Physics and Engineering of Radiation Detection

5.1. Semiconductor Detectors 291

dielectric constant is 12. Hence we have

CA =

[

eNA

2 V 0

] 1 / 2

=

[(

1. 602 × 10 −^19

)

(12)

(

8. 854 × 10 −^12

)(

1015 × 106

)

(2)(150)

] 1 / 2

=7. 5 × 10 −^6 Fm−^2

The absolute capacitance can be obtained by multiplying this value by the

surface area of the diode, that is

C = CAA

=

(

7. 5 × 10 −^6

)(

0. 01 × 10 −^4

)

=7. 5 pF.

H.2 SignalGeneration

We saw earlier that radiation passing through the depletion region produces free
charge carriers that constitute a current under the influence of the externally applied
electric field. This current can be estimated using Ramo’s theorem, which for a
planar geometry states that the instantaneous current can be obtained through the
relation

i=qv

dVw

dx

, (5.1.74)

whereqis the charge produced at positionxand moving with a velocityvandVw
is theweighting potentialthat for a certain electrode is obtained simply by setting
its potential to 1 and potentials on all other electrodes to 0. In terms ofweighting
electric fieldEw=dVw/dx, the above equation can be written as

i=qvEw. (5.1.75)

To use this theorem we need to know the velocity of the charge carriers. We saw
earlier that the drift velocity of charges in a semiconductor is proportional to the
electric field. Hence we can write

v = μE or

v = μ

V 0

d

, (5.1.76)

whereμis the mobility of the charge carrier,V 0 is the applied reverse bias, anddis
the width of the depletion region.
If we apply unit potential to the electrodes where we are measuring the current,
then the weighting field is given by

Ew=

1

d

(5.1.77)