Theory of photoabsorption in modulation-doped semiconductor quantum wells

A systematic study of the electronic and optical properties of modulation-doped GaAs-Alₓ{Ga}_{1{{-}}x}$As quantum wells is undertaken. We consider cases in which the ${Al}ₓGa_1-xAs barriers are doped either n or p type and the GaAs wells are filled with a gas of free carriers. The electronic band structure, exciton binding energy, exciton oscillator strength, and interband absorption are studied as functions of well width and doping concentration. A multiband effective-mass method is used which takes coupling between heavy- and light-hole states into account. In our model for excitons we include effects of valence-subband nonparabolicity, free-carrier screening, and the k dependence of optical matrix elements. The interband optical absorption is obtained using Fermi's golden rule with a correction made for the screened final-state interaction. Our theoretical results are compared with available experimental data.