Impurity states in quantum wells and superlattices and their influence in the intersubband absorption spectra

Intersubband absorption in quantum wells (QW) and superlattices usually requires the presence of doping atoms, inevitably giving rise to disorder by randomly distributed hydrogenic impurity states (Coulomb potentials). It has been shown that in particular the 1s-2pz transition plays the role of an impurity-shifted intersubband transition, clearly observed in superlattices at low temperature, but recently also in isolated quantum wells.
In an attempt to understand the inter-miniband absorption spectra in doped superlattices on a more profound level than the usual variational approach for the impurity states, we have performed numerical calculations of the absorption spectra, by exactly diagonalizing the fully three-dimensional Schrödinger equation for a certain number of N coupled QWs (N=1..20), in an areal sheet of 100 x 100 nm2. The impurities are placed in the middle of each QW, but randomly distributed in the xy plane. The resulting energy levels and wave functions are used to calculate the absorption spectra.
For the case of a single QW the well known results for a quasi 2D impurity are reproduced, in particular the 2pz state (or 2p0, i.e. m=0) lies just below the second subband. More interesting is the double QW. Here it turns out that each subband level gets “its own” m=0 type impurity level, all of which can be optically reached from the 1s ground state.
It is now most interesting to observe how this evolves into a superlattice (SL). We find that, at low temperature, there remain two absorption peaks even at low doping, when only the 1s ground state is occupied: the transition to the 2pz-type excited state, just below the second miniband, but also a transition to an impurity state pinned to the top of the second miniband (and a weaker continuum in between). This result requires re-interpretation of data reported in the past: at low temperature and low doping, the high-energy peak in the SL absorption spectrum is not the miniband transition at kz=0, but an impurity transition to the state near the top of the excited miniband. This also explains a hitherto not understood behavior: the high-energy peak does not disappear, when the SL is driven through the metal-insulator transition by a magnetic field into the insulating regime, when only the impurity states are occupied, but the miniband states are empty. This is the first calculation which treats quantum well and random impurity potential on the same footing. At higher doping, screening and impurity band formation sets in, and the resulting Mott transition can be treated by the same method.