Physics and Engineering of Radiation Detection

292 Chapter 5. Solid State Detectors

Hence according to Ramo’s theorem the induced current will be

i = qμ

V 0

d

1

d

= qμ

V 0

d^2

. (5.1.78)

This expression can be used to deduce the corresponding total charge induced on the
electrode provided we know the charge collection time. Because of linear dependence
of the velocity of charge carriers on the electric field, we can find the transit timete
of an electroncreated at a distancexfrom the collection electrode simply by using
(see also Fig.5.1.28)

te =

x

ve

=

x

μeE

=

xd

μeV 0

. (5.1.79)

The hole is also created at the same position but moves in opposite direction. Since
it travels a distanced−xbefore being collected by the opposite electrode, we can
write its transit timethas

th =

d−x

vh

=

d−x

μhE

=

(d−x)d

μhV 0

. (5.1.80)

The total charge induced by electronsQecan then be calculated from the relation
Qe=iete. Using the relations for the current and the transit time, we get

Qe = iete

= qμe

V 0

d^2

xd

μeV 0

= q

x

d

. (5.1.81)

Similarly the charge induced by the hole is given by

Qh = ihth

= qμh

V 0

d^2

(d−x)d

μhV 0

= q

(

1 −

x

d

)

. (5.1.82)

It is apparent from above expressions that the amount of charges induced on the
electrodes by electrons and holes depends on the position of the charge pair creation.
Also since the mobility of electrons is approximately three times higher than that