Physics and Engineering of Radiation Detection

286 Chapter 5. Solid State Detectors

il

il

Depletion Region

−

−

−−

+ −

++

+

+

p n

i

V

(a)

(b)

ReverseBias ForwardBias

− +

Figure 5.1.24: (a) Reverse biased pn-

junction. (b) Current-voltage curve of

a typical pn-junction. If the junction is

reverse biased, a small leakage current

il flows through it, which stays almost

constant as the voltages is increased up

to a point at which the potential is high

enough to overcome the potential barrier

(not shown here). At forward bias, how-

ever, the current increases with applied

voltage.

H.1 CharacteristicsofaReverse-Biasedpn-Diode

In a semiconductor detector, the depletion region is used as the active medium
for creating electron-hole pairs by incident radiation. This region is almost devoid
of free charge carriers at operating temperatures and therefore very small leakage
current flows through it in the absence of radiation. The charge pairs created by the
radiation move in opposite directions under the influence of the effective junction
electric field and constitute an electric current that can be measured. Under carefully
maintained working conditions such as temperature, this current is proportional to
the energy deposited by the radiation. In this respect a semiconductor detector has
the same working principle as a gas filled chamber except that the number of charge
pairs created in the former is far more than the latter and consequently the output
signal is of higher strength.
The output signal of a semiconductor detector and its dynamic range depends on
several factors, most notably the effective electric field strength, the capacitance, and
the depth of the depletion region. For the typical planar geometry, these parameters
can be fairly easily estimated using the Poisson’s equation

^2 Φ=−

ρ



, (5.1.54)

where Φ is the electric potential,is the permittivity of the semiconductor material,
andρis the charge density profile in the depletion region. The permittivity in this
equation can be written as a product of the dielectric constant of the materialr
(also sometimes referred to as the relative permittivity) and the permittivity of free
space 0 ,thatis
=r 0. (5.1.55)

The dielectric constant or relative permittivity is a dimensionless constant and is
extensively quoted in literature. Its value depends on the type of material and
varies considerably from material to material. for example the dielectric constant
for silicon is around 12 while that of germanium is about 16. For computations,