Fundamentals of the Absorption and Emission Processes

To understand the recombination processes clearly, one should start from the absorption, particularly the absorption coefficient If I(x) represents the optical intensity at point x in a semiconductor, the spatial rate of change of the intensity at the same point is proportional to the intensity and is given by 

If N2 and Nj represent the populations (or photon occupation numbers) of levels 2 and 1, respectively, under thermodynamic equilibrium, we can write the rate of change in the population of level 2 through spontaneous emission (decay for population which is why the - sign) as ]34] 

Note that spontaneous emission is not coupled to the optical field and therefore does not depend on the photon density in the system having the same energy. The above rate equation simply indicates that the photon population in level 2 would decrease with a rate of J 2i = l ii + B2iP(v)]N2 by which we can argue that the spontaneous emission lifetime is r p = (A2i). Typically, this lifetime is on the order of 10 s. Similarly, the rate equation for the stimulated emission that involves transitions from level 2 to level 1 can be written as 

Note that this process is coupled to the photons having the same energy in the system, which is the genesis for the Pe(v) term. The product Pe(v)N2dv represents the photon energy density in the frequency range of v and v + dv. A decrease in the N2 population due to transition from level 2 to level 1 would be accompanied by an equal increase in Ni, which means that Equation 3.8 can also be written as 

Stimulated absorption also takes place and has a proportionality constant of J 2i = [A21 + B2iP(v)]N2 (as absorption involves excitation of an electron from level 1 to level 2)  

---