Seebeck Coefficient in N-Type Germanium-Silicon Alloys: "Competition" Region

The Seebeck coefficient $Q$ of arsenic-doped germanium-silicon alloys was measured as a function of silicon content from 0 to 20 at.%. The values of $Q$ were found to go through a maximum at the alloy ${\mathrm{Ge}}_{85}$ ${\mathrm{Si}}_{15}$; furthermore, they were smaller on the germanium side of that composition than they were on the silicon side. The behavior of $Q$ as a function of alloy composition, in the case of lightly doped samples, can be accounted for in terms of the changes in the density-of-states: at ${\mathrm{Ge}}_{85}$ ${\mathrm{Si}}_{15}$ the structure of the conduction-band minima passes from that of germanium, with four valleys along the $〈111〉$ directions, to that of silicon, with six valleys along the $〈100〉$ directions; and at ${\mathrm{Ge}}_{85}$ ${\mathrm{Si}}_{15}$ all ten valleys are equi-energetic. In the case of the heavily doped samples, there is also a contributory effect due to the decrease in the relative strength of the ionized-impurity scattering ($\tau \sim E^{\frac{3}{2}}$) as alloy-disorder scattering ($\tau \sim E^{-\frac{1}{2}}$) increases with the addition of silicon.