Modelling the optical constants of Si xGe 1-x alloys in the range 1.7-5.6 eV

Abstract

Optical constants of Si xGe 1-x alloys are modelled over the spectral range from 0.7 eV to 5.6 eV for all compositions 0≤x≤1. The employed model is the modified Adachi's model, which utilizes variable line broadening instead of the conventional Lorentzian one. The model takes into account transitions at the indirect band gap E g id, and critical points E 0, E 0+Δ 0, E 1, E 1+Δ 1, E′ 0, E 2(X), and E 2(Σ). Excitonic effects are not considered. The model parameters are determined using a global optimization routine, namely an acceptance-probability-controlled simulated annealing algorithm. Excellent agreement with the experimental data is obtained in the entire investigated energy and composition ranges. The obtained relative root mean square errors are below 4.5% and 6.5% for the real and imaginary parts of the index of refraction, respectively.