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Method of performing parametric sensitivity analysis in optical spectroscopic measurements

IP.com Disclosure Number: IPCOM000239617D
Publication Date: 2014-Nov-19
Document File: 4 page(s) / 122K

Publishing Venue

The IP.com Prior Art Database

Abstract

Disclosed is a modified method to evaluate the sensitivity of optical model parameters based on a solution of the inverse problem. The obvious improvement is to allow all model parameters simultaneous variance, and then evaluate the sensitivity based on the solution of the inverse problem using real measurement data

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Title

Method of performing parametric sensitivity analysis in optical spectroscopic measurements

Abstract

Disclosed is a modified method to evaluate the sensitivity of optical model parameters based on a solution of the inverse problem.  The obvious improvement is to allow all model parameters simultaneous variance, and then evaluate the sensitivity based on the solution of the inverse problem using real measurement data. 

Problem

Most of the modern analysis and modeling software packages for optical characterization have some modules to perform what is referred to as sensitivity analysis (SA) of the model parameters.  This problem of sensitivity is central to the understanding of the model behavior in which the ill-defined parameters (e.g., cross-correlated parameters) will severely influence the accuracy of complex film stacks and/or two-dimensional (2D) and three-dimensional (3D) microelectronic structure measurements (e.g., critical dimensions, sidewall angles, grating, and underlying thin film thicknesses).  SA determines the relative importance of the parameters and helps to optimize a range of variations for each sensitive parameter; the efficiency of all optimization algorithms can be greatly improved if the parameter search space has reasonable bounds.

In this way, it is more likely for an optimization algorithm to find the unique global optimal solution rather than the multiple local minima, which do not adequately describe the results.  Another advantage is that SA indicates which parameters have a negligible influence on model behavior and, therefore, might simplify the model and reduce number of model parameters needed in the optical analysis.

Although all well-established analysis software packages include sensitivity analysis as an option, it is based on a solution of a well-posed forward problem.  In that case, the sensitivity is estimated by calculating changes in the model’s output.  That output, namely, is the spectra when varying one selected parameter at a time by a small amount from its baseline (or nominal) value while holding all other parameters fixed at their nominal values.

This approach relies on an assumption that the solution of an ill-posed inverse problem will agree within negligible quantity.  However, it is not valid in vast majority of real situations.  For instance, the model parameters might be correlated (expressed in terms of two- or multiple-parameter correlation coefficients) and vary only one of the parameters while holding all others fixed, which may produce some delusive results.  Moreover, in general, the three required Hadamard conditions - existence, uniqueness, and stability of a solution - do not hold, since different solutions can give the same resulting spectra and due to measurement noise, the solutions can be unstable.

Solution/Novel Contribution

The novel contribution is a method to evaluate an importance of various model parameters in optical characterization.  The obvious im...