**4.5 The p-n junction capacitance**

Table of Contents -
1
2
3
4
5
6
7
8
9
R
S
¬
®

In this Section:
- Introduction
- The junction capacitance
- The diffusion capacitance
- Capacitance measurement
and parameter extraction

## 4.5.1 Introduction

Any variation of the charge within a p-n diode with an applied
voltage variation yields a capacitance wich must be added to the
circuit model of a p-n diode. The capacitance
associated with the charge variation in the depletion layer is
called the junction capacitance, while
the capacitance associated
with the excess carriers in the quasi-neutral region is called the
diffusion capacitance.

Both types of capacitances are non-linear so that we will derive
the small-signal capacitance in each case. We will find that the junction
capacitance dominates for reverse-biased diodes, while the
diffusion capacitance dominates in strongly forward-biased diodes.
The total capacitance is the sum of both.

Expressions for the capacitances are obtained by calculating
the change in charge for a change in applied voltage, or:

(pn19)

## 4.5.2 The junction capacitance

The junction capacitance is calculated using the expression for the
parallel plate capacitance. This might at first seem unexpected since
the charge is distributed throughout the depletion layer. However,
when applying small voltage variations one finds that charge is only
added and removed at the **edge** of the depletion region so that
the capacitance simply depends on the dielectric constant, the area
and the depletion layer width, yielding:

(pn14)

where the depletion layer width, *w*, was obtained from the
electrostatic analysis.

## 4.5.3 The diffusion capacitance

## 4.5.4 Capacitance measurement and parameter
extraction

A capacitance versus voltage measurement can be used to
obtain the built-in voltage and the doping density of a one-sided
p-n diode. Plotting one over the capacitance squared one expects a
linear dependence as expressed by:

(pn15)

A calculated capacitance-voltage and corresponding
1/*C*^{2} curve is shown in the figure below:

pncap.xls - pncap.gif

**Fig. 4.5.1** *Capacitance and 1/C*^{2}
versus voltage of a p-n diode with N_{a} =
10^{16} cm^{-3}, N_{d} =
10^{17} cm^{-3}
and an area of 10^{-4} cm^{2}

The built-in voltage is obtained at the intersection of the
1/*C*^{2} curve
and the horizontal axis, while the doping density is obtained from the slope
of the curve.
A capacitance-voltage measurements also provides the doping
density profile of
one-sided p-n diodes. For a p^{+}-n diode one obtains the
doping density from:
(pn16)

while the depth equals the depletion layer width which is otained
from *w* = e_{s}*A*/*C*_{j}.
Both the doping density and the corrresponding depth can be obtained at each
voltage yielding a doping profile.

4.4
¬
®
s 4.6

© Bart J. Van Zeghbroeck, 1996, 1997