Excess Carrier Generation and Recombination

Excess Carrier Generation and Recombination :

The net rate of change in electron concentration is given by:

$$\frac{dn(t)}{dt}=$$ Thermal generaton rate-Recombination Rate

$$\frac{dn(t)}{dt}=\alpha _r[n_i^2-n(t)p(t)]$$

How is Thermal generation rate given by $$\alpha _rn_i^2$$ and Recombination Rate given by $$\alpha _r n(t)p(t)$$ ?

• Just because your first 'equation' is written as (Thermal-Recombination) does not mean that you can take the terms in the second equation and separate them as you do. The thermal generation rate is whatever it is such that for the given recombination rate you end up with the intrinsic carrier concentration. For any $np$ not equal to $n_{i}^{2}$ you have a change in the recombination rate since you are not in thermal equilibrium. – Jon Custer Feb 25 at 16:38