Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, Al<i>x</i>Ga1−<i>x</i>As, and In1−<i>x</i>Ga<i>x</i>As<i>y</i>P1−<i>y</i>

Abstract

A method is described for calculation of the optical constants (the refractive index, extinction coefficient, and absorption coefficient) of some III-V binaries (GaP, GaAs, GaSb, InP, InAs, and InSb), ternaries (AlxGa1−xAs), and quaternaries (In1−xGaxAsyP1−y) in the entire range of photon energies (0–6.0 eV). The imaginary part of the dielectric function [ε2(ω)] is derived first from the joint density-of-states functions at energies of various critical points (CPs) in the Brillouin zone; then its real part [ε1(ω)] is obtained analytically using the Kramers–Kronig relation. The indirect band-gap transitions are also assumed to provide a gradually increasing ε2 spectrum expressed by a power law of (ℏω−EIDg)2, where ℏω is the photon energy and EIDg is the indirect band-gap energy. The optical dispersion relations are expressed in terms of these model dielectric functions. The present model reveals distinct structures in the optical constants at energies of the E0, E0+Δ0 [three-dimensional (3-D) M0 CP], E1, E1+Δ1 [3-D M1 or two-dimensional (2-D) M0 CP], and E2 or E′0 (triplet) (damped harmonic oscillator). Excellent agreement is achieved between our calculations and published experimental data for these semiconductors over a wide range of the photon energies.