Thomas–Fermi–Dirac theory of the hole gas of a double p-type δ-doped GaAs quantum wells

We present the hole subband structure of two coupled p-type δ-doped GaAs quantum wells as a function of the impurity concentration and the distance l between them, including exchange effects. We present an analytical expression for the Hartree–Fock potential as a function of these two magnitudes, by using the Thomas–Fermi–Dirac approximation. The numerical results for a double Be-δ-doped GaAs quantum well show that many body effects are important when the concentration is low and the energy levels are degenerate for l⩾100 Å and an impurity concentration of 5 × 1012 cm−2, while without exchange effects the energy levels are degenerated for l⩾150 Å and the same impurity concentration. We present an expression for the relative electronic mobility, that is, we calculate the ratio of the electronic mobility of a double δ-doped quantum well and that of a simple δ-doped quantum well. The theoretical results agree quite well with the experimental data available.