Ab initio study of HfPdY (Y = Si, Ge, Sn): insights into electronic, optical, and thermoelectric behavior

This work presents a comprehensive first-principles investigation of the structural, electronic, optical, and thermoelectric properties of half-Heusler alloys HfPdX (X = Si, Ge, Sn) using density functional theory within the generalized gradient approximation, as implemented in the Quantum ESPRESSO package. Structural optimization confirms the thermodynamic stability of the compounds, with lattice parameters in good agreement with available literature. Electronic band structure calculations reveal that all three materials exhibit indirect narrow band gaps of approximately 0.69 eV (HfPdSi), 0.57 eV (HfPdGe), and 0.40 eV (HfPdSn), classifying them as narrow-gap semiconductors. Projected density of states analysis shows that the electronic states near the Fermi level are dominated by hybridized Hf-5d and Pd-4d orbitals, while the p states of the X element mainly contribute to the deeper valence bands and influence band gap narrowing along the Si → Ge → Sn trend. The calculated optical properties indicate strong interband transitions in the visible and ultraviolet regions, with HfPdSn exhibiting a well-defined absorption onset consistent with its semiconducting character, whereas HfPdSi and HfPdGe display enhanced low-energy optical response due to their narrow band gaps. Thermoelectric transport properties were evaluated using semiclassical Boltzmann transport theory within the constant relaxation time approximation. Among the studied compounds, HfPdSi shows the highest Seebeck coefficient, power factor, and overall thermoelectric performance, leading to the largest figure of merit (ZT) over the temperature range of 300–800 K. The results suggest that HfPdX alloys, particularly HfPdSi, are promising candidates for thermoelectric and optoelectronic applications, with further performance enhancement achievable through carrier concentration optimization and lattice thermal conductivity reduction.