Voltage dependence of the differential capacitance of a $p^+$–$n$ junction

The dependences of the differential capacitance and current of a $p^+$–$n$ junction with a uniformly doped $n$ region on the voltage in the junction region are calculated. The $p^+$–$n$ junction capacitance controls the charge change in the junction region taking into account a change in the electric field of the quasi-neutral $n$ region and a change in its bipolar drift mobility with increasing excess charge-carrier concentration. It is shown that the change in the sign of the $p^+$–$n$ junction capacitance with increasing injection level is caused by a decrease in the bipolar drift mobility as the electron-hole pair concentration in the $n$ region increases. It is shown that the $p^+$–$n$ junction capacitance decreases with increasing reverse voltage and tends to a constant positive value.