Determination of accurate critical-point energies and linewidths from optical data.

Abstract

It is not possible to obtain accurate critical-point linewidths or energies directly from spectroscopic ellipsometry, reflectance, or even thermoreflectance or piezoreflectance line shapes without first differentiating those line shapes. On the other hand, the numerical differentiation of experimental line shapes before fitting them to parametrized theoretical functional forms introduces systematic distortion and broadening, which affects the values found for critical-point energies and linewidths. For that reason, low-field electroreflectance, which within the Franz-Keldysh-Aspnes theory is a third-derivative modulation technique, has long been considered a preferable technique for the determination of critical-point energies and linewidths. However, more recently it has been shown that electroreflectance often contains substantial first- and second-derivative contributions and that it is especially sensitive to sample surfaces, interfaces, and highly defectuous regions. For that reason, it may not yield accurate values for bulk critical-point energies and linewidths. Thus, spectroscopic ellipsometry would be the most reliable method for obtaining accurate bulk critical-point energies and linewidths if the systematic distortion and broadening introduced by numerical differentiation and smoothing could be eliminated. In this paper we present a simple method for doing so. We present several examples to show that this method gives accurate undistorted differentiated line shapes and hence accurate values for critical-point energies and linewidths.