PATENT APPLICATION

MODELING FOR SEMICONDUCTOR FABRICATION

PROCESS EFFECTS

Cross References to Related Applications

This application claims priority from U.S. Utility Patent Application Serial No. [to be determined], entitled GATE MODELING FOR SEMICONDUCTOR FABRICATION PROCESS EFFECTS, filed on February 16, 2007 and U.S. Utility Patent Application Serial No. [to be determined], entitled INTERCONNECTION MODELING FOR SEMICONDUCTOR FABRICATION PROCESS EFFECTS, filed on February 16, 2007, both of which claim priority from U.S. Provisional Patent Application Serial No. 60/774,511, entitled CONTOUR DERIVATION FOR LFD AND EXTRACTION, filed on February 17, 2006, all of which are hereby incorporated by reference as if set forth in full in this application for all purposes.

Background

[01] Particular embodiments generally relate to modeling for photolithographic processing and more particularly to contour generation for integrated circuit designs due to process variations.

[02] In a conventional integrated circuit design process, a circuit designer begins with a conceptual idea of what functions an integrated circuit is to perform. The circuit designer then creates a circuit design on a computer and verifies it using one or more simulation tools to ensure that the circuit will operate as desired. The design at this stage may be represented by what is commonly viewed as a circuit schematic, but may also be represented by higher level abstractions within the computer.

[03] These abstract designs are then converted to physical definitions of the circuit elements to be fabricated. These definitions, often called the drawn design of the circuit

layout, represent the geometric boundaries for the physical devices to be fabricated- transistor gates, capacitors, resistive interconnecting wires, etc. A number of data formats have been created to represent these physical layouts, including Graphic Data System (GDS) II and OASIS ^IM . Often, each physical layer of the circuit has a corresponding data layer to represent the polygonal boundaries of the elements in that layer.

[04] Once the circuit layout has been defined, additional verification checks are performed. Some of these verification checks are to insure that the physical structures will correctly represent the desired electrical behavior. The devices in the layout may be extracted by a tool, such as an LVS, for Layout vs. Schematic or Layout vs. Source tool. Additional extraction of parasitic resistances and capacitances can be done, and the dynamic behavior of the circuit can be estimated for the layout as well. This step is traditionally called parasitic extraction. Then, the electrical behavior of the extracted device may be tested using a simulation tool, such as a Simulation Program with Integrated Circuit Emphasis (SPICE) tool. This is typically referred to as a parametric simulation.

[05] In a parametric simulation, the width and length of a gate in a circuit layout may be used in a model to simulate the electrical behavior of the transistor. For example, the layout of a transistor may be back-annotated using the LVS. The SPICE simulator uses the width and length to simulate the electrical behavior of the transistor to verify its electrical behavior in silicon.

[06] Due to process variations, the geometric shapes that are actually manufactured using a photolithographic process may vary from the circuit layout in the drawn design. Because of the process variations, the width and length from the drawn design may not provide an accurate simulation of the transistor. One solution for taking into account the process variations includes breaking up the area of the gate into an N number of segments. The width and length for each of these segments is then used in verifying the electrical behavior. This process, however, feeds N number of segments into the simulation. This is a computationally expensive and thus is undesirable.

[07] Also, in a parametric simulation, a series of widths and lengths of an interconnect in a circuit layout may be used in a model to simulate the electrical behavior of the interconnect. For example, the layout of an interconnect may be back-annotated using the

LVS. The SPICE simulator uses the widths and lengths of the interconnect to verify its electrical behavior in silicon.

[08] Due to process variations, the geometric shapes that are actually manufactured using a photolithographic process may vary from the circuit layout in the drawn design. The widths and lengths of the drawn design for an interconnect may be used to verify the electrical behavior of the interconnect. However, because of the process variations, the widths and lengths from the drawn design may not provide an accurate simulation of the interconnect.

Summary

[09] In one embodiment, a method for determining a contour for an object is provided. An object in a layout of a transistor design to be created with the photolithographic process is determined. The object includes a width and a length in the layout. A contour generation is performed to estimate the dimensions of the object after processing. The contour generation includes parametric variations that may occur in the photolithographic process. An adjusted width and adjusted length of the object is then determined based on the contour. The adjusted width and the adjusted length are usable to determine a parametric model for simulation of the electrical behavior of the object. For example, a layout versus schematic (LVS) tool may back-annotate the layout. Then, a SPICE simulation may use the output of the LVS tool to verify the electrical behavior of the transistor using the adjusted width and adjusted length.

[10] The adjusted length and adjusted width represent the contoured edges that may result due to processing variations. This may result in a more accurate simulation of what actually is manufactured using a photolithographic process. Also, a SPICE simulation may expect to receive width and length values for an object, such as a gate area. Thus, by providing an adjusted width and adjusted length, the simulation methodology does not have to be significantly changed.

[11] In another embodiment, an interconnect object in a layout of an integrated circuit design to be created with a photolithographic process is determined. The interconnect object includes a width and a length in the layout. The interconnect design may be in a

drawn design in the layout. A contour generation of the interconnect object in the drawn design is determined based on processing variation factors for the photolithographic process, which produces a generated contour. An object that includes the generated contour may be referred to a generated contour object. A plurality of segments in the generated contour object may be determined based on processing variations. For example, contouring of the edges of the interconnect may result due to processing variations. Segments are then broken up based on the processing variations that result. An adjusted width and adjusted length for each of the plurality of segments of the generated contour object are then determined. The adjusted width and adjusted length may be used by layout verse schematic (LVS) tools to back annotate the layout. For example, resistances and capacitances may be extracted using the adjusted widths and adjusted lengths. Then, the output of the LVS tool may be sent to a SPICE simulation to verify the electrical behavior of the interconnect.

[12] The adjusted lengths and adjusted widths represent the contoured edges that may result due to processing variations. This may result in a more accurate simulation of what actually is manufactured using a photolithographic process. Also, a SPICE simulation may expect to receive multiple resistances and capacitances for an interconnect object. Thus, by providing resistances and capacitances from adjusted widths and adjusted lengths, the simulation methodology does not have to be significantly changed.

[13] A further understanding of the nature and the advantages of particular embodiments disclosed herein may be realized by reference of the remaining portions of the specification and the attached drawings.

Brief Description of the Drawings

[14] FIG. IA illustrates a simplified integrated circuit layout of a transistor including a pair of objects or features to be created on a semiconductor wafer.

[15] FIG. IB illustrates the objects of Fig. IA after modeling for process variations to more accurately predict the shape the transistor will have after undergoing a photolithographic process according to one embodiment.

[16] Fig. 2 depicts an example of a system for providing contour-based simulation

according to a particular embodiment.

[17] Fig. 3 A shows an example of a contour simulated object used for determining an adjusted length according to one embodiment.

[18] Fig. 3B shows an example of a contour simulated object used for determining an adjusted width according to one embodiment.

[19] Fig. 4 depicts a simplified flowchart of a method for determining the adjusted length according to one embodiment.

[20] Fig. 5 depicts a simplified flowchart of a method for determining an adjusted width according to one embodiment. . .

[21] Fig. 6A shows an example of an interconnect design in a layout according to one embodiment.

[22] Fig. 6B shows an interconnect design after undergoing a photolithographic process according to one embodiment.

[23] Fig. 7 depicts an example of a system for providing contour-based simulation according to a particular embodiment.

[24] Fig. 8 shows an example of generated contour object used for determining an adjusted length and adjusted width for a plurality of segments according to one embodiment.

[25] Fig. 9 depicts a simplified flowchart of a method for determining a contour simplification for an interconnect design.

Detailed Description of Embodiments

[26] Contour generation for a gate will now be described. FIG. IA illustrates a simplified integrated circuit layout of a transistor including a pair of objects or features 10, 12 to be created on a semiconductor wafer. In conventional lithographic processing, a layout for an Integrated Circuit (IC) design is stored in a layout format, such as GDS-II or OASIS , that defines the objects as a number of vertices that in turn define corresponding polygons. The edges of the polygons defined between the vertices can then

be further fragmented into additional, smaller edge segments and adapted to ensure the manufacturability of the polygons on a wafer.

[27] Fig. IA shows a transistor layout that models a drain, polysϊlicon line, and source. The region where the polysilicon line is between the source and drain is the transistor gate. Although this layout is described, it will be understood that other objects in integrated circuit designs may be used.

[28] As shown in Fig. IA, a width, W, and length, L ₅ of gate object 102 in the layout can be determined. This may be considered the drawn design, or ideal design, of the width and length as it does not take into account any process variations that may occur in a photolithography process. In one example, the width and length is for a critical dimension (CD) of the gate of a transistor; however, it will be understood that other width and length measurements may be used. The critical dimension may be a portion of the gate that is ^λ electrically sensitive to process variations. Although a gate is described, it will be understood that other objects of an integrated circuit design may be used. For example, the object may be any element that captures a design-intent and process condition. Due to process variations, the electrical behavior can be affected if variations occur in electrically sensitive areas of the design (e.g., polysilicon gate width differences between a pair of\ matched transistors). Accordingly, these areas may be simulated to determine if the process variations will affect the electrical behavior.

[29] FIG. IB illustrates the objects of Fig. IA after modeling for process variations to more accurately predict the shape the transistor will have after undergoing a photolithographic process according to one embodiment. As shown in Fig. IB, contoured edges 104 of object 10 and contoured edges 105 of object 12 are modeled as deviating from the drawn design due to process variations. As discussed above, process conditions can vary from wafer to wafer or from chip to chip within a wafer. Examples of process conditions that may vary include, but are not limited to, focus, dose, etch processing, polishing variations, etc. Variations can occur in the focus of the image on the wafer, the dose of illumination light through the mask or reticle, the overlay of the stepper or ■scanner, the thickness of materials on the wafer, the resist development and processing conditions, as well as other process conditions that affect how the circuit will be created on the wafer.

[30] In a parametric simulation, the width and length of object 102 in a circuit layout may be used in a model to simulate the electrical behavior of the transistor. Devices in the layout may be extracted from a layout using the LVS. For example, the width and length of a gate is used to back-annotate the gate in the layout. The SPICE simulator uses the width and length to simulate the electrical behavior of the transistor to verify its electrical behavior in silicon.

[31] Accordingly, if the width and length of object 102 shown in Fig. IA is used in a model of a simulation to verify the electrical behavior of the transistor, then the simulation may not accurately simulate how the transistor will electrically behave after undergoing photolithography processing. This is because the width and length of object 102 in Fig. IA may not accurately represent the contouring of edges 104 that may occur due to processing variations. Thus, the parametric simulation using the width and length of object 102 in Fig. IA may not be useful.

[32] To take into consideration how process variations may affect the objects created on a wafer, particular embodiments determine an adjusted width W _a φ and adjusted length L _adj that represent the processing variations that may occur during a photolithographic process. The adjusted width and adjusted length represent an object 102 shown in Fig. IB. The width and length in Fig. IB vary from the uneven contouring that may result. As will be described in more detail below, the length and width may vary depending upon where it is measured due to the uneven contouring. Thus, particular embodiments determine an adjusted width and adjusted length that represent the feature with contouring.

[33] In one embodiment, a single value for an adjusted width and a single value for an adjusted length are determined for an object. Thus, segmenting the object into N segments and using the width and length values for each the N segments in a parametric simulation is not necessary. Rather, only the adjusted width and adjusted length is needed to perform the parametric simulation. Because the parametric simulation tools are typically configured to receive one width and length for the object, changes to the methodology for performing the parametric simulation are not needed. However, if the object is segmented into N segments and a series of widths and lengths for each segment is needed for the parametric simulation, then resources use is expensive in addition to having to change the parametric simulation methodology.

[34] Fig. 2 depicts an example of a system 200 for providing contour-based simulation according to a particular embodiment. As shown, a contour generator 202, a contour simplification gate determiner 204, a device extraction tool 206, and a transistor simulator 208 are provided.

[351 Contour generator 202 is configured to perform a contour generation by simulating process variations that may occur in a lithographic process. Contour generator 202 receives a layout of a transistor. For example, the layout may represent geometric boundaries for physical devices to be fabricated, such as transistor gates, capacitors, resistive-interconnecting wires, etc. Any data format may be used to represent the physical layout, such as GDS-II ₃ OASIS™, etc.

[36] Contour generator 202 uses process variation factors to generate a contour representation of the layout. The process variation factors may be any information that models process variations that may occur in the photolithographic process. As shown in Fig. IB, a possible contour simulation shows contours in the geometric shapes of a transistor layout that may occur.

[37] The electrical behavior of a portion of the contour representation of the layout may be tested. The portion may be referred to as a generated contour object. The simulation using generated contours may be an expensive computation. Thus, if it is done full chip, then the cost in time may be exorbitant. Accordingly, in some embodiments, a selective simulation may be determined. For example, a method for determining which areas of an integrated circuit may be tested is provided. These areas of interest may be where variation between the contour and drawn edges may have a good chance to be significantly different due to process variations.

[38] Fig. 3 A shows an example of a generated contour object 300 used for determining an adjusted length according to one embodiment. As shown, drawn edges 302-1 and 302-2 represent edges in the drawn design of the transistor layout. That is, these edges 302-1 and 302-2 are the edges in the layout without taking into account any processing variations. Contoured edges 304-1 and 304-2, however, show the contoured edges that may result after processing variations factors are modeled in a photolithographic process.

[39] As shown in Fig. 3 A, contoured edges 304 differ from drawn edges 302. Thus, using a length from drawn edges 302 may not yield an accurate parametric simulation of the object. Accordingly, contour simplification gate module 204 is configured determine an adjusted length for generated contour object 300. The adjusted length may be used to represent the generated contour object 300 based on processing variation factors for the photolithographic process.

[40] As shown in Fig. 3 A, a drawn length would be the length of an edge from drawn edge 302-1 to drawn edge 302-2. However, due to process variations, contoured edges 304-1 and 304-2 vary from drawn edges 302-1 and 302-2. Thus, using the drawn length does not accurately represent the length in generated contour object 300. Contoured edges 304 may deviate from drawn edges 302 differently at various points along contour simulated object 300. For example, a segment 312-1 is a different length from a segment 312-3. Thus, a determination of the adjusted length takes into account the variations in contoured edges 304. Different ways of calculating the adjusted length may be appreciated. In one embodiment, the object 300 may be broken up into segments 306 as shown in Fig. 3 A. In one embodiment, the adjusted length of generated contour object 300 is determined based on the measured length of CD edges 312 and the area of the segments. For example, the following equation 1.1 may be used:

[41] In equation 1.1, the area of a segment 306 is determined, such as the area of segment 306-1. The area of segment 306-1 is the area between contoured edges 304-1 and 304-2 and CD edges 312-1 and 312-2. The lengths of CD edges 312-1 and 312-2 are then determined. The lengths may be determined using line scan techniques or any other techniques known in the art. Accordingly, the area of segment 306-1 and the lengths of CD edges 312-1 and 312-2 are determined. This process continues for each segment 306 in generated contour object 300. The adjusted length is then determined based on the

areas of each segment 306 and lengths of the CD edges 312. In one embodiment, equation 1.1 optimally provides the adjusted length over a small range of L (<5nm) where Ids (Drain to source current) is linearly proportional to the W/L.

[42] A process for determining the adjusted width will now be described. Fig. 3B shows an example of a generated contour object 300 used for determining an adjusted width according to one embodiment. As shown, drawn edges 302-3 and 302-4 represent edges in the drawn design of the transistor layout. Contoured edges 304-3 and 304-4, however, show the contoured edges that may result after processing variations factors are simulated in a photolithographic process.

[43] A drain 314, a gate 316, and a source 318 are provided. The adjusted width may be determined based on process variation factors. For example, the minimum width between contoured edges 304-3 and 304-4 may be used as the adjusted width. In one embodiment, the following equation may be used to determine the adjusted width:

W _ad j ^{= MIN} (W ora, _n W _Sourc > S _aφ (1-2)

where

[44] In equation 1.2, the adjusted width may be determined based on sampling the various widths from 304-3 to 304-4 at various positions between drain 314 and source 318 and selecting the minimum. For example, moving from contoured edge 304-1 to contoured edge 304-2, width values between contoured edges 304-3 and 304-4 are determined. The minimum of the width values determined is then selected as the adjusted width. A SPICE adjustment coefficient may be determined from customer requirements. The SPICE adjustment adjusts the width of the drawn design to match a silicon-measured I _DS (current between the drain and source) and compensates for R _DS (resistance between the drain and source) variation due to non-uniform width. The SPICE adjustment is between 1 and the maximum width/minimum width. Although the minimum width determined is described as being selected, other methods of determining the adjusted width may also be appreciated.

[45] The adjusted width and adjusted length reflect the contoured edges that are simulated due to process variations in generated contour object 300. Once the adjusted

width and adjusted length are determined ₅ they may be outputted for use in a simulation. For example, the adjusted width and adjusted length may be sent to device extraction tool 206. Also, the adjusted width and adjusted length may be stored, displayed, etc. for other uses.

[46] Devices in the layout may be extracted using device extraction tool 206. A LVS check compares the connectivity and consistency between the logic and the physical objects in the layout. Then, additional extraction of parasitic resistances and capacitors can also be performed. The output of device extraction tool 206 is then input into transistor simulator 208.

[47] Transistor simulator 208 is configured to perform a parametric simulation based on the adjusted length and width to verify the electrical behavior for the transistor. The parametric simulation may ensure that the physical structures will exhibit the desired electrical behavior. In one embodiment, transistor simulator 208 is a SPICE simulator that uses models to perform the simulation; however, it will be understood that other simulators may be used. The model uses the adjusted width and adjusted length determined in performing the parametric simulation. Transistor simulator 208 outputs a simulation result, which may simulate the electrical behavior of the transistor. The result may be used to verify the electrical behavior and may be stored, displayed, etc.

[48] In one embodiment, the simulation receives only one adjusted width and one adjusted length per generated contour object 300. For example, for the object being simulated, the adjusted width and adjusted length are the only width and length values that are provided. Accordingly, the SPICE simulation methodology does not need to be significantly changed because it traditionally received one width value and one length value for an object. This is different than segmenting the object into N segments and sending multiple width and length values for each segment. Then, the results of the N simulations may be summed together to verify the objects electrical behavior. However, particular embodiments, allow transistor simulator 308 to perform the simulation using only one value for each of the adjusted width and adjusted length. Accordingly, the SPICE model may operate as it normally operates when parametric process variations are not taken into account.

[49] Fig. 4 depicts a simplified flowchart 400 of a method for determining the

adjusted length according to one embodiment. Step 402 determines a plurality of segments in the generated contour object. For example, from the top of the gate, the method may move down the gate subdividing the gate into segments 306 until the bottom of the gate is reached.

[50] Step 404 determines lengths for two sides of a segment 306. The length is measured in between contoured edges 304-1 and 304-2 shown in Fig. 3A.

[51] Step 406 determines the area for a segment in the contour-simulated object. For example, the area between contours edges 304-1 and 304-2 is determined for a segment.

[52] Step 408 determines if additional segments need to be processed. If so, the process reiterates to step 404 where the area of another segment is determined.

[53] When the process is finished, and the areas and lengths for all the segments have been determined, equation 1.1 is used to determine the adjusted length in step 410.

[54] Fig. 5 depicts a simplified flowchart 500 of a method for determining an adjusted width according to one embodiment. Step 502 determines a series of widths between contoured edges 304-3 and 304-4 shown in Fig. 3B from drain 314 to source 318. Any number of widths may be determined.

[55] Step 504 selects the minimum width determined in step 502. Although the minimum width is selected, it will be understood that widths other than the minimum width may be selected.

[56] Step 506 then applies a SPICE adjustment coefficient to the minimum width, if desired. It should be noted that the coefficient may just be one so it has no effect.

[57] Accordingly, particular embodiments provide many advantages. For example, a simulation methodology does not need to be significantly changed. A SPICE simulation receives an adjusted length and adjusted width for a gate and can use those values to simulate the electrical behavior of the gate. This is an efficient process for taking into account processing variation factors in a parametric simulation.

[58] Contour generation for an interconnect will now be described. Fig. 6A shows an example of an interconnect design 600 in a layout according to one embodiment.

Interconnect design 600 may be a drawn object that will be created with a photolithographic process. In conventional lithographic processing, a layout for an IC design is stored in a layout format, such as GDS-II or OASIS™, that defines the objects as a number of vertices that in turn define corresponding polygons. The edges of the polygons defined between the vertices can then be further fragmented into additional, smaller edge segments and adapted to ensure the manufacturability of the polygons on a wafer.

[59J Fig. 6A shows a layout that models an interconnect according to one embodiment. An interconnect may be any connecting structure in an integrated circuit design. For example, devices in an integrated circuit may be interconnected using layers of metal. Although this layout is described, it will be understood that other objects in integrated circuit designs may be used.

[60] As shown in Fig. 6A, a width and length of an object 602 in the layout can be determined. This may be considered the drawn design of the width and length as it does not take into account any process variations that may occur in a photolithography process. The width and length may be for any object in the layout. For example, the object may be any element that captures a design-intent and process condition. Due to process variations, the electrical behavior can be affected if variations occur in electrically sensitive areas of the design (e.g., where there is contextual difference between drawn and generated contour). Accordingly, these areas may be simulated to determine if the process variations will affect the electrical behavior. Although an interconnect is described, it will be understood that other objects may be used in particular embodiments.

[61] Fig. 6B shows interconnect design 600 modeling for process variations to more accurately predict the shape the interconnect will have after undergoing a photolithographic process according to one embodiment. Object 602\represents a portion of interconnect design 600. The portion of interconnect design is shown for descriptive purposes; it will be understood that any portion (or all of) interconnect design may be included as object 602.

[62] As shown, drawn edges 604-1 and 604-2 represent edges in the drawn design. That is, these edges are the edges in the layout without taking into account any processing variations. Contoured edges 606-1 and 606-2, however, show the contouring that may

result after processing variations occur in a photolithographic process. As discussed above, process conditions can vary from wafer to wafer or from chip to chip within a wafer. Examples of process conditions that may vary include, but are not limited to, focus, dose, etch processing, polishing variations, etc. Variations can occur in the focus of the image on the wafer, the dose of illumination light through the mask or reticle, the overlay of the stepper or scanner, the thickness of materials on the wafer, the resist development and processing conditions, as well as other process conditions that affect how the interconnect will be created on the wafer.

[63] In a parametric simulation, the width and length of object 602 in a circuit layout may be used in a model to simulate the electrical behavior of the interconnect. For example, the width and length of the interconnect in the layout may be used to extract resistance and capacitance values using an LVS tool. A SPICE simulator uses the resistance and capacitance values to verify the interconnect' s electrical behavior in silicon.

[64] Accordingly, if the width and length of object 602 shown in Fig. 6A is used in a model of a SPICE simulation to verify the electrical behavior of the interconnect, then the simulation may not accurately simulate how the interconnect will electrically behave after undergoing photolithography processing. This is because the width and length of object 602 in Fig. 6A may not accurately represent the contouring of contoured edges 606 that may occur due to processing variations. Thus, the parametric simulation using the width and length of object 602 in Fig. 6A may not be useful. To take into consideration how process variations may affect the objects created on a wafer, particular embodiments determine an adjusted width W _adj and adjusted length L _aι φ for multiple segments of the interconnect that model the processing variations that may occur during a photolithographic process.

[65] Fig. 7 depicts an example of a system 700 for providing contour-based simulation according to a particular embodiment. As shown, a contour generator 702, a contour simplification interconnect determiner 704, a device extraction tool 706, and an interconnect simulator 708 are provided.

[66] Contour generator 702 is configured to perform a contour generation by simulating process variations that may occur in a lithographic process. Contour generator 702 receives a layout of an integrated circuit design that includes an interconnect. For

example, the layout may represent geometric boundaries for physical devices to be fabricated, such as transistor gates, capacitors, resistive-interconnecting wires, etc. Any data format may be used to represent the physical layout, such as GDS-II, OASIS™, etc.

[67] Contour generator 702 uses process variations factors to generate a contour generation of the layout. The process variation factors may be any information that models process variations that may occur in the photolithographic process. As shown in Fig. 6B, a possible contour generation shows contours in the geometric shapes of an interconnect layout that may occur.

[68] The electrical behavior of a portion of the contour simulated layout may be tested. The portion may be referred to as a generated contour object. The contour generation may be an expensive computation. Thus, if it is done full chip, then the cost in time may be exorbitant. Accordingly, in some embodiments, a selective simulation may be determined. For example, a method for determining which areas of an integrated circuit may be tested is provided. These areas of interest may be where variation between the contour and drawn edges may have a good chance to be significantly different due to process variations

[69] Fig. 8 shows an example of a generated contour object 800 used for determining an adjusted length and adjusted width for a plurality of segments according to one embodiment. As shown, drawn edges 604-1 and 604-2 represent edges in the drawn design of the interconnect layout. That is, these edges 604-1 and 604-2 are the edges in the layout without taking into account any processing variations. Contoured edges 606-1 and 606-2, however, show the contouring that may result after processing variations factors are represented in a photolithographic process.

[70] Contour simplification interconnect determiner 704 is configured to determine a plurality of segments 808 in a generated contour object 800. Generated contour object 800 may be the object that is defined by contoured edges 606. The breaking up of generated contour object 800 into segments is determined based on the processing variation factors. For example, the segments may be broken based on area changes, slope changes, curvature of contoured edges 606, local maximum/local minimum of contoured edges 606, etc.

[71] In one example, contour simplification interconnect determiner 704 uses area changes to determine how to segment generated contour object 800. For example, an area of a drawn segment 810 using drawn edges may be determined. A contoured segment 808 using contoured edges 806-1 and 806-2 is then determined. Different sized segments may be determined until the area of the contoured segment 808 becomes greater or less than a threshold as compared with the area of a drawn segment 810. A segment break may be determined at that point. In one example, the following equations 1.1 and 1.2 may be used:

PlNarca ≥ PlDarca • (l + Aseg) (1.1)

PlNarea ≤ PlDarea • (l - As*) . (1.2)

where 0 <= Aseg <= 1

[72] In equation 1.1, if the contoured segment area (CS _are a) is greater than the drawn segment area (DS _are a) times a variable (A _seg ) set by a user, then the segment is determined at that point. An example of a contoured segment that illustrates an area greater than the drawn segment area times the.variable is contoured segment 808-2. In this case, an adjusted length Ll and an adjusted width Wl are used. The adjusted length and width represent the edges of contoured segment 808-2.

[73] In equation 1.2, if the contoured segment area (CSarea) is less than the drawn segment area (DS _are a) times a variable set by a user, then the segment is determined at that point. An example of a contoured segment that illustrates an area greater than the drawn segment area times the variable is segment 808-3. In this case, an adjusted length L2 and an adjusted width W2 are used. The adjusted length and width represent the edges of contoured segment 808-2.

[74] The adjusted length and adjusted width of contoured segments 808 are the lengths and widths of the dotted rectangles shown. Although the adjusted lengths and adjusted widths using contoured edges 806-2 may not exactly follow the contouring, they may yield more accurate parametric simulations of object 602 because they approximate the contouring. If the processing variations are not taken into account, then the same length and width would be used for object 602 using drawn edges 604. However,

contoured segments 808 may vary in size based on the processing variations that are simulated (the deviation of contoured edges 606 from drawn edges 604).

[75] Although using area for breaking generated contour object 800 into segments 808 is described, it will be understood that other methods will be used. For example, the slope of contoured edges 806 may be used. Referring to segment 808-1, the difference between drawn edge 604-1 and contoured edge 606-1 is small. Also, the difference between drawn edge 604-2 and contoured edge 606-2' is also small. When contoured edges 606-1 and 606-2 start to slope inward, then the difference from drawn edges 604-1 and 604-2 becomes larger. Accordingly, a segment is then broken around the point at which the difference starts becomes larger than a desired threshold.

[76J Generated contour object 800 may be segmented more frequently when the deviations from drawn edges 604 become greater. This is because an adjusted width and an adjusted length are determined for the segments 808. If large changes in the contour slope occur, then it may be more accurate to have smaller segments with adjusted widths and lengths rather than a larger segment.

[77] Thus, as shown, a large segment 808-1 is first included where the deviation is not very large between drawn edge 604 and contoured edge 606. However, the segments become smaller as the slope of contoured edges 606 becomes steeper. Then, as the slope becomes less gradual, larger segments, such as segment 808-N, may be determined.

[78] It should be noted that the segments in generated contour object 800 are not arbitrarily determined. For example, fixed-size segments are not just determined. Rather, the processing variations are taken into account to determine the segments. Although this may result in fixed-size segments being determined, the segments are determined based on the processing variations.

[79] Once the adjusted width and adjusted length are determined for each segment, they may be outputted for use in a simulation. For example, the adjusted width and adjusted length may be sent to device extraction tool 706. Also, the adjusted width and adjusted length may be stored, displayed, etc. for other uses.

[80] Devices in the layout may be extracted using device extraction tool 706. A LVS

check compares the connectivity and consistency between the logic and the physical objects in the layout. Then, additional extraction of parasitic resistances and capacitors using the adjusted widths and adjusted lengths can also be performed for the interconnect. For example, the adjusted width and adjusted length may be used to determine the resistances and capacitances for each segment of generated contour object 800. The output of device extraction tool 706 is then input into interconnect simulator 708.

[81] Interconnect simulator 708 is configured to perform a parametric simulation to verify the electrical behavior for the interconnect. The parametric simulation may ensure that the physical structures will exhibit the desired electrical behavior. In one embodiment, interconnect simulator 708 is a SPICE simulator that uses models to perform the simulation. The model uses the resistance and capacitance for each segment 808 to perform the parametric simulation. In one embodiment, the simulation receives a series of resistances and capacitances per generated contour object 800. Interconnect simulator 708 outputs a simulation result, which may simulate the electrical behavior of the interconnect. The result may be used to verify the electrical behavior and may be stored, displayed, etc.

[82] For an interconnect that does not take into account process variations, a series of resistances and capacitances are conventionally input into a SPICE simulator. Accordingly, the SPICE simulation methodology does not need to be significantly changed because it is used to receiving a series of resistances and capacitances for an object. However, particular embodiments provide resistances and capacitances that take into account process variations, which yields more accurate simulations.

[83] Fig. 9 depicts a simplified flowchart 900 of a method for determining a contour representation for an interconnect design. Step 902 determines an object in an interconnect design. For example, the object may be a portion of an interconnect in a layout.

[84] Step 904 determines a generated contour object 800 using a contour generation. The contour generation determines a generated contour object 800 based on the process variation factors that may occur in a photolithographic process. Generated contour object 800 can be a portion of interconnect design 700 or the entire interconnect design. For example, for ease of simulation, interconnect design may be broken up into portions.

[85] Step 906 determines a plurality of segments 808 in generated contour object 800 based on processing variation factors. For example, plurality of segments 808 may be determined based on area deviation from a drawn design.

[86] Step 908 then determines an adjusted width and adjusted length for each of the plurality of segments. The adjusted width and adjusted length model the width and length of the segment found in generated contour object 800. This takes into account the contoured edges 606 that may result from processing variations. The adjusted width and adjusted length may be used to determine a parametric model for simulation of the object. For example, as described above, generated contour object 800 may be back-annotated using LVS tool 606. The adjusted width and adjusted length may then be used to determine resistances and capacitances for an interconnect model in a parametric simulation.

[87] Accordingly, particular embodiments provide many advantages. For example, a simulation methodology does not need to be significantly changed. A SPICE simulation receives resistances and capacitances that were determined using adjusted lengths and adjusted widths for an interconnect and can use those values to simulate the electrical behavior of the interconnect. This is an efficient process for taking into account processing variation factors in a parametric simulation.

[88] Although the description has been described with respect to particular embodiments thereof, these particular embodiments are merely illustrative, and not restrictive. Although particular embodiments are described with respect to the creation of integrated circuits, it will be appreciated that the techniques of particular embodiments may be applied to any manufacturing process that is subject to process variations. Examples of processes include, but are not limited to, mask bias, overlay errors, film stack thickness variations, mask phase errors, post-exposure bake temperatures, resist development times and post exposure bake times. Other devices fabricated lithographically where particular embodiments may be applied may include Micro- electromechanical systems (MEMS), magnetic heads for disk drives, photonic devices, diffractive optical elements, nanochannels for transporting biological molecules, etc.

[89] Any suitable programming language can be used to implement the routines of particular embodiments including C, C++, Java, assembly language, etc. Different

programming techniques can be employed such as procedural or object oriented. The routines can execute on a single processing device or multiple processors. Although the steps, operations, or computations may be presented in a specific order, this order may be changed in different particular embodiments. In some particular embodiments, multiple steps shown as sequential in this specification can be performed at the same time. The sequence of operations described herein can be interrupted, suspended, or otherwise controlled by another process, such as an operating system, kernel, etc. The routines can operate in an operating system environment or as stand-alone routines occupying all, or a substantial part, of the system processing. Functions can be performed in hardware, software, or a combination of both. Unless otherwise stated, functions may also be performed manually, in whole or in part.

[90] In the description herein, numerous specific details are provided, such as examples of components and/or methods, to provide a thorough understanding of particular embodiments. One skilled in the relevant art will recognize, however, that a particular embodiment can be practiced without one or more of the specific details, or with other apparatus, systems, assemblies, methods, components, materials, parts, and/or the like. In other instances, well-known structures, materials, or operations are not specifically shown or described in detail to avoid obscuring aspects of particular embodiments.

[91] A "computer-readable medium" for purposes of particular embodiments may be any ^~ medium that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, system, or device. The computer readable medium can be, by way of example only but not by limitation, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, system, device, propagation medium, or computer memory.

[92] Particular embodiments can be implemented in the form of control logic in software or hardware or a combination of both. The control logic, when executed by one or more processors, may be operable to perform that what is described in particular embodiments.

[93] A "processor" or "process" includes any human, hardware and/or software system, mechanism or component that processes data, signals, or other information. A

processor can include a system with a general-purpose central processing unit, multiple processing units, dedicated circuitry for achieving functionality, or other systems. Processing need not be limited to a geographic location, or have temporal limitations. For example, a processor can perform its functions in "real time," "offline," in a "batch mode," etc. Portions of processing can be performed at different times and at different locations, by different (or the same) processing systems.

[94] Reference throughout this specification to "one embodiment", "an embodiment", "a specific embodiment", or "particular embodiment" means that a particular feature, structure, or characteristic described in connection with the particular embodiment is included in at least one embodiment and not necessarily in all particular embodiments. Thus, respective appearances of the phrases "in a particular embodiment", "in an embodiment", or "in a specific embodiment" in various places throughout this specification are not necessarily referring to the same embodiment. Furthermore, the particular features, structures, or characteristics of any specific embodiment may be combined in any suitable manner with one or more other particular embodiments. It is to be understood that other variations and modifications of the particular embodiments described and illustrated herein are possible in light of the teachings herein and are to be considered as part of the spirit and scope.

[95] Particular embodiments may be implemented by using a programmed general purpose digital computer, by using application specific integrated circuits, programmable logic devices, field programmable gate arrays, optical, chemical, biological, quantum or nanoengineered systems, components and mechanisms may be used. In general, the functions of particular embodiments can be achieved by any means as is known in the art. Distributed, networked systems, components, and/or circuits can be used. Communication, or transfer, of data may be wired, wireless, or by any other means.

[96] It will also be appreciated that one or more of the elements depicted in the drawings/figures can also be implemented in a more separated or integrated manner, or even removed or rendered as inoperable in certain cases, as is useful in accordance with a particular application. It is also within the spirit and scope to implement a program or code that can be stored in a machine-readable medium to permit a computer to perform any of the methods described above.

[97] Additionally, any signal arrows in the drawings/Figures should be considered only as exemplary, and not limiting, unless otherwise specifically noted. Furthermore, the term "or" as used herein is generally intended to mean "and/or" unless otherwise indicated. Combinations of components or steps will also be considered as being noted, where terminology is foreseen as rendering the ability to separate or combine is unclear.

[98] As used in the description herein and throughout the claims that follow, "a", "an", and "the" includes plural references unless the context clearly dictates otherwise. Also, as used in the description herein and throughout the claims that follow, the meaning of "in" includes "in" and "on" unless the context clearly dictates otherwise.

[99] The foregoing description of illustrated particular embodiments, including what is described in the Abstract, is not intended to be exhaustive or to limit the invention to the precise forms disclosed herein. While specific particular embodiments of, and examples for, the invention are described herein for illustrative purposes only, various equivalent modifications are possible within the spirit and scope , as those skilled in the relevant art will recognize and appreciate. As indicated, these modifications may be made to the present invention in light of the foregoing description of illustrated particular embodiments and are to be included within the spirit and scope.

[100] Thus, while the present invention has been described herein with reference to particular embodiments thereof, a latitude of modification, various changes and substitutions are intended in the foregoing disclosures, and it will be appreciated that in some instances some features of particular embodiments will be employed without a corresponding use of other features without departing from the scope and spirit as set forth. Therefore, many modifications may be made to adapt a particular situation or material to the essential scope and spirit. It is intended that the invention not be limited to the particular terms used in following claims and/or to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include any and all particular embodiments and equivalents falling within the scope of the appended claims.