Abstract

We propose a high temperature version of Afromowitz' model to calculate the refractive index at growth temperature (600-700°C typical), since this information is indispensable for optical thickness monitoring¹ during the crystal growth. To extend the Afromowitz' model into the high temperature region, it is assumed that the imaginary part of the dielectric function ε₂(E) shifts with temperature at the same rate as the lowest band gap energy without changing its shape. This approximation is plausible to the first order, because the linear temperature coefficients or ΔE/ΔT are all negative and nearly the same at all the interband critical-point energies of GaAs.² In other words, ε₂(E) can be written simply as where E_g(T) is the lowest direct band gap energy. In this case, the Kramers-Kronig integration yields the refractive indices which include the temperature as an implicit variable through E_g(T).

© 1994 Optical Society of America