Lightly doped and compensated quantum wells: The density of states in the dipole model

Abstract

%e present a calculation of the density of states (DOS} of electrons bound to donor impurities in a lightly doped and compensated quantum well. %e use a quasiclassical treatment suitable for low compensation in which we apply the dipo1e model. If the fu11 electron-electro~Coulomb interactions were taken into account, instead of the short-range dipole interaction, a Coulomb gap should appear around the Fermi level. But this model is able to describe the small peak of unoccupied states that appear, as a result of compensation, in the high-energy side of the DOS. In this work we show how the additional peak varies with the well width, impurity concentration, and compensation in the small-impurity-concentration limit.It is well established by now that a gap in the density of states (DOS) occurs at the Fermi level in a lightly doped and compensated semiconductor. In the past Efros, Van Lien, and Shklovskii' have calculated the DOS, using a numerical simulation method due to Baranovskii et al.to obtain the ground state of this system, in the so-called classical impurity band model. In fact, when the impurity concentration is very small the electrons are in the completely localized regime. The overlap of the wave functions representing the one-electron ground state is negligible as the average distance between impurities is much greater than the localization length. In that case the donors and acceptors can be assumed as point charges.At suSciently low temperatures a11 acceptors are ionized. If n; represents the occupancy of a donor i, r;" stands for the distance between that donor and an acceptor p; the system can be described by the classical Hamiltonian:For low compensation the ionized donors are those near an acceptor, resulting in unoccupied electron states with higher energies than those occupied at neutral donors.It turns out that a simple way to treat that problem analytically is the dipole model: each acceptor ionizes its nearest-neighbor donor and the pair does not perturb the states of neutral donors as its potential rapidly decays. A bandwidth appears in this additional peak at the DOS located at e /kr, where r is the distance between atoms in the pair, corresponding to the unoccupied "dipole states. " The spread in energy is due to randomness in the dipole moment. Using this simplified picture, a two-peaked DOS comes out: a deltalike peak due to states in neutral donors and a separated broad peak of the unoccupied states in the donors forming dipoles with ionized acceptors. Actually, Auctuations of the electrostatic potential at the neutral donors are responsible for a considerable broadening of the delta peak. However the DOS does not change qualitatively and indeed the dipole model was shown" to give very good results in the caIculation of the electric field distribution.In this work we extend the dipole model to treat a lightly doped and compensated semiconductor heterostructure: the Ga, Al As/GaAs quantum well (QW). We assume that hydrogenlike donor and acceptor impurities occur in the small gap layer o...

Impurity bound states in a compensated quantum well

“…They have also investigated the Fermi level, the charge distribution, and the distribution of the electric fields at neutral donors. Emmel, de Andrada e Silva and da Cunha Lima [3] have presented a calculation of the density of states of electrons bound to donor impurities in a lightly doped and compensated quantum well. They have used a quasiclassical treatment suitable for low compensation in which they apply the dipole model.…”