Transport Equations for Semiconductor Solar Cells

In the most general situation, the current density in semiconductors and in solar cells is composed of electron and hole contributions jq = jh+ Je The relevant carrier concentrations ne(x) and rih(x) are subject to generation and recombination and have to obey continuity equations 

Furthermore, electron and hole densities ne(x) and r ,h(x) are coupled by Poisson s equation with the electrostatic potential t x)  

Because of this coupling of the carrier concentrations with the electrostatic potential, it is customary to decompose the current into two components, one of which is due to the gradient of the electrostatic potential. 

We expand the current density equations for electrons and holes and, for example, for electrons, we replace 

We then reintroduce —grad[ c(a )] = eE(x) as the electric field strength, convert the reciprocal electron concentration 

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