Optical Absorption and Emission in Semiconductors

The above treatment can be extended to a semiconductor with the additional conditions that momentum conservation and Pauli s exclusion principle must hold [36]. As described in Equation 3.6, modifying the rate equations for semiconductors would for stimulated absorption lead to (rates are given in units s m ) 

Electron can also make the transition from level 2 to level 1 via spontaneous emission, which can be formulated as 

note the involvement of the optical field in the absorption and stimulated emission by the term p( 2i) but not in the spontaneous emission process. Under thermal equilibrium, as in the case of Equation 3.12 but modified for a semiconductor, the downward transition rate must be equal to the upward transition rate 

By solving p( 2i) from Equation 3.46 and equating it to that of Equation 3.34 (by substituting 21 for ) while ignoring the dispersion in the refractive index, we obtain 

As we have done for the derivation of Equation 3.39, we will set B21 = Bi2 which allows us to derive an expression for relating Einstein s A and B coefficients as 

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