Classical theory of impurity bands in δ-doped n-i-p-i superlattices

We investigate the density of localized states (DOS) of the classical two-dimensional impurity band in lightly doped δ-n-i-p-i structures. The donor DOS distribution of the ground state of the n-i-p-i superlattice is simulated for T=0 K as a function of the compensation level K and the interlayer distance d, which permits an artificial reduction of the donor-acceptor Coulomb interaction. We compare the position of the Fermi level with analytical results in the case of low and high compensation. In the limit of low compensation and large interlayer distance Wigner crystallization is observed. The analysis of the Coulomb gap in the vicinity of the Fermi level shows significant deviations from the universal slope postulated for two-dimensional systems in the large disorder limit. Furthermore, the impurity bandwidth’s dependence on the interlayer distance and the influence of residual three-dimensional background doping is disussed. Finally, we investigate the donor and acceptor impurity band in excited δ-n-i-p-i structures and thus take advantage of the possibility to tune the electron filling factor F in one system of given compensation. A static model is compared with a dynamic one in which recombination, capture, and intralayer hopping processes are considered. The excitation-induced heating of the impurity system is described by introducing effective temperatures.