Physics and Engineering of Radiation Detection

290 Chapter 5. Solid State Detectors

whereμis the mobility of majority charge carrier andNis the dopant concentration.
For the caseND>> NA, the majority charge carriers are electrons and therefore
the depletion depth in terms of resistivity becomes

d[2ρnμeV 0 ]^1 /^2. (5.1.71)

Similar expression can be derived for the case when acceptor impurity level is much
higher than the donor level. Of course in such a situation the majority charge
carriers will be holes.
In the absence of radiation, except for a minute leakage current, the depletion
region of a pn junction essentially acts as an insulator sandwiched between positive
and negative electrodes. The capacitance of this configuration can be easily esti-
mated for the usual case of planar geometry if we assume the idealized charge density
profile of Fig.5.1.25. This is the configuration of a simple parallel plate capacitor
with a capacitance of

C=

A

d

, (5.1.72)

whereAis the surface area of the junction anddis the depletion width. A convenient
parameter generally used for comparison is the capacitance per unit areaCA=C/A,
which we can compute if we substitute the values ofdfrom Equations 5.1.68 and
5.1.69 into the above expression. Hence we get

CA=

⎧

⎪⎨

⎪⎩

(

eND

2 V 0

) 1 / 2

forNA>> ND

(

eNA

2 V 0

) 1 / 2

forNA<< ND

(5.1.73)

It should be noted that although the capacitance of a usual pn junction is very
small, of the order of a few pico Farads (see example below), still together with the
load resistor of the signal readout circuit, it can limit the frequency response of the
detector. Therefore in practical detectors it is ensured that the capacitance is kept
at a minimum. This can be done by simply increasing the reverse bias, as apparent
from the above expressions forCA.

Example:

Compute the capacitances per unit area of a silicon pn diode having donor

and acceptor impurities of 10^17 cm−^3 and 10^15 cm−^3 respectively when a bias

of 150V exists across its junction. Also compute the absolute capacitance if

the surface area of the diode is 0.01cm^2.

Solution:

Since we haveND >> NA, therefore according to equation 5.1.73 we can

estimate the capacitance per unit area using only the acceptor impurity con-

centration. Since the material is silicon therefore we will assume that the