Metal-semiconductor interfaces are ubiquitous in many types of devices, especially in electronics where Schottky contacts are widespread. In this work we investigate both the phonon and electron transport at an interface between a metal, titanium, and a semiconductor, silicon, by means of the Boltzmann transport equation solved with the discrete ordinate method. The Boltzmann equation is solved in energy intensity for each of the phonon and electron baths, with an average mean free path for each bath [1].

We first apply a temperature difference and then add on top a voltage bias. The aim is to analyse the nonequilibrium of electrons and phonons close to the interface. While it has already been studied with the two-temperature model, the local nonequilibrium of each of the energy carriers due to the presence of the boundary could not be systematically included. Here we therefore analyse the interplay between this ‘ballistic’ nonequilibrium and the nonequilibrium between the electron and phonon baths. The electron-phonon coupling length acts as a third mean free path in addition to the electron (few to tens of nanometers) and phonon average (~200 nm) mean free paths. When the materials on both sides of the interface are thin films, the electron-phonon coupling can be suppressed and the temperature field becomes complex. Finally, we study the case of a limited contact zone of extension smaller than the mean free paths, associated with ballistic dissipation.

This work sheds light on the thermal boundary resistance at semiconductor-metal interface and thermoelectric coefficients when the thickness of the layers is decreased to the nanometric size.

[1] Y. Wang et al., J. Appl. Phys. 119, 065103 (2016)

We acknowledge the support of projects EFICACE (ANR-20-CE09-0024), THACOS (ANR-24-CE50-1843-02) and EFINED (H2020-GA-766853). We thank S. Merabia for useful discussions.