Light holes band

We do this by using the k p method, (called k-dol-p), which is based upon the perturbation theory of Eq. (1-14). In this method, energy is calculated near a band maximum or minimum by considering the wave number (measured from the extremum) as a perturbation. (The method is described in many solid state texts, such as Kittel, 1963, p. 186, or Harrison, 1970, p. 140.) The method was used for a study of effective masses by Cardona (1963, 1965). It was also usetl in the more extensive study by Lawaetz (1971) referred to in the discussion of heavy-hole bands. We shall discuss here only the conduction band and the light-hole band where the effects of interaction are great. 

Here the matrix element is that of the momentum operator p, in the x-direction, since we have chosen k to lie in the x-direction. The matrix element is taken between the state Fi of the conduction-band minimum and any other state T at r the denominator is the energy difference between the two states. We drop all terms in this sum except those with the valence-band maximum, for which the energy denominator is the smallest and the contribution the largest. It can be shown by symmetry that the matrix clement vanishes for the two heavy-hole bands (they correspond to p orbitals with an orientation perpendicular to the x-axis), so only the matrix element between wave functions for the conduction band and the light-hole band remains. The denominator is the band gap Eq, so wc may extract a conduction-band mass from Eq. (6-26). This mass is given by... 

The hole states are more complicated as there are both heavy hole and light hole bands to consider. Nevertheless, conceptually it is very similar to the classic particle-in-the-box problem. The allowed optical transitions occur between energy levels in which An = 0, i.e. transitions between electron and hole states with the same quantum number. Since the energy levels of the electron and hole states scale the same with length, the shift in the exciton transitions show a very good correlation with the 1/L dependence expected from the simple particle-in-the-box picture. 

The states u> and c> are obtained from solution of the Hamiltonian matrix, Eq. (6-10), for k = 0, in which case all off-diagonal matrix elements take the same value. It can be easily verified that the two eigenvectors (other than the doubly degenerate ones corresponding to heavy holes) are (1, 1, 1, l)/2 and (1, 1, — 1, — l)/2. The Bond Orbital Approximation turns out to be exact for these states at r. The second of these eigenvectors corresponds to the light-hole band (the first corresponds to the bottom of the valence band). Thus the valence-band state at T that enters the calculation can be written as a sum of bond orbitals, as in Eq. (3-20), with k = 0 ... 

In p-t)fpe GaSb, a multiellipsoidal model has to be used at low temperatures, taking into account the shift of the heavy- and light-hole bands away from k = 0. At high temperatures, a warped-sphere model (as in the case of Si and Ge) is adequate. 

The most exciting property, that is coupled with the coexistence of a heavy-hole and a light-hole band, is the occurrence of superconductivity in GeTe [192] with hole concentration p>8x 10 °cm , reaching a critical temperature Tc of 0.3 K at p = 1.5 X 10 cm . It is however not the lattice distortion that is responsible for superconductivity, as superconductivity was found also in the rocksalt-type SnTe. 

Auger processes encompass Auger recombination and its opposite impact ionization. Beattie defined ten basic Auger processes in material with a single conduction band and with a heavy holes and light holes band. In the processes of nonradiative interband recombination phonon states, localized states and impurity levels may take part. Landsberg described 70 such secondary Auger processes [30]. 

In narrow-bandgap direct semiconductor of the Hgi cCd cTe and InSb type the dominant processes are Auger 1 (CCCH) and Auger 7 (CHHL) (Fig. 1.4). Here, the letters in the notation denote the bands containing the carrier taking part in the Auger process. The first two letters denote the initial state, and the second two the final one. C means the conduction band, H is the heavy holes band, and L is the light holes band. S means the spin split-off band. 

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