# US 11,079,687 B2 · Process window based on defect probability > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,079,687 B2 - Document ID: US11079687B2 - Status: Granted - Kind: B2 - Application number: 16/955,483 - Filed: 2018-12-17 - Published: 2021-01-21 - Granted: 2021-08-03 - Earliest claimed: 2017-12-22 - Assignees: ASML Netherlands B.V. - Applicants: Asml Netherlands B.V. - Inventors: Abraham Slachter; Stefan Hunsche; Wim Tjibbo Tel; Anton Bernhard Van Oosten; Koenraad Van Ingen Schenau; Gijsbert Rispens; Brennan Peterson - Web page: https://patentgrep.com/patent/US11079687B2 ## CPC - G03F 7/70633: {Overlay, i.e. relative alignment between patterns printed by separate exposures in different layers, or in the same layer in multiple exposures or stitching} - G03F 7/705: {Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions} - G03F 7/70558: {Dose control, i.e. achievement of a desired dose} - G03F 7/70625: {Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness} - G03F 7/70641: {Focus} - 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 A method including obtaining (i) measurements of a parameter of the feature, (ii) data related to a process variable of a patterning process, (iii) a functional behavior of the parameter defined as a function of the process variable based on the measurements of the parameter and the data related to the process variable, (iv) measurements of a failure rate of the feature, and (v) a probability density function of the process variable for a setting of the process variable, converting the probability density function of the process variable to a probability density function of the parameter based on a conversion function, where the conversion function is determined based on the function of the process variable, and determining a parameter limit of the parameter based on the probability density function of the parameter and the measurements of the failure rate. ## Claims ### Claim 1 A method for determining a parameter limit of a feature on a substrate, the method comprising: obtaining (i) a functional behavior of a parameter of the feature defined as a function of the process variable based on measurements of the parameter and data related to a process variable of a patterning process used to generate the feature, (ii) measurements of a failure rate of the feature, and (iii) a probability density function of the process variable for a setting of the process variable; converting, by a hardware computer system, the probability density function of the process variable for the setting to a probability density function of the parameter for the setting based on a conversion function, wherein the conversion function is determined based on the function of the process variable; and determining, by the hardware computer system, a parameter limit of the parameter based on the probability density function of the parameter for the setting and the measurements of the failure rate of the feature. ### Claim 2 (depends on 1) The method according to claim 1, wherein the probability density function of the process variable for the setting is determined based on a variance of the process variable that is computed from a measured variance of the parameter for the setting of the process variable and a local derivative of the function of the process variable with respect to the process variable determined for the setting of the process variable. ### Claim 3 (depends on 1) The method according to claim 1, wherein the conversion function is a conversion factor, wherein the conversion factor is an absolute value of a local derivative of an inverse of the function of the process variable determined for the setting of the process variable. ### Claim 4 (depends on 1) The method according to claim 1, further comprising: determining, by the hardware computer system, an estimated failure rate of the feature based on the parameter limit and the probability density function of the parameter; and identifying, by the hardware computer system, a process window related to the process variable such that the estimated failure rate of the feature is less than a predetermined threshold. ### Claim 5 (depends on 4) The method according to claim 4, wherein the predetermined threshold is based on a selected yield of the patterning process. ### Claim 6 (depends on 1) The method according to claim 1, wherein the failure rate is related to one or more failures of the feature, the one or more failures having one or more failure modes comprising a physical failure mode of the feature, a transfer failure mode of the feature, and/or a postponed failure mode of the feature. ### Claim 7 (depends on 6) The method according to claim 6, wherein the failure rate is related to a postponed failure mode of the feature and the postponed failure mode of the feature is a failure that occurs in a next step of the patterning process due to defect in a current processing step, and/or wherein the one or more failures of the feature are weighted based on a frequency of a particular failure to generate a weighted failure rate of the feature. ### Claim 8 (depends on 1) The method according to claim 1, further comprising: obtaining a weighted function of the process variable based on a correlation between one or more failures of the feature and the process variable; determining, by the hardware computer system, a weighted parameter limit of the parameter based on the weighted function of the process variable; and determining, by the hardware computer system, a process window based on the weighted parameter limit. ### Claim 9 (depends on 8) The method of claim 8, further comprising optimizing, by the hardware computer system, a resist thickness and/or resist type using a resist model of a resist process, by simulation, based on one or more postponed failures associated with the resist process. ### Claim 10 (depends on 1) The method of claim 1, further comprising: obtaining the parameter limit for each feature type of a plurality of feature types, and an estimated failure rate of each feature type of the plurality of feature types based on the corresponding parameter limit; and determining, by the hardware computer system, an overlapping process window based on the estimated failure rate of each feature type of the plurality of feature types. ### Claim 11 (depends on 10) The method according to claim 10, further comprising iteratively determining an optical proximity correction, by modelling and/or simulation, based on a maximum of the estimated failure rate of each feature type of the plurality of feature types. ### Claim 12 (depends on 1) The method according to claim 1, further comprising determining, by the hardware computer system, a refined variance of the parameter from a measured variance of the parameter, wherein the refined variance accounts for variance due to factors unrelated to the process variable. ### Claim 13 (depends on 12) The method according to claim 12, wherein the refined variance is computed by removing the variance due factors unrelated to the process variable from the measured variance. ### Claim 14 (depends on 12) The method according to claim 12, further comprising determining a process window based on the refined variance. ### Claim 15 (depends on 1) The method of claim 1, further comprising: obtaining a transfer function of a post pattern transfer step of the patterning process, and a probability density function of another process variable based on the transfer function; and determining, by the hardware computer system, a process window based on the probability density function of the another process variable. ### Claim 16 A computer product comprising a non-transitory computer-readable medium having instructions, the instructions, upon execution by a computer system, configured to cause the computer system to at least: obtain (i) a functional behavior of a parameter of a feature on a substrate defined as a function of the process variable based on measurements of the parameter and data related to a process variable of a patterning process used to generate the feature, (ii) measurements of a failure rate of the feature, and (iii) a probability density function of the process variable for a setting of the process variable; convert the probability density function of the process variable for the setting to a probability density function of the parameter for the setting based on a conversion function, wherein the conversion function is determined based on the function of the process variable; and determine a parameter limit of the parameter based on the probability density function of the parameter for the setting and the measurements of the failure rate of the feature. ### Claim 17 (depends on 16) The computer product according to claim 16, wherein the probability density function of the process variable for the setting is determined based on a variance of the process variable that is computed from a measured variance of the parameter for the setting of the process variable and a local derivative of the function of the process variable with respect to the process variable determined for the setting of the process variable. ### Claim 18 (depends on 16) The computer product according to claim 16, wherein the conversion function is a conversion factor, wherein the conversion factor is an absolute value of a local derivative of an inverse of the function of the process variable determined for the setting of the process variable. ### Claim 19 (depends on 16) The computer product according to claim 16, wherein the instructions are further configured to cause the computer system to: determine an estimated failure rate of the feature based on the parameter limit and the probability density function of the parameter; and Identify a process window related to the process variable such that the estimated failure rate of the feature is less than a predetermined threshold. ### Claim 20 (depends on 16) The computer product according to claim 16, wherein the instructions are further configured to cause the computer system to: obtain a weighted function of the process variable based on a correlation between one or more failures of the feature and the process variable; determine a weighted parameter limit of the parameter based on the weighted function of the process variable; and determine a process window based on the weighted parameter limit.