Classical Size Effect on In-plane Thermoelectric Transport at Low Dimension

Abstract

Previous models on low-dimensional thermoelectric investigation deal with the quasi twodimensional electron transport due to quantum confinement effect. The formation of sub-bands in quantum well requires that electron wave reflections or transmissions at the interface are strictly in the specular direction and the superimposed wave function keeps phase coherence. However, due to the interface non-ideality or roughness, electrons can lose coherence such that their transport will deviate from that described by two-dimensional quantum well limit theories. In this paper, we report a theoretical approach to investigate the classical size effect on in-plane thermoelectric transport at low dimensions. A theoretical model based on Boltzmann equation is established with interface scattering treated as partial specular and partial diffuse scattering boundary condition. With the infinite quantum well assumption, the classical size effect in the quantum-classical mixed regime is quantitatively demonstrated. Factors that affecting classical size effect, such as quantum well width and relaxation length, are discussed.