Dispersion of the refractive index of GaAs and Al<inf>x</inf>Ga<inf>1-x</inf>As

Abstract

The real part of the complex refractive index near the fundamental absorption edge is calculated for the ternary compound Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> As, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0 \leq x \leq 0.3</tex> , as a function of frequency. An analytical expression for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is given which is derived from a quantum mechanical calculation of the dielectric constant of a semiconductor assuming the band structure of the Kane theory. The expression obtained is a function of bandgap energy, effective electron and heavy hole masses, the spin orbit splitting energy, the lattice constant, and the carrier concentration for n-type or p-type materials. The refractive index at the absorption edge is found as a function of the material parameters above. This enables one to express theoretical results in terms of basic material parameters only, with no adjustable constants. Comparison of theory with available experimental data is given for various reported values of the bandgap energy and effective masses as functions of mole fraction <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> .