### Overview

1. The lifetime of a semiconductor is contingent upon the recombination rate, which is dependent upon the concentration of minority carriers.
2. The lifetime of the material takes into account the different types of recombination.
3. Lifetime is an indicator of the efficiency of a solar cell, and thus is a key consideration in choosing materials for solar cells.

If the number of minority carriers is increased above that at equilibrium by some transient external excitation (such as incident sun), the excess minority carriers will decay back to that equilibrium carrier concentration due to and through the process of recombination. A critical parameter in a solar cell is the rate at which recombination occurs. Such a process, known as the "recombination rate" depends on the number of excess minority carriers. If for example, there are no excess minority carriers, then the recombination rate must be zero. Two parameters that are integral to recombination rate are the minority carrier lifetime and the minority carrier diffusion length. The first will be discussed here.

The minority carrier lifetime of a material, denoted by τn or τp, is the average time which a carrier can spend in an excited state after electron-hole generation before it recombines.  It is often just referred to as the "lifetime" and has nothing to do with the stability of the material. Stating that "a silicon wafer has a long lifetime" usually means minority carriers generated in the bulk of the wafer by light or other means will persist for a long time before recombining. Depending on the structure, solar cells made from wafers with long minority carrier lifetimes will usually be more efficient than cells made from wafers with short minority carrier lifetimes. The terms "long lifetime" and "high lifetime" are used interchangeably.

In low level injected material (where the number of minority carriers is less than the doping), the lifetime is related to the recombination rate by:

$$\tau=\frac{\Delta n}{R}$$

where τ is the minority carrier lifetime, Δn is the excess minority carriers concentration and R is the recombination rate.

$$\frac{1}{\tau_{\text {bulk}}}=\frac{1}{\tau_{\text {Band}}}+\frac{1}{\tau_{\text {Auger}}}+\frac{1}{\tau_{S R H}}$$

Auger lifetime is a function of the carrier concentration and is given by:

$$\tau_{\text {Auger}}=\frac{1}{C N_{A}^{2}}$$

Where the auger coefficient, C, for silicon is typically given as: 1.66 × 10-30cm6/s 1, 2