Minibands in semiconductor superlattices modelled as Dirac combs (significance of band non-parabolicity)

A generalization of the Kronig-Penney problem is put forward with the potential energy V(x) = gamma Sigma(j) delta(x - ja), gamma > 0. A periodic multi-layer ... ABABABA ... is considered: layers A of thickness a are intercalated between layers B of much smaller thickness. In this superlattice, A and B symbolize, respectively, narrow-gap semiconductor layers and barrier layers. The conduction band of the semiconductor A is defined by the dispersion function E(k) which was derived in the Kane two-band theory. Owing to the non-zero value of the parameter gamma, the electron energies inside the interval corresponding to the conduction band of the semiconductor A are organized in minibands separated by forbidden gaps. With E(k) taken in the Kane form, the dispersion law epsilon = E(k) is non-parabolic if E-g (the width of the forbidden gap of the semiconductor A) is finite. This non-parabolicity affects the positions and widths of the minibands. If E-g tends to infinity, the original Kronig-Penney problem is recovered. If E-g decreases, the density of the minibands increases.