Past exam of the materials science course of the University of Cambridge / 2016 / Paper 1 / 2 / a / Solution

Assume one temperature-independent activation energy over this interval and an unchanged dopant-controlled carrier population. Write the Arrhenius equation as $D=D_0\exp [-Q/(k_{B}T)]$. The two measurements giveUsing $D(T)=10^{-13}\exp [(Q/k_B)(1/1000-1/T)]$ yieldsThe Nernst-Einstein relation includes the factor $1/T$: $\sigma =n{q}^{2}D/(k_{B}T)$. For fixed $n$ and a fixed correlation correction,Using conductivity proportional to $D$ alone would miss the temperature factor. Carrier association, a changing vacancy population or a changing diffusion correlation factor would invalidate this simple extrapolation.