Temperature dependence of the intersubband transitions of doped quantum wells

Numerical calculations are presented for the temperature dependence of the intersubband transition energies of uniformly doped quantum wells. Both the Hartree and exchange interactions cause the transition energy ${\mathit{E}}_{12}$ between the two lowest conduction subbands to depend on the dopant density. For a chosen dopant density, ${\mathit{E}}_{12}$ initially decreases with increasing temperature T. This decrease in ${\mathit{E}}_{12}$ as T increases compares well with the shift observed in the peak position of the infrared absorption coefficient (a blueshift as the temperature is decreased) of Si-doped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple quantum wells. Our calculations also show an interesting dependence of the intersubband transition energies due to the competition between the exchange and Hartree interactions as a function of the dopant density within the quantum well.