Question

For an abrupt PN junction diode, small signal capacitance is 1nF/cm^2 at zero bias condition.If the built in voltage, Vbi is 1V, the capacitance at reverse bias of 99V is?

(a) 0.1nF/cm^2

(b) 1nF/cm^2

(c) 1.5nF/cm^2

(d) 2nF/cm^2

This question was addressed to me in examination.

I need to ask this question from Diode Capacitances in section Semiconductor-Diode Characteristics of Electronic Devices & Circuits

Answer 1

The correct answer is (a) 0.1nF/cm^2

Easiest explanation: Cjo is the capacitance at zero bias, that is VR=0V, Cjo=Cj for VR=0V. We know, Cj = Cjo/(1+(VR/Vbi))m , m=1/2 for abrupt. So, putting  Cj=0.1nF/cm^2 where, VR=99V and  Vbi=1V we get, Cjo= 0.1(1+99)^1/2 = 0.1nF/cm^2.