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, $S\propto \left(\frac{D}{2}\right)\ln T$ in non-degenerate regimes (e.g. $\left(S\right)\ge 200\mu V{K}^{-1}$ ) and $S\propto n^{-2/D}$ in degenerate regimes (e.g. $\left(S\right)\le 150\mu V{K}^{-1}$ ). Applying this approach to SrTiO₃, few-layer Bi₂O₂Se and Pb_1-xSn_xTe 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.