Capacitance of p-n Junctions: depletion capacitance
There are basically two types of capacitance associated with a junction:
(1) the junction capacitance due to the dipole in the transition region and
(2) the charge storage capacitance arising from the lagging behind of voltage as current changes, due to charge storage effects.
Depletion capacitance:
The junction capacitance is dominant under reverse-bias conditions, and the charge storage capacitance is dominant when the junction is forward biased. In many applications of p-n junctions, the capacitance is a limiting factor in the usefulness of the device. Instead of the common expression C = Q/V, which applies to capacitors in which charge is a linear function of voltage, we must use the more general definition
since the charge Q on each side of the transition region varies nonlinearly with the applied voltage (Fig.a).The equilibrium value of W was found to be
Since we are dealing with the nonequilibrium case with voltage V applied, we must use the altered value of the electrostatic potential barrier (V0 - V). The proper expression for the width of the transition region is then
The value of Q can be written in terms of the doping concentration and transition region width on each side of the junction
Relating the total width of the transition region W to the individual widths xn0 and xp0
and therefore the charge on each side of the dipole is
Then the junction capacitance Cj