APPARATUS

The present invention relates to an optical device for a lithography apparatus and to a lithography apparatus.

The present application claims the priority of the German patent application DE 10 2015 225 263.9 (filed on December 15, 2015), the entire content of which is incorporated by reference herein.

Microlithography is a process used in microfabrication to pattern parts of a thin film of the bulk of a substrate. In particular, microlithography is used in the fabrication of integrated circuits. The lithography process is carried out using a lithography apparatus comprising an illumination system and a projection system. A geometric pattern is transferred using light from a reticle to a light- sensitive chemical layer known as photoresist on the substrate. The reticle is illuminated by the illumination system. The projection system projects the geometrical pattern onto the substrate which is located at the image plane of the projection system.

Driven by Moore's law and the pursuit of ever smaller structures, particularly in the production of integrated circuits, EUV lithography apparatuses are currently being developed which use light with a wavelength in the region of 5 nm to 30 nm, in particular 13.5 nm. "EUV" denotes "Extreme Ultraviolet". As a result of most materials exhibiting high absorption of light at this wavelength, it is necessary to use reflective optical elements, i.e. mirrors, in place of - as previously— refractive optical elements, i.e. lenses, in such EUV lithography apparatuses. The mirrors in EUV lithography apparatuses may, for example, be fastened to a so-called force frame. Each mirror may be manipulated in up to six degrees of freedom. This allows the mirrors to be positioned highly accurately with respect to one another, e.g. in the pnvrange. In this manner, changes in optical properties, for example as a result of thermal influences, may be compensated during operation of the lithography apparatus. More recently, it has been found that more advanced optical error correction may be obtained by deforming optical elements, such as mirrors, during operation of the lithography apparatus, i.e. in real time.

For example, DE 10151919 Al describes - see Figures 1 and 2 of said document - a mirror 1 comprising four posts 2. An actuator 4 either pulls opposite posts 2 towards an optical axis 3 of the mirror 1, or pushes opposite posts 2 away from the optical axis 3. As a result, the optical element 1 is deformed.

JP 2013-106014 A discloses a deformable mirror 22 in Fig. 2. Multiple mirror posts 24 are arranged on a rear face 22e of the mirror 22. A load supply system 58 is configured to displace a tip of a respective mirror post 24 in order to induce a load into the rear face 22e of the mirror 22 and thus deform the reflective surface 22d of the mirror 22. An object of the present invention is to provide an improved optical device for a lithography apparatus.

This object is achieved by an optical device for a lithography apparatus

comprising an optical element, an actuator and a compensation unit. The optical element has a positive stiffness when deformed in at least one direction. The actuator is configured for deforming the optical element in the at least one direction. The compensation unit has a negative stiffness in the at least one direction at least partially compensating the optical element's positive stiffness. "Negative stiffness" is defined as a stiffness producing a force or moment which tends to deform the optical element in the at least one direction, and increases (or remains constant) with increasing deformation of the optical element in the at least one direction. The negative stiffness thus counteracts the positive stiffness, therefore reducing (or even eliminating) the force required to deform the optical element. Another characteristic of the negative stiffness is that it, preferably, does not require any external supply of energy. Rather, the negative stiffness relies on energy stored in a mechanical system or magnetic field and is

independent of any external supply of energy.

One concept on which the present invention is based consists of dividing the force required to deform the optical element into two components, i.e. a quasi-static force and a dynamic force. The quasi-static force is required to deform the optical element itself. It is noted that herein "deforming the optical element" is to say that either the entire optical element is deformed or one or multiple parts thereof are deformed. The quasi- static force is mainly dependent on the optical element's (positive) stiffness. The stiffness is determined by the E-modulus of the material that the optical element is made of, e.g. glass or ceramics, as well as the optical element's geometry. The dynamic force is required to accelerate the mass of the optical element. This force is mainly dependent on the density of the optical element, the geometrical deformation profile and the deformation trajectory as a function of time.

Since the amount of movement of the optical element required for optical correction is small, typically ranging within a few micrometers, and, at the same time, the time window for optical correction being fairly large, e.g. l/30 ^th of a second, the dynamic force required is small. On the other hand, the stiffness of the optical element is relatively large, thus requiring a quasi- static force for deforming the optical element which is much larger than the dynamic force.

With a (close to) zero stiffness arrangement as presently provided, the actuator now only needs to deliver the kinetic energy and the energy required to

compensate any friction losses. E.g. to move a mirror mass of 1 kg over 1 μηι in 10 ms move time, requires an acceleration of 10 mm/s ² . Thus, a force of 10 mN is required, which can be easily delivered by, for example, a Lorentz actuator (also known as voice coil actuator) with under 1 mW power dissipation.

The required negative stiffness to compensate the optical element's positive stiffness will typically be in the order of 10 ⁵ to 10 ⁶ N/m. For a l-μηι excursion, this will require a force of 1 N. In the present example, this corresponds to 100 times the required dynamic force, and is thus much larger.

As a result of this design, the actuator in accordance with the present invention only needs to provide the dynamic force, and, if at all, a small quasi-static force. Thus, the total force provided by the actuator is significantly smaller compared to known solutions.

Generally speaking, all types of actuators produce significant heat which cannot be extracted without adding disturbances, such as cooling water vibrations. Yet, since the forces required in accordance with the present solution are much reduced, substantially no additional heat removal is needed.

The actuator of the present invention is, preferably, a Lorentz actuator. However, other types of actuators, such as piezoelectric actuators or pneumatic actuators, may also be feasible in some applications.

Another advantage of Lorentz actuators is their small response time, which makes them particularly suitable for real-time optical error corrections, for example "die to die" or even "intra-die". "Die to die" refers to deforming the optical element in the time window between exposures of two consecutive dies on a single wafer. "Intra-die" refers to deforming the optical element for optical correction in the time window during the scans of a single die. Yet another advantage of Lorentz actuators compared to, e.g. piezoelectric actuators, is that they may be operated in an open-loop control system, since they exhibit less or no hysteresis, drift or other inaccuracies. In accordance with one embodiment, the compensation unit is configured to produce a first maximum force on the optical element in the at least one direction, and the actuator is configured to produce a second maximum force on the optical element in the at least one direction, wherein a first maximum force is N times larger than the second maximum force, wherein N is > 5, preferably > 10 and more preferably > 50.

"Maximum force" refers to a maximum force found over the cycle of fabricating a single die or a complete wafer using the optical device. It was found that N > 5, preferably > 10 and more preferably > 50 gives a small enough actuator force, and, at the same time, good system stability for easy open-loop control.

According to a further embodiment, the compensation unit is configured to produce a first force on the optical element in the at least one direction, and the actuator is configured to produce a second force on the optical element in the at least one direction, wherein the first force had a first maximum time derivative, and the second force has a second maximum time derivative, wherein the second maximum time derivative is M times larger than the first maximum time derivative, wherein M is > 10, preferably > 100.

"Maximum time derivative" is the maximum derivative found over the cycle of fabricating a single die or a complete wafer using the optical device. The given values of M were found to give highly dynamic deformation, while at the same time keeping the compensation unit simple.

According to a further embodiment, the compensation unit's negative stiffness is 0.9 to 0.99 times the optical element's positive stiffness. This ratio of negative stiffness to positive stiffness was found to give a small actuator force and, at the same time, good dynamic stability. Ideally, one should wish to have 100% compensation, such that the ratio negative to positive stiffness should be equal to 1. In such case, the positive stiffness due to the optical element's elasticity is fully compensated by the negative stiffness of the compensation unit. However, this also means that the mirror is in force equilibrium at any deformed state, and will remain at such deformed state. This may not be desirable, since in case of a malfunction, one would wish to have the mirror returned to a specific original shape. Thus, it is desirable to have the negative stiffness compensation to be slightly less than 100%, e.g. 90% to 99%.

According to a further embodiment, the difference between the optical element's positive stiffness and the compensation unit's negative stiffness is larger than zero.

Thus, in the neutral state, i.e. when the actuator is switched off (no power) or is malfunctioning and for this reason does not provide a force, the state of the optical element, in particular its degree of deformation, is always defined. The optical element will always return to its original shape.

According to a further embodiment, the deforming of the optical element in the at least one direction is obtained by out-of-plane bending of the optical element.

"Out-of-plane bending" presently refers to bending about an axis perpendicular to the optical element's optical axis.

According to a further embodiment, the compensation unit comprises magnets, in particular permanent magnets, or at least one spring.

Such components are well suited to obtain a negative stiffness. The spring may be a mechanical spring such as a leaf or helical spring. According to a further embodiment, the compensation unit, in particular the at least one spring, is configured to preload the optical element in plane. "In plane" is to say that the force generated by the compensation unit acts in a direction parallel to the optical element's plane of extension. Thus, negative stiffness is obtained by using a buckling effect. According to a further embodiment, the optical device comprises a base, wherein the magnets are comprised of a first magnet fastened to the optical element and a second and a third magnet fastened to the base, respectively, the first magnet being movable between the second and third magnet. This configuration is well suited to obtain a negative stiffness with a zero offset force. While the second and third magnets are stationary, the first magnet moves along with a portion of the optical element in order to obtain the required deformation of the optical element. According to a further embodiment, the optical device comprises a base, wherein the magnets are comprised of a first magnet fastened to the optical element and a second magnet fastened to the base, wherein either the first magnet or the second magnet is formed as a ring magnet and the other magnet is movable along the ring magnet's central axis.

This embodiment describes a further configuration of magnets to obtain negative stiffness with a zero offset force. Again, the second magnet is stationary, and the first magnet moves along with a portion of the optical element as the optical element is deformed.

According to a further embodiment, the optical device comprises an adjusting unit for adjusting the compensation unit's negative stiffness.

Because of the reduced system's stiffness, resonance modes of the optical device may deteriorate. This may lead to an unacceptable dynamic performance when the actuator is switched off or does not provide a suitable force due to

malfunctioning. This can be counteracted, however, by including a switching mechanism that can turn the negative stiffness on or off. This is also advantageous during, for example, transport of the optical device or the lithography apparatus comprising such a device. Typically during transport, resonance frequencies could inflict damage to the optical device. By now including the adjusting unit allows the optical element to have its (normal) positive stiffness or at least a substantial positive stiffness, which will prevent damage to the optical element during transport or the like. On the other hand, the adjusting unit may even adjust the negative stiffness in real time so as to keep the required actuator force at a minimum during operation of the optical device. The adjusting unit may be configured to adjust the negative stiffness continuously.

According to a further embodiment, the adjusting unit is configured for

preloading the at least one spring, adjusting the relative position of the first, second and/or third magnet, adjusting a magnetic field coupling between the first, second and/or third magnet or adjusting the first, second and/or third magnet's magnetic field using at least one electro-permanent magnet.

Depending on the mechanism by which negative stiffness is obtained, different ways of adjusting the negative stiffness appear to be suitable. When a spring is used as the source of negative stiffness, a preload acting on the spring may be changed in order to adjust the negative stiffness. Preloading may, for example, be performed by using a pneumatic cylinder. When using magnets to obtain negative stiffness, repulsion and attraction forces between the magnets and thereby the negative stiffness may be changed by adjusting their relative position. To this end, for example a set screw or the like may be used. Further, when using magnets to obtain negative stiffness, magnetic field coupling between the magnets can be changed by, for example, using a moving iron as a short circuit. For example, a horseshoe-type moving iron may be used. Even further, when using magnets to obtain negative stiffness, attraction and repulsion forces between magnets may be changed by adjusting the magnetic fields of respective magnets. To this end, electro-permanent magnets may be used. An "electro-permanent magnet" is presently defined as a magnetic unit comprising at least a first magnet with an adjustable permanent magnetization and a means to adjust the permanent magnetization of at least one magnet.

The at least one magnet can be made of, for example, ferromagnetic or

ferrimagnetic material.

"Permanent magnetization" is to say that the at least one magnet does not lose its magnetization (for example expressed as A/m) by more than 5%, preferably not more than 2% and even more preferably by not more than 0.5% per year, when the means for adjusting the permanent magnetization does not produce a magnetic field.

The permanent magnetization is adjustable. This is to say that, for example, the means for permanent magnetization of the at least one magnet is switchable between two states of magnetization. These two states may comprise, for example, one demagnetized (magnetization is zero) and one magnetized state. In other embodiments, this is to say that the means for permanent magnetization is switchable between more than two, preferably more than ten, states of

magnetization. Switching may also be performed continuously. The means for permanent magnetization may be formed as a coil. By adjusting the current in the coil, the external field for magnetizing the at least one magnet may be adjusted.

In one example, the at least one magnet has a medium coercivity field strength. "Coercive field strength" refers to the field strength required to fully demagnetize the magnetic material of the at least one magnet after magnetic saturation of said material. Medium coercivity materials are known in the art and, for example, comprise iron, aluminium, cobalt, copper and/or nickel. For example, the medium coercivity field strength corresponds to a field strength of 10 to 300 kA/m, preferably 40 and 200 kA/m, more preferably 50 to 160 kA/m. In particular, the material of medium coercivity is AlNiCo. AlNiCo refers to an alloy of iron, aluminium, nickel, copper and cobalt.

Further, the magnetic unit may comprise a further magnet whose permanent magnetization may not be changed by the means for changing the permanent magnetization. This characteristic may be obtained by using a high- coercivity material for the further magnet (second magnet). The first and the second magnet may together produce the negative stiffness required. In other

embodiments, the first magnet alone produces the negative stiffness required.

By controlling the means for adjusting the permanent magnetization of the first magnet, the negative stiffness may be adjusted appropriately.

According to a further embodiment, the optical element has a first positive stiffness when deformed in a first direction and a second positive stiffness when deformed in a second direction, wherein the actuator is configured for deforming the optical element in the first and second direction and wherein the

compensation unit has a first negative stiffness in the first direction at least partially compensating the optical element's positive stiffness in the first direction and a second negative stiffness in the second direction at least partially compensating the optical element's positive stiffness in the second direction.

In this manner, the basic principle of the invention can be applied to systems with multiple axes. The response of such systems may be described using a stiffness matrix where the non- diagonal terms describe the coupling between axes. If the system is significantly coupled, local negative stiffness as described in the previous paragraph will no longer suffice to compensate all stiffness forces and an equivalent negative stiffness matrix needs to be built to compensate the positive stiffness matrix. I.e. not only the diagonal (local) stiffness needs to be compensated, but also cross-talk between neighboring actuators. Depending on the geometry, the resulting mechanical system is usually a somewhat banded stiffness matrix, where actuators close together will have some coupling stiffness and actuators far apart will have (near) zero coupling stiffness. A typical negative stiffness matrix is given in equation 1 below, where k _p is the local actuator negative stiffness and k _c is the coupling stiffness between the degrees of freedom, δι... 5i gives the deformation in a respective direction, and Fi...Fi gives the negative stiffness force produced by a respective actuator.

[Equation l]

For example, a negative stiffness matrix with properties as described in equation 1 may be obtained by using an appropriate topology of magnets. According to a further embodiment, the actuator is configured for deforming the optical element for optical correction.

Generally speaking, optical correction may comprise any type of image error correction, in particular in overlay and/or in focus correction.

According to a further embodiment, the optical element is a mirror, a lens, a grating or a lambda plate.

Lambda plates are also known as wave plates or retarders, i.e. optical devices which alter the polarization state of the light wave traveling through it.

The mirror may be plane or curved. Further, the mirror may be a facet of a mirror comprising multiple facets. Further, a lithography apparatus is provided comprising the optical device described above.

The lithography apparatus may be a EUV- or DUV lithography apparatus. EUV stands for "Extreme Ultraviolet" and refers to a wavelength of the exposure light between 0.1 and 30 nm. DUV stands for "Deep Ultraviolet" and refers to a wavelength of the exposure light between 30 and 250 nm.

The optical device may be integrated into an objective of the lithography apparatus. The objective may be immersed in a fluid at least during exposure of the waver (immersion lithography).

Further exemplary embodiments will be explained in more detail with reference to the attached Figures of the drawings.

Fig. 1A shows a schematic view of an EUV lithography apparatus!

Fig. IB shows a schematic view of a DUV lithography apparatus!

Fig. 2 shows a perspective view of an optical device integrated into the

lithography apparatus of Fig. 1A or IB, for example!

Fig. 3 shows schematically a section IITIII from Fig. 2!

Fig. 3A showing a force diagram pertaining to Fig. 3!

Fig. 4A shows a diagram illustrating a force vs. displacement diagram for the optical device of Fig. 3 according to a first embodiment;

Fig. 4B illustrates a force vs. displacement diagram for the optical device of Fig. 3 according to a second embodiment; Figs. 5A - 5C illustrate, in a schematic side view respectively, an optical device using a mechanical compensation system to obtain negative stiffness!

Fig. 6A shows, in a schematic side view, an optical device using a magnetic compensation system to obtain negative stiffness!

Fig. 6B shows a variation of the embodiment of Fig. 6A!

Figs. 7A - 7D illustrate different embodiments to obtain an optical device having an adjustable negative stiffness! and

Fig. 8 illustrates in a schematic side view an optical device comprising negative stiffness compensation along multiple axes. In the Figures, like reference numerals designate like or functionally equivalent elements, unless otherwise indicated.

Fig. 1A shows a schematic view of an EUV lithography apparatus 100A

comprising an illumination system 102 and a projection system 104 (also referred to as "POB"). EUC stands for "Extreme Ultraviolet" and denotes wavelengths of the exposure light between 0.1 and 30 nm. The illumination system 102 and the projection system 104 are integrated into a vacuum housing evacuated by means of an evacuation device (not shown). The vacuum housing is enclosed by a machinery room (not shown). The machinery room includes devices for

positioning the optical elements. Further, the machine room may include control devices and other electrical equipment.

The EUV lithography apparatus 100A comprises an EUV light source 106A. The EUV light source 106A may be formed as a plasma source or synchrotron emitting light 108A in the EUV range, for example light at a wavelength between 0.1 nm to 30 nm. The EUV light 108A is bundled inside the illumination system 102, and the desired operational wavelength is filtered out. The EUV light 108A has a low transmissivity in air which is why the illumination system 102 and the projection system 104 are evacuated.

The illumination system 102 shown in Fig. 1A has, for example, five mirrors 110, 112, 114, 116, 118. After passing through the illumination system 102, the EUV light 108A is guided onto a reticle 120. The reticle 120 is also configured as a reflective optical element and may be arranged outside the systems 102, 104. Further, the EUV light 108A may be directed towards the reticle 120 using a mirror 126 outside either of the systems 102, 104. The reticle 120 comprises a structure, a much smaller image of which is projected onto a waver 122 or the like by the projection system 104.

The projection system 104 may comprise, for example, six mirrors Ml— M6, for projecting the structure onto the waver 122. Some of the mirrors Ml - M6 of the projection system 104 may be arranged symmetrically with respect to the optical axis 124 of the projection system 104. The number of mirrors of the EUV lithography apparatus 100A is not limited to the number shown in Fig. 1A, of course. Further, the mirrors may be of different shapes, for example some may be formed as curved mirrors, while others may be formed as facet mirrors.

Fig. IB shows a schematic view of a DUV lithography apparatus 100B, also comprising an illumination system 102 and a projection system 104. DUV refers to "Deep Ultraviolet" and designates a wavelength of the exposure light between 30 and 250 nm. The illumination system 102 and the projection system 104 may — as explained with reference to Fig. 1A— be arranged in a vacuum housing and/or machine room.

The DUV lithography apparatus 100B comprises a DUV light source 108B. The DUV light source 108B may be configured as an ArF excimer laser emitting light 108b at, for example, 193 nm wavelength. The illumination system 102 guides the DUV light 108B onto a reticle 120. The reticle 120 is configured as a transmissive optical element and may be arranged outside the systems 102, 104, respectively. Again, the reticle 120 has a structure, a much smaller image of which is projected onto a waver 122 or the like by the projection system 104.

The projection system 104 may comprise multiple lenses 132 and/or mirrors 134 for projecting the structure of the photomask 120 onto the waver 122. The lenses 132 and/or mirrors 134 may be arranged symmetrically with respect to an optical axis 124 of the projection system 104. Again, the number of lenses or mirrors of the DUV lithography apparatus 100B is not limited to the number of lenses and mirrors shown in Fig. IB.

The air gap between the final lens 132 and the wafer 122 may be replaced with a liquid medium 136 that has a refractive index greater than 1. As a liquid medium highly purified water may be used, for example. This setup is referred to as immersion lithography which is characterized by an enhanced photolithographic resolution. Fig. 2 illustrates, in a perspective view, an optical device 200 comprising a base 202 supporting an optical element 204 which may be formed as a mirror, for example.

The optical device 200 may be integrated into one of the lithography apparatuses shown in Fig. 1A and Fig. IB. The optical element 204 may correspond to, for example, one of the mirrors Ml - M6 (Fig. 1A) or one of the lenses or mirrors 132, 134 (Fig. IB). In other embodiments (not shown), the optical element 204 is configured as an optical grid or lambda plate. The base 202 may be fastened to a stationary structure of the lithography apparatus 100A, 100B, for example, to a force frame (not shown). To this end, the base 202 may be equipped with fastening holes 206 or the like. The base 202 may comprise a rectangular or any other suitable shape.

The mirror 204 (reference is made to a mirror hereinafter in order to facilitate understanding— this is not to be construed as a limitation to only a mirror but any other suitable optical element may be used) reflects incoming light 108A, 108B. A corresponding optical axis of the mirror 204 is designated with reference numeral 208. At least the front face 210 at which the light 108A, 108b is reflected, or the entire mirror 204, may be curved (as shown) or straight.

Fig. 3 shows a section IITIII from Fig. 2. The mirror 204 is depicted in an undeformed state (solid line) and in a deformed state (dot- dash line). The mirror 204 is shown to have a planar shape in its undeformed state. Yet, the mirror 204 may have any shape— for example a curved shape— in its undeformed state.

The mirror 204 may be supported, for example, at two locations, for example by supports 300, 302. The supports 300, 302 may support the mirror 204 or a portion thereof at its rear face 304. In this simply supported configuration, the support 300 may be configured so as to allow relative rotation of the mirror 204, yet fixedly connects the mirror 204 to the base 202 in a direction perpendicular to the optical axis 208. On the other hand, the support 302 allows for relative rotation of the mirror 204, and allows movement of the mirror 204 perpendicularly with respect to the optical axis 208. "Perpendicular" as used herein may include deviations from exactly perpendicular of up to 10°, preferably up to 5° and more preferably up to 1°.

However, any other type of support of the mirror 204 or parts thereof is feasible. For example, the mirror 204 may be supported at more than two locations, for example five, ten or twenty or more locations. Further, the supports may be configured for producing a force or moment or both at the locations where they connect to the mirror 204. Further, the optical device 200 comprises an actuator 306. The actuator 306 is configured to deform the optical element 204 (or a portion thereof) between the two states shown in Fig. 3. The actuator 306 is, on the one hand, fastened to the mirror 204 and, on the other hand, to the base 202 or any other suitable reference. The actuator 306 may, for example, be configured as a Lorentz-type actuator, i.e. comprising a voice coil (not shown) and a magnet (not shown) to produce a resulting force F _r (see Fig. 3A showing a force diagram pertaining to Fig. 3) on the mirror 204 for deforming the same. The direction in which the force F _r acts is designated with δ.

Instead of a Lorentz actuator, in principle, any other actuator, for example a piezoelectric actuator or a pneumatic actuator, may be used. Yet, using Lorentz actuator, specifically when used in an open-loop control system, may provide a system of low complexity which may be cost-effective.

When a Lorentz actuator is used, the magnet may be fastened to the mirror 204, specifically to its rear side 304, and the voice coil may be fastened to the base 202. Other arrangements, where the voice coil 306 is fastened to the mirror 204, and the magnet is fastened to the base 202 are also conceivable.

The actuator 306 may be controlled by a controller 308. The controller 308 may be configured to control the actuator 306 so as to deform the mirror 204 to provide optical correction. I.e., by deforming the mirror 204, the angle of incidence of the light 108A, 108B is changed. Optical corrections may comprise image error corrections, such as in overlay or in focus corrections. "Image" refers to the image projected onto the waver 122 (see Figs. 1A and IB).

The controller 308 may be configured to deform the mirror 204 in real time, for example inside the time window between exposing two different dies on the wafer 122 or even intra-die, i.e. during scans of a single die on the wafer 122. Scanning of respective dies on the wafer 122 may take place at, for example, 30 Hz. Thus, the time window for changing the deformation of the mirror 204 may be smaller than l/30 ^th of a second.

In the example of Fig. 3, deforming the mirror 204 in the direction δ is obtained by out-of-plane bending of the mirror 204. This is a result of the actuator 306 acting on the mirror 204 at a location between the two supports 300, 302 in the direction δ parallel to the optical axis 208. "Parallel" may include deviations from exactly parallel of up to 10°, preferably up to 5° and more preferably up to 1°. When the mirror 204 is deformed by a force acting in the direction δ, this force will, generally speaking, be made up of two components. First, a quasi-static force FQ (see Fig. 3A) required to deform the mirror 204 itself. This quasi- static force is a function of the E-modulus of the material of the mirror 204 as well as its geometry, thus corresponding to the (positive) stiffness of the mirror 204. On the other hand, the force will be made of a dynamic force FD required to accelerate the mass of the mirror 204. This dynamic force depends on the density of the mirror 204, the geometrical deformation profile, and the deformation trajectory (as a function of time). In order to reduce the resulting force F _r that needs to be expended by the actuator 306 to deform the mirror 204, the mirror's positive stiffness is paired with a corresponding negative stiffness. To this end, the optical device 200 comprises a compensation unit 310 having a negative stiffness in the direction δ at least partially compensating the positive stiffness of the mirror 204. Fig. 3A shows a schematic diagram of the forces acting on the mirror 204 at the location of the actuator 306 and the compensation unit 310. The mirror's positive stiffness k _p results in a positive force F _p when the mirror 204 is deformed in the direction δ. This is also illustrated in Fig. 4A showing a diagram of force F vs. deformation δ. On the other hand, the negative stiffness of the compensation unit 310 results in a force F _n , as the mirror is deformed in the direction δ which opposes the force F _p . The resulting force is the force FQ which is the quasi-static force required to deform the mirror 204 in the direction δ. In addition to the quasi- static force FQ, the actuator 306 needs to exert the dynamic force FD on the mirror 204 to accelerate the same. The sum of the forces FQ and FD equals the resulting force F _r exerted by the actuator 306. Since F _n and F _p are much larger than FQ, FD and F _r , they are not drawn to scale in Fig. 3A which is indicated by a dotted line respectively.

Since the amount of deformation of the mirror 204 in the direction δ is typically small, for example within the micrometer range, and, at the same time, the time window for deformation being fairly large, for example l/30 ^th of a second (see the explanations regarding the scanning trajectory above), the dynamic force FD required is small in comparison to the quasi-static force FQ. Further, the resulting force F _r (= FQ + FD) is given to be much smaller than the force F _n produced by the compensation unit by way of appropriate system design. Clearly, the forces F _p , F _n , FD may vary over time as a die or a wafer is produced. Yet, the forces will typically show to be cyclic over the fabrication of a single die or an entire waver. It has been found that the system can be designed such that the negative stiffness force F _n has, when looking at a single cycle, a maximum which is N times larger than the maximum resulting force F _r that needs to be produced by the actuator 306, where N is preferably > 5, more preferably > 10 and even more preferably > 50.

This kind of system design gives an actuator 306 with low energy consumption. This in turn makes corresponding heat losses small, thus avoiding thermal expansion problems and corresponding cooling issues.

In order to improve system design even more, the "large" forces F _p and F _n may be designed to change little compared to the "small" dynamic force FD. TO this end, a maximum time derivative of the dynamic force FD over one cycle (see explanation above) may be M times larger than the maximum time derivative of the negative stiffness force F _n , wherein M is preferably larger than 1, more preferably larger than 2 and even more preferably larger than 10. To improve the energy efficiency of the system even more, the actuator 306 may be designed so as to recover the dynamic energy in the mirror 204. In other words, when the mirror 204 needs to be slowed down, the work done by the mirror 204 on the actuator 306 is transformed into electrical energy, which is returned to an electrical energy storage. Thus, heat losses of the actuator 306 can be reduced even more.

Now returning to Fig. 4A, it can be seen that the positive stiffness force F _p , the negative stiffness force F _n and the resulting force F _r are respectively dependent on the stiffnesses k _p (positive stiffness), k _n (negative stiffness), k _r (resulting stiffness) and the deformation δ. Preferably, the resulting stiffness k _r and the corresponding resulting force F _r are designed to be positive and unequal to zero. For example, the negative stiffness k _n may equal to 0.9 to 0.99 times the positive stiffness k _p . This will ensure that, when the actuator 306 is not producing a force, for example when the actuator 306 is switched off (no power) such as during transport of the optical device 200 or the lithography apparatus 100A, 100B, or when there is an unforeseen failure of the actuator 306, the deformation of the mirror 204 in the direction δ will be defined. By choosing the resulting stiffness k _r positive, the mirror 204 will return to its undeformed state without action of the actuator 306 (actuator 306 switched off or malfunctioning).

Fig. 4B shows a force vs. deformation diagram according to another embodiment of the optical device 200. In this embodiment, the negative stiffness force F _n may be switched on or off, as will be explained in more detail referring to Figs. 7A to 7D hereinafter. Thus, when the negative stiffness k _n is switched off, the resulting stiffness will correspond to the positive stiffness k _p which is large enough to prevent, for example, damage to the mirror 204 during transport due to

vibrations or other movements. As a result, the resulting stiffness k _r during normal operation of the optical device 200, i.e. during the fabrication of wafers, can be designed to be even smaller (or equal zero) than in the embodiment described in Fig. 4A. For example, in the embodiment of Fig. 4B, the negative stiffness k _n may be designed to be 0.99 to 0.999 times the positive stiffness k _p . Example ^: If the mirror mass is assumed to be 1 kg which is moved over 1 μπι in 10 ms moving time, this requires an acceleration of 10 mm/s ² . The corresponding dynamic force FD thus equals 10 mN which can be delivered by Lorentz actuator with under 1 mW power dissipation.

The required negative stiffness k _n to compensate the mirror's positive stiffness k _p will be of the order of 10 ⁵ to 10 ⁶ N/m. For a 1 μηι excursion, this will thus require a negative stiffness force F _n of 1 N. This corresponds to 100 times the dynamic force FD. TO get into the same order of magnitude of the dynamic force FD, the negative stiffness force F _n needs to be very accurate. Preferably, the negative stiffness force can be adjusted in real time, i.e. dynamically during operation of the optical device 200. Ways of adjusting the negative stiffness will be explained with regard to Figs. 7A to 7D hereinafter.

Now, an embodiment of an optical device 200 using mechanical compensation to obtain the desired negative stiffness k _n will be explained with reference to Figs. 5A to 5C. The compensation unit 310 of Fig. 5A includes, for example, a mechanical spring 500, for example, a leaf or helical spring, and a preloading unit 502, for example, a pneumatic cylinder, configured to preload the spring 500. The spring 500, acting, for example, on the side 504 of the mirror 204, is preferably configured to be fairly long. A long spring 500 ensures a more or less constant preloading force Fc as the mirror 204 is deformed since this deformation will also causes the mirror 204 to move laterally, i.e. in a direction normal to the optical axis 208. Instead of using a pneumatic cylinder 502, the spring 500 could, in its

compressed state, be attached to the base 202 so as to produce the force F _c . In other embodiments, the force F _c may be exerted directly (without using a mechanical spring) by a pneumatic cylinder or using magnets, for example. The mirror 204 of Fig. 5A is preloaded in plane, i.e. at right angles to the optical axis 208, with the compensation force F _c . The force F _c tends to buckle the mirror 204, and thus bend the same out of plane. This force F _c may be exerted, for example, by a mechanical spring 500.

Since the mirror 204 is symmetrical, half of the mirror 204 can be considered as a simple cantilever subjected to a force at its end as shown in Fig. 5B.

The deflection is given by ' [Equation 2]

where L corresponds to the width of the mirror 204 between the supports 300, 302 as shown in Fig. 5A, F _p corresponds to the positive stiffness force required to overcome the mirror's positive stiffness 204, E corresponds to the E-modulus of the material of the mirror 204 (for example glass or ceramics) and I corresponds to the moment of inertia (which depends on the geometry of the cross- section of the mirror 204).

Thus, the positive stiffness k _p of the mirror 204 is given by:

[Equation 3] The compressive force F _c (preload) applied to the cantilever (Fig. 5B and 5C), at a deflection δ, results in a bending moment with a magnitude of F _c · δ. This moment creates a deflection δ' such that

δ' = (Fc · δ) [Equation 4] When δ = δ' (corresponding to zero stiffness, i.e. when the positive stiffness k _p equals the negative stiffness k _n ), the required compressive force F _c is given by

2 ^■ E ^■ I

Fc = [Equation 5]

Thus, it has been shown above that a constant preload force F _c is suitable to provide a negative or near negative stiffness which will compensate the positive stiffness of the mirror 204. For example, the near constant compensation force F _c may be provided by a long spring 500 which is preloaded.

Figs. 6A and 6B illustrate a first and a second embodiment of a compensation unit 310 comprising magnets.

The compensation 310 of Fig. 6A comprises a first magnet 600 fastened to the mirror 204 to produce the negative stiffness force F _n . A connection between the first magnet 600 and the mirror 204 is indicated at 602. The magnet 600 is arranged between a second and a third magnet 604, 606 which are stationary. To this end, the second and third magnet 604, 606 may be fastened to the base 202. The first magnet 600 may be guided mechanically in the direction δ. The magnets 600, 604, 606 may be configured as block magnets, and may have the same polarization (indicated by "N" for North, and "S" for South) with respect to the direction δ. Thus, when the first magnet 600 is positioned halfway between the second and third magnet 604, 606, the first magnet 600 produces a zero offset force on the mirror 204. Also, as the deformation of the mirror 204 increases in the direction δ, the force F _n increases accordingly. Thus, the negative stiffness k _n is produced.

In the example of Fig. 6B, the compensation 310 comprises a first magnet 600 connected to the mirror 204 by a connection 602. Further, the compensation unit 310 comprises a second magnet 604 configured as a ring magnet. The ring magnet 604 has a central axis 608. The first magnet 600 is, for example, mechanically guided to move along the central axis 608 as the mirror 204 is deformed in the direction δ. The first magnet 600 and the second magnet 604 have an opposed polarity along the axis 608. When the first magnet 600 is arranged on the axis of symmetry 610 of the second magnet 604 along the axis 608, the first magnet 600 produces a zero offset force on the mirror 204. As deformation of the mirror 204 increases in the direction δ, so does the negative stiffness force F _n produced by the first magnet 600, as the first magnet 600 is displaced from its position at the axis of symmetry 610. Fig. 7A to 7D illustrate four different embodiments of an adjusting unit 700.

In the example of Fig. 7 A, the adjusting unit has a pneumatic cylinder 700 configured to be switched on or off. In the "off state, the pneumatic cylinder 700 does not produce the preload force F _c on the spring 500. On the other hand, a controller 702 may be provided configured to control the preload force F _c (even continuously) based on input to the controller 702. For example, a sensor 704 may be provided, sensing an optical error requiring correction. The controller 702 may receive a corresponding input signal from the sensor 704 and control the pneumatic cylinder 700 to produce a preload force F _c which will result in a deformation of the mirror 204 leading to appropriate optical correction.

Setting of a desired preload force F _c by the controller 702 may be performed by measuring e.g. the current of the (Lorentz) actuator 306 during a slow

deformation move. Since this is slow, there is negligible acceleration force, and the Lorentz force is only due to the residual stiffness kr. If both F _r and δ are measured, k _r can be determined and F _c adjusted accordingly until the desired k _r value is reached.

The embodiments of Figs. 7B to 7D may also include a controller 702 and, as the case may be, also a sensor 704. They merely differ in the way in which the negative stiffness force F _n is adjusted. In the embodiment of Fig. 7B, the adjusting unit 700 may comprise mechanical means, for example a set screw, to move the second magnet 604 along the central axis 608 from an initial position PI to a position P2, in which the first magnet 600 produces an initial offset force on the mirror 204. Instead of a set screw or the like, also electromagnetic means may be used to adjust the position of the second magnet 604, for example.

In the embodiment of Fig. 7C, the adjusting unit 700 is configured to adjust the magnet field coupling between the first magnet 600 and the second magnet 604. To this end, the adjusting unit 700 may comprise a, e.g. U-shaped, mover magnet which is moved perpendicular to the central axis 608 to change the field coupling between the magnets 600, 604. In the position PI, the magnets 600, 604 are arranged inside the mover magnet 700. Thus, there is maximum field coupling between the magnets 600, 604. In the position P2, the mover magnet 700 is moved to a position with the magnets 600, 604 arranged outside the mover magnet 700. Hence, there is no (additional) field coupling between a magnet 600, 604. This changes the forces working between the first and second magnet 600, 604 when the magnet 600 is moved along the central axis 608 as the mirror 204 is deformed.

In the example of Fig. 7D, the adjusting unit 700 comprises an electro-permanent magnet 706. The electro-permanent magnet 706 is comprised of at least a first magnet 708 made of a medium coercivity material and a coil 710 configured to change the magnetization of the magnet 708 depending on, for example, an input signal received from the controller 702 (see Fig. 7A). Further, the adjusting unit 700 may comprise a second magnet 712 of a high coercivity material, and, in addition or alternativly, an iron core 714 to increase overall field strength. The magnet 708 and, if provided, the magnet 712 form the second magnet 604 described in Fig. 6B. By adjusting the magnetization of the first magnet 708, the magnetic field produced by the second magnet 604, and thus the negative stiffness F _n may be adjusted. Fig. 8 shows an optical device 200 having multiple axes 51, 52, 53 along which deformation may take place. The mirror 204 is connected through, for example, three connectors 602a, 602b, 602c to first magnets 600a, 600b, 600c, respectively. The first magnet 600a, 600b, 600c are respectively arranged between first and second magnets 604a, 604b, 604c and 606a, 606b, 606c. Each first, second and third magnet 604a...606c associated with a respective connector 602a, 602b, 602c forms a compensation sub unit 310a, 310b, 310c. Together, the compensation sub unit 310a, 310b, 310c form the compensation unit 310. The negative stiffness of the compensation unit 310 of Fig. 8 is described by the negative stiffness matrix given below^

The stiffness matrix should be built not only to produce the required diagonal (local) stiffness, but also needs to compensate cross-talk terms of the mirror 204 by generating the appropriate negative crosstalk between neighboring magnets 604a...606c. Even though the present invention has been described with reference to specific embodiments, numerous modifications and variations are possible, and still the result will come within the scope of the invention. No limitation with respect to specific embodiments disclosed herein is intended or should be inferred. LIST OF REFERENCE NUMERALS

100A EUV lithography apparatus

100B DUV lithography apparatus

102 illumination system

104 projection system

106A EUV light source

106B DUV light source

108A EUV light

108B DUV light

110 mirror

112 mirror

114 mirror

116 mirror

118 mirror

120 reticle

122 wafer

124 optical axis

126 mirror

132 lens

134 mirror

136 fluid

200 optical device

202 base

204 mirror

206 hole

208 optical axis

210 front face

300 support

302 support

304 rear face

306 actuator

308 controller 310 compensation unit

310a-310b compensation sub unit

500 spring

502 pneumatic cylinder

504 side face

600 first magnet

600a-600c first magnets

602 connection

602a-6002c connections

604 second magnet

604a-604c second magnets

606 third magnet

606a-606c third magnets

608 central axis

610 axis of symmetry

700 adjusting unit

702 controller

704 sensor

706 electro-permanent magnet

708 first permanent magnet

710 coil

712 second permanent magnet

714 iron core

F, Fi, F2, F3 force

Fc preload force

F _D dynamic force

F _n negative stiffness force

Fp positive stiffness force

FQ quasi- static force

F _r resulting force

resulting stiffness k _n negative stiffness k _p positive stiffness

M1-M6 mirror δ, δι, δ2, δ3 displacement / direction