Dimensional transport crossovers in thermoelectrics revealed by a simple transport model

Quantum confinement gives low-dimensional materials distinctive electronic behaviour, but assessing their effective band structure dimensionality (D) is difficult. Conventional probes such as angle-resolved photoemission spectroscopy (ARPES) or scanning tunneling microscopy (STM) demand ultra clean surfaces and expensive facilities. We introduce a generalized transport model that functions as an internal dimensionality meter: by tracking how the Seebeck coefficient varies with carrier concentration or temperature, we deduce D from two scaling laws, S ∝ D 2 ln T in non-degenerate regimes (e.g. S ≥ 200 μ V K - 1 ) and S ∝ n - 2 / D in degenerate regimes (e.g. S ≤ 150 μ V K - 1 ). Applying this approach to SrTiO₃, few-layer Bi₂O₂Se and Pb1-xSnxTe uncovers temperature-, doping- and alloy-induced crossovers between three-dimensional and lower-dimensional transport. The method offers a rapid, scattering independent framework to design quantum and thermoelectric properties.