Heat Capacities Study of Semiconductors CuMX2 (M = Ga, In; X = S, Se, Te) from the Einstein–Debye Approximation

— The ternary chalcopyrite semiconductors CuMX2 (M = Ga, In; X = S, Se, Te) have attracted considerable attention due to their promising applications in optoelectronic and thermoelectric devices. In the present work, the temperature dependence of the heat capacities at constant volume ( $${{C}_{V}}$$ ) and constant pressure ( $${{C}_{P}}$$ ) of CuMX2 (M = Ga and In; X = S, Se, and Te) semiconductors is systematically investigated within the framework of the combined Einstein–Debye approximation. The Einstein–Debye approximation, one of the recently refined methods for describing lattice vibrational contributions, provides improved accuracy over single-model descriptions by combining the strengths of the Debye and Einstein treatments. Calculations are carried out over a wide temperature range, and the contributions of both acoustic and optical phonon modes are incorporated through the Einstein–Debye formalism. The calculated heat capacities exhibit consistent trends among the studied compounds, reflecting the influence of atomic mass and lattice stiffness. A comparison with available theoretical and experimental literature data demonstrates good agreement, confirming the reliability of the present approach.