Investigation of mis-estimation of structure of amorphous silicon films in ellipsometric modeling

Abstract

Dielectric functions for thin films of hydrogenated amorphous silicon (a-Si 1− x :H x ) with varying hydrogen content x, void concentration and surface roughness may be constructed from measured dielectric functions for amorphous silicon (a-Si) by use of the tetrahedron model, scaling procedures, dielectric formulation, and the effective medium approximation (EMA). The measured dielectric functions may correspond to relaxed or unrelaxed (ion-implanted) a-Si. Ellipsometric measurements on thin films of a-Si 1− x :H x are often fitted with such dielectric functions to obtain film parameters such as void concentration and surface roughness, with the fit quality being assessed from the value of the unbiased estimator σ. Due to the strong preparation dependence of the a-Si 1− x :H x lattice structure, it may not be clear whether it is relaxed or unrelaxed dielectric functions which are appropriate for the fit. In this work, dielectric functions are constructed for a-Si 1− x :H x thin films using unrelaxed a-Si dielectric functions, and fitted using relaxed a-Si 1− x :H x dielectric functions and Levenberg–Marquardt non-linear regression. It is demonstrated that a small value of σ may be obtained despite the incorrect choice of relaxation state. Comparison of the input and output void concentration and surface roughness shows significant mis-estimation in the fits.