  Transverse thermoelectric power generation has emerged as a topic of immense
interest in recent years owing to the orthogonal geometry which enables better
scalability and fabrication of devices. Here, we investigate the thickness
dependence of longitudinal and transverse responses in film-substrate systems
i.e., the Seebeck coefficient, Hall coefficient, Nernst coefficient and
anomalous Nernst coefficient in a unified and general manner based on the
circuit model, which describes the system as the parallel setup. By solving the
parallel circuit model, we show that the transverse responses exhibit a
significant peak, indicating the importance of a cooperative effect between the
film and the substrate, arising from circulating currents that occur in these
multilayer systems in the presence of a temperature gradient. Finally, on the
basis of realistic material parameters, we predict that the Nernst effect in
bismuth thin films on doped silicon substrates is boosted to unprecedented
values if the thickness ratio is tuned accordingly, motivating experimental
validation.
