If the number of minority carriers is increased above that at equilibrium by some transient external excitation, the excess minority carrier will decay back to the equilibrium carrier contraction due to recombination processes. 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. The "minority carrier lifetime" of a material, denoted by tn or tp, is the average time which a carrier can spend in an excited state after electron-hole generation before it recombines. A related parameter, the "minority carrier diffusion length" is the average distance a carrier can move from point of generation until it recombines.
The minority carrier lifetime and the diffusion length depend strongly on the type and magnitude of recombination processes in the semiconductor. For many types of silicon solar cell, SRH recombination is the dominant recombination mechanism. The recombination rate will depend on the number of defects present in the material, so that as doping the semiconductor increases the defects in the solar cell, doping will also increase the rate of SRH recombination. In addition, since Auger recombination is more likely in heavily doped and excited material, the recombination process is itself enhanced as the doping increases. The method used to fabricate the semiconductor wafer and the processing also have a major impact on the diffusion length.
Color chart of a high efficiency multicrystalline PERL solar cell. The percentage refers to the fraction of light-generated carrier and the variations between one region and another are due to variations in the diffusion length in the solar cell caused by the grain boundaries in the multicrystalline material.
In silicon, the lifetime can be as high as 1 msec. For a single crystalline silicon solar cell, the diffusion length is typically 100-300 mm. These two parameters give an indication of material quality and suitability for solar cell use.
The diffusion length is related to the carrier lifetime by the diffusivity according to the following formula:
,
where L is the diffusion length in metres, D is the diffusivity in m²/s and t is the lifetime in seconds. All of the minority carriers. The following calculator provides a way of converting between lifetime and diffusion length using more familiar units. The diffusivity can be found in the appendices.