252 Chapter 5. Solid State Detectors
of conduction and valence bands. It has been found that the density of states of
conduction bandNcand valence bandNvvary with absolute temperature according
to
Nc ∝ T^3 /^2 (5.1.2)
and Nv ∝ T^3 /^2. (5.1.3)The intrinsic charge concentration, however, has a much stronger temperature
dependence, which certainly is a major operational problems of semiconductor de-
tectors. The intrinsic charge concentration can be written as
ni=[ncnv]^1 /^2 exp[
−
Eg
2 kBT]
, (5.1.4)
wherencandnv represent the charge concentrations in conduction and valence
bands respectively. This expression shows that the intrinsic charge concentration
asymptotically reaches a saturation value, which is characterized by the density of
states of conduction and valence bands only.
As states above, an intrinsic material is called an ideal semiconductor, which
essentially means that it simply does not exist in nature. This is a true statement
since, in reality, due to crystal defects and impurities, there are also other energy
states within the forbidden gap that significantly change the electrical conduction
properties of the material. These crystal imperfections lower the energy threshold
needed for transitions and consequently the electron and hole densities change from
an ideal semiconductor having equal number of free electron and hole pairs. Hence
a naturally found or grown semiconductor does not possess intrinsic properties.
However, through the process of impurity addition one can turn any semiconductor
into an intrinsic type, which then is referred to as acompensatedmaterial.
Whenever impurity is added to a semiconductor, its electrical conduction prop-
erties change. The material is then referred to as anextrinsicsemiconductor. The
impurity addition ordopingis an extremely useful process that dramatically im-
proves the performance of semiconductors.
5.1.D Doping
The electrical conduction properties of semiconductors can be drastically changed
by adding very small amounts of impurities, a process known as doping. In this
process, another element with different number of electrons in its outer atomic shell
than the semiconductor atom is added in a very small quantity to the bulk of the
material. The net effect of this process is the creation of additional energy levels
between valence and conduction bands of the crystal. The locations of these levels
in the energy band diagram depend on the type of impurity added. The impurity
that creates abundance of positive charges in the material is known asacceptor
impurity and it creates energy levels near the valence band. The resulting material
is known as p-type semiconductor. On the other hand adonorimpurity makes the
material abundant in negative charges and creates additional energy levels near the
conduction band. Such a material is referred to as n-type semiconductor.
To use semiconductors as radiation detectors, generally very small quantities
of impurities are added to the bulk of material. for example the typical ratio of