometric profile is a 3-D profile. In an embodiment, the nominal profile comprises information regarding one or more materials properties of one or more layers making up the physical target.

[0142] So, in an embodiment, the nominal profile can be considered as a center of gravity for the values of various parameters of the profile of the target (and thus the unit cell) obtained from measuring numerous instances of the target across the substrate and optionally on more than one substrate. But, in an embodiment, the nominal profile can have different forms and be more specific. For example, the nominal profile can be defined for one or more particular instances of a target (e.g., by using values from the same target location(s) from multiple substrates). As another example, the nominal profile can be defined for a particular substrate (e.g., by using values from only that substrate). In an embodiment, the nominal profile can be tuned for a particular target and/or substrate as part of the process of Figure 12. For example, when the target and/or substrate is measured as part of the process of Figure 12, a reconstruction technique can be used with the measured data to fine tune the nominal profile for that target and/or substrate, the fine- tuned nominal profile can then be used as the nominal profile herein to determine weights and which weighs can then be used with the same measured data to yield one or more overlay values.

[0143] The reconstructed nominal profile 1140 is then provided to process 1110. Thus, in an embodiment, process 1110 uses a derived nominal profile of the target, e.g., a geometric after-etch profile of the unit cell of a device derived from measured data. In an embodiment, the nominal profile can be in the form of a parameterized model, like model 206 parameterized in accordance with the measured unit cell. Thus, in an embodiment, process 1110 uses a derived profile model of the unit cell, e.g., a model of the geometric after-etch profile of the physical instance of a unit cell of a device derived from measured data.

[0144] The basic engine of the reconstruction technique described herein is used in process 1110, along with the derived profile or the derived profile model, to derive the weightings. In an embodiment, the derived profile model or a derived profile model derived from the derived profile is used to determine pupil pixels sensitive to overlay in the unit cell. In particular, in an embodiment, the sensitivity to overlay of pupil response is determined by, using simulations (e.g., the Maxwell solver), to determine a change in pupil response to an induced change in overlay for the nominal profile.

[0145] This can be accomplished by causing the derived profile model to be changed such that an overlay change of a certain amount is induced (e.g., 1 nm) in the model, leaving all other parameters/variables of the derived profile model unchanged. This effectively causes a symmetric unit cell to become asymmetric or causes an already asymmetric unit cell ell can be symmetric) to change symmetry (including to become further asymmetric or to become symmetric from an asymmetric situation). In one embodiment, a target having one or more unit cells with a pre-defined overlay may be employed such that an overlay change of a prescribed amount is known.

[0146] A pupil as would be expected in the metrology apparatus (e.g., for radiation at a certain measurement beam wavelength, measurement beam polarization, measurement beam intensity, etc.) can then be derived (e.g., using a Maxwell solver, a library search or other reconstruction technique) based on the derived profile model with the induced overlay change. Where the physical instance of the unit cell is smaller than a beam spot, the reconstruction can treat the beam spot as being filled with physical instances of the unit cell. In an embodiment, the derived pupil can be a simulated pupil image 1060 and/or a derived pupil image 1065 based on the simulated pupil image.

[0147] The derived pupil can be then used to determine the sensitivities of the intensity in a plurality of the pupil pixels to overlay change, for example by comparison with a derived pupil for the unit cell without the induced overlay (for example, the derived pupil for the unit cell without the induced overlay can be a simulated pupil image 1030 and/or a derived pupil image 1035 based on the simulated pupil image). In an embodiment, these sensitivities form the basis of the weightings.

[0148] In an embodiment, the pixels of the pupil (and thus the pixel intensities, signal components S i , etc.) can be expressed as a vector. In an embodiment, the weightings can then be derived from a Jacobian matrix generated in the modelling. In an embodiment, the weightings can be derived from a Moore-Penrose pseudo inverse of the Jacobian matrix generated in the modelling. Therefore, the weights are effectively determined for the term of equation (3). The weightings derived from the Jacobian matrix or the Moore-Penrose pseudo inverse of the Jacobian matrix appear to apply well for the relatively modest overlay variations (e.g., within ± 3 nm or within ± 4 nm or within ± 5 nm).

[0149] In an embodiment, the weights can be extended to be determined for the erm as well as

the (and typically other comparable terms for other parameters, such as CD, sidewall angle, etc.).

In this case, the weightings are, or can be derived from, a Hessian matrix generated in the modelling in addition to the Jacobian matrix. The Hessian shows how the response to the overlay changes due to a change of a certain amount of another (symmetric) parameter (such as CD). So, for every such parameter there is a column in the Hessian. In an embodiment, to be (more) robust, the weights could be altered such that they become more orthogonal to the column (parameter) for which the unit cell is sensitive. To become more orthogonal, the one or more sensitive columns can be concatenated to the Jacobian, and then the Moore-Penrose pseudo inverse can be computed from this Jacobian with one or more columns from the Hessian concatenated thereto. From this computation, the weights follow. However, this calculation can be more complex and thus may be suitable for those situations where overlay values in practice are expected to exceed the overlay variation range for which the weightings derived from the (Moore-Penrose pseudo inverse of) Jacobian matrix show good results.

[0150] In an embodiment, the weights can be extended to be determined for other terms of equation (3). In that case, the weightings are, or can be derived from, third order derivatives generated in the modelling in addition to the Jacobian matrix.

[0151] As noted above, the nominal profile could be a fine-tuned nominal profile per target or substrate. For example, when the particular target or substrate is measured as part of the process of Figure 12, a reconstruction technique can be used with the measured data to fine tune the nominal profile for that target or substrate. Now, depending on the fine-tuning, the weights can be (re-)determined and/or a choice made between the type of weighting being made (e.g., Jacobian or a combination of the Jacobian and Hessian). For example, weights, based on a nominal profile that wasn’t fine-tuned, may have been previously selected to suppress the effect of but if the fine-tuning identifies and updates the∆ for the target and/or

substrate, the effect of∆ may not need to be suppressed. Thus, weights could be chosen that more favor

precision over robustness.

[0152] So, from process 1110, a collection (e.g., a vector) of weights : 1150 can be output. The weights : ! themselves can act as a conversion factor of intensity to overlay or they can be combined with a conversion factor from intensity to overlay (which conversion factor can be derived as part of the same modelling). As will be appreciated from pupil image 1065, the pixels in the regions 1075 and 1080 have relatively higher sensitivity to overlay than pixels outside of regions 1075 and 1080 and thus their weightings will be noticeably different (e.g., higher) than the weighting of pixels outside of region 1075 and 1080 (which pixels have relatively low sensitivity to overlay). So, when the weights are combined (such as according to equation (4)) with measured intensity values of a target having one or more physical instances of the unit cell, an overlay signal can be obtained for the particular target (such as a device pattern having a physical instance of the unit cell).

[0153] Further, one or more measurement parameters can be determined to form a measurement strategy for use in obtaining the measured intensity values of the target. One or more measurement parameters can affect the overlay sensitivity of pixels. For example, overlay sensitivity varies across different measurement beam wavelengths. So, in an embodiment, one or more measurement parameters (such as wavelength, polarization, dose, a number of optical characteristic readings taken by a detector sensor of a particular one illumination of the target (the readings typically averaged to provide an averaged optical characteristic value for the measurement of the target)) can be varied as part of the modelling process 1110. For example, one or more measurement parameters can be examined for a particular induced overlay change to determine a value of the one or more measurement parameters that reduces an error residual, for example between an overlay obtained when the weightings are for one value of the one or more parameters in relation to overlay obtained when the weightings are for another value of the one or more parameters, to a minimum or below a certain threshold. So, a value of one or more measurement parameters can then be obtained that improve precision.

[0154] Further, robustness to process variations differs across different values of one or more measurement parameters. For example, in particular, robustness to process variations differs across different values of measurement beam wavelength and/or measurement polarization. Thus, in an embodiment, the weighting scheme should address at least a dominant contributor to lack of robustness to process variation. So, additionally or alternatively to determining a value of one or more measurement parameters for improved precision, one or more measurement parameters can be examined for different particular induced overlay change values (and/or for particular induced changes of one or more other parameters of the derived profile model, such as a change in CD, side wall angle, etc.) to obtain a value of one or more measurement parameters that enables results using the weightings that have enhanced robustness to process variation. For example, for different amounts of induced overlay change, various values of the one or more measurement parameters can be evaluated to determine a value of the one or more measurement parameters that causes a minimum (or below a threshold) variation in the determined overlay using the weightings associated with the value of the one or more measurement parameters. Of course, a balance can be used in selection of the value of the one or more measurement parameters between precision and enhanced robustness. For example, a weighting can be applied between a value of the one or more measurement parameters determined for precision (e.g., a weight applied to a performance metric that measures precision) and a value of the one or more measurement parameters determined for enhanced robustness (e.g., a weight applied to a performance metric that measures robustness) and then a largest, top ranked, etc., combination can be selected. And of course, a plurality of values of one or more measurement parameters can be determined such that there is in effect a plurality of different measurement strategies in the overall measurement strategy. The plurality of values could be ranked according to one or more performance metrics. Thus, optionally, a measurement strategy can be output from process 1110 for use in obtaining measured intensity values of a target having one or more physical instances of the unit cell.

[0155] Further, one or more non-overlay parameters, such as CD, sidewall angle, etc., can affect the weights used for mapping the intensity signal to overlay. As noted above, an example manner of determining the weights in this context is to use a Hessian matrix and/or third order derivatives. So, in an embodiment, various possible weighting schemes are possible to take account of one or more non-overlay parameters so as to still maintain a good overlay value. In an embodiment, the overlay informative overlay pixels and their weightings can be optimized for overlay determination precision. This may require good model quality, i.e., good estimates of the non-overlay parameters. In an embodiment, the overlay informative pixels and their weights can be optimized for increased robustness to process variations such as in the non-overlay parameters. This may be at the expense of precision.

[0156] In an embodiment, estimates of the one or more non-overlay parameters can be made using, for example, the reconstruction techniques described in relation to Figure 9, and fed-forward to tune the derived profile or derived profile model. For example, a CD reconstruction can estimate a CD of a target at a particular location at a substrate and/or for a particular combination of patterning process settings (e.g., exposure dose, exposure focus, etc.) and use that CD estimate to tune the CD parameter of the derived profile or derived profile model. In an embodiment, iterative reconstructions of the exact derived profile or derived profile model parameters can be performed.

[0157] Referring to Figure 12, a method of determining an overlay value for a target having one or more physical instances of a unit cell capable of being geometrically symmetric is described. This method involves two processes 1200 and 1210. Process 1200 involves obtaining a measurement of the target having the one or more physical instances of the unit cell. Process 1210 involves determining an overlay value for the measured target based on the measurement of the target from process 1200.

[0158] Process 1200 takes as an input the target 1220 to be measured including one or more physical instances of a unit cell as described herein capable of being geometrically symmetric. In an embodiment, a substrate with one or more instances of the target is provided to a metrology apparatus, such as the metrology apparatus of Figure 7.

[0159] Optionally, process 1200 takes as input a particular measurement strategy 1230 specified for the target. In an embodiment, the measurement strategy can specify a value of one or more measurement parameters, such as one or more selected from: measurement beam wavelength, measurement beam polarization, measurement beam dose, and/or a number of optical characteristic readings taken by a detector sensor of the metrology apparatus of a particular one illumination of the target. In an embodiment, the measurement strategy can comprise a plurality of measurement strategies, each specifying a value of one or more measurement parameters. The measurement strategy can be used to measure the target.

[0160] Process 1200 then measures the target using a metrology apparatus according to the optional measurement strategy. In an embodiment, the metrology apparatus obtains a pupil representation of the redirected radiation. In an embodiment, the metrology apparatus can produce a pupil representation such as pupil image 1030 (if, for example, the target has no error in overlay) or pupil image 1060 (if, for example, the target has an error in overlay). Thus, in an embodiment, the process 1200 outputs optical information 1240 regarding the redirected radiation from the target, such as a pupil representation of the radiation.

[0161] Process 1210 then receives the optical information 1240 and processes the optical information to determine an overlay value 1260 for the target. In an embodiment, the process 1210 receives as input the weightings 1250 determined from the method of Figure 11, which then are combined with one or more optical characteristic values (e.g., intensities) obtained or derived from the optical information 1240.

[0162] In an embodiment, the process 1210 (or process 1200) can process the optical information to derive a raw overlay signal from the optical information. In an embodiment, the raw overlay signal comprises a differential of the optical information, i.e., a difference in optical characteristic values between symmetric pixels across an axis or point of symmetry. In an embodiment, the derived pupil image 1035 (if, for example, the target has no error in overlay) or derived pupil image 1065 (if, for example, the target has an error in overlay) can be obtained.

[0163] In an embodiment, the weightings and optical information with respect to radiation redirected by the target (e.g., the optical information from process 1200 or a processed version of the optical information from process 1200 such as the raw overlay signal) are combined to determine the overlay value. In an embodiment, the use of a combination of redirected measurement beam intensities linearly combined with associated weightings can lead to a quick determination of overlay. For example, in an embodiment, the overlay value can be derived using equation (4) wherein the overlay value M is calculated as the weighted combination of signal components S i from the raw overlay signal using respective weights : ! for each of the signal components Si.

[0164] In an embodiment, the optical information collected from process 1200 can be used additionally to derive one or more target related parameters other than overlay. For example, the optical information collected from process 1200 can be used in a reconstruction process to derive any one or more geometric profile parameters of the target, such as CD, sidewall angle, bottom floor tilt, etc., So, in an embodiment, a same set of optical information collected from a target, such as an in-die after-etch target, can be used to determine overlay, CD and/or one or more other geometric profile parameters of the target (such as a device structure).

[0165] While, as noted above, focus has been on intensity, in an embodiment, the optical characteristic can be reflectivity, the radiation can be polarized and the measurements can be cross-polarization measurements. For example, a target exposed to a certain linear polarization can be measured with that polarization or at a different polarization. So, for symmetric pixels > ! and > 3

! (where the apostrophe denotes the symmetric location), then reflectivity R for those pixels can be measured as follows:

wherein s denotes s polarization and p denotes p polarization. Thus, the reflectivity ? BB corresponds to reflectivity R of s polarized radiation measured when the target was illuminated using s polarization, reflectivity ? BC corresponds to reflectivity R of s polarized radiation measured when the target was illuminated using p polarization, and so on. Moreover, these measurements can be taken at different wavelengths. And, it has been discovered that, in certain embodiments, the overlay for a symmetric unit cell that changes its symmetry in response to overlay change can be found and determined from the congruents ?

[0166] Further, non-linearity can arise from overlay and/or from other parameters. As discussed above, certain non-linearity can be addressed through appropriate selection of weightings, e.g., by deriving the weightings using a Hessian matrix and/or third order derivatives. In an embodiment, the non-linearity can be addressed by using a non-linear solution to derive the overlay from the measured optical information of redirected radiation from a target.

[0167] In an embodiment, the overlay can be determined through using the reconstruction engine as described above used to derive the nominal profile. For example, a non-linear solver working from a model based on the derived nominal profile and/or a derived nominal profile model can be used to derive a simulated version of the optical information expected from redirected radiation from a target of interest, which can be compared to the measured optical information of the target of interest. As noted above, the target of interest comprises one or more physical instances of a unit cell that can be symmetric and that changes its symmetry when subject to overlay. Then, if there is not agreement within a certain threshold, a geometric profile parameter (e.g., overlay) can be varied and the simulated version of the optical information re-computed and compared to the measured optical information until there is agreement within a threshold. Similarly, measured optical information of a target of interest can be compared against a library of the optical information expected from redirected radiation from the target of interest (which library would typically be derived using a non-linear solver). Then, if there is not agreement within a certain threshold, a geometric profile parameter (e.g., overlay) can be varied and the library can be consulted again for a simulated version of the optical information which is compared to the measured optical information until there is agreement within a threshold.

[0168] In an embodiment, the use of the reconstruction engine with the measured optical information from a target of interest uses measured optical information from which a symmetric distribution of radiation has been removed as described above, e.g., by subtracting from the optical characteristic value at each pixel the optical characteristic value at a pixel symmetrically located across a point or axis of symmetry. Thus, the optical information relates to substantially only the asymmetric distribution of radiation. Similarly, the simulated or library version of the optical information relates to substantially only the asymmetric distribution of radiation. This will facilitate the speed of calculation and/or comparison as a significant portion of optical information won’t need to be calculated or evaluated since it will eliminate through the differencing.

[0169] In a further embodiment of a non-linear solution, the expansion of equation (3) can be solved with a non-linear solver to derive n particular, the values o etc., (as applicable) in equation (3) can be determined as part of the determination of the derived nominal profile and/or the derived nominal profile model of a unit cell of interest. For example, once the derived nominal profile has been determined as part of the non-linear reconstruction, simulated or library optical information for a pupil corresponding to the derived nominal profile (e.g., corresponding to a perturbation of the derived nominal profile for a particular change in overlay can be obtained and then the values of a, b, c, etc., (as applicable) can be determined for each pixel in the pupil with a non-linear solver that, e.g., iterates through solutions (e.g., responsive to one or more perturbations in overlay ( in order to

minimize the residual. The result is a vector of a values for the pupil (each a value corresponding to a pixel of the pupil), a vector of b values for the pupil (each b value corresponding to a pixel of the pupil), a vector of c values for the pupil (each a value corresponding to a pixel of the pupil), and so on as applicable. These vectors can then be combined with a vector of 5 ! values determined from a measured pupil of a target having the unit cell of interest. A non-linear solver that, e.g., iterates through solutions in order to minimize the residual, can take these input vectors and then solve for the overlay

[0170] While the discussion above has focused on using a model that models the physical profile of the unit cell, in an embodiment, the weightings can be derived using a data driven technique that does not require physical profile modelling or can be derived with a data driven technique that supplements physical profile modeling. So, in an embodiment, the data driven technique can advantageously not require a physical profile model; this can be useful, for example, for limiting the sharing of confidential information because the physical profile modeling starts with, and determines, details regarding the unit cell (and thus the target) which can be sensitive information if the unit cell is a device pattern structure. In an embodiment, the data driven technique can be enable relatively quick determination of, for example, the weights as discussed above to translate measured optical information (e.g., pupil intensity) into a patterning process parameter (e.g., overlay). In an embodiment, the data driven technique enables determination of the patterning process parameter in an early stage since as discussed below the data technique driven may need only measured data and an associated reference.

[0171] So, in an embodiment, the data driven technique involves processing data measured (“get” data) from one or more substrates having physical instances of the unit cell of interest patterned thereon as one or more targets, with one or more certain set values of the patterning process parameter (e.g., overlay) of interest. This combination of“set” intentional values of a certain patterning process parameter (e.g., overlay) to create patterns along with data measured from those patterns (“get” data) is referred to as a“set-get” process. For example, an overlay of a particular amount of the physical instance of unit cell is created as part of the patterning process and then the target having the physical instance of the unit cell is measured to obtain, e.g., a pupil image thereof (i.e.,“get” data). In an embodiment, a plurality of substrates can be patterned and measured in this manner. In an embodiment, a plurality of different set values of overlay are created, which different values of overlay can be on one substrate, can be across different substrates, etc., In an embodiment, each substrate will have a plurality of targets measured, yielding, e.g., a plurality of pupil images. In an embodiment, the overlay can be created by inducing a magnification change from the design magnification between patterning different parts of the physical instance of the unit cell. In an embodiment, the overlay can be created by providing an intentional translation from the design positioning between patterning different parts of the physical instance of the unit cell. Thus, the result is a deliberate applied overlay in targets that are, e.g., induced by the lithographic apparatus.

[0172] In an embodiment, in general, there is obtained measurement data and associated reference values. So, in an embodiment, deliberate overlay need not be provided if there are different overlays but those overlays are determined by another means (e.g., from a scanning electron microscope). In an embodiment, critical dimension uniformity substrates with corresponding reference data (e.g., coming from a CD-SEM) can be used as the input data. With the measured data and the reference values, the data-driven approach can find, as discussed herein, weights such that inferred overlay values resemble the reference values. So, while the discussion of the data-driven technique will focus on measured optical information and pupil representations obtained at intentionally set overlay value, they can be generally applied to more general measurement data and associated reference values (whether measured or intentionally set).

[0173] Further, while the techniques here relate to a particular overlay (e.g., an overlay in the X- direction), it will be appreciated that the techniques here can be repeated for different overlays (e.g., an overlay in the Y-direction, overlay between structures in different layers, etc.) using corresponding measurement data and reference values. Thus, different weights sets can be determined for different overlays.

[0174] So, referring to Figure 13, a high-level flow of an embodiment of a data driven technique is depicted. At 1300, a calculation is performed to derive the weights as discussed above to translate measured optical information (e.g., pupil intensity) into a patterning process parameter (e.g., overlay). In particular, the calculation uses several inputs. One of the inputs is the set values 1320 of a set-get process for a target having a physical instance of the unit cell of interest. As noted above, a plurality of instances of a target can be measured across one or more substrates, wherein one or more instances of the target have a different value of intentional set value of a patterning process parameter than one or more other instances of the target. A further input is measured optical information 1310 for those instances of the target at different set values. In an embodiment, the optical information 1310 is a plurality of pupil representations, each corresponding to an instance of the target. Then, inputs 1310 and 1320 are processed in a data driven technique to arrive at the weights 1330. Examples of such a data driven technique are described hereafter. [0175] In an embodiment, an example of a data driven technique to find a vector of the weights : is to minimize the following objective or merit function to arrive at the weights

wherein : is a vector of the weights for combination with values of a measured optical characteristic (e.g., intensity) to determine a patterning process parameter (e.g., overlay), each weight corresponding to a pixel value of the pupil, P ! is a matrix with each column containing the pixel values of the measured optical characteristic from a measured pupil of an instance of a target obtained from a substrate W patterned so as to obtain a particular set value of the patterning process parameter (which matrix is then transposed so that the columns becomes the pixels of the pupil, the rows become the one or more instances of the target on the substrate, and the values in the matrix are the values of measured optical characteristic at the respective pixels), R ! is a vector containing the corresponding set values of the patterning process parameter for the one or more instances of the target on the one or more substrates W, each set value corresponding to a patterning process parameter value, 1 is a unit vector of the size of the number of set values, and 4 ! is an offset difference between the set-values of the patterning process parameter and inferred values of the patterning process parameter (P Q

! :) for each substrate, and D is the number of substrates measured. The matrix P ! can be combination of different results for each instance of the target. For example, a target can be measured with different wavelengths, different polarizations, etc., So, these results can be concatenated to each column so, for example, a single column can have values for the pixels of a pupil a target measured with a first wavelength and a first polarization, which are followed by values in the column for pixels of a pupil of the target measured with a second different wavelength or followed by values in the column for pixels of a pupil of the target measured with a second different polarization (and which can then be followed by further values at one or more different polarizations and/or wavelengths).

[0176] So, in effect, this function finds the weight vector :, such that the inferred values P for each substrate W looks as similar as possible (in a L2 regularization norm sense) as the set-values R part from an offset 4 ! . In principle, the optimal weights and offsets can be computed by a matrix inversion. Since the pixel values of the measured optical characteristic are taken with one or more particular metrology apparatuses, the obtained weights can be normalized by calibration data to reduce the impact of the particular metrology apparatus itself on the results.

[0177] Instead of or in addition to finding the weights as described above using an objective or merit function as the data driven technique, the data driven technique can use a machine learning algorithm, like a neural network, or a non-linear method to determine the weights based on measured pupils of targets with intentionally provided difference in the patterning process parameter (e.g., overlay) of interest.

[0178] In an embodiment, after the training (i.e., using the objective or merit function or the machine learning algorithm), the weights can checked using other data. There is a chance that the training results in an overfit; the data driven approach“just” fits the data to the set values. Therefore, a cross validation is done. New data with known set values are used to check the weights. This new data can also be a subset of the substrates at hand. Therefore, in an embodiment, the training is done on a subset of substrates, and the validation is done on another (disjunct) subset of substrates.

[0179] Figure 14 depicts a high-level flow of an embodiment of a data driven technique in combination with a physical geometric model. In this embodiment, a data driven technique as described in relation to Figure 13 can be used to derive weights, which are used to tune a physical geometric model (e.g., by using the Hessian to obtain better model nominal values, by changing the model nominal values, etc.) such that weights from physical geometric model (e.g., the (Moore-Penrose pseudo inverse of the) Jacobian of the physical geometric model) are the same or similar (e.g., in value, statistically, etc.) to the weights determined by the data driven technique. Thus, in an embodiment, a (scaled) weight vector : can be used to fine-tune the physical geometric model such that the physical geometric model is tuned so that the (Moore-Penrose pseudo inverse of) the Jacobian is similar to the (scaled) weight vector :.

[0180] So, in an embodiment, at 1400, a data driven technique (examples of which are described above) is performed to derive the weights as discussed above. The calculation uses several inputs. One of the inputs is the set values 1420 of a set-get process for a target having a physical instance of the unit cell of interest. As noted above, a plurality of instances of a target can be measured across one or more substrates, wherein one or more instances of the target have a different value of intentional set value of a patterning process parameter than one or more other instances of the target. A further input is measured optical information 1410 for those instances of the target at different set values. In an embodiment, the optical information 1410 is a plurality of pupil representations, each corresponding to an instance of the target. Then, inputs 1410 and 1420 are processed in a data driven technique to arrive at the weights 1430.

[0181] The weights 1430 are input to a process 1440 to fine-tune a physical geometric model using the weights 1430. The process 1440 obtains a physical profile 1450 for the unit cell (which the process 1440 uses to derive a physical profile model) or obtains a physical profile model 1450 for the unit cell (which the process 1440 uses). In an embodiment, the physical profile is the derived nominal profile and/or the derived nominal profile model of a unit cell as discussed above.

[0182] The process 1440 uses the physical geometric model to derive weights that correspond to weights 1430. Those weights are then compared to the weights 1430. The comparison can involve a matching of magnitudes, a statistical analysis, a fitting evaluation, etc., If there is a significant difference (e.g., by evaluation of the comparison against a threshold), one or more parameters of the physical profile can be tuned. For example, one or more physical profile parameters (e.g., CD, sidewall angle, material heights, etc.) can be tuned so that the results of the comparison come closer than or equal to, e.g., a certain threshold. In an embodiment, the Hessian can be used to do this fine-tuning, or can be done using a non- linear solver (including one or more forward calls (e.g., a Maxwell solver)). The tuning and comparison can be iterated until the threshold is met or crossed. Then, the tuned physical geometric model can output updated weights 1460 for use in combining with measured optical information of a target of interest to derive a patterning process parameter value.

[0183] Figure 15 depicts a high-level flow of a further embodiment of a data driven technique in combination with a physical geometric model. When a physical geometric model behaves similarly as measured data, the physical geometric model can be used to predict the impact of process variations. So, in an embodiment, the Hessian of the physical geometric model can be used to tune the weights such that the weights become (more) orthogonal to process variations that were not in the data used in the data driven technique to obtain the weights used to tune the physical geometric model.

[0184] This approach of using the Hessian to tune the weights can also be done without the data driven technique. That is, this technique to use the Hessian to update the weights can be done with a physical geometric model approach described in association with Figure 11. In this case, for example, the weights can be tuned such that the weights become (more) orthogonal to process variations that were not in the data used to obtain the derived nominal profile and/or the derived nominal profile model of a unit cell as discussed above. Through such tuning, the weights become more robust to process variations not observed in measured data used to create the physical geometric model.

[0185] So, in an embodiment, at 1500, a data driven technique (examples of which are described above) is performed to derive the weights as discussed above. The calculation uses several inputs. One of the inputs is the set values 1510 of a set-get process for a target having a physical instance of the unit cell of interest. As noted above, a plurality of instances of a target can be measured across one or more substrates, wherein one or more instances of the target have a different value of intentional set value of a patterning process parameter than one or more other instances of the target. A further input is measured optical information 1505 for those instances of the target at different set values. In an embodiment, the optical information 1505 is a plurality of pupil representations, each corresponding to an instance of the target. Then, inputs 1505 and 1510 are processed in a data driven technique to arrive at the weights 1515.

[0186] The weights 1515 are input to a process 1520 to fine-tune a physical geometric model using the weights 1515. The process 1520 obtains a physical profile 1525 for the unit cell (which the process 1520 uses to derive a physical profile model) or obtains a physical profile model 1525 for the unit cell (which the process 1520 uses). In an embodiment, the physical profile is the derived nominal profile and/or the derived nominal profile model of a unit cell as discussed above.

[0187] The process 1520 uses the physical geometric model to derive weights that correspond to weights 1515. Those weights are then compared to the weights 1515. The comparison can involve a matching of magnitudes, a statistical analysis, a fitting evaluation, etc., If there is a significant difference (e.g., by evaluation of the comparison against a threshold), one or more parameters of the physical profile can be tuned. For example, one or more physical profile parameters (e.g., CD, sidewall angle, material heights, etc.) can be tuned so that the results of the comparison come closer than or equal to, e.g., a certain threshold. In an embodiment, the Hessian can be used to do this fine-tuning, or can be done using a non- linear solver (including one or more forward calls (e.g., a Maxwell solver)). The tuning and comparison can be iterated until the threshold is met or crossed.

[0188] But, as will be appreciated, a patterning process can vary during execution and differently for different executions of the patterning process. Thus, data obtained for the data driven technique doesn’t account for all the possible patterning process variations. However, when the tuning of the physical geometric model has made it so that behaves similarly as measured data, the physical geometric model can be used to predict the impact of process variations and adjust the weights accordingly.

[0189] So, in an embodiment, the tuned physical geometric model 1530 is used to compute the Hessian of the tuned physical geometric model at 1535. The Hessian 1540 is then used to tune the weights at 1545 such that the weights become (more) orthogonal (i.e., robust) to process variations that were not in the data used in the data driven technique to obtain the weights used to tune the physical geometric model. In other words, the weights are tuned to be more likely to yield an accurate result when combined with measurement data from a substrate even when the substrate is subject to process variation.

[0190] A non-limiting example of how the Hessian can be used to fine-tune the weights is described here in the context of overlay; a different patterning process parameter could be used as appropriate. In this example, it is assumed only one overlay type is evaluated (e.g., overlay in the X direction). Fine-tuning with multiple overlay types is also possible.

[0191] In this embodiment of using the Hessian to fine-tune the weights, an overlay response is estimated from data measured from one or more set-get substrates by applying a single value decomposition to the data. It is assumed that an eigenvector + (which has length 1) corresponds to the overlay response. Then the following equation is solved to find vector∆>:

wherein \ is the Jacobian with respect to the overlay parameter, and the Hessian [ is a matrix where the columns contain the partial derivatives with respect to a process variation (e.g., a variation in CD, material height, etc.) and the overlay parameter (both the Jacobian and the Hessian are obtained from the model as described above). The determined vector∆> then corresponds to the delta parameters to be applied to the non-overlay parameters in the model to obtain an updated (e.g., better) model.

[0192] To make the weights robust to process variations (i.e., orthogonal to the process variations), the following technique can be used. A pupil can be defined by the following second order Taylor expansion: where \ is the Jacobian with respect to the overlay parameter, and [ is a matrix where the columns contain the partial derivatives with respect to a process variation (e.g., a variation in CD, material height, etc.) and the overlay parameter. The vector∆> contains the corresponding process variations. Thus, for a given structure and for a given process variation instance∆> with an overlay value o, the pupil equals (approximately) . As will be appreciated, the above formulation can be extended to more overlay parameters by adding these contributions as well. Moreover, this formulation is an approximation because the higher orders in the Taylor expansion are neglected.

[0193] Now, if the impact of the process variations is small, the weights are computed using the Penrose-Moore inverse of the Jacobian \. In the case of only one overlay parameter, the weights equal to

And indeed, the weighted average (inner product) with the pupil results in the overlay value o

However, when the process variations have a large impact, the overlay response changes:

To make the weights robust to these variations,

This can be achieved by taking the weights : equal to the first row of the pseudo inverse of the matrix other words, the Hessian matrix [ is concatenated to the Jacobian before the inversion. In this

way, the weights become orthogonal to the process variations (but at some cost of precision).

[0194] Thus, from tuning 1545, tuned weights 1550 are output for use in combining with measured optical information of a target of interest to derive a patterning process parameter value.

[0195] Figure 16 depicts a high-level flow of a further embodiment of a data driven technique in combination with a physical geometric model. In this embodiment, the data input to the data driven technique is extended by including synthetic optical information (e.g., pupil representations) that contains process variations for the patterning process (e.g., the patterning process variation can be obtained from CD measurements). The synthetic optical information alone or in combination with the measured optical information can be used to find new weights using the data driven technique.

[0196] So, in an embodiment, at 1500, a data driven technique (examples of which are described above) is performed to derive the weights as discussed above. The calculation uses several inputs. One of the inputs is the set values 1510 of a set-get process for a target having a physical instance of the unit cell of interest. As noted above, a plurality of instances of a target can be measured across one or more substrates, wherein one or more instances of the target have a different value of intentional set value of a patterning process parameter than one or more other instances of the target. A further input is measured optical information 1505 for those instances of the target at different set values. In an embodiment, the optical information 1505 is a plurality of pupil representations, each corresponding to an instance of the target. Then, inputs 1505 and 1510 are processed in a data driven technique to arrive at the weights 1515.

[0197] The weights 1515 are input to a process 1520 to fine-tune a physical geometric model using the weights 1515. The process 1520 obtains a physical profile 1525 for the unit cell (which the process 1520 uses to derive a physical profile model) or a physical profile model 1525 for the unit cell (which the process 1520 uses). In an embodiment, the physical profile is the derived nominal profile and/or the derived nominal profile model of a unit cell as discussed above.

[0198] The process 1520 uses the physical geometric model to derive weights that correspond to weights 1515. Those weights are then compared to the weights 1515. The comparison can involve a matching of magnitudes, a statistical analysis, a fitting evaluation, etc., If there is a significant difference (e.g., by evaluation of the comparison against a threshold), one or more parameters of the physical profile can be tuned. For example, one or more physical profile parameters (e.g., CD, sidewall angle, material heights, etc.) can be tuned so that the results of the comparison come closer than or equal to, e.g., a certain threshold. The tuning and comparison can be iterated until the threshold is met or crossed.

[0199] So, in an embodiment, the tuned physical geometric model 1530 is used to compute the Hessian of the tuned physical geometric model at 1535. The Hessian 1600 is then used to generate at 1610 synthetic optical information (e.g., one or more pupil representations). Synthetic optical information is simulated optical information. The synthetic optical information is intended to mimic one or more expected process variations in the patterning process. In an embodiment, data 1620 regarding one or more process variations in the patterning process can be used in combination with the Hessian 1600 to derive the synthetic optical information. In an embodiment, a synthetic pupil can be generated by substituting different overlay values o and different parameter variations in the equation (8) above, wherein the weights correspond to : = Y

While equation (8) described above is directed to a single overlay parameter, the technique can be

extended to more overlay parameters by adding those contributions as well. Furthermore, the technique using equation (8) is an approximation, because the higher orders in the Taylor expansion are neglected. The data 1620 can comprise, for example, information that describes the kind and extent of a process variation (e.g., an indication that overlay, CD, etc., can vary by a certain percentage). The data 1620 can be obtained by a measurement in the patterning process, e.g., overlay, CD, etc., measurement. The data 1620 is thus used with the Hessian 1600 to generate simulated optical information 1630 that includes an expected process variation. The synthetic optical information 1630 can also include one or more associated estimated set values associated with the synthetic optical information 1630. The synthetic optical information 1630 (and any associated set values) is then input to the data driven technique 1500 for analysis alone or in combination with the measured optical information, to find new weights using the data driven technique.

[0200] Figure 17 depicts a high-level flow of a further embodiment of a data driven technique in combination with a physical geometric model. This embodiment is similar to the embodiment of Figure 16 except that instead of computing a Hessian a forward call is made to a non-linear solver (e.g., a Maxwell solver) for every process variation to obtain the synthetic optical information.

[0201] So, in an embodiment, at 1500, a data driven technique (examples of which are described above) is performed to derive the weights as discussed above. The calculation uses several inputs. One of the inputs is the set values 1510 of a set-get process for a target having a physical instance of the unit cell of interest. As noted above, a plurality of instances of a target can be measured across one or more substrates, wherein one or more instances of the target have a different value of intentional set value of a patterning process parameter than one or more other instances of the target. A further input is measured optical information 1505 for those instances of the target at different set values. In an embodiment, the optical information 1505 is a plurality of pupil representations, each corresponding to an instance of the target. Then, inputs 1505 and 1510 are processed in a data driven technique to arrive at the weights 1515.

[0202] The weights 1515 are input to a process 1520 to fine-tune a physical geometric model using the weights 1515. The process 1520 obtains a physical profile 1525 for the unit cell (which the process 1520 uses to derive a physical profile model) or a physical profile model 1525 for the unit cell (which the process 1520 uses). In an embodiment, the physical profile is the derived nominal profile and/or the derived nominal profile model of a unit cell as discussed above.

[0203] The process 1520 uses the physical geometric model to derive weights that correspond to weights 1515. Those weights are then compared to the weights 1515. The comparison can involve a matching of magnitudes, a statistical analysis, a fitting evaluation, etc., If there is a significant difference (e.g., by evaluation of the comparison against a threshold), one or more parameters of the physical profile can be tuned. For example, one or more physical profile parameters (e.g., overlay, CD, sidewall angle, etc.) can be tuned so that the results of the comparison come closer than or equal to, e.g., a certain threshold. The tuning and comparison can be iterated until the threshold is met or crossed.

[0204] So, in an embodiment, the tuned physical geometric model 1700 is used to compute at 1720 synthetic optical information like as discussed above. Like as discussed above, data 1710 regarding one or more process variations in the patterning process can be used in combination with the tuned physical geometric model 1700 to derive the synthetic optical information. For example, the data 1710 can comprise information that describes the kind and extent of a process variation (e.g., an indication that overlay, CD, etc., can vary by a certain percentage). The data 1710 can be obtained by a measurement in the patterning process, e.g., overlay, CD, etc., measurement. As noted above, the process at 1720 can use a forward call to a non-linear solver (e.g., a Maxwell solver) for the process variation to obtain the synthetic optical information. The data 1710 is thus used with the tuned physical geometric model 1700 to generate simulated optical information 1730 that includes an expected process variation. The synthetic optical information 1730 can also include one or more associated estimated set values associated with the synthetic optical information 1730. The synthetic optical information 1730 (and any associated set values) is then input to the data driven technique 1500 for analysis alone or in combination with the measured optical information, to find new weights using the data driven technique.

[0205] In Figures 10A-10C, a relatively simple example of a unit cell was presented in which an overlay in essentially only one direction caused a change in the symmetry of the unit cell. In particular, in the unit cell of Figures 10A-10C, an overlay change in the X direction resulted in a change in the symmetry/asymmetry of the unit cell, while an overlay change in the Y direction does not result in a change in the symmetry of the unit cell. This is a consequence of the unit cell of Figures 10A-10C having two structures 1000, 1005 that are configured in a particular geometric way such that an overlay in essentially only one direction caused a change in the symmetry of the unit cell. Of course, this can be designed in this manner by appropriate selection of structures. However, it could be that an existing structure, such as a device structure, can be identified that has a particular geometry such that an overlay in essentially only one direction causes a change in the symmetry of the unit cell. Therefore, various unit cells can be chosen or designed that enable determination of an overlay in essentially only one direction (which need not be in the X direction).

[0206] However, advantageously, a unit cell can be identified or designed that is configured so that a change in the symmetry of the unit cell results for two or more different overlays. In an embodiment, the different overlays can be in different directions. Specifically, in an embodiment, a first overlay can be in the X direction, while a second overlay can be in the Y direction. In an embodiment, the different overlays can each be between a different combination of structures or parts of the unit cell. In an embodiment, those structures can be in a same layer and/or in different layers of the target. Specifically, in an embodiment, a first overlay can be between a first structure and a second structure of the unit cell and a second overlay can be between the first structure (or second structure) and a third structure of the unit cell or between a third structure and a fourth structure of the unit cell. In this case, the first overlay and second overlay can be in the same direction. Naturally, there can be a combination of different overlays in different directions and different overlays from combinations of structures of the unit cell. For example, a first overlay can be in the X direction for a first structure in a first layer and a second structure in a second lower layer and a second overlay can be in the Y direction for the first structure in the first layer and a third structure in the a third layer lower than the second layer. Thus, numerous combinations of overlay can be determined through appropriate identification or design of the unit cell (and thus the target).

[0207] Moreover, as will be appreciated, a determination of an overlay in the X direction and the Y direction can enable through appropriate combination determine a total overlay (in X and Y). Similarly, to enable the determination of total overlay for multiple different structures between which overlay can occur, the overlay for each of those structures needs to be determined. So, as an example, for a unit cell that has 4 distinct structures in 4 layers between which overlay can occur (with one of the layers being a reference layer), then 6 overlays (X and Y for each layer) could be determined to enable determination of the total overlay for the unit cell. Of course, a sub-combination could be determined as desired to arrive at one or more different overlays of interest among the 4 layers.

[0208] Figure 18 depicts an example embodiment of a multiple overlay unit cell of a target. Like the unit cells of Figures 10A-10C, this unit cell comprises a first structure 1000 and a second structure 1005. Additionally, this unit cell has a third structure 1800 that is in this embodiment in a layer above, in the Z direction, the first and second structures 1000, 1005. In this embodiment, asymmetry of this unit cell can be created by one or more different overlays. For example, a relative shift between the structure 1005 and the structure 1800 in the X direction can yield an overlay in the X direction, which causes asymmetry. As another example, a relative shift between the structure 1005 and the structure 1000 in the Y direction can yield an overlay in the Y direction which causes asymmetry. As a further example, a relative shift between the structure 1000 and the structure 1800 in the Y direction can yield a further overlay in the Y direction, which causes asymmetry.

[0209] Figure 19 depicts a further example embodiment of a multiple overlay unit cell of a target. Like the unit cells of Figures 10A-10C, this unit cell comprises a first structure 1000 and a second structure 1005. Additionally, like the unit cell of Figure 18, this unit cell has a third structure 1800 that is in this embodiment in a layer above, in the Z direction, the first and second structures 1000, 1005. Further, this unit cell has a fourth structure 1900 that is in this embodiment in a layer above, in the Z direction, the first, second and third structures 1000, 1005, 1800. Like the unit cell of Figure 18, in this embodiment, asymmetry of this unit cell can be created by one or more different overlays. For example, a relative shift between the structure 1005 and the structure 1800 in the X direction can yield an overlay in the X direction, which causes asymmetry. As another example, a relative shift between the structure 1005 and the structure 1900 in the X direction can yield an overlay in the X direction, which causes asymmetry. As another example, a relative shift between the structure 1005 and the structure 1000 in the Y direction can yield an overlay in the Y direction, which causes asymmetry. As a further example, a relative shift between the structure 1000 and the structure 1800 in the Y direction can yield a further overlay in the Y direction, which causes asymmetry.

[0210] Thus, in an embodiment, measurement of an illuminated physical instance of the unit cell of Figure 18 or of Figure 19 will yield optical information that could potentially include multiple different overlays if there are in fact multiple different overlays. For example, referring to Figure 18, if the symmetry of the unit cell of Figure 18 represents zero overlay and there is a shift in the X and Y of the structure 1005 (e.g., a shift in direction that is not 0, 90, 180 or 270 degrees) from its zero overlay position relative to its overlying structures, that shift would cause an asymmetry due to the relative shift between the structure 1005 and the structure 1800 in the X direction and the relative shift between the structure 1005 and the structure 1000 in the Y direction. Therefore, it would be desirable to determine both the overlay for structure 1005 in the X and Y directions (which combination will yield the total overlay of structure 1005).

[0211] As discussed hereafter, a technique is presented that can determine, from the optical characteristic values, a value of a first overlay for the physical instance of the unit cell separately from a second overlay for the physical instance of the unit cell that is also obtainable from the same optical characteristic values, wherein the first overlay is in a different direction than the second overlay (e.g., X direction overlay and Y direction overlay) or between a different combination of parts of the unit cell than the second overlay (e.g., a first overlay between structure 1005 and structure 1800 and a second overlay between structure 1005 and structure 1000 or between structure 1000 and structure 1800, where the first overlay and the second overlay could possibly be in the same direction).

[0212] That is, in an embodiment, weights are determined to decouple first overlay information in an optical characteristic value from second (or more) overlay information in the same optical characteristic value. Thus, in an embodiment, by applying specially selected weights, the combination of the weights with optical characteristic values will yield a particular overlay of interest as distinguished from other possible overlay information in the same optical characteristic values. In effect, the weights will feature the overlay of interest and lessen one or more other overlays. Of course, different sets of weights can be constructed for each overlay of interest such that the optical characteristic values can be processed to yield different values for each of the different overlays of interest.

[0213] This technique will be described in respect of the graph of Figure 20. The graph of Figure 20 presents a graphical presentation of the technique but in practice the graph need not be constructed as all the processing can be done mathematically without the need to create the graph. Further, the technique is described in respect of the model of Figure 11. However, models (and associated other techniques) described in respect of other Figures herein could be used.

[0214] Further, this example is presented in terms of deriving the linear version of the weights from the model. That is, in an embodiment, the weights are derived from the (Moore-Penrose pseudo inverse of) the Jacobian.

[0215] So, in this linear case, to reconstruct a particular parameter such as an overlay in a certain direction, the Jacobian can be inverted. But, how the column of the parameter of interest is correlated to the remaining columns determines how easily it will be to reconstruct this parameter.

[0216] So, having, e.g., the nominal profile model for a unit cell of interest (e.g., the unit cell of Figure 18), at least two vectors can be generated. A first overlay vector > V represents a first overlay of interest (e.g., a X-direction overlay) within the unit cell and a second overlay vector > . represents a second overlay of interest (e.g., a Y-direction overlay). As will be appreciated, further vectors can be created for additional overlays of interest.

[0217] Further, for each of the two overlay vectors, one or more pixels of a pupil representation corresponding to an expected measurement of the physical instance of the unit cell are selected. In this embodiment, a pair of pixels is selected for each overlay vector, wherein each pair of pixels comprises symmetrically located pixels as described earlier. Desirably, the pairs of pixels are selected from the asymmetric radiation distribution portion of the pupil representation as discussed above.

[0218] Now, the first overlay vector > V corresponds to the response (in this case, asymmetric signal between the pixels creating a pair) in the pairs of pixels to a change in the first overlay of interest for the first overlay vector (leaving all other parameters unchanged, i.e., no change in the second overlay of interest). This response can be generated using the nominal profile model by inducing a change in the first overlay of interest (e.g., 1 nm change) and then calculating the optical response (e.g., intensity) in the pairs of pixels to that change.

[ 0219] Similarly, the second overlay vector > . corresponds to the response (in this case, asymmetric signal between the pixels creating a pair) in the pairs of pixels to a change in the second overlay of interest for the second overlay vector (leaving all other parameters unchanged, i.e., no change in the first overlay of interest). This response can be generated using the nominal profile model by inducing a change in the second overlay of interest (e.g., 1 nm change) and then calculating the optical response (e.g., intensity) in the pairs of pixels.

[0220] The resulting vectors are graphed in Figure 20 wherein the horizontal axis h corresponds to the asymmetric intensity (Ii - Ii’) between symmetrically positioned pixels of the first pixel pair and the vertical axis i corresponds to the asymmetric intensity (Ii - Ii’) between symmetrically positioned pixels of the second pixel pair. So, Figure 20 shows two highly correlating vectors > V and > . .

[0221] So, to decouple and separate the contributions of the first and second overlays of interest to the pixel pairs, the vector > V is back-projected onto a vector P . j , which is a vector orthogonal to the vector > . , to form vector > V 3 and the length of projected vector > V 3 is divided by the cosine of the angle k V between vector > V and P . j . This vector then helps to isolate the first overlay of interest from the intensity of the pixel pairs (and by extension other pixel pairs in the pupil representation).

[0222] Additionally or alternatively, the vector > . is back-projected onto a vector P V j , which is a vector orthogonal to the vector > V , to form vector > . 3 and the length of projected vector > . 3 is divided by the cosine of the angle k . between vector > . and P V j . This vector then helps to isolate the second overlay of interest from the intensity of the pixels pairs (and by extension other pixel pairs in the pupil representation). [0223] So, referring back to equations (3) and (4), Si represents the asymmetric intensity (Ii - Ii’) between symmetrically positioned pixels of a pixel pair. So, the first overlay vector > can correspond to the response in a first pixel pair having d a second pixel pair having ) a change in the

first overlay of interest. Similarly, the second overlay vector can correspond to the response in those first and second pixel pairs to a change in the second overlay of interest. Accordingly, the vector > and/or the vector > can be constructed; here both are constructed for explanatory purposes. The vector > and t he vector 3 are defined in terms of the intensity h corresponding to the first pixel pair corresponding to ) and in terms of the intensity i corresponding to the second pixel pair corresponding vector and vector > 3 can be specified as:

So, now in the linear context described above and referring to equation (4), an overlay value of the first overlay of interest can then be defined based on l and vectors as follows:

Additionally or alternatively, an overlay value of the second overlay of interest can then be defined based on ) ) nd vectors as follows

So, from equation (14), the weights to determine the first overlay of interest are, for respectively

the following:

Further, from equation (15), the weights to determine the second overlay of interest are, for respectively l ) and the following:

So, as will be appreciated, this can be repeated for all, or substantially all, of the pixel pairs in the pupil representation so as to arrive at a set of weights : ! for the first overlay of interest and/or to arrive at a

set of weights for the second overlay of interest One or both of these can then applied to measure optical characteristic values in accordance with equation (4) to arrive at an overlay value for the respective overlay of interest. Of course, one or more further overlays of interest can be evaluated and one or more appropriate weight sets determined for them. As will be appreciated, in an embodiment, the sensitivity (e.g., Jacobian) to all of the different overlays of interest is included in the weights definition for a particular overlay of interest.

[0224] So, for example for a unit cell having 4 layers (with one of the layers being a reference layer) wherein a shift in each of the layers in the X and Y directions could cause a change in symmetry (e.g., cause an asymmetry, or cause a further asymmetry, or cause an asymmetric unit cell to become symmetric), then 6 vectors can be created (each being associated with a different pixel pair), the 6 vectors comprising a X- direction overlay vector for each of the layers and a Y-direction overlay vector for each of the layers. There could thus be 6 sets of weights to derive the respective overlays. Of course not all of the weight sets need to be derived if one of the vectors is not of interest (but in an embodiment, the sensitivity (e.g., Jacobian) to all of the different overlays of interest is included in the weights definition for the particular overlay of interest). Any other overlay can then be determined by appropriate mathematical combination of two or more of these overlays.

[0225] As will be appreciated, some shifts of a layer in a unit cell would not cause a change in symmetry and so the overlay corresponding to that shift cannot be determined from the unit cell. So, obviously, no vector would be defined for such a shift. So, taking Figure 18 as an example, three vectors could be defined for that unit cell– one for the X-direction overlay and two for the different Y-direction overlays. So, one sets of weights can be determined that will give the overlay in the X-direction when combined with measured optical characteristic values. Or, a set of weights can be determined that will give one of the overlays in the Y-direction when combined with measured optical characteristic values and/or a set of weights can be determined that will give the other of the overlays in the Y-direction when combined with measured optical characteristic values. Of course, all three sets of weights can be determined or just two.

[0226] The discussion above has focused on a target formed by one or more instances of a symmetrical unit cell made up of structures of a device. Such a target can enable, through on-product measurement of radiation redirected by the on-product target, determination of an on-product value of a patterning process parameter. However, as described above, the target need not be made up of only device structures. In other words, a non-product target can be provided whose structures don’t exclusively comprise device structures. For example, in an embodiment, a target can be specially created of structures that are not used to form the device but rather are merely used for measurement. Such a target can be provided, e.g., in a scribe lane away from the device (and thus provided in a part of a device patterning pattern away from the device pattern). In an embodiment, the target can be provided in among the device pattern (and thus provided among the features of a device pattern of a patterning device pattern). Where appropriate, a non-product target can comprise one or more device structures and one or more specially created structures that are not used to form the device but rather are merely used for measurement.

[0227] A non-product target can be useful if, for example, a patterning process parameter is being determined for a device pattern that cannot present symmetric unit cell instances. As another example, a non-product target can be useful if, for example, a patterning process parameter is being determined for a portion of a device pattern that doesn’t have a symmetrical unit cell as described above that can give a measure of that patterning process parameter. For example, there can be cases of a structure for overlay after etch is desired to be determined using the symmetrical unit cell methods described above but has no symmetry. For example, logic circuits or structures have many process layers\steps that are each able to introduce a different overlay component that can break the symmetry of the structure. In the case of logic circuits for example, measurement on the device pattern typically cannot be performed due to the lack of a symmetric unit cell of logic circuit structures.

[0228] As a further example, the non-product target can be used in association with a device pattern that can present symmetric unit cell instances (and even if the unit cell can give a measure of all patterning process parameters of interest). This can be, for example, if the device pattern is complex, which can require significant computation time. Further, the device pattern may present potential cross-talk with signals of patterning process parameters not of interest. As an example, the pupil correlations of different overlay components might be so large that it is impossible to separate the different overlay errors.

[0229] Thus, a non-product target can be used with a device pattern that has instances of a symmetrical unit cell for a beam spot or with a device pattern that can’t present instances of a symmetrical unit for the beam spot.

[0230] So, in an embodiment, a non-product target can be designed such that a particular type of patterning process parameter (e.g., overlay) of interest breaks a certain type of (pupil) symmetry of the non- product target; this is similar to the techniques described above. And, while overlay will be a focus of the discussion, like as discussed above, one or more different patterning process parameters than overlay may be determined.

[0231] Of course, for the non-product target to give a measure of the patterning process parameter, the non-product target will follow those process steps that are considered to be the main contributor to the patterning process parameter at issue. Thus, as discussed above, if, e.g., an overlay between two structures created in separate patterning processes are of interest, then the non-product target comprises a structure created in each of the separate patterning processes and desirably by a same or comparable process.

[0232] Further, breaking a certain type of geometric symmetry (e.g., Y-symmetry) leads to breaking the same type of symmetry in the pupil domain. So, a non-product target can be designed for a particular type of geometric symmetry such that a corresponding particular patterning process parameter value causes a break in the symmetry. For example, a Y-symmetry broken by an X-overlay. Further, where there is symmetry in more than one direction using a target that is designed such that a different type of patterning process parameter (e.g., different overlay type such as overlay in X and overlay in Y) breaks a different type of symmetry enables monitoring the induced asymmetry (according to the relevant type of symmetry) to determine one patterning process parameter (e.g., overlay) at a time.

[0233] A non-product target can have one or more advantages. For example, a non-product target design can have reduced or minimized pupil correlations compared to using a measurement of radiation from an on-product target and, as a consequence, a patterning process parameter of interest is easier to determine from the measured radiation. In an embodiment, the non-product target design can reduce or minimize cross-talk between different types of a same patterning process parameter or between different kinds of patterning process parameter. Thus, a cleaner signal can be obtained. The non-product target design can have of advantage of measuring a patterning process parameter for a device pattern that doesn’t have instances of a symmetric unit cell for a beam spot. Thus, the non-product target design can enable the extension of the measurement and determination techniques described herein to applications like logic and/or advanced memory where the device pattern may not have instances of a useful symmetric unit cell. A non-product target design can have a relatively simplified structure, which can, e.g., make it easier for modeling as described herein. This can make it easier to separate and determine more than one patterning process parameter type from a single target. Further, a non-product target design can be specially configured to determine just a single patterning process parameter type or determine a specific combination of patterning process parameter types.

[0234] However, oversimplification in a non-product target design may kill critical contributors to the patterning process parameter (e.g., overlay). To mitigate this risk, the non-product target design should assume the substantially same process steps as the device product pattern. Further, main contributors to the patterning process parameter of interest should be identified so that they can be factored into the non- product target design and/or and associated modeling.

[0235] So, like an on-product target design, an embodiment of a non-product target design is defined in terms of a unit cell comprising structures having a geometric symmetry. In an embodiment, the symmetry can be in a first direction (e.g., X-direction), in a second orthogonal direction (e.g., Y-direction), or both. In an embodiment, the unit cell is created such that a change in physical configuration of the structures in the unit cell causes a break in symmetry, which break in symmetry results in a particular radiation distribution, which can be processed to determine a value of a patterning process parameter of interest as described above. Thus, the unit cell effectively as the metrology target and, in an embodiment, contains a minimum area of structures used to provide the signal to determine the patterning process parameter of interest.

[0236] In an embodiment, the non-product target design comprises structures created in at least two patterning processes (e.g., at least two executions of a same type of patterning process, at least two executions of different types of patterning processes, etc.). In an embodiment, where the plurality of patterning process executions result in structures in different layers for which a patterning process parameter of interest is being determined, the non-product target design unit cell comprises a structure from each of the plurality of layers of interest. In an embodiment, where the patterning process executions result in structures in a same layer for which a patterning process parameter of interest is being determined, the non-product target design unit cell comprises a structure from each of the applicable different patterning process executions of interest. In an embodiment, a first structure created by a first patterning process and/or a second structure created by a second patterning process is not used to create a functional aspect of a device pattern.

[0237] So, in an embodiment and in terms of the unit cell, structures from a plurality of patterning processes together form an instance of the unit cell and the unit cell has geometric symmetry at a nominal physical configuration, wherein the unit cell has a feature that causes, at a different physical configuration than the nominal physical configuration due to, e.g., a relative shift in pattern placement in the first patterning process, the second patterning process and/or another patterning process, an asymmetry in the unit cell. An example of such a feature is one that causes asymmetry in the unit cell in response to an offset of a structure in one layer relative a structure to another layer.

[0238] In an embodiment, the non-product target design comprises a repetition of the unit cell. That is in an embodiment, a beam spot on a physical instance of the non-product target would illuminate a plurality of instances of the unit cell filling up the beam spot. In an embodiment, the non-product target design comprises at least 4 instances, at least 8 instances, at least 10 instances, at least 20 instances, at least 40 instances, at least 80 instances, at least 100 instances, at least 200 instances, at least 400 instances, or at least 1000 instances of the unit cell.

[0239] In an embodiment, the non-product target as produced on a substrate has a small size. For example, the non-product target can have an area of 100 square microns or less, 50 square microns or less, or 25 square microns or less. In an embodiment, the non-product target has a cross-wise dimension of 10 microns or less or 5 microns or less. In an embodiment, the beam spot for the non-product target has a cross-wise dimension smaller than the maximum cross-wise dimension of the target. In an embodiment, the beam spot for a non-product target has a cross-wise dimension of 10 microns or less, 5 microns or less or 2 microns or less. In an embodiment, the beam spot for a non-product target has a cross-sectional area of less than or equal to 100 square microns, 50 square microns or less, or 25 square microns or less. In an embodiment, the unit cell of a non-product target has an area of 250,000 square nanometers or less, 150,000 square nanometers or less, 100,000 square nanometers or less, or 50,000 square nanometers or less. In an embodiment, the unit cell of a non-product target has a cross-wise dimension of 500 nanometers or less, 300 nanometers or less, 200 nanometers or less or 150 nanometers or less. In an embodiment, the unit cell of the non-product target has a smaller size than a unit cell of a device pattern associated with the non- product target.

[0240] In an embodiment, the unit cell comprises a feature (e.g., a structure, a void (e.g., a gap), etc.) that corresponds to a feature (e.g., a structure, a void, etc.) of a device made using a first patterning process and a feature (e.g., a structure, a void, etc.) that corresponds to a feature (e.g., a structure, a void, etc.) of a device made using a second patterning process. For example, a structure of the unit cell is created by a first patterning process that creates a corresponding device feature of a device and another structure of the unit cell is created by a second patterning process that creates a corresponding device feature of the device. In an embodiment, one or more features created in a unit cell share key process steps of a feature in a device for which the unit cell feature is being used to determine a patterning process parameter. In an embodiment, the features of the unit cell created by the respective corresponding patterning processes correspond to, e.g., one or more features (e.g., structures such as lines) of the device that extend or are elongate in a direction essentially parallel to the features (e.g., lines) of the unit cell. So, for example, the unit cell comprises structures extending in a Y-direction can be used to determine overlay of corresponding structures in the device extending in the Y-direction.

[0241] In an embodiment, as described further in examples presented below, the unit cell can enable determination of multiple different types of a same patterning process parameter (e.g., overlay). For example, a unit cell enable determination of 2 or more types of overlay, 3 or more types of overlay, etc., For example, besides types of overlay in different directions (e.g., in X and Y), the unit cell can enable determination of overlay between different combinations of features and/or between different combinations of layers.

[0242] In an embodiment, the unit cell has features that have comparable dimensions (e.g., widths and/or pitches) to corresponding features of a device. Comparable dimensions means identical or within ±5% from the device feature dimension (i.e., 95% to 105% of the device feature dimension), within ±10% from the device feature dimension, within ±15% from the device feature dimension, within ±20% from the device feature dimension, or within ±25% from the device feature dimension. In an embodiment, the dimensions of one or more the unit cell features can be selected to improve the measurement signal and thus not match the corresponding dimension of a feature of the device pattern. This can be done, for example, by evaluating the sensitivity of signal output to change in dimension of the target feature and so the dimension can be selected in the particular circumstance to maximize signal or provide a signal meeting or crossing a threshold.

[0243] In an embodiment, the non-product target can be used in conjunction with an on product target. For example, an overlay can be determined using the non-product target and the result can be fed-forward to determination of the overlay using an on-product target.

[0244] Figure 21 is an illustrative diagram of an overlay between two layers of a substrate, in accordance with various embodiments. Scenario 2100, in the illustrative embodiment, includes a side- profile of two layers of a target T. Target T, which may correspond to a substrate, may include a first layer L1 and a second layer L2. Layers L1 and L2 may each include one or more features arranged in a pattern, as described in greater detail above with reference to Figures 10A-C. Layers L1 and L2 are separated by a distance, and target T may include additional layers above and/or below layers L1 and L2, respectively, each separated by the same distance or a slightly different distance.

[0245] In one embodiment, each layer’s features correspond to a grating– which may be a substantially block-like configurations, however this is merely exemplary. For instance, layer L1 may include a first set of features 1000 and a second set of features 2000. In scenario 2100, a relationship between features 1000 and features 2000 may be characterized by a first parameter of interest having a first value. For example, as described by scenario 2100, an overlay OV exists between features 1000 and 2000 of first layer L1 and second layer L2, respectively. Additional overlays may exist for the other features 1000 and 2000 of layers L1 and L2, and, furthermore, overlays may also exist between features of other layers of target T. Scenario 2100, therefore, depicts a single overlay for simplicity and is not intended to be limiting. In an embodiment, overlay OV is shown as being one dimensional, however persons of ordinary skill in the art will recognize that overlay may also exists in additional dimensions, and the aforementioned is merely illustrative.

[ 0246] Overlay OV may be described, for example, in terms of reflectivity coefficients R 0 , as seen by Equation 17.

[0247] More generally, the reflectivity coefficient R may be described as:

[0248] As described above, the reflectivity may be associated with the intensity of the radiation beam (e.g., zeroth order, first order.

[ 0249] of Equation 17 and of Equation 18 describe the reflectivity coefficients per

pupil point In one embodiment, these values may be given ahead of time (e.g., data obtained prior

to intensity calculations being performed). may describe, for example, a nominal CD profile. In

other words, may provide an optimal description of the layers and shapes on the wafer based on

the CD application. for instance, may be related to characteristics of the wafer. In the illustrative embodiment, describes the reflectivity based on the CD profile of the target as a function of

parameter p at an overlay OV=0 (e.g., no overlay). on the other hand, describes the reflectivity

based on the CD profile as a function of parameter p and overlay, for overlays not equal to zero.

[0250] In one application, the nominal CD profile may be used to determine how the modeled intensities, as measured by a calibrated sensor (e.g., 19 of Figure 3A), respond to a change in a value of overlay OV. The overlay sensitivity may be described by }

[0251] The overlay sensitivity may, as seen by Equation 19, reflects a change in sensitivity in relation to a change in the asymmetry of the target’s features. In Equation 19, the modeled intensities and may be represented by Equation 20, where

asymmetric pupil points.

[0252] In Equation (20) 8 may correspond to an output illumination as function of pupil poin may correspond to the effects of the sensor coming in and/or being detected at

each pupil point In one embodiment, may be related to the sensor (e.g.,

sensor 19 and/or sensor 23), and may be given based on calibrations performed to the sensor(s) prior to intensity measurements. Further, corresponds to the Hermitian of such that

[0253] As seen in Equation 20, the modeled intensity is therefore determined by the trace of at each pupil point. may reflect how the

intensities change at different pupil points with variations to these parameters. Therefore, the OV sensitivity may include errors due to calibration of the measurement components.

[0254] Characterization of a target wafer using the nominal CD-profile, as seen by Equation 17, may yield measured intensitie To determine the measured overlay OV, the anti-symmetry between the measured intensities may be performed (e.g., differences between (f, g) and (-f, -g)), and multiplied by the sensitivities the result of which is described by Equation 21.

[ 0255] In Equation 21, the intensity difference (e.g.,

characterizing the anti-symmetry (if present), may correspond to a difference between the measured intensity at one pupil point (f, g) and the measured intensity at the antisymmetric pupil point (-f, -g). Thus, as indicated by Equation 21, in one embodiment, accurately measuring the sensitives and will provide an accurate overlay measurement.

[0256] Figure 22 is an illustrative diagram of an exemplary substrate include a predicted amount of overlay between layers of the substrate, in accordance with various embodiments. In one embodiment, the exemplary substrate may correspond to a get-set wafer 2200, which has a predicted amount of overlay between features of two or more layers of the substrate. Get-set wafer 2200 may include information, or information may be known about get-set wafer 2200, that indicates a known overlay OV for that substrate. For example, each point on the substrate may be defined by its x and y coordinates (however different dimensions may be employed (e.g., (x, z), (y, z)), and an overlay associated with that point on the substrate may be known. In one embodiment, the overlay may be a function of the coordinates. For example, overlay value OV per point on the wafer may be represented by Equation 22.

[0257] Alternatively, or additionally, the overlay value per point on the wafer may be represented by a corresponding reflectivity at that particular point, as seen by Equation 23.

[0258] In Equation 23, the reflectivity, also referred to, as mentioned above, as the reflectivity coefficient (e.g., see Equation 18), may be related to the CD profile, which may be a function of parameters

[0259] After performing the intensity measurements, as detailed above, a determination may be made as to whether the measured overlay value OV equals the input overlay value, defined by If the

measure OV value does not match the input then parameters of the CD profile, such as, for

example, may be adjusted. In one embodiment, the only parameters being affected are associated with the CD profile however, this is merely exemplary.

[0260] Adjustment of parameter may cause a change in the modeled intensity difference associated

with the modeled OV sensitivity per pupil point as described above by Equation 19. After

an adjustment is made to the model, the process may be repeated, and the newly acquired measured OV may then compared with the newly modeled OV. This process may repeat until a difference between the measured (e.g., get) OV value and the modeled (e.g., set) OV value are minimized. In some embodiments, the process may be repeated twice (e.g., once to check to see an amount of error associated with the modeled OV sensitivity, and a second to check to see if the adjustment made to the parameters mitigates the errors). For instance, when the difference is less than a threshold value, which may be pre-set or configurable, for example. The minimization process may be reflected by Equation 24:

In Equation 24, the modeled intensities may be described by:

[0261] In Equation 25, as compared to Equation 20, the reflectivity coefficient and may further be based on the wafer point that the measurement is associated with in addition

to the pupil point. Furthermore, both may remain dependent on the pupil point.

[0262] Equations 24 and 25 illustrate that a discrepancy may arise between a base description of a wafer layer’s thickness and the shapes on the wafer as seen by the CD application and at-resolution-overlay (“ARO”) application. This may indicate inaccuracies in tool calibration, and in particular, inaccurate calibrated sensory asymmetry.

[0263] Using the information associated with the substrate having predicted overlay (e.g., get set wafer 2200), the CD profile and the tool calibration may simultaneously be optimized. This may be accomplished by updating parameter > and calibration matrices Therefore, Equation 24 is

modified to account for this, yielding Equation 26. [0264] By employing Equation 26, a co-optimization between parameter > and calibration matrices may be achieved. This may prevent the non-linear solver from transferring the changes

associated with parameter to matrices Further, this may allow new information associated

with the at-resolution overlay application to effect the tool calibration.

[0265] The minimization, as seen by Equation 26, may also be represented by Equation 27 by including, for Imodel, Equation 25.

[0266] For small changes in the modeled intensities as a function of small changes in the parameters, may be represented by Equation 28.

[0267] In Equation 28, J and H correspond to the Jacobian and the Hessian, respectively. In an embodiment, certain parameters are restricted from change to prevent transfer from parameter > to matrices The parameters that are restricted from change correspond to parameters that are solely dependent on pupil point and do not include any positional dependency (e.g., coordinates x and y). For i nstance,

a re prevented from exchanging.

[0268] To update the nominal tool, the following terms may be used:

Furthermore, the terms:

m ay be optimized.

Previously, only terms

h ad been employed to optimize the sensitivity model. The additional terms

m ay now be added to the

optimization scheme to optimize the sensitivity model. In these terms, wafer information may cross talk between the sensor and the CD profile. Generally speaking, the terms that may be modified, may correspond to characteristics of the sensitivity model that may be adjusted based on the results of the measured overlay in relation to the predicted overlay. The solution of the solver, in an embodiment, may be restricted to the calibration results and to the CD profile with some elastic constraints that may be determined.

[0269] Figure 23 is an illustrative flow chart of an exemplary process for determining an adjustment to one or more characteristics of a metrology apparatus, in accordance with various embodiments. Process 2300, in a non-limiting embodiment, may begin at step 2302. At step 2302, a substrate may be obtained, where the substrate includes first features on a first layer and second features on a second layer, where a relationship between the first features and the second features is characterized by a parameter of interest having a first value. having a predicted amount of overlay may be obtained. For example, a get- set wafer 2200 may be obtained. Get-set wafer 2200 may include a predicted, predefined, and/or known amount of overlay, which may correspond to an overlay between features 1000 and features 2000.

[0270] At step 2304, a metrology apparatus may be applied to the substrate, where the metrology apparatus is operated in accordance with at least one characteristic having a first setting. For instance, the metrology apparatus of FIG.3A may be applied to substrate 2200. By applying the metrology apparatus to the substrate, an incident radiation beam (e.g., ray of illumination I) may incident on the features (e.g., the first features and the second features) present on the substrate. In some embodiments, the at least one component may be related to a sensitivity model used to determine the parameter of interest (e.g., an amount of overlay), and/or any other suitable parameter associated with the metrology process.

[0271] At step 2306, intensity data may be received. The intensity data may represent first intensity, or intensities, of a first portion of the incident radiation beam scattered by the first features and the second features. In some embodiments, the intensity data may correspond to information obtained by sensor 19 and/or sensor 23 in response to the incident radiation beam (e.g., ray of illumination I) being applied to the substrate. For example, particles of ray I may scatter off the features (e.g., features 1000 and 2000) of substrate 2200, and may be detected by sensor 19 and/or sensor 23. The intensity data may represent a magnitude and location of the detected scattering, which may provide information relevant to determining an amount of overlay between features 1000 and 2000. In some embodiments, one or more pre-processing techniques (e.g., filters) may be applied to the intensity data after being received.

[0272] At step 2308, a second value for the parameter of interest may be determined. For example, a measured amount of overlay may be determined based on the intensity data. As an illustrative example, the measured amount of overlay may, for instance, indicate an error in the settings of one or more component associated with the metrology apparatus. In some embodiments, the measured amount of o verlay may be determined using Equation 21. As seen above, Equation 21 may include and

F urthermore, as seen from Equation 19, is a function of and

Therefore, a measured amount of overlay is likely due to one of two factors: an actual

overlay that is present, or the settings associated with one or more components of the sensitivity model of the metrology apparatus that need to be adjusted. In the illustrative embodiment, because the substrate has a first value for the parameter of interest (e.g., a predicated/known amount of overlay), if the second value of the parameter of interest determined from the intensity data does not equal the first value, then this may indicate one or more errors in the settings associated with one or more components for the sensitivity model. For example, if the measured amount of overlay differs from the predicted amount of overlay, then this may indicate that one or more components of the sensitivity model for the metrology apparatus need to be adjusted. Alternatively or additionally, the error may be due to calibration to physical parameters associated with metrology apparatus.

[0273] At step 2310, a difference between the first value of the parameter of interest and the second value of the parameter of interest may be determined. For example, a difference between the measured amount of overlay and the predicated amount of overlay may be determined. In one embodiment, as mentioned above, the first value of the first parameter for the substrate that was used at step 2302 is known. The difference between the second value and the known first value should be substantially small (e.g., zero difference) if the settings associated with the one or more components of the sensitivity model are calibrated correctly. However, if there is a difference is not substantially small (e.g., 10^-9), then this may indicate that one or more settings associated with at least one of the one or more parameters related to sensitivity model for the metrology apparatus need to be adjusted.

[0274] At step 2312, one or more adjustments may be determined, where the one or more adjustments are to be applied to the one or more components. In particular, the one or more adjustments to the at least one characteristics are such that a setting of the one or more characteristics changes from the first setting to a second setting, which differs from the first setting. Furthermore, the one or more adjustments may be determined, as described above, based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest. For example, as described in greater detail above with reference to Equation 28, certain terms of the modeled intensity may be associated with cross talk between the sensor and the CD profile. The particular terms whose values are adjusted may be determined based on the measured different between the predicted overlay value and the measured overlay value. At step 2314, the one or more adjustments to the settings of the one or more characteristics may be applied.

[0275] At step 2316, a new substrate including third features on a third layer and fourth features on a fourth layer, where a relationship between the third features and the fourth features may be characterized by the parameter of interest having a third value, may be obtained. For instance, a second get-set wafer having an predicted/known overlay between features on a first layer of the new substrate and features on a second layer of the new substrate may be obtained. At step 2318, the incident radiation beam may be applied to the new substrate by the metrology apparatus, where the metrology apparatus is operated, in the illustrative embodiment, in accordance with the at least one characteristic having the second setting. For example, the same, the metrology apparatus, configured with the adjustments to the settings as described above with respect to steps 2312 and 2314, may apply ray of illumination I to the new substrate.

[0276] At step 2320, second intensity data representing second intensity of a second portion of the incident radiation beam scattered by the third features and the fourth features may be received. For instance, sensor 19 and/or sensor 23, in response to the incident radiation beam (e.g., ray of illumination I) being applied to the new substrate with the metrology apparatus having the at least one characteristic being the second setting, may receive intensity data indicating the magnitudes and directions of the scattered particles by the features of the new substrate. In some embodiments, step 2320 may be substantially similar to step 2306, with the exception that the intensity data received at step 2320 may be in response to the ray of illumination, from the metrology apparatus configured with the at least one characteristic having the second setting as opposed to the first setting, being applied to the new substrate.

[0277] At step 2322, a fourth value for the parameter of interest for the new substrate may be determined. In some embodiments, the fourth value may be determined based on the second intensity data that was received at step 2320. For example, a new amount of measured overlay may be determined. The new measured amount of overlay may be based, in one embodiment, the intensity data received at step 2320.

[0278] At step 2324, a second difference between the third value of the parameter of interest for the second substrate and the fourth value of the parameter of interest for the second substrate may be determined. For example, a difference between the predicated amount of overlay for the new substrate and the measured amount of overlay for the new substrate may be determined. At step 2326, a determination may be made as to whether the at least one characteristic of the metrology apparatus has been calibrated. The metrology apparatus may be determined to be calibrated if the second difference is less than a threshold value. For example, if the difference between measured amount of overlay for the new substrate and the predicted/known amount of overlay for the new substrate is less than a threshold value (e.g., 10^-9). If so, then process 2300 may proceed to step 2328, where the process ends. In some embodiments, the threshold may be preset based on the particular substrates used at steps 2302 and 2316. If, however, it is determined that the metrology apparatus has not been calibrated for the at least one characteristic having the second swatting, the process 2300 may proceed to step 2330. In some embodiments, at step 2330, a determination is made as to whether process 2300 is to repeat for another new substrate. If so, then process 2300 may return to step 2302, where another new substrate, having a parameter of interest with a new value, which is predicted/known, may be obtained. However, process 2300, at step 2330, may alternatively end. For instance, another substrate, having a different predicated overlay than the substrates of steps 2302 and 2316, may be obtained, and the process may be repeated. [0279] While discussion in this application considers an embodiment of a metrology process and metrology target designed to measure a parameter of interest of a substrate, such as an overlay, the embodiments herein are equally applicable to other metrology processes and targets, such as process and targets to measure various other asymmetries in symmetrical structures, such as sidewall angle asymmetry, asymmetry in bottom floor tilt angle, asymmetries in CD, etc. Accordingly, the references herein to overlay metrology targets, overlay data, etc. should be considered as suitably modified to enable other kinds of metrology processes and targets.

[0280] In an embodiment, there is provided a method including: applying, by a metrology apparatus, an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting; receiving first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features; determining, based on the first intensity data, a second value of the parameter of interest for the first substrate; and applying one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

[0281] In the embodiment, the method further includes: applying the incident radiation beam to a second substrate comprising third features on a third layer and fourth features on a fourth layer, a second relationship between the third features and the fourth features being characterized by the parameter of interest having a third value, wherein the metrology apparatus is operated in accordance with the at least one characteristic having the second setting; receiving second intensity data representing second intensity of a second portion of the incident radiation beam scattered by the third features and the fourth features; determining, based on the second intensity data, a fourth value of the parameter of interest for the second substrate; and determining a second difference between the third value of the parameter of interest and the fourth value of the parameter of interest.

[0282] In the aforementioned embodiment, the method further includes: determining, based on the second difference being less than a threshold value, that the metrology apparatus is calibrated for the at least characteristic having the second setting.

[0283] In the aforementioned embodiment, the method further includes: performing an additional calibration for the metrology apparatus by modifying the second setting at least one characteristic in response to determining that the second difference is equal to or greater than a threshold value. [0284] In the embodiment, where the second value of the parameter of interest is determined, the method includes: obtaining an intensity model that indicates an expected intensity distribution for the metrology apparatus for the at least one characteristic having the first setting; identifying one or more components of the intensity model associated with the first features of the first layer and the second features of the second layer; and determining the second value of the parameter of interest by calculating a second difference between the expected intensity distribution and the first intensity data based on the one or more components.

[0285] In the aforementioned embodiment, the one or more components of the intensity model relate to a pupil point of the metrology apparatus and a feature position.

[0286] In the embodiment, the method further includes: updating an intensity model indicating an expected intensity distribution for the metrology apparatus such that the intensity model reflects the at least one characteristic having the second setting.

[0287] In an embodiment, there is provided a metrology apparatus including memory and at least one processor operable to: apply an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting; receive first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features; determine, based on the first intensity data, a second value of the parameter of interest for the first substrate; and apply one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

[0288] In the embodiment, the at least one processor of the metrology apparatus is further operable to: apply the incident radiation beam to a second substrate comprising third features on a third layer and fourth features on a fourth layer, a second relationship between the third features and the fourth features being characterized by the parameter of interest having a third value, wherein the metrology apparatus is operated in accordance with the at least one characteristic having the second setting; receive second intensity data representing second intensity of a second portion of the incident radiation beam scattered by the third features and the fourth features; determine, based on the second intensity data, a fourth value of the parameter of interest for the second substrate; and determine a second difference between the third value of the parameter of interest and the fourth value of the parameter of interest.

[0289] In the aforementioned embodiment, the at least one processor is further operable to: determine, based on the second difference being less than a threshold value, that the metrology apparatus is calibrated for the at least characteristic having the second setting.

[0290] In the aforementioned embodiment, the at least one processor is further operable to: perform an additional calibration for the metrology apparatus by modifying the second setting at least one characteristic in response to determining that the second difference is equal to or greater than a threshold value.

[0291] In the embodiment, the second value of the parameter of interest being determined corresponds to the at least one processor being operable to: obtain an intensity model that indicates an expected intensity distribution for the metrology apparatus for the at least one characteristic having the first setting; identify one or more components of the intensity model associated with the first features of the first layer and the second features of the second layer; and determine the second value of the parameter of interest by calculating a second difference between the expected intensity distribution and the first intensity data based on the one or more components.

[0292] In the embodiment, the one or more components of the intensity model relate to a pupil point of the metrology apparatus and a feature position.

[0293] In the embodiment, the at least one processor is further operable to: update, stored in the memory, an intensity model indicating an expected intensity distribution for the metrology apparatus such that the intensity model reflects the at least one characteristic having the second setting.

[0294] In an embodiment, there is provided a non-transitory computer readable medium comprising instructions that, when executed by at least one processor of a computing device, causes the computing device to: apply, by a metrology apparatus, an incident radiation beam to a first substrate comprising first features on a first layer and second features on a second layer, a first relationship between the first features and the second features being characterized by a parameter of interest having a first value, wherein the metrology apparatus is operated in accordance with at least one characteristic having a first setting; receive first intensity data representing first intensity of a first portion of the incident radiation beam scattered by the first features and the second features; determine, based on the first intensity data, a second value of the parameter of interest for the first substrate; and apply one or more adjustments to the at least one characteristics such that the at least one characteristics has a second setting different from the first, the one or more adjustments being determined based on a first difference between the first value of the parameter of interest and the second value of the parameter of interest.

[0295] In the embodiment, the instructions, when read by the at least one processor, further cause the computing device to: apply the incident radiation beam to a second substrate comprising third features on a third layer and fourth features on a fourth layer, a second relationship between the third features and the fourth features being characterized by the parameter of interest having a third value, wherein the metrology apparatus is operated in accordance with the at least one characteristic having the second setting; receive second intensity data representing second intensity of a second portion of the incident radiation beam scattered by the third features and the fourth features; determine, based on the second intensity data, a fourth value of the parameter of interest for the second substrate; and determine a second difference between the third value of the parameter of interest and the fourth value of the parameter of interest.

[0296] In the aforementioned embodiment, the instructions, when read by the at least one processor, further cause the computing device to: determine, based on the second difference being less than a threshold value, that the metrology apparatus is calibrated for the at least characteristic having the second setting.

[0297] In the aforementioned embodiment, the instructions, when read by the at least one processor, further cause the computing device to: perform an additional calibration for the metrology apparatus by modifying the second setting at least one characteristic in response to determining that the second difference is equal to or greater than a threshold value.

[0298] In the embodiment, the instructions comprising the second value of the parameter of interest being determined, when read by the at least one processor, cause the computing device to: obtain an intensity model that indicates an expected intensity distribution for the metrology apparatus for the at least one characteristic having the first setting; identify one or more components of the intensity model associated with the first features of the first layer and the second features of the second layer; and determine the second value of the parameter of interest by calculating a second difference between the expected intensity distribution and the first intensity data based on the one or more components.

[0299] In the embodiment, the one or more components of the intensity model relate to a pupil point of the metrology apparatus and a feature position.

[0300] In the embodiment, the instructions, when read by the at least one processor, further cause the computing device to: update an intensity model indicating an expected intensity distribution for the metrology apparatus such that the intensity model reflects the at least one characteristic having the second setting.

[0301] Referring to Figure 24, a computer system 2400 is shown. The computer system 2400 includes a bus 2402 or other communication mechanism for communicating information, and a processor 2404 (or multiple processors 2404 and 3205) coupled with bus 2402 for processing information. Computer system 2400 also includes a main memory 2406, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 2402 for storing information and instructions to be executed by processor 2404. Main memory 2406 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 2404. Computer system 2400 further includes a read only memory (ROM) 2408 or other static storage device coupled to bus 2402 for storing static information and instructions for processor 2404. A storage device 2410, such as a magnetic disk or optical disk, is provided and coupled to bus 2402 for storing information and instructions.

[0302] Computer system 2400 may be coupled via bus 2402 to a display 2412, such as a cathode ray tube (CRT) or flat panel or touch panel display for displaying information to a computer user. An input device 2414, including alphanumeric and other keys, is coupled to bus 2402 for communicating information and command selections to processor 2404. Another type of user input device is cursor control 2416, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 2404 and for controlling cursor movement on display 2412. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A touch panel (screen) display may also be used as an input device.

[0303] The computer system 2400 may be suitable to function as a processing unit herein in response to processor 2404 executing one or more sequences of one or more instructions contained in main memory 2406. Such instructions may be read into main memory 2406 from another computer-readable medium, such as storage device 2410. Execution of the sequences of instructions contained in main memory 2406 causes processor 2404 to perform a process described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 2406. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, embodiments are not limited to any specific combination of hardware circuitry and software.

[0304] The term“computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor 2404 for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 2410. Volatile media include dynamic memory, such as main memory 2406. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus 2402. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH- EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read. [0305] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 2404 for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 2400 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 2402 can receive the data carried in the infrared signal and place the data on bus 2402. Bus 2402 carries the data to main memory 2406, from which processor 2404 retrieves and executes the instructions. The instructions received by main memory 2406 may optionally be stored on storage device 2410 either before or after execution by processor 2404.

[0306] Computer system 2400 may also include a communication interface 2418 coupled to bus 2402. Communication interface 2418 provides a two-way data communication coupling to a network link 2420 that is connected to a local network 2422. For example, communication interface 2418 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 2418 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface 2418 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0307] Network link 2420 typically provides data communication through one or more networks to other data devices. For example, network link 2420 may provide a connection through local network 2422 to a host computer 2424 or to data equipment operated by an Internet Service Provider (ISP) 2426. ISP 2426 in turn provides data communication services through the worldwide packet data communication network, now commonly referred to as the“Internet” 2428. Local network 2422 and Internet 2428 both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 2420 and through communication interface 2418, which carry the digital data to and from computer system 2400, are exemplary forms of carrier waves transporting the information.

[0308] Computer system 2400 can send messages and receive data, including program code, through the network(s), network link 2420, and communication interface 2418. In the Internet example, a server 2430 might transmit a requested code for an application program through Internet 2428, ISP 2426, local network 2422 and communication interface 2418. In accordance with one or more embodiments, one such downloaded application provides for a method as disclosed herein, for example. The received code may be executed by processor 2404 as it is received, and/or stored in storage device 2410, or other non-volatile storage for later execution. In this manner, computer system 2400 may obtain application code in the form of a carrier wave.

[0309] An embodiment of the disclosure may take the form of a computer program containing one or more sequences of machine-readable instructions describing a method as disclosed herein, or a data storage medium (e.g., semiconductor memory, magnetic or optical disk) having such a computer program stored therein. Further, the machine readable instruction may be embodied in two or more computer programs. The two or more computer programs may be stored on one or more different memories and/or data storage media.

[0310] Any controllers described herein may each or in combination be operable when the one or more computer programs are read by one or more computer processors located within at least one component of the lithographic apparatus. The controllers may each or in combination have any suitable configuration for receiving, processing, and sending signals. One or more processors are configured to communicate with the at least one of the controllers. For example, each controller may include one or more processors for executing the computer programs that include machine-readable instructions for the methods described above. The controllers may include data storage medium for storing such computer programs, and/or hardware to receive such medium. So the controller(s) may operate according the machine readable instructions of one or more computer programs.

[0311] Although specific reference may be made in this text to the use of a metrology apparatus in the manufacture of ICs, it should be understood that the metrology apparatus and processes described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin film magnetic heads, etc., The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms“wafer” or“die” herein may be considered as synonymous with the more general terms “substrate” or“target portion", respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology tool and/or one or more various other tools. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0312] Although specific reference may have been made above to the use of embodiments of the disclosure in the context of optical lithography, it will be appreciated that the disclosure may be used in other applications, for example nanoimprint lithography, and where the context allows, is not limited to optical lithography. In the case of nanoimprint lithography, the patterning device is an imprint template or mold.

[0313] The terms“radiation” and“beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams.

[0314] The term“lens”, where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components.

[0315] References herein to crossing or passing a threshold may include something having a value lower than a specific value or lower than or equal to a specific value, something having a value higher than a specific value or higher than or equal to a specific value, something being ranked higher or lower than something else (through e.g., sorting) based on, e.g., a parameter, etc.

[0316] References herein to correcting or corrections of an error include eliminating the error or reducing the error to within a tolerance range.

[0317] The term“optimizing” and“optimization” as used herein refers to or means adjusting a lithographic apparatus, a patterning process, etc., such that results and/or processes of lithography or patterning processing have more a desirable characteristic, such as higher accuracy of projection of a design layout on a substrate, a larger process window, etc., Thus, the term“optimizing” and“optimization” as used herein refers to or means a process that identifies one or more values for one or more variables that provide an improvement, e.g., a local optimum, in at least one relevant metric, compared to an initial set of one or more values for those one or more variables. "Optimum" and other related terms should be construed accordingly. In an embodiment, optimization steps can be applied iteratively to provide further improvements in one or more metrics.

[0318] In an optimization process of a system, a figure of merit of the system or process can be represented as a cost function. The optimization process boils down to a process of finding a set of parameters (design variables) of the system or process that optimizes (e.g., minimizes or maximizes) the cost function. The cost function can have any suitable form depending on the goal of the optimization. For example, the cost function can be weighted root mean square (RMS) of deviations of certain characteristics (evaluation points) of the system or process with respect to the intended values (e.g., ideal values) of these characteristics; the cost function can also be the maximum of these deviations (i.e., worst deviation). The term“evaluation points” herein should be interpreted broadly to include any characteristics of the system or process. The design variables of the system can be confined to finite ranges and/or be interdependent due to practicalities of implementations of the system or process. In the case of a lithographic apparatus or patterning process, the constraints are often associated with physical properties and characteristics of the hardware such as tunable ranges, and/or patterning device manufacturability design rules, and the evaluation points can include physical points on a resist image on a substrate, as well as non-physical characteristics such as dose and focus.

[0319] While specific embodiments of the disclosure have been described above, it will be appreciated that the disclosure may be practiced otherwise than as described. For example, the disclosure may take the form of a computer program containing one or more sequences of machine-readable instructions describing a method as disclosed above, or a data storage medium (e.g., semiconductor memory, magnetic or optical disk) having such a computer program stored therein.

[0320] In block diagrams, illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems in which the functionality described herein is organized as illustrated. The functionality provided by each of the components may be provided by software or hardware modules that are differently organized than is presently depicted, for example such software or hardware may be intermingled, conjoined, replicated, broken up, distributed (e.g., within a data center or geographically), or otherwise differently organized. The functionality described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine readable medium. In some cases, third party content delivery networks may host some or all of the information conveyed over networks, in which case, to the extent information (e.g., content) is said to be supplied or otherwise provided, the information may be provided by sending instructions to retrieve that information from a content delivery network.

[0321] Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout this specification discussions utilizing terms such as“processing,”“computing,”“calculating,” “determining” or the like refer to actions or processes of a specific apparatus, such as a special purpose computer or a similar special purpose electronic processing/computing device.

[0322] The reader should appreciate that the present application describes several inventions. Rather than separating those inventions into multiple isolated patent applications, applicants have grouped these inventions into a single document because their related subject matter lends itself to economies in the application process. But the distinct advantages and aspects of such inventions should not be conflated. In some cases, embodiments address all of the deficiencies noted herein, but it should be understood that the inventions are independently useful, and some embodiments address only a subset of such problems or offer other, unmentioned benefits that will be apparent to those of skill in the art reviewing the present disclosure. Due to costs constraints, some inventions disclosed herein may not be presently claimed and may be claimed in later filings, such as continuation applications or by amending the present claims. Similarly, due to space constraints, neither the Abstract nor the Summary of the Invention sections of the present document should be taken as containing a comprehensive listing of all such inventions or all aspects of such inventions.

[0323] It should be understood that the description and the drawings are not intended to limit the invention to the particular form disclosed, but to the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

[0324] Modifications and alternative embodiments of various aspects of the invention will be apparent to those skilled in the art in view of this description. Accordingly, this description and the drawings are to be construed as illustrative only and are for the purpose of teaching those skilled in the art the general manner of carrying out the invention. It is to be understood that the forms of the invention shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, certain features may be utilized independently, and embodiments or features of embodiments may be combined, all as would be apparent to one skilled in the art after having the benefit of this description of the invention. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as described in the following claims. Headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description.

[0325] As used throughout this application, the word“may” is used in a permissive sense (i.e., meaning having the potential to), rather than the mandatory sense (i.e., meaning must). The words “include”,“including”, and“includes” and the like mean including, but not limited to. As used throughout this application, the singular forms“a,”“an,” and“the” include plural referents unless the content explicitly indicates otherwise. Thus, for example, reference to“an” element or "a” element includes a combination of two or more elements, notwithstanding use of other terms and phrases for one or more elements, such as “one or more.” The term "or" is, unless indicated otherwise, non-exclusive, i.e., encompassing both "and" and "or." Terms describing conditional relationships, e.g., "in response to X, Y," "upon X, Y,",“if X, Y,” "when X, Y," and the like, encompass causal relationships in which the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributory causal condition of the consequent, e.g., "state X occurs upon condition Y obtaining" is generic to "X occurs solely upon Y" and "X occurs upon Y and Z." Such conditional relationships are not limited to consequences that instantly follow the antecedent obtaining, as some consequences may be delayed, and in conditional statements, antecedents are connected to their consequents, e.g., the antecedent is relevant to the likelihood of the consequent occurring. Statements in which a plurality of attributes or functions are mapped to a plurality of objects (e.g., one or more processors performing steps A, B, C, and D) encompasses both all such attributes or functions being mapped to all such objects and subsets of the attributes or functions being mapped to subsets of the attributes or functions (e.g., both all processors each performing steps A-D, and a case in which processor 1 performs step A, processor 2 performs step B and part of step C, and processor 3 performs part of step C and step D), unless otherwise indicated. Further, unless otherwise indicated, statements that one value or action is“based on” another condition or value encompass both instances in which the condition or value is the sole factor and instances in which the condition or value is one factor among a plurality of factors. Unless otherwise indicated, statements that“each” instance of some collection have some property should not be read to exclude cases where some otherwise identical or similar members of a larger collection do not have the property, i.e., each does not necessarily mean each and every.

[0326] To the extent certain U.S. patents, U.S. patent applications, or other materials (e.g., articles) have been incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is only incorporated by reference to the extent that no conflict exists between such material and the statements and drawings set forth herein. In the event of such conflict, any such conflicting text in such incorporated by reference U.S. patents, U.S. patent applications, and other materials is specifically not incorporated by reference herein.

[0327] The descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made to the disclosure as described without departing from the scope of the claims set out below.