# US 2010/0169060 A1 · Method, system, and computer program prodcut for lithography simulation in electronic design automation > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2010/0169060 A1 - Document ID: US20100169060A1 - Status: Published application - Kind: A1 - Application number: 12/347,926 - Filed: 2008-12-31 - Published: 2010-07-01 - Earliest claimed: 2008-12-31 - Assignees: Cadence Design Systems, Inc. - Inventors: Zhenhai Zhu - Web page: https://patentgrep.com/patent/US20100169060A1 ## CPC - G03F 7/705: {Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions} - G03F: PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR; (phototypographic composing devices B41B; photosensitive materials or processes for photographic purposes G03C; electrophotography, sensitive layers or processes therefor G03G) ## Abstract Disclosed are improved methods, systems, and computer program products for lithographic simulation of an electronic circuit design. Various embodiments of the present invention identifies a mask pattern, performs offline precharacterization for the mask pattern by solving an equation which models a solution for the mask pattern and an interaction between the mask pattern and one or more effects, performs online evaluation based at least upon a parameterized form of the equation, determines a field around the mask pattern based at least upon the act of performing the online evaluation, and stores a result of the act of determining an electromagnetic field around the mask pattern in a tangible computer readable or usable medium ## Claims ### Claim 1 A machine-implemented method for lithographic simulation of an electronic circuit design, the method comprising: identifying a mask pattern; performing offline precharacterization for the mask pattern to generate or modify a reduced parameterized model for the mask pattern; performing online evaluation based at least upon a parameterized form of the equation; determining a field around the mask pattern based at least upon a result of the act of performing the online evaluation; and displaying the result of the act of determining an electromagnetic field around the mask pattern on a display apparatus or storing the result in a tangible computer readable medium. ### Claim 2 (depends on 1) The machine-implemented method of claim 1, in which the act of performing offline precharacterization comprises: identifying an equation which models a solution for the mask pattern and an interaction between the solution and one or more effects; identifying the mask pattern; and solving the equation for an instance of the mask pattern to generate or modify the reduced parameterized model for the mask pattern. ### Claim 3 (depends on 2) The machine-implemented method of claim 2, in which the act of solving the equation for an instance of the mask pattern to generate or modify the reduced parameterized model for the mask pattern comprises: transforming a discretized form of the equation into a parameterized form based at least on at least one parameter; performing a number of stochastic sampling solves on the parameterized form by using a number of values for the at least one parameter; and generating or modifying a reduced parameterized model for the mask pattern based upon a criterion. ### Claim 4 (depends on 2) The machine-implemented method of claim 2, in which the act of identifying the mask pattern comprises: identifying the mask pattern from a library of a plurality of mask patterns; and determining whether an adjustment is need for the mask pattern. ### Claim 5 (depends on 2) The machine-implemented method of claim 2, in which the act of identifying the mask pattern comprises: identifying the mask pattern from a mask layout of the electronic circuit design. ### Claim 6 (depends on 3) The machine-implemented method of claim 3, in which the one or more effects comprise a diffraction effect, a coupling effect between an aperture of the mask pattern and another feature of the mask pattern, or a polarization effect. ### Claim 7 (depends on 3) The machine-implemented method of claim 3, in which the at least one parameter comprises a width, a height, a thickness, or a profile of a mask feature, a transmission coefficient, or one or more illumination parameters. ### Claim 8 (depends on 3) The machine-implemented method of claim 3, in which the criterion comprises determining whether the number of values for the at least one parameter is sufficient to form the reduced parameterized model. ### Claim 9 (depends on 3) The machine-implemented method of claim 3, further comprising: storing a result of performing the number of stochastic sampling solves in a projection matrix. ### Claim 10 (depends on 3) The machine-implemented method of claim 3, in which the parameterized form comprises an affine form or a rational function form. ### Claim 11 (depends on 1) The machine-implemented method of claim 1, in which the act of performing online evaluation comprises: identifying a known mask pattern from a mask layout of the electronic circuit design; and determining the near field for the known mask pattern identified by using the reduced parameterized model. ### Claim 12 (depends on 11) The machine-implemented method of claim 11, in which the act of determining the near field for the known mask pattern comprises: determining a plurality of parameter values for a first parameter in the known mask pattern; solving the reduced parameterized model with the plurality of parameter values to obtain a solution; and projecting a result of the act of solving the reduced parameterized model to an original space. ### Claim 13 (depends on 12) The machine-implemented method of claim 12, further comprising: predicting a printed image on wafer for the known mask pattern. ### Claim 14 (depends on 12) The machine-implemented method of claim 12, in which the act of determining the plurality of the parameter values comprises: extracting the parameter value from a layout of the electronic circuit design. ### Claim 15 A system for lithographic simulation of an electronic circuit design, the system comprising: means for identifying a mask pattern; means for performing offline precharacterization for the mask pattern to generate or modify a reduced parameterized model for the mask pattern; means for performing online evaluation based at least upon a parameterized form of the equation; means for determining a field around the mask pattern based at least upon a result of the act of performing the online evaluation; and a display apparatus configured for displaying the result of the act of determining an electromagnetic field around the mask pattern or a tangible computer usable medium or a storage device configured for storing the result. ### Claim 16 (depends on 15) The system of claim 15, in which the means for performing offline precharacterization comprises: means for identifying an equation which models a solution for the mask pattern and an interaction between the solution and one or more effects; means for identifying the mask pattern; and means for solving the equation for an instance of the mask pattern to generate or modify the reduced parameterized model for the mask pattern. ### Claim 17 (depends on 16) The system of claim 16, in which the means for solving the equation comprises: means for transforming a discretized form of the equation into a parameterized form based at least on at least one parameter; means for performing a number of stochastic sampling solves on the parameterized form by using a number of values for the at least one parameter; and means for generating or modifying a reduced parameterized model for the mask pattern based upon a criterion. ### Claim 18 A computer program product comprising a computer-usable storage medium having executable code to execute a process for lithographic simulation of an electronic circuit design, the process comprising: identifying a mask pattern; performing offline precharacterization for the mask pattern to generate or modify a reduced parameterized model for the mask pattern; performing online evaluation based at least upon a parameterized form of the equation; determining a field around the mask pattern based at least upon a result of the act of performing the online evaluation; and displaying the result of the act of determining an electromagnetic field around the mask pattern on a display apparatus or storing the result in a tangible computer readable medium. ### Claim 19 (depends on 18) The computer program product of claim 18, in which the act of performing offline precharacterization of the process comprises: identifying an equation which models a solution for the mask pattern and an interaction between the solution and one or more effects; identifying the mask pattern; and solving the equation for an instance of the mask pattern to generate or modify the reduced parameterized model for the mask pattern. ### Claim 20 (depends on 19) The computer program product of claim 19, in which the act of solving the equation of the process comprises: transforming a discretized form of the equation into a parameterized form based at least on at least one parameter; performing a number of stochastic sampling solves on the parameterized form by using a number of values for the at least one parameter; and generating or modifying a reduced parameterized model for the mask pattern based upon a criterion.