An analytical model of dark saturation current of silicon solar cell considering both SRH and Auger recombination

The analytical modeling of dark saturation current of a solar cell conventionally incorporates either SRH (Schokley-Reed-Hall) recombination or Auger recombination, since simultaneous consideration of both these mechanisms results in mathematical complexity. On the other hand, non-uniform doping profile is used in the practical solar cells for which a retarding electric field is introduced and as a result, the dark saturation current is reduced. Moreover, the doping level increases day by day to meet the requirements for the improvement of solar cell performances. However, the heavy doping level as well as the non-uniformity of the doping profile lead to the position and field dependency of the carrier mobility and also, to the doping dependency of the carrier lifetime. Moreover, the bandgap narrowing effects also become significant at such heavy doping levels. This later effect causes the retarding electric field for the dark saturation current to reduce and hence, increases the dark saturation current. Therefore, all these effects should be incorporated in the analytical modeling of the dark saturation current of modern solar cells. However, consideration of all these effects especially simultaneous consideration of both SRH and Auger recombination mechanisms leads the governing equation to a second order, nonlinear, variable-coefficient differential equation and hence, causes the differential equation to be analytically intractable. In this paper, the analytical intractability problem has been resolved by using an exponential approximation technique, which can approximate any exponential-like profile (Gaussian, complementary error function etc.) or any doping dependent transport parameter (mobility, lifetime etc.) into a simple exponential function. Therefore, this technique can be used for any doping level and for arbitrary doping profile. The developed model shows that the changes in the dark saturation current due to the simultaneous consideration of SRH and Auger recombination becomes significant compared to the consideration of any one recombination mechanism. The model results also show that the change in the dark saturation current considering both recombination mechanisms increases with the doping level.