The Valence Sub-Bands of Biased Semiconductor Heterostructures

Abstract

It is now recognised that the envelope function framework^(1–3) is a versatile and convenient method to calculate the electronic states of semiconductor heterostructures. In essence this computational scheme relies on the separation between the rapidly varying periodic parts of the Bloch functions, assumed to be the same in each kind of layer, and the more slowly varying envelope functions. The latter experience the potentials arising from the band bending due to charges and the band edge steps when one goes from one layer to the next. Thus, a great deal of the computational complexities is of bulk like origin, i.e. depends upon the fact that the extrema around which one is interested to build the heterolayer eigenstates is non degenerate or degenerate, the local effective mass tensor is scalar or not etc. In this respect, for III–V or II–VI heterolayers which retain the zinc blende lattice, there is a marked difference between the conduction and valence bands. The former is non degenerate (apart from spin) and displays small anisotropy and non parabolicity. The valence band edge instead is fourfold degenerate at the zone center (Γ₈ symmetry), which leads to complicated dispersion relations (although quadratic upon the wavevector k)⁽⁴⁾.