5.1. Semiconductor Detectors 273
pendence of electron and hole mobilities for silicon can be written as (44)
μe ∝ T−^2.^5 (5.1.34)
μh ∝ T−^2.^7. (5.1.35)Typical curves showing the dependence of temperature on electron and hole mobili-
ties are shown in figures 5.1.13 and 5.1.14. We will see later that this behavior is not
typical of only silicon and for almost all semiconductors the temperature dependence
of mobility can be approximated by
μ∝T−n, (5.1.36)wherenis a real number that depends on the type of the semiconductor material
and the particle (electron or hole). Of course the value ofncan be significantly
different from one material to the other. Even for the same material the value may
differ for electrons and holes, as we will see later for germanium.
Figure 5.1.13: Dependence of hole
mobility on the absolute temper-
ature (9). Solid line represents
the theoretical prediction while the
points represent the experimental
data.Example:
Determine the percentage change in intrinsic charge concentration in silicon
if the temperature is decreased from 27^0 Cto− 100 C.Solution:
Let us first determine the band gap energiesEg 1 andEg 2 at the two temper-
aturesT 1 = 300KandT 2 = 263Kusing equation 5.1.29. The energy at 300