Atomistic origin of low thermal conductivity in quaternary chalcogenides Cu(Cd, Zn)$_2$InTe$_4$

TL;DR

This study investigates the atomistic origin of ultralow lattice thermal conductivity in CuCd2InTe4 and CuZn2InTe4 by integrating electronic structure calculations with a unified phonon-transport framework that includes both particle-like and coherence channels. It identifies filled antibonding states below the Fermi level as the driver of enhanced phonon anharmonicity and increased three-phonon phase space, yielding a suppressed lattice thermal conductivity dominated by $\mathcal{K}_P$ with negligible $\mathcal{K}_C$. CuCd2InTe4 shows stronger acoustic–OPTical overlap and higher scattering than CuZn2InTe4, leading to lower $\mathcal{K}$, and grain-boundary scattering further reduces transport to match experimental values. The results offer atomistic design principles for engineering intrinsically low $\mathcal{K}$ semiconductors among quaternary chalcogenides and related materials.

Abstract

Crystalline semiconductors with intrinsically low lattice thermal conductivity ($\mathcal{K}$) are vital for device applications such as barrier coatings and thermoelectrics. Quaternary chalcogenide semiconductors such as CuCd$_2$InTe$_4$ and CuZn$_2$InTe$_4$ are experimentally shown to exhibit low $\mathcal{K}$, yet its microscopic origin remains poorly understood. Here, we analyse their thermal transport mechanisms using a unified first-principles framework that captures both the Peierls (particle-like propagation, $\mathcal{K}_P$) and coherence (wave-like tunneling, $\mathcal{K}_C$) mechanisms of phonon transport. We show that extended antibonding states below the Fermi level lead to enhanced phonon anharmonicity and strong scattering of heat-carrying phonon modes, suppressing $\mathcal{K}$ in these chalcogenides. We show that $\mathcal{K}_P$ dominates the total thermal conductivity, while $\mathcal{K}_C$ remains negligible even under strong anharmonicity of the phonon modes. The heavier Cd ions in CuCd$_2$InTe$_4$ induce greater acoustic-optical phonon overlap and scattering compared to CuZn$_2$InTe$_4$, further lowering thermal conductivity of the former. Additionally, grain boundary scattering in realistic samples contributes to further suppression of thermal transport. Our findings establish the atomistic origins of low $\mathcal{K}$ in quaternary chalcogenides and offer guiding principles for designing low-thermal-conductivity semiconductors.

Figures (6)

• Figure 1: Zinc-blende like crystal structure of (a) CuCd$_2$InTe$_4$, (f) CuZn$_2$InTe$_4$. (b, g) Electronic structures (left) and density of states (DOS) (right) show the semiconducting gap for both materials. The crystal orbital Hamilton population (COHP) in figures (c, d, e, h, i, j) represent the bonding (+ve) and antibonding (-ve) nature between any pair of nearest neighbour cation and anion. Large DOS of Cu and Te ions with a significant contribution from Cd/Zn and their antibonding states below the Fermi energy for both the compounds influence the thermal transport.
• Figure 2: The upper and lower rows depict the results for CuCd$_2$InTe$_4$ and CuZn$_2$InTe$_4$, respectively. The phonon dispersions (a, e) and atom-projected phonon DOS (b, f) are shown, respectively. The mode Grüneisen parameters ($\gamma$) (c, g) and the mode resolved phonon scattering rates (d, h) are shown for 300 K. Softer phonon modes due to heavier Cd atoms and the presence of antibonding states leads to high mode Grüneisen parameters and large scattering rates.
• Figure 3: Calculated lattice thermal conductivity for (a) CuCd$_2$InTe$_4$ and (b) CuZn$_2$InTe$_4$ at different temperatures. LBTE and Wigner represent the particle-like contribution ($\mathcal{K}_P$), coherences contribution ($\mathcal{K}_C$), respectively. The total thermal conductivity is the sum of both these terms, i.e., $\mathcal{K}$ = $\mathcal{K}_P$ + $\mathcal{K}_C$. The grain boundary sizes (diameters) are mentioned as mean free paths (mfp) by the numbers in nm units. CuCd$_2$InTe$_4$ shows lower thermal conductivity as predicted by our theoretical analysis, and our results also support the experimental findings for both the compounds.
• Figure 4: The upper and lower rows depict the results for CuCd$_2$InTe$_4$ and CuZn$_2$InTe$_4$, respectively. (a, c) The mode resolved particle-like contribution to thermal conductivity ($\mathcal{K}_P$) by solving LBTE. (b, d) The cumulative particle-like contribution to thermal conductivity ($\mathcal{K}_P^c$). Mode resolved contributions are dominating in the first region of phonon dispersions [CuCd$_2$InTe$_4$ (0 - 60 cm$^{-1}$) and CuZn$_2$InTe$_4$ (0 - 75 cm$^{-1}$)].
• Figure A1: (a) The convergence of thermal conductivity ($\mathcal{K}$) with respect to q-mesh ($n\times n \times n$) for CuCd$_2$InTe$_4$ at a temperature of 300 K. (b) Comparison of lattice thermal conductivities (particle-like solution of linear Boltzmann transport equation (LBTE) and Wigner coherence contributions) considering two different ranges of atomic interactions. The two ranges, $r_C =$ 4.5 Å and 5.4 Å, contain upto four and six nearest neighbor atoms, respectively.