Long-Time Tail of the Autocorrelation Function for Electron Drift in High Electric Fields in Silicon

The velocity autocorrelation $\varphi \mathrm{}\left(t\right)\mathrm{}$ function is calculated for electrons moving along a high electric field in $n$-type silicon. For short times $t$, it varies as $\exp (-\frac{t}{{\tau }_0})$, but for times greater than approximately $1.5{\tau }_0$, the short-time exponential decay appears to go over to a $t^{-\frac{3}{2}}$ decay. This representation covers the initial relaxation, but a second exponential also appears as relaxation to the nonequilibrium steady state occurs.