5.1. Semiconductor Detectors 253
impurity atomic density to the semiconductor atomic density for silicon is of the
order of 10−^10 cm−^3. This means that for each impurity atom there are around 10^10
semiconductor atoms. Although most of the semiconductor detectors are made with
small impurity additions, there is also a special class of detectors that are made
withheavily dopedsemiconductors. Typical impurity atomic concentration in such
materials is 10^20 cm−^3 in the bulk semiconductor with a density of the order of
1022 cm−^3.
An interesting aspect of doping agents is that their ionization energies depend
on where their energy levels lie within the energy band structure of the bulk of
the semiconductor material. This implies, for example that the ionization energy
of boron impurity in silicon will be different than that in germanium. Typical
ionization energies for the doping agents used in semiconductor detector materials
range between 0.01eV and 0.1eV. If we compare this with the typical ionization
energies of several electron volts for the semiconductors, we can conclude that the
doping agents should ionize very quickly after their introduction into the material.
If the material did not have significant impurities beforehand then it can be said
that the free charge carrier density in the bulk of the material is, to a large extent,
characterized by the acceptor and donor impurity concentrations. Ifnaandndare
the acceptor and donor impurity concentrations, then the acceptor and donor charge
concentrations can be written as
Na,− ≈ na (5.1.5)
Nd,+ ≈ nd, (5.1.6)where the (−) and (+) signs represent the ionization states of the impurity atoms.
Note thatNdoes not represent the free charge density, rather the number of ion-
ized atoms. A donor gives off its electron and becomes positively ionized while an
acceptor becomes negatively charged after accepting an electron.
Since there are always donor and acceptor impurities present in a material, there-
fore the characterization of a material as n or p type depends on the difference of
charges, which as we just saw, depends on the difference of number density of ionized
atoms. Hence we can say that a material is of type n if
nn=Nd,+−Na,−>> ni, (5.1.7)wherennis the charge carrier density of the n-type material andnirepresents the
charge carrier density of the pure material. This is the carrier density of the material
before being doped. Similarly aptype material is defined as the one that satisfies
the condition
np=Na,−−Nd,+>> ni. (5.1.8)
Herenpis the charge carrier density of p type material.
The reader should note that, since the amount of impurity needed to modify the
semiconductor into n- or p-type is very small, all the semiconductor crystals are
naturally of either n- or p-type. An absolutely pure semiconductor material does
not exist. However it is possible to dope the material such that its positive and
negative charge carrier densities become nearly equal, that is
nn≈np. (5.1.9)Such compensated materials show bulk properties similar to an ideally pure semi-
conductor. To develop semiconductor detectors, generally shallow doping is done.