Method and system for three-dimensional modeling of stochastic variations of lithographic process

One or more non-transitory computer-readable media storing computer-executable instructions for causing one or more processors performance of a method comprising:

• accessing a random field model configured to model stochastic randomness in one or both of exposure or resist process, the random field model configured to receive inputs of at least one light exposure parameter, at least one resist model parameter associated with resist used in a lithographic process, and at least one success criterion or failure criterion, the random field model configured to generate a probability distribution function of deprotection concentration indicative of success probability or failure probability of the lithographic process;
• inputting the at least one light exposure parameter, the at least one resist model parameter, and the at least one success criterion or failure criterion to the random field model;
• using the random field model to model the stochastic randomness for a plurality of levels based on one or both of the at least one light exposure parameter or the at least one resist model parameter, wherein the plurality of levels are discrete from one another in a resist thickness direction;
• analyzing the stochastic randomness across the plurality of levels;
• outputting, based on the analysis of the stochastic randomness across the plurality of levels, the indication of the success probability or the failure probability of the lithographic process;
• and
• based on the indication of the success probability or the failure probability of the lithographic process, modifying at least one aspect in the lithographic process in order to reduce an effect of the stochastic randomness in the lithographic process.

A system comprising:

• one or more processors, the one or more processors programmed to perform:
• accessing a random field model configured to model stochastic randomness in one or both of exposure or resist process, the random field model configured to receive inputs of at least one light exposure parameter, at least one resist model parameter associated with resist used in a lithographic process, and at least one success or failure criterion, the random field model configured to generate a probability distribution function of deprotection concentration indicative of success probability or failure probability of the lithographic process;
• inputting the at least one light exposure parameter, the at least one resist model parameter, and the at least one success or failure criterion to the random field model;
• using the random field model to model the stochastic randomness for a plurality of levels based on one or both of the at least one light exposure parameter or the at least one resist model parameter, wherein the plurality of levels are discrete from one another in a resist thickness direction;
• analyzing the stochastic randomness across the plurality of levels;
• outputting, based on the analysis of the stochastic randomness across the plurality of levels, the indication of the success probability or the failure probability of the lithographic process;
• and
• based on the indication of the success probability or the failure probability of the lithographic process, modifying at least one aspect in the lithographic process in order to reduce an effect of the stochastic randomness in the lithographic process.