# 7 Appendix 2: Temperature dependence of $$E_g$$

Experimental results consistently shows that the energy gap depends on temperature and for Germanium we can find in the literature the following empirical law:

$$$E_{ g }(T)=0.742-\frac { 4.8\cdot 10^{ -4 }T^{ 2 } }{ T+235 } \quad \quad [eV] \tag{7.1}$$$

This may be approximated, in the high temperature region, by a linear law as follows:

$E_g (T) = A \cdot BT$

where the constants $$A$$ is the value of $$E_g$$ linearly extrapolated to $$T=0$$: $E^0_g = A = 0.78eV$

Since in the intrinsic region (high temperature) the resistance depends on the absolute temperature $$T$$ as $$exp( \frac{E_G}{2kT})$$, a plot of $$ln( R )$$ vs $$\frac{1}{2 K T}$$ using a linear approximation for $$E_g(T)$$ results in a straight line with slope $$E^0_g$$