Physics and Engineering of Radiation Detection

5.1. Semiconductor Detectors 265

F.1 DriftofElectronsandHoles..................

The semiconductor detectors are almost always operated in the so calledphotocon-
ductive mode. Such an operation involves establishment of an electric field across the
material. When the incident radiation produces electron hole pairs along its track
in the detector, the charges start moving in opposite directions under the influence
of the applied electric field. The velocity with which the charges move depends on
the electric field. I has been found that for low fields the velocity increases almost
linearly with the field strength, that is

v=μE, (5.1.23)

whereμis a proportionality constant called mobility. Its value depends on the type
of the material, for example in silicon it is 1350cmV−^1 s−^1 for electrons and 480
cmV−^1 s−^1 for holes.
As the field is further increased the velocity of the carriers starts showing de-
viation from the above relation and eventually saturates (see Fig.5.1.7). Most of
the detectors are built such that the charges could very quickly (within a few pico
seconds) attain the saturation velocity.

Electric Field

Electron/Hole Drift Velocity

Figure 5.1.7: Typical variation of drift ve-

locity with respect to the applied electric

field intensity.

Based on the drift of electrons and holes, let us now discuss a simple scheme
that could assure us the proportionality of a measurable quantity with the energy
deposited by the incident radiation. As the charges move in opposite directions,
they constitute an electric current with a current densityJ, which follows Ohm’s
law
J=σE, (5.1.24)

whereEisσis a proportionality constant known as conductivity. Since current
density can also be written as
J=ρv, (5.1.25)

withρbeing the charge density, the above three equations can be combined to give

σ=μρ. (5.1.26)
We saw earlier that the mobility of electronsμediffers significantly from that of
holesμh. Hence the effective conductivity of the material has two separate compo-
nents for each type of charge and hence we can write the above equation as

σ=e(μene+μhnh), (5.1.27)