Kane matrix element

In the analyses of conventional zincblende (ZB) semiconductors, we frequently assume a parabolic band for the conduction bands, and the 6 x 6 Luttinger-Kohn Hamiltonians are used to describe the upper valence bands [1,2], In treating the valence bands together with the conduction bands on an equal footing, as when estimating the momentum matrix elements, we often make use of the 8 x 8 Kane Hamiltonian [3], However, the form of the Hamiltonians reflects the crystal symmetry, and Kane Hamiltonians are constructed under the condition of cubic symmetry. For wurtzite (WZ) materials, therefore, we must consider hexagonal symmetry in the effective Hamiltonian. Let us consider the 8 x 8 k.p Hamiltonian for WZ structure [4,5],... 

For matrix elements between CB and VB Bloch functions (i.e. y = 1, 2 and f = 3,4,5,6), following Kane s work, the mutual interaction between conduction and valence bands (the k p interaction) are treated exactly, ... 

Here all the conduction band-edge , and valence-edges , are put into an absolute energy scale. It is clearly shown in the matrix elements of (28) that 3/2, 3/2) heavy-hole (HH) band-edges are shifted by SE =-P -Q and 13/2, 1/2) light-hole (LH) band-edges are shifted by SE =-P +Q, and conduction band-edges are shifted by SE =P from their previous unstrained positions. The corrections to the Kane inteiband matrix element/ on both in-plane and perpendicular directions are trivial. 

The results are presented of an investigation of the optical infrared transmission and reflection spectra of the alloy 0.7 InSb-0.3 InAs, doped with tellurium to obtain different electron densities (n). The optical width of the forbidden band (AE) and the optical effective mass of the electrons (mn) were determined from the spectra and their dependence on n studied. It was established that the conduction bands of InSb-InAs solid solutions are nonparabolic. Attempts were made by extrapolation to obtain an estimate of the limiting values of AE and mg in the region of low values of n, and an estimate of the matrix element P was made. It is concluded that there is general agreement between the structure of the energy bands of the semiconductor alloys considered and the Kane model. 

Use of relationships based on Kane s theory enables the matrix element to be determined from the slope of this straight line [9]. The value of was found to be close to 20 eV. Unfortunately, the scatter of the experimental points did not enable P to be determined sufficiently accurately to test the recent data of Woolley and van Tongerloo [6], which indicate an e q)ected change in the matrix element with the composition in InSb-InAs alloys along a curve having a slight minimum. 

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