Valence band heavy hole

The revealed optical absorption coefficient in the range of 0.48-0.83 eV followed a squared relationship that is typical for indirect interband transitions. Generation of the photocurrent at the energy 0.48-0.56 eV was explained by indirect electron transitions from the valence band heavy hole levels of Ge... 

Ep = 2 edcv /wto is approximately 21 meV for most of the III-V and II-VI semiconductors, no is the linear refractive index, and Kpi, is a material independent constant (1940 cm (eV) for a two-parabolic-band model). It should be mentioned that the above model does not correctly account for the degeneracy of the valence band (heavy hole, light hole, and spin-orbit/crystal-field split-off bands) and assumes single parabolic conduction and valence bands. Using the Kane band structure with three valence bands and including excitonic effects have been shown to produce larger TPA coefficients [227]. 

Fig. 5. Energy levels of electrons and heavy holes confined to a 6-nm wide quantum well, Iuq 53GaQ 4yAs, with InP valence band, AE and conduction band, AE barriers. In this material system approximately 60% of the band gap discontinuity Hes in the valence band. Teasing occurs between the confined...

Calculations [104] show that for L7 > A (the heavier transition metal ions) the gap is of the charge-transfer type, whereas for 1/ < A (the lighter transition metal ions) the gap is of the d-d type. In our nomenclature this may be translated as MMCT LMCT. In the charge-transfer semiconductors the holes are light (anion valence band) and the electrons are heavy (d bands). Examples are CuClj, CuBrj, CuO, NiClj, NiBrj and Nil2. 

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.

In equation 3, ran is the effective mass of the electron, h is the Planck constant divided by 2/rr, and Eg is the band gap. Unlike the free electron mass, the effective mass takes into account the interaction of electrons with the periodic potential of the crystal lattice thus, the effective mass reflects the curvature of the conduction band (5). This curvature of the conduction band with momentum is apparent in Figure 7. Values of effective masses for selected semiconductors are listed in Table I. The different values for the longitudinal and transverse effective masses for the electrons reflect the variation in the curvature of the conduction band minimum with crystal direction. Similarly, the light- and heavy-hole mobilities are due to the different curvatures of the valence band maximum (5, 7). 

The valeuce bands, which arise from p atomic orbitals, have sixfold degeneracy and contain at 0 K the six p-orbital Se valence electrons. Due to spiu-orbit coupliug, this degeneracy is split at k = 0 into a fourfold degenerate J = 312 band and a twofold degenerate J = 1/2 split-off valence band where Jis the total unit cell angular momeutum. For ki= = 3/2 band splits into two doubly degenerate components the heavy hole... 

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... 

Figure 1. Conduction and valence band profiles of the dilute-N W" InAsN/GaSb/InAsN and "M" GaSb/InAsN/GaSb laser structures on InAs substrate. On the upper part, fundamental electron (ei) and heavy hole (hhi) presence probability densities are reported. Tbe ei-hhi optical transitions are expected at 3.3 pm at RT.

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. 

According to Fig. 1.5, the conduction as well as the valence band consists of several bands. Some valence bands are degenerated around k = 0 (the F point). Since the curvature differs from one band to another, each band is associated with a different effective mass (see also Appendix D). Rather flat energy profiles correspond to heavy holes... 

Fig. 3.8. Direct magnetoabsorption in germanium at RT. The polarization condition is usually referred as n polarization. The calculated peaks 1 and 2 correspond to transitions from spin-split levels of the Landau ladder of the heavy hole valence band and the 1+ and 2+ ones to corresponding transitions for light hole VIS. With the ordinate scale used, the indirect absorption is barely visible (after [13])...

We calculated the size dependence of the zero-temperature Huang-Rhys factors (4) using parameters of GaAs [7]. Fig. 1(a) shows the optic Huang-Rhys factors of 2D-excitons (flat dot) as a function of the QD lateral size. The Froehlich interaction is seen to dominate over the optic deformation potential interaction (caused by the heavy hole interaction in a p-like valence band). The total optic Huang-Rhys factor gradually increases with the decreasing QD lateral size. 

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 ... 

Peterson and Casselman [8.71] have been extending Petersen s earlier calculations of Auger recombination in n-type Hg, jjCd,Te to p-type material. The purpose is to determine how important Auger recombination in fact is in p-type Hg, jjCd Te. Their calculations assume Au r transitions involving the light-hole valence band as well as the heavy-hole valence band. The result will help determine the maximum Z)J really possible in Hg, Cd Te photovoltaic detectors. 

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. 

Silicon (Si). The electronic transport is due exclusively to electrons in the [100] conduction band minima and holes in the two uppermost (heavy and light) valence bands. In samples with impurity concentrations below 10 cm , the mobilities are determined by pure lattice scattering down to temperatures of about 10 K (n-type) or 50 K (p-type), for electrons and holes, respectively. Higher impurity concentrations lead to deviations from the lattice mobility at corresponding higher temperatures. For electrons, the lattice mobility below 50 K is dominated by deformation-potential coupling... 

An additional complication is seen in the valence band structures in Fig. 2.13. Here, two different E k valence bands have the same minima. Since their curvatures are different, the two bands correspond to different masses, one corresponding to heavy holes with mass mn and the other to light holes with mass m/. The effective scalar mass in this case is m = (m]j + Such light and heavy holes occur in several... 

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