Bandgap narrowing in zincblende III–V semiconductors: Finite-temperature full random-phase approximation and general analytical model

The bandgap narrowing (BGN) in zincblende III–V semiconductors is calculated in a finite-temperature full Random-Phase Approximation (RPA) formalism based on an isotropic dispersion model. The cases of n-type and p-type quasi-neutral regions and the case of a neutral electron–hole plasma are elaborated for the technologically important materials GaAs, AlAs, InAs, GaP, InP, GaSb, InSb, zb-GaN, zb-InN, Al0.3Ga0.7As GaAs0.5Sb0.5, InP0.69Sb0.31, InAs0.4P0.6, InAs0.4Sb0.6, In0.52Al0.48As In0.49Ga0.51P, In0.53Ga0.47As In0.5Ga0.5Sb, and zb-Ga0.5In0.5N (60 cases). In quasi-neutral regions, the correlation energy of the interaction between carriers and ionized dopants adds two terms to the total BGN. At low temperatures, inefficient screening makes the hole term dominant in n-type materials with a large ratio of the valence band to the conduction band (CB) density-of-states. The inclusion of the CB nonparabolicity is decisive here, as it prevents a diverging BGN at high concentrations. For all 60 cases, the BGN is evaluated in the temperature range from 0 to 500 K. A strong temperature dependence over the whole density range is observed in all direct n-type materials. Otherwise, the temperature dependence quickly ceases with increasing density. An analytical model of BGN without material-dependent free fit parameters is derived and compared with the full-RPA results.