Semiconductor Measurement Technology: A Software Program for Aiding the Analysis of Ellipsometric Measurements, Simple Spectroscopic Models

摘要

MAIN2 is a software program for analyzing spectroscopic ellipsometric measurements. MAIN2 consists mainly of subroutines written in FORTRAN that are used to invert the standard reflection ellipsometry equations for simple systems. Here, a system is said to be simple if the solid material sample is characterized by models which assume at least the following: (1) materials are nonmagnetic; (2) samples exhibit depth-dependent optical properties, such as one with layered or laminar structure atop a substrate that behaves like a semi-infinite half-space; (3) layers are flat and of uniform thickness; and (4) the optical medium within each ambient/layer/substrate is isotropic, homogeneous, local, and linear. The ambient region refers to that region of space which lies external to the layer/substrate structure of the sample. Each layer is characterized by a thickness and a dielectric function. The dielectric function of a region, i.e., ambient, layer, or substrate, is represented by the Bruggeman effective medium approximation (EMA). Within the EMA, the effective medium of a region is characterized by an aggregate mixture of constituent media, and the dielectric function of each constituent medium is known a priori. The ellipsometric equations are formulated as a standard damped nonlinear least-squares problem and then solved by an iterative method when possible. The program is sufficiently modular to allow one to modify some of the models used in the calculations.