Electric Properties ofn-Type Liquid Alloys of Thallium and Tellurium

Measurements have been made of the electrical conductivity $\sigma$ and Seebeck coefficient $S$ of Tl-Te liquid alloys as a function of the composition $X$ (at.% Tl) and temperature $T$ for $67<X<\mathrm{}72\mathrm{}$. Also, the effects of doping the $n$-type binary solution with relatively small amounts of a third element were studied, with Ag, Cd, In, Sn, or Sb as the third element. In most ranges of $T$ and $X$, there was little dependence of $\sigma$ and $S$ on $T$. It was possible to fit isothermal data to conventional transport theory in a rather comprehensive way. Plots of all data for $\sigma$ versus $S$, including solutions containing a third element, fell on a single theoretical curve based on Fermi-Dirac integrals, corresponding to $\mathcal{r}=-\frac{1}{2}$, viz., $\tau ={\tau }_{\perp }{\epsilon }^r$, where $\tau$ is the scattering time and $\epsilon$ is the kinetic energy of the electrons. This value of $\mathcal{r}$, together with the finding that ${\tau }_1$ is independent of $T$, indicates that scattering is caused by the intrinsic (nonthermal) disorder of the liquid. Comparison of the experimental dependence of $S$ on the composition of Tl-Te solutions, with the theoretical dependence of the electron concentration $n$ on $S$, shows that $n$ is proportional to the concentration of Tl in excess of the composition ${\mathrm{Tl}}_2$Te. Use of the same theoretical curve for the dependence of $S$ on the concentration $A$ of the various doping elements showed again a linear dependence. Comparison of the relative slopes $\frac{\mathrm{dn}}{\mathrm{dA}}$ for the different elements indicates that one could assign integral valences as follows: Tl, +3; Ag, +1; Cd, +2; In, +1; Sn, +2; Sb, -1. Consideration of other aspects of transport theory, particularly the relative magnitudes of the de Broglie wavelength and the scattering distance, suggests that a large fraction of the electron charge in the conduction band is localized as the result of screening of the potential of the donor and acceptor ions. Solutions of the nonlinear Thomas-Fermi screening equation indicate that physically reasonable magnitudes of the effective dielectric constant $K$ leads to value of $\alpha$, the fraction of free-electron charge, which are consistent with the range of values required by the transport parameters. We deduce that $0.15\widetilde{<}\alpha \widetilde{<}0.5$, and the effective-mass ratio $\frac{m^{*}}{m}$ lies between 1.0 and 2.0, corresponding to $K<\mathrm{}10\mathrm{}$.