Abstract

The use of optical proximity correction (OPC) as a resolution enhancement technique (RET) in microelectronic photolithographic manufacturing demands increasingly accurate models of the systems in use. Model building and inference techniques in the data science community have seen great strides in the past two decades in the field of Bayesian statistics. This work aims to demonstrate the predictive power of using Bayesian analysis as a method for parameter selection in lithographic models by probabilistically considering the uncertainty in physical model parameters and the wafer data used to calibrate them. We will consider the error between simulated and measured critical dimensions (CDs) as Student’s t-distributed random variables which will inform our likelihood function, via sums of log-probabilities, to maximize Bayes’ rule and generate posterior distributions for each parameter. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, the model’s parameter space is explored to find the most credible parameter values. We use an affine invariant ensemble sampler (AIES) which instantiates many walkers which semi-independently explore the space in parallel, which lets us exploit the slow model evaluation time. Posterior predictive checks are used to analyze the quality of the models that use parameter values from their highest density intervals (HDIs). Finally, we explore the concept of model hierarchy, which is a flexible method of adding hyperparameters to the Bayesian model structure.

Library of Congress Subject Headings

Microlithography--Mathematics; Photolithography--Mathematics; Bayesian statistical decision theory; Microelectronics

Publication Date

6-19-2017

Document Type

Thesis

Student Type

Graduate

Degree Name

Microelectronic Engineering (MS)

Department, Program, or Center

Microelectronic Engineering (KGCOE)

Advisor

Bruce W. Smith

Advisor/Committee Member

Robert Pearson

Advisor/Committee Member

Dale Ewbank

Campus

RIT – Main Campus

Plan Codes

MCEE-MS

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