Physics and Engineering of Radiation Detection

282 Chapter 5. Solid State Detectors

where bothNcandNvare in units ofcm−^3. The energy gapsELandEXcorre-
sponding toLandXvalleys respectively can be evaluated from (47)

EL=1. 815 − 6. 05 × 10 −^4

T^2

T+ 204

(5.1.48)

EX=1. 981 − 4. 60 × 10 −^4

T^2

T+ 204

. (5.1.49)

The intrinsic charge carrier density can now be calculated by substitutingNcand
Nvfrom equations 5.1.46 and 5.1.47 into equation 5.1.30. Hence we get

ni=3. 974 × 1014 T^3 /^2

[

1 − 1. 93 × 10 −^4 T− 4. 19 × 10 −^8 T^2

+21exp

(

−

EL

2 kBT

)

+44exp

(

−

EX

2 kBT

)] 1 / 2

e−Eg/^2 kBT, (5.1.50)

whereEg,EL,andEXare given by equations 5.1.45, 5.1.48, and 5.1.49 respectively.
The plot of the above equation (see Fig.5.1.22) can now be compared to the similar
plots for silicon and germanium (see figures 5.1.10 and 5.1.17). It is clear that,
in terms of intrinsic charge carriers, gallium arsenide is much superior than silicon
and germanium. Such low intrinsic carrier concentration even at room temperature
makes it possible to operateGaAsbased detectors without or with very minimal
cooling.

T (K)

250 260 270 280 290 300 310

-3)

(cmi

n

103

104

105

106

Figure 5.1.22: Dependence of

intrinsic charge concentration

in gallium arsenide on absolute

temperature.

Let us now have a look at the electrical conduction properties of GaAs. It is
apparent from Table 5.1.8 that the electron mobility inGaAsis more than 20 times
higher than the hole mobility. This behavior is in contrast with germanium and
silicon where the mobilities differ by only about a factor of 2 to 3. However, inter-
estingly enough, the temperature dependence of the hole mobility inGaAsis about
the same as in germanium, that is (44)

μh∝T−^2.^3. (5.1.51)

On the other hand the electron mobility inGaAsfollows (7)

μe∝T−^0.^66. (5.1.52)