Concentration-dependent absorption and spontaneous emission of heavily doped GaAs

Abstract

A model for the calculation of the absorption and emission spectra for GaAs at carrier concentrations in excess of 1×10¹⁸ cm⁻³ is described. This model utilizes a Gaussian fit to Halperin‐Lax band tails for the concentration‐dependent density of states and also includes an energy‐dependent matrix element. The calculated absorption and emission spectra are compared to previous experimental results. All results are for 297 K. For p‐type GaAs, the agreement is very good. The concentration dependence of the effective energy gap is obtained and can be expressed as E_g (eV) =1.424−1.6×10⁻⁸ [p (cm⁻³)]^1/3. The concentration‐dependent thermal equilibrium electron‐hole density product n₀p₀ and the radiative lifetime τ_r are calculated for p‐type GaAs. The value of n₀p₀ increases from the low‐concentration value of 3.2×10¹² cm⁻⁶ to 1.2×10¹³ cm⁻⁶ at p=1.6×10¹⁹ cm⁻³. This value of n₀p₀, together with the thermal generation rate obtained from the experimental absorption coefficient, gives τ_r as 0.37 nsec at p=1.6×10¹⁹ cm⁻³.