By Jacques I. Pankove
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Extra resources for Optical processes in semiconductors
2-B Temperature Effects As the temperature of a semiconductor increases, the lattice expands and the oscillations of the atoms about their equilibrium lattice points increase. We have already seen how dilation leads to a change (increase or decrease) in the energy gap. Besides this shift of the band edges, the increased motion of the atoms broadens the energy levels. Just as in the case of pressure-induced deformation, temperature will affect the potential assigned to an impurity level via the band edge with which it is associated, keeping the ionization energy constant.
1-2 Parabolic dependence of energy vs. momentum. Let us first consider how the energy varies with momentum along one direction of momentum space. Figure 1-2 illustrates the parabolic dependence of E on k. Hence such a distribution of states is called a parabolic valley—the pictorial impact is even more pronounced in a three-dimensional representation of E vs. kx and ky. In a three-dimensional momentum space, a constant-energy surface forms a closed shell and, with every increment in momentum, the energy of successive shells increases quadratically.
The changes in energy. are given by the elastic coefficients of a strain tensor. Thus compression of a silicon crystal along the  axis decreases the energy gap in the direction of the compression; but because of a simultaneous dilation in the transverse directions, the conduction-band valleys lying in the transverse plane move to a higher energy (Fig. 2-2). The redistribution of the states causes a rearrangement of the electrons which spill into the lower-energy states made available by the strain.