5.1. Semiconductor Detectors 255
shell electrons is added to this lattice, it tries to fit into the structure but since it
has one electron less therefore it can form only three covalent bonds with silicon
atoms. The fourth location can then be thought to have a positive hole since it has
strong affinity to attract a free electron. In fact if this hole is filled by a free electron
in the lattice it would essentially move the hole to the original site of the electron.
Since in an intrinsic silicon lattice there are a very few free electrons therefore even
a small number of boron atoms in the bulk of the lattice can make it abundant in
p-type charges and turn the material into a p-type semiconductor.
The distribution function of acceptors in a semiconductor is given by
fA(EA)=1
1+4e(EA−EF)/kBT, (5.1.10)
whereEArepresents the acceptor energy level. Note that this distribution is some-
what different from the Boltzmann distribution we saw earlier for for free charge
carriers (cf. equation 5.1.1).
D.2 DopingwithDonorImpurity
If the impurity has more electrons than the semiconductor atoms in the outermost
shell, the excess electrons are not able to make covalent bonds with the lattice atoms
and are thus free to move around. Such an impurity is calleddonorimpurity since
it donates free charge carriers to the bulk of the material. In the energy band
structure the net effect is the lowering of the conduction band (see Fig. 5.1.3).
Since the energy gap is reduced with more free electrons in the conduction band,
the electrical conduction properties of the semiconductor are greatly enhanced. Such
a material is known as n-type semiconductor due to the abundance of free negative
charges.
As with acceptors, the distribution function of donors also differs from the Boltz-
mann distribution given in equation 5.1.1. In this case it is given by
fA(ED)=1
1+0. 5 e(ED−EF)/kBT, (5.1.11)
whereEDrepresents the donor energy level.
5.1.E Mechanism and Statistics of Electron-Hole Pair Production
Radiation passing through a semiconductor material is capable of causing the fol-
lowing three distinct phenomena to occur in the bulk of the material.
Lattice Excitation:This occurs when the incident radiation deposits energy
to the lattice increasing the lattice vibrations.Ionization:In semiconductors ionization means production of an electron hole
pair.Atomic Displacement:This non-ionizing phenomenon is the major contrib-
utor to the bulk of the damage caused by radiation. We’ll discuss this in detail
later in the Chapter.