The Absorption Edge for Direct Transitions

In Appendix A1 we have determined that for the general case of parabolic bands, p ci ) is given by 

Several III-V semiconductors, such as ALP, GaAs, luSb, AlAs, and InAs, show direct absorption edge transitions. The next example shows the analysis of the fundamental absorption edge for indium arsenide. 

Equation (1.4). Assuming that the beam size is conserved, the attenuation of the laser power is given by 

For some direct-gap materials, the quantum electronic selection rules lead to = 0. However, this is only strictly true at / = 0. For 0, it can be assumed, in a first order approximation, that the matrix element involving the top valence and the bottom conduction states is proportional to k that is, Pif k. Within the simplified model of parabolic bands (see Appendix Al), it is obtained that Tuo = Tuog + flp., and therefore Pif k co — cog). Thns, according to Equations (4.31) and (4.32), the absorption coefficient for these transitions (called forbidden direct transitions) has the following spectral dependence  

Some complex oxides, such as Si02 or CuOa, show forbidden direct transitions. 

---