As discussed elsewhere, there are various recombination mechanisms within even a uniformly doped piece of semiconductor. In the bulk of the material the carriers recombine by either radiative (also known as band-to-band) recombination, Auger recombination or defect recombination (via traps within the energy gap).

The lifetime of carriers in the material bulk τ_{b} is composed of radiative lifetime τ_{rad}, Auger lifetime τ_{A} and a SRH lifetime τ_{SRH} with the relation:

$$ \frac{1}{\tau_{b}}=\frac{1}{\tau_{rad}}+\frac{1}{\tau_{A}}+\frac{1}{\tau_{defect}} $$

For an indirect bandgap semiconductor such as silicon τ_{rad} is very large and usually neglected.

The Auger lifetime time can be calculated using theoretical models 1, however, the defect lifetime depends on the level of defects in the crystal lattice and so is difficult to calculate theoretically. The bulk lifetime for extrinsic silicon can be determined using semi-empirical models based on lifetime measurements of float-zone silicon with very low defect levels. The lifetime is dependent on the excess carriers and doped-atom concentrations. The models presented here are based on 2 but a more recent model was developed3. Most silicon wafers have higher levels of contaminants and so lower lifetimes than calculated here. Further details on silicon properties are in the appendices.

### Bulk Lifetime for p-type Silicon

### Bulk Lifetime for n-type Silicon

- 1. , “Coulomb-enhanced Auger recombination in crystalline silicon at intermediate and high injection densities”, Journal of Applied Physics, vol 88, pp 1494-1497, 2000.
- 2. , “Generalized analysis of quasi-steady-state and transient decay open circuit voltage measurements”, Journal of Applied Physics, vol 91, p 399, 2002.
- 3. , “Improved quantitative description of Auger recombination in crystalline silicon”, Physical Review B, vol 86, 호 16, 2012.