Role of crystal symmetry in band structure optimization for enhanced thermoelectric transport in Cr and Se modified GeTe

GeTe-based degenerate semiconductors offer a promising platform for thermoelectric optimization owing to their responsive electronic structure and intrinsically low lattice thermal conductivity. However, neither the pure rhombohedral nor the pure cubic GeTe phase offers optimal band degeneracy for maximizing the thermoelectric power factor. Here, we demonstrate that defect-engineered co-doping enables simultaneous control of crystal symmetry and thereby electronic band structure in GeTe. Cr substitution suppresses the rhombohedral phase fraction and induces valence band convergence, leading to an enhanced ${m}_{\text{DOS}}^{*}$ and nearly 35% increase in the power factor (53 $\textmu{}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\text{K}}^{\ensuremath{-}2}$) at 750 K, while excessive Cr (3.5%) destabilizes the rhombohedral phase. Temperature-dependent synchrotron x-ray diffraction further elucidates the role of Cr in lowering the onset temperature of cubic symmetry ($\ensuremath{\sim}663$ K). A simple two-band phenomenological model incorporating the L--$\mathrm{\ensuremath{\Sigma}}$ valence-band offset offers a transparent framework to rationalize the contrasting thermopower evolution in GeTe as compared to 2.5% Cr doped GeTe. In contrast, Se substitution stabilizes the rhombohedral lattice and suppresses the bipolar activation of minority carriers. Specifically, 2% Cr, 5% Se co-doped GeTe exhibits significant suppression of bipolar transport in the high-temperature thermoelectric transport. Ultraviolet photoelectron spectroscopy reveals a deeper Fermi level and increased work function upon Se incorporation, consistent with an increased minority carrier activation energy. These results establish defect-engineered co-doping as an effective strategy to couple phase evolution with valence band convergence, enabling enhanced thermoelectric performance in GeTe across a broad temperature range.