Total G-R Rate of Narrow-Bandgap Semiconductors

Net recombination rate can be calculated as the sum of separate net recombination rates caused by independent mechanisms (denoted here by an index k), where each net recombination rate is equal to the difference between the generation and the recombination rate for the given mechanism 

If excess concentrations are small enough compared to the equilibrium values, (1.83) transforms into a sum of separate and independent generation-recombination rates defined by minority carrier lifetimes for each separate fc-th mechanism [8] 

In the same approximation, the reciprocal value of the resulting lifetime is given as a sum of reciprocal values of each separate mechanism (a ratio between the generation-recombination rate and the excess concentration of carriers). 

The total generation-recombination rate for narrow-bandgap direct semiconductors in the dark (i.e., without optical generation) is obtained as the sum of the rates for CCCH and CHHL Auger processes, radiative generation-recombination and single-level SR generation-recombination in the form 

If external IR flux is present, we add the optical generation term (1.79) or (1.81) into (1.85). If we take into account background generation as well, we add (1.82). 

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