1. Lifetime and Doping
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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 through the process of recombination. Furthermore, we have a recombination rate that 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 minority carrier lifetime of a material, denoted by τn or τp, is the average time 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. Recombination rate is an important solar cell parameter; 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.
The low level injected material (where the number of minority carriers is less than the doping) the lifetime is related to the recombination rate by:
where τ is the minority carrier lifetime, Δn is the excess minority carrier concentration and R is the recombination rate.
We will discuss in the next few pages various types of recombination processes which all have associated lifetimes. Therefore, to obtain a total lifetime for a minority charge carrier we must include all contributions from the various processes that are to be discussed in more detail:
So, we have that because all these lifetimes depend to some degree on dopant concentration, we see that the doping level of a material will determine it’s the total lifetime of the charge carrier and therefore the solar efficiency of the material in question. We have the following dependencies1:
- For doping less than 1017 cm-3 (normal for most Silicon devices) radiative combination plays a negligible role and carrier lifetime is predominantly determined by the impurity level.
- At doping levels greater than 1018 cm-3, Auger recombination becomes dominant.
1. Goetzberger, Adolf et.al. Crystalline Silicon Solar Cells. Chichester: John Wiley & Sons Ltd., 1998.