The junction capacitance of a p-n junction depends on

A diode can have two different capacitances namely Junction capacitance and diffusion capacitance.

Junction Capacitance:

It is dominant when the diode is reverse biased and is the result of the charge stored in the Depletion layer.

The junction capacitance is given by the formula:

\({C_j} = \frac{{A\epsilon}}{W}\)   ---(1)

W = Width of the depletion region calculated as:

\(W= \sqrt {\frac{{2\epsilon_s(V_{bi}-V_a)(N_a+N_d)}}{N_aN_d}} \)   ---(2)

V_a = Applied Voltage

N_a and N_d are the acceptor and donor doping concentrations respectively.

Substituting the above in Equation (1), we get:

\(C=\frac{A\epsilon}{ \sqrt {\frac{{2\epsilon_s(V_{bi}-V_a)(N_a+N_d)}}{N_aN_d}} }\)

\(C=\sqrt {\frac{{{A^2\epsilon_s}{N_A}{N_D}}}{{2\left( {{V_{bi}} - {V_a}} \right)\left( {{N_A} + {N_D}} \right)}}} \)

∴ The junction capacitance of a p-n junction depends on both the doping concentration and the applied voltage.

Diffusion Capacitance:

It is dominant when the diode is forward and is the result of storage charges when forward biased.

The diffusion capacitance is given by the formula:

\({C_d} = \frac{{{I_{DQ}}\times\tau }}{{η {V_T}}}\)

IDQ = Quiescent current of the diode.

τ = Minority carrier lifetime

VT = Thermal voltage

η = Constant = 2 for silicon and 1 for germanium