Acceptor resonances in zero-gap and small-gap semiconductors

An extension of the Koster-Slater theory is performed to study the effect of a localized perturbing potential in zero-gap and small-gap semiconductors. According to this two-band model, the existence of resonant energies depends upon the ratio of the effective mass of the valence and conduction bands, respectively. Owing to the large value of this ratio, it is shown that donors do not lead to any quasidiscrete level. On the contrary, acceptors lead to resonances in the conduction band, provided that the perturbing potential is strongly repulsive. We find that the interband coupling potential mainly results in a dependence of the location of the resonance upon the density of conduction-band states. Experiments performed on ${\mathrm{Hg}}_{1-x}{\mathrm{Cd}}_x \mathrm{Te}$ alloys are shown to be in good agreement with these theoretical results.