Thermal conductivity switch: Optimal semiconductor/metal melting transition

Abstract

Scrutinizing distinct solid/liquid ($s/l$) and solid/solid ($s/s$) phase transitions (passive transitions) for large change in bulk (and homogenous) thermal conductivity, we find the $s/l$ semiconductor/metal (S/M) transition produces the largest dimensionless thermal conductivity switch (TCS) figure of merit ${Z}_{\text{TCS}}$ (change in thermal conductivity divided by smaller conductivity). At melting temperature, the solid phonon and liquid molecular thermal conductivities are comparable and generally small, so the TCS requires localized electron solid and delocalized electron liquid states. For cyclic phase reversibility, the congruent phase transition (no change in composition) is as important as the thermal transport. We identify $X\mathrm{Sb}$ and $X\mathrm{As}$ ($X=\text{Al}$, Cd, Ga, In, Zn) and describe atomic-structural metrics for large ${Z}_{\text{TCS}}$, then show the superiority of S/M phonon- to electron-dominated transport melting transition. We use existing experimental results and theoretical and ab initio calculations of the related properties for both phases (including the Kubo-Greenwood and Bridgman formulations of liquid conductivities). The $5p$ orbital of Sb contributes to the semiconductor behavior in the solid-phase band gap and upon disorder and bond-length changes in the liquid phase this changes to metallic, creating the large contrast in thermal conductivity. The charge density distribution, electronic localization function, and electron density of states are used to mark this S/M transition. For optimal TCS, we examine the elemental selection from the transition, basic, and semimetals and semiconductor groups. For CdSb, addition of residual Ag suppresses the bipolar conductivity and its ${Z}_{\text{TCS}}$ is over 7, and for ${\mathrm{Zn}}_{3}{\mathrm{Sb}}_{2}$ it is expected to be over 14, based on the structure and transport properties of the better-known $\ensuremath{\beta}\ensuremath{-}{\mathrm{Zn}}_{4}{\mathrm{Sb}}_{3}$. This is the highest ${Z}_{\text{TCS}}$ identified. In addition to the metallic melting, the high ${Z}_{\text{TCS}}$ is due to the electron-poor nature of II-V semiconductors, leading to the significantly low phonon conductivity.