Effects of high carrier concentrations on some optical properties of semiconductors
Many semiconductor devices, such as heterostructure lasers and silicon bipolar transistors, require large concentrations of free carriers in the conduction and/or valence band of an active region. Under these conditions the band gap of the material is reduced by the many-body interactions of the carrier gas. The band gap narrowing results from a lowering of the conduction and raising of the valence band edge energies and is evaluated for a range of carrier concentrations. (10(^17) - 10(^22) cm_^-3)) in p-type Si and P- and n-type GaAs, Ga(_0.47) In(_0.53) As and Ga(_0.28) In(_0.72) As(_0.6) P(_0.4) at T = OK. A plasmon-pole approximation for the carrier gas dielectric function is used in the calculations. For all these materials, the largest energy shift occurs in the band containing the free carriers. For comparison the band edge shifts in all four materials are evaluated at finite temperature (300 K). The band gap narrowing at finite and zero temperatures differ notably only for low carrier concentrations (p < 5 x 10(^19) cm (^-3) in p-type Si) where the thermal excitation of the carriers reduces their screening effect so producing smaller band gap reduction. High hole concentrations also lead to increased optical losses in semi-conductor lasers due to intervalence band absorption (IVBA) transitions. These losses, which are considered to be partially responsible for the temperature dependence of threshold current densities in some semiconductor lasers, are evaluated in bulk laser materials using a pseudopotential band structure model. The temperature dependencies of the IVBA coefficients in GaAs, Ga(_0.47) In(_0.53) As and Ga(_0.28) In(_0.72) As(_0.6) P(_0.4) are shown to be either small or the coefficients themselves are negligible. Intervalence band absorption is also calculated for a 100/200 A GaAs/Ga(_0.7) al(_0.3) As quantum well laser structure for which the electronic band structure is determined using a variational k^-p approach. The wavelength dependence of the IVBA coefficients differs notably from corresponding results derived using simpler effective mass and pseudopotential models. In particular the k.p model gives significant contributions to the total loss, from certain 'forbidden' transitions.