Recombination
A useful way to think about recombination rate in semiconductors follows from the equation,
$$ R = An + Bnp + Cpn^2 - G + I/q $$
where $n$ and $p$ are the electron and hole density.
The first term deals with the non-radiative recombination. In your question you mentioned Shockley-Reed-Hall (SRH), think of this term as a very simple non-radiative recombination model where $A=\tau_{nr}^{-1}$ is the inverse of the non-radiative lifetime.
The second term deals with the radiative (bimolecular) recombination rate.
The third term deals with Auger recombination.
The fourth term deals with the generation of electron (and holes) due to the absorption of light.
The fifth term deals with an electrical current being extracted from the material (the current could be negative for injection).
The $A$, $B$, and $C$ are coefficients which control contribution of each term to the total recombination rate $R$. They are material constants.
What you will notice is that different recombination mechanisms dominate at different carrier density regimes:
- at low carrier density, the non-radiative term dominates,
- at moderate carrier density, radiative recombination dominates,
- and at extreme carrier density, Auger recombination dominates.
The way that recombination is controlled is by bringing together different semiconductor materials to:
- control the electron and hole concentrations
- exploit the different material properties (i.e. the $A$, $B$, and $C$ coefficients).
Heterostructure design
When different semiconductors are brought together in a single device it is called a semiconductor heterostructure. Heterostructures are predominately designed to control the electron and hole concentration at different regions of a device to achieve a given outcome.
A solar cell heterostructure is designed to achieve a good balance between optical generation ($G$) such that the extracted current $I$ is maximised. This is done by making the absorbing layer as thick as possible, but thin enough that carriers can cross the junction in a time quicker than $\tau_{nr}$. Similarly, the carrier density should be low enough that the extraction rate (given by $I/q$) is faster than the radiative recombination rate.
In an LED you want to inject current into the device (i.e. the $I$ term) and make the carrier density of electrons and holes to be very high in a small volume of the device to increase the radiative recombination rate. However, the carrier density should not be too high that carriers are lost via non-radiative Auger recombination.
So, in summary, you can control recombination by clever design of semiconductor hereostructures to control the electron and hole concentrations and take advantage of the natural material properties of the semiconductor (i.e the $A$, $B$, and $C$ coefficients). Usually this is a trade off between two other recombination processes, as with the two examples discussed above.
