Physics and Engineering of Radiation Detection

278 Chapter 5. Solid State Detectors

Some of the important electrical properties of germanium are listed in Table 5.1.7.
Comparison of these values with those of silicon (see Table 5.1.5) clearly shows that
the overall charge collection efficiency in a detector based on germanium will be
higher than in silicon. However charge collection efficiency is not the only criterion
for selecting a material as detection medium. Other factors include intrinsic charge
carrier density, crystal defects and imperfections, impurities, availability, and cost.

Table 5.1.7: Mobilities (μe,μh,) velocities (ve,vh), and diffusion coefficients (De,Dh)
of electrons and holes in germanium (47).

Property Symbol Value

Electron Mobility μe ≤ 3900 cm^2 V−^1 s−^1

Hole Mobility μh ≤ 1900 cm^2 V−^1 s−^1

Electron Thermal Velocity ve 3. 1 × 105 ms−^1

Hole Thermal Velocity vh 1. 9 × 105 ms−^1

Electron Diffusion Coefficient De ≤ 100 cm^2 s−^1

Hole Diffusion Coefficient Dh ≤ 50 cm^2 s−^1

Let us now turn our attention to the temperature and electric field dependence
of electrical conduction properties of germanium. Fig.5.1.18 shows the dependence
of drift velocity on electric field intensity at two different temperature settings. The
important thing to note here is the proportionality of the drift velocity to the electric
field intensity at least up to moderate electric fields. Hence the relation

vd=μeE, (5.1.42)

holds well up to about an electric field of 1000V/cm.Herevdis the drift velocity
of electrons,E is the applied electric field, andμeis the mobility of electrons in
germanium.
As in case of silicon, in germanium too the electron mobility has a temperature
dependence, which can be approximately written as (44)

μe∝T−^1.^66. (5.1.43)

Fig.5.1.19 shows mobility of electrons in germanium as a function of absolute tem-
perature. Though the graph does not cover a wide temperature range going up to
the room temperature, but the trend of the graph is qualitatively similar to the one
shown.
So far we are happy that the electrons in germanium behave in an orderly fashion
with a drift velocity that is proportional to the applied electric field. But the output
signal depends not only on electrons but also on how holes behave. Since movement
of holes is coupled with the movement of electrons, we would expect that their drift