Physics and Engineering of Radiation Detection

280 Chapter 5. Solid State Detectors

Figure 5.1.19: Dependence of

electron mobility on absolute

temperature in germanium (20).

Solid line represents theoretical

prediction while the points rep-

resent experimental data.

magnitude higher than that of silicon. This, of course, is a very desirable feature as
far as its use as detection medium is concerned.
The temperature dependence of band gap of gallium arsenide is given by (47)

Eg=1. 519 − 5. 405 × 10 −^4

T^2

T+ 204

, (5.1.45)

whereT is the absolute temperature andEgis ineV. This equation has been
plotted in Fig.5.1.21. The reader would note that the variation in band gap energy
with temperature for gallium arsenide is not much different than that for silicon or
germanium. The distinguishing feature ofGaAsis the width of the band gap itself,
which at each temperature is far higher than the other two materials.
The evaluation of intrinsic carrier density of gallium arsenide is not as simple
as that of silicon or germanium. The reason can be understood by examining its
band structure diagram (see Fig.5.1.20). The conduction band ofGaAshas two
additional valleys (X and L) whose contribution to the overall density of states of
the conduction band can not be ignored. The valence band density of states has a
simple temperature dependence, though. The density of states of conduction and