Resonant Impurity Bands in Semiconductor Superlattices

It is shown that the $2p_z$ confined impurity state of a semiconductor quantum well develops into an excited impurity band in the case of a superlattice. This is studied by following theoretically the transition from a single to a multiple quantum well or superlattice by exactly diagonalizing the three-dimensional Hamiltonian for a quantum well system with random impurities. Intersubband absorption experiments, which can be nearly perfectly reproduced by the theory, corroborate this interpretation, which also requires reinterpretation of previous data.

Figure 1

Schematic of a superlattice with minibands (hatched) and impurity bands (shaded blue area), slightly lower in energy than the minibands (see later in the text).

Figure 2

Calculated infrared absorption spectra of a double quantum well for different temperatures as indicated. A sketch of the structure is shown in the inset with the relevant transitions.

Figure 3

Contour plot of the squared moduli of the states $j=391$ and $415$ in the $xy$ plane (integrated over the $z$ coordinate). The positions of the impurities (one in each QW) are indicated by crosses.

Figure 4

Calculated infrared absorption spectra of a superlattice for different temperatures as indicated.

Figure 5

Experimental infrared absorption spectrum of a $\mathrm{GaAs}/{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ superlattice with 9 nm well width and 2.5 nm barrier thickness. The cutoff at 70 meV is due to the detector employed in the measurement.