Theory of optical transitions in inversion layers of narrow-gap semiconductors

The theory of electric sub-bands in MOS structures involving InSb-type narrow-gap semiconductors is developed and used to resolve a long-standing problem concerning a possibility of inter-sub-band resonance excitations with light polarisation parallel to the interface. k.p p theory is formulated for electrons in inversion layers, taking into account the main features of the InSb-type band structure and assuming a triangular model potential near the interface. It is shown that the interband k.p coupling and the small value of the gap make it possible to excite inter-sub-band optical transitions with light polarisation parallel to the interface. The transition probability is proportional to k/sub ///2, where k/sub /// is the electron wavevector parallel to the interface. Numerical estimations are carried out using variational functions for electric sub-bands. For typical experimental conditions in InSb MOS structures one obtains the optical transition probability for parallel light polarisation to be a few percent of that for the transverse one. Both the k/sub ///2-dependence and the numerical values agree with existing experiments. The possibility of excitation with parallel light polarisation is interpreted in terms of an analogy between free relativistic particles and electrons in narrow-gap semiconductors.