SbroR io

where (T) and (V) are kinetic and potential energies.

For transitions from the first valence level to a donor impurity level, we have, for the initial and final states, sin (k^r)

where u(r), Uf (r) are the periodic parts of the Bloch states for the initial and final states.

Taking the energy origin at the first conduction subband as depicted in Figure 50, we have for the energy of the initial (first valence level) state where Eg is given by

2 mi with sg being the bulk GaAs bandgap. The energy of the final state is

The transition probability per unit time for valence-to-donor transitions associated with a donor impurity located at R is proportional to the square of the matrix element of the electron-photon interaction Hd between the wavefunctions of the initial state (first valence level) and final (impurity) states. That is,

with Hel = Cer p, where er is the polarization vector in the direction of the electric field of the radiation, p is the momentum operator, and C is a prefactor which contains hm i z hm 2

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