Heavy holes band

Fig. 24. The computed valence band dispersion E(k) computed from the 6 x 6 Luttinger model for the wave vector parallel and perpendicular to the Mn spin magnetization in (Ga,Mn)As. assuming that the spin splitting of the heavy-hole band at the f point is 0.15 eV.

Eq. (6-24). We see that they are in reasonably good agreement, though the values given by Lawaetz are preferred. Using them, it is appropriate in many circumstances to treat these two heavy-hole bands as isotropic and identical. 

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... 

We begin by expanding the LCAO bands for small /c we can, for example, expand the expressions in Eqs. (6-11) and (6-12). Expansion of Eq. (6-11), with b taken from (6-16), gives the heavy-hole bands,... 

Spin-orbit coupling splits off one of the otherwise degenerate heavy-hole bands, as shown by the lowest solid line. Equations are given for each, with parameters given in Tables 6-3 and 6-4 (and with m taken equal to m ). The heavy-hole band that is split, away then becomes mixed with the... 

The valence band has its maximum at the P point (symmetry Pg), the light- and heavy-hole bands being degenerate at this point. Both bands are warped. The third, spin-orbit spUt-off band has P symmetry. In contrast to silicon the spin-orbit splitting energies are considerable. Thus, the symmetry notation of the double group of the diamond lattice is mostly used for Ge. 

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. 

The threshold energy for the Auger 1 and Auger 7 processes is the lowest, and their total density of states, and thus their probability of occurrence, the largest. In the CCCH Coulomb interaction appears between two electrons in conduction band (states 1 and 2). Due to this, an electron crosses into the heavy holes band and... 

M.G. Burt, S. Brand, C. Smith, R.A. Abram, Overlap integrals for Auger recombination in direct-bandgap semiconductors calculations for conduction and heavy-hole bands in GaAs and htP. J. Phy. C SoUd Stale Phys. 17(35), 6385-6401 (1984)... 

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