Physics and Engineering of Radiation Detection

276 Chapter 5. Solid State Detectors

Because of the low band gap energy, intrinsic charge carrier concentration of
germanium is about three order of magnitude higher than than of silicon. Certainly
this is not a very desirable feature as far as radiation detection is concerned since
it would imply larger intrinsic noise and the need to more aggressive cooling. The
resistivity of the germanium is about four order of magnitude lower than that of
silicon. The temperature dependence of germanium’s energy gap is given by (47)

Eg=0. 742 − 4. 8 × 10 −^4

T^2

T+ 235

, (5.1.38)

whereTis the absolute temperature andEgis ineV. This equation has been plotted
in Fig.5.1.16. This figure when compared with that of silicon (Fig.5.1.9) does not
reveal any dramatic difference between the temperature dependence of the band gap
energies of the two materials. The only important thing here is that the band gap
for germanium also increases with decrease in temperature.

T (K)

250 260 270 280 290 300 310

(eV)g

E

0.66

0.665

0.67

0.675

0.68

Figure 5.1.16: Variation of ger-

manium band gap energy with

absolute temperature.

Just like silicon, the intrinsic carrier concentration of germanium is also governed
by equation 5.1.30. The temperature dependences of density of states in conduction
and valence bands of germanium are given by (47)

Nc =1. 98 × 1015 T^3 /^2 (5.1.39)

Nv =9. 6 × 1014 T^3 /^2 , (5.1.40)

whereTis the absolute temperature and the density of states are incm−^3. Substi-
tuting these in equation 5.1.30 gives the expression for the intrinsic carrier concen-
tration.
ni=1. 38 × 1015 T^3 /^2 e−Eg/^2 kBT (5.1.41)

Here, as before,niis incm−^3 ,Tis the absolute temperature, andkBis the Boltz-
mann’s constant. The plot of this equation (Fig.5.1.17) when compared with that of
silicon (Fig.5.1.17) reveals that quantitatively there is a difference of several orders
of magnitude between the intrinsic charge carrier densities of the two materials in
the same temperature range. Of course this can be attributed to the lower band gap
energy in germanium, which allows more electrons in the valence band to jump to
the conduction band due to thermal agitation.