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In this work, a theoretical study is carried out on the effects of the thickness of a semiconductor thin film on the transport of heat and particles under the action of an external temperature difference. The dependence of the Seebeck effect on the thickness is considered. The thickness film is introduced through the transport coefficients of the material, namely, the thermal and electrical conductivities and the intrinsic Seebeck coefficient, by resorting to known results of irreversible thermodynamics. Graphs of the generated electric potential difference by an external temperature difference versus film thickness are obtained in the range 0.1 µm–1 µm. We compare the results of two slightly doped materials, namely, silicon and bismuth telluride of the  n - and  p - types. The  n -type silicon shows an optimal thickness where the generated electric potential difference is maximum, while the electric potential difference in the  n -type bismuth telluride decreases with decreasing thickness. The electric response of  p -type silicon and  p -type bismuth telluride also worsens as the thickness decreases. The results presented may be useful in the design of thermoelectric devices on the sub-micrometer length scale.

Size scaling effects on heat and particle transport in semiconductor thin films: a near-equilibrium thermodynamic approach