Investigation on structure and energy band of vacancy-containing type-Ⅰ tin-based clathrates A₈Sn₄₄□₂

Density functional theory (DFT) calculations within the LDA framework were utilized to examine the electronic structure and tuning mechanisms of vacancy-containing Type-Ⅰ tin-based clathrates A₈Sn₄₄□₂ (A = K, Rb, Cs, or mixed alkali atoms). The computational results indicate that the materials have a higher structural stability when the vacancies preferentially occupy the Wyckoff 6c crystallographic sites. The unfilled Sn₄₄□₂ framework demonstrates characteristics of a p-type degenerate semiconductor, with a pseudo-bandgap of approximately 0.4 eV. Dangling-bond states induced by the vacancies dominate the electronic behavior near the Fermi level. Upon incorporating alkali metal guest atoms, charge transfer saturates these defect states, resulting in a transition from a degenerate semiconductor to a narrow-bandgap semiconductor. All clathrate compounds analyzed conform to the RBM. The study reveals that Cs atoms, rather than K counterparts, exhibit a higher charge transfer capability, compressing Sn—Sn bond lengths to 0.276 nm. Such compression enhances bond strength and facilitates fine-tuning of lattice parameters. Boltzmann transport calculations further demonstrate anisotropic electronic transport properties. Notably, Cs₈Sn₄₄□₂ exhibits a high Seebeck coefficient (about 180 μV·K⁻¹) and substantial electrical conductivity under p-type doping conditions, indicating its potential for achieving a high power factor. This research elucidates the collaborative mechanism between vacancies and guest atoms, aiding researchers in designing PGEC (phonon glass-electron crystal) thermoelectric materials with low thermal conductivity and tunable bandgaps.