Finite-temperature full random-phase approximation of bandgap narrowing in quasi-neutral regions: Theory including nonparabolicity and application to silicon and InGaAs

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The bandgap narrowing (BGN) in quasi-neutral regions of semiconductors is calculated in a finite-temperature full random-phase approximation formalism based on a simple isotropic dispersion model including band nonparabolicity. The total quasi-particle shift (QPS) is determined by the exchange-correlation self-energy of the free carriers and the correlation energy of the interaction between carriers and ionized dopants. At cryogenic temperatures, the latter part results in giant shifts of the minority band edge in n-type semiconductors with a large ratio of valence to conduction band density of states, as often present in III–V materials. However, at room temperature, the BGN does not exceed common values. The reason for this behavior is explained analytically. Whereas the exchange-correlation energy of free carriers is known to be insensitive to band structure details, the nonparabolicity of the conduction band (CB) has a strong effect on the ionic QPS of the minority carriers in n-type III–V materials. It strongly reduces the BGN at cryogenic temperatures compared to the case of a parabolic CB. This is demonstrated numerically and also analytically for n-type InGaAs. The BGN in n-type silicon becomes independent of temperature at high concentrations, but in p-type silicon, a weak temperature dependence re-emerges above the Mott density, which also can be attributed to the ionic QPS of the minority electrons. The calculated BGN for quasi-neutral regions in silicon is in good agreement with earlier photoluminescence and more recent photo-conductance measurements.