Electronic Transport Processes in Heavily Doped Uncompensated and Compensated Silicon as Probed by the Thermoelectric Power

The thermoelectric power $S$ and electrical resistivity $\rho$, measured between 1.5 and 30 K, of just insulating, heavily doped Si show distinct differences between uncompensated and compensated samples. $S\left(T\right)$ of Si:P exhibits a sign change from $S<\mathrm{}0\mathrm{}$ to $S>\mathrm{}0\mathrm{}$ with decreasing $T$ at a temperature $T_{S=0\mathrm{}}$ which increases sharply with decreasing carrier concentration $N$ below $N_0=2.78\mathrm{}\times {10}^{18}{\mathrm{cm}}^{-3\mathrm{}}$. Below $N_0$, $\rho \left(T\right)$ shows activated conduction over an energy gap $E_2$ which has the same $N$ dependence as $T_{S=0\mathrm{}}$. This is attributed to the splitting of the two Hubbard bands. In contrast, $S\left(T\right)$ of Si:(P,B) is negative in the whole $N$ and $T$ range investigated and $\rho \left(T\right)$ shows Efros-Shklovskii variable-range hopping down to the lowest $N$.