1s-2${\mathit{p}}_{\pm }$ infrared-absorption spectra of donor-doped quantum wells under electric and magnetic fields

We present a theoretical study of the intradonor infrared-absorption properties associated with transitions between the 1s-like ground state and 2${\mathit{p}}_{\pm }$-like excited states of hydrogenic donors in a GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum well under electric and magnetic fields, both applied along the growth direction of the heterostructure. Donor energies and envelope wave functions of 1s-like and 2${\mathit{p}}_{\pm }$-like states are obtained within a variational procedure in the effective-mass approximation, and the line strengths for intradonor 1s-2${\mathit{p}}_{\pm }$ transitions are obtained for x-polarized radiation and for donor positions along the quantum well. The 1s-2${\mathit{p}}_{\pm }$ absorption spectra are calculated and theoretical results compare rather well with experimental data by Jarosik et al. [Phys. Rev. Lett. 54, 1283 (1985)] and Yoo et al. [Phys. Rev. B 44, 13 152 (1991)]. Also, the present work unambiguously shows that a calculation of the absorption spectra with the appropriate doping profile is needed if one aims to a full understanding of experimental measurements.