B.1
B
Derivation of homojunction J-V curves
In this appendix we present the derivations for the J-V curves in the dark and under
illumination for p-n homojunctions, as introduced in Section 8.1.
The J-V characteristic in the dark
When an external voltage, V a , is applied to a p-n junction the potential difference between
the n-type and p-type regions will change and the electrostatic potential across the spacecharge region will become (ψ 0 − V a ). Under the forward-bias condition an applied external
voltage decreases the electrostatic-potential difference across the p-n junction. The
concentration of the minority carriers at the edge of the space-charge region increases
exponentially with the applied forward-bias voltage but it is still much lower than the
concentration of the majority carriers (low-level injection conditions). The concentration
of the majority carriers in the quasi-neutral regions do not change significantly under
forward bias. The concentration of charge carriers in a p-n junction under forward bias is
schematically presented in Fig. B.1
Figure B.1: Concentration profiles of mobile charge carriers in a p-n junction under forward bias (red lines).
Concentration profiles of carriers under thermal equilibrium are shown for comparison (black lines).
The concentrations of the minority carriers at the edges of the space-charge region,
electrons in the p-type semiconductor and holes in the n-type semiconductor, after
applying forward-bias voltage are described by
B
Derivation of homojunction J-V curves
In this appendix we present the derivations for the J-V curves in the dark and under
illumination for p-n homojunctions, as introduced in Section 8.1.
The J-V characteristic in the dark
When an external voltage, V a , is applied to a p-n junction the potential difference between
the n-type and p-type regions will change and the electrostatic potential across the spacecharge region will become (ψ 0 − V a ). Under the forward-bias condition an applied external
voltage decreases the electrostatic-potential difference across the p-n junction. The
concentration of the minority carriers at the edge of the space-charge region increases
exponentially with the applied forward-bias voltage but it is still much lower than the
concentration of the majority carriers (low-level injection conditions). The concentration
of the majority carriers in the quasi-neutral regions do not change significantly under
forward bias. The concentration of charge carriers in a p-n junction under forward bias is
schematically presented in Fig. B.1
Figure B.1: Concentration profiles of mobile charge carriers in a p-n junction under forward bias (red lines).
Concentration profiles of carriers under thermal equilibrium are shown for comparison (black lines).
The concentrations of the minority carriers at the edges of the space-charge region,
electrons in the p-type semiconductor and holes in the n-type semiconductor, after
applying forward-bias voltage are described by