Static and dynamic Monte Carlo simulations of phonon drag effects on thermoelectric properties in silicon nanostructures

Thermoelectric transport in silicon nanofilms is investigated using a self-consistent electro-thermal Monte Carlo simulator that couples electron dynamics to a phonon bath with spatially varying temperature. A key novelty of this work is the explicit inclusion of the phonon-drag contribution, implemented by modifying the electron-phonon momentum exchange based on the local deviation of the phonon distribution from equilibrium. The method is validated against bulk silicon data and extended to incorporate rough boundary scattering for both electrons and phonons, yielding excellent agreement with experimental measurements on nanofilms. We also analyze the transient regime and show that a temperature bias produces a slower current response than a voltage bias, although the phonon-drag effect itself tends to accelerate the response. These results demonstrate that the proposed framework provides a powerful tool for predicting both steady-state and time-dependent thermoelectric behavior in semiconductor nanostructures.