Calculations of Dielectric Constant for AlGaInAs Quaternary Semiconductor Alloy in the Transparent Region and Above (0.4
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Calculations of Dielectric Constant for AlGaInAs Quaternary Semiconductor Alloy in the Transparent Region and Above (0.4-4.0eV) M. Linnik and A. Christou Department of Materials and Nuclear Engineering and Materials Research Science and Engineering Center, University of Maryland, College Park MD 20742 ABSTRACT The modeling of the spectral behavior of the refractive index of AlGaInAs quaternary IIIV semiconductor alloy in the energy range from 0.4 to 4eV, including the transparent region, is presented. The extended model of interband transition contributions incorporates not only the fundamental absorption edge contribution to the dielectric function, but also contributions from higher energy and indirect transitions. It is demonstrated that indirect energy transitions must be included in the calculations of the complex dielectric function of the material in the transparent region. Indirect transitions from different critical points in the Brillouin zone are treated separately. The comparison between the theoretical refractive indices and the experimental data for AlGaInAs alloy is presented. These calculations have been applied to the design of Bragg mirrors with the highest refractive index contrast for heterostructure lasers. INTRODUCTION The design and analysis of such devices as injection lasers, photodiodes, detectors, solar cells, multilayer structures, and microcavities requires the exact knowledge of the optical constants of III-V compound semiconductors in the region near the fundamental absorption edge as well as at the higher photon energies. In modeling of the optical constants of semiconductors in the fundamental optical region, several approaches are typically used: (1) empirical formulas, (2) damped harmonic oscillator (DHO) models, (3) standard critical point (SCP) models. Optical constants determined from empirical formulas (such as the Sellmeier dispersion equations for the refractive index and Urbach’s rule for the absorption coefficient [1], or the expression for n based on interpolation of a dielectric quantity using Vegard’s rule by Burkhard et al.[2]) are not related through the Kramers-Kronig dispersion relation and are valid only over a very limited energy range. A semi-empirical single effective oscillator model based on quasi-classical Boltzmann equation or Drude theory proposed by Wemple et al.[3] does provide an analytical expression for the dispersion of the semiconductor refractive index at photon energies significantly below the direct band edge. The Drude theory ignores the carrier related effects around the band gap, and thus the results are valid only in the low optical frequency region. This model also lacks the agreement with experimental data at the band edge, which is the energy range of the most interest for semiconductor laser devices. The standard critical point (SCP) model can determine the position of critical points of the semiconductor band structure, but cannot accurately predict the dielectric function [4]. The modified SCP model was initially proposed by Korovin [5] a
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