The open-circuit voltage is the voltage at which the forward bias diffusion current is exactly equal to the short circuit current. The forward bias diffusion current is dependent on the amount recombination in a p-n junction and increasing the recombination increases the forward bias current. Consequently, high recombination increases the forward bias diffusion current, which in turn reduces the open-circuit voltage. The material parameter which gives the recombination in forward bias is the diode saturation current. The recombination is controlled by the number of minority carriers at the junction edge, how fast they move away from the junction and how quickly they recombine. Consequently, the dark forward bias current, an hence the open-circuit voltage is affected by the following parameters:
- the number of minority carriers at the junction edge. The number of minority carriers injected from the other side is simply the number of minority carriers in equilibrium multiplied by an exponential factor which depends on the voltage and the temperature. Therefore, minimising the equilibrium minority carrier concentration reduces recombination. Minimizing the equilibrium carrier concentration is achieved by increasing the doping;
- the diffusion length in the material. A low diffusion length means that minority carriers disappear from the junction edge quickly due to recombination, thus allowing more carriers to cross and increasing the forward bias current. Consequently, to minimise recombination and achieve a high voltage, a high diffusion length is required. The diffusion length depends on the types of material, the processing history of the wafer and the doping in the wafer. High doping reduces the diffusion length, thus introducing a trade-off between maintaining a high diffusion length (which affects both the current and voltage) and achieving a high voltage;
- the presence of localised recombination sources within a diffusion length of the junction. A high recombination source close to the junction (usually a surface or a grain boundary) will allow carriers to move to this recombination source very quickly and recombine, thus dramatically increasing the recombination current. The impact of surface recombination is reduced by passivating the surfaces.
The net effect of previous trade-offs is shown in the graphs below.