Phonon transport in a silicon film with presence of an aluminum dot in the film

Phonon transport in a two-dimensional silicon film with presence of an aluminum quantum dot is studied in the presence of temperature excitation at the aluminum dot. Frequency-dependent Boltzmann equation is solved numerically to obtain phonon intensity distribution in the silicon film. Temperature at the edges of the aluminum dot is varied exponentially and the phonon transport characteristics are examined in the silicon film. Equivalent equilibrium temperature is introduced to assess the phonon intensity distribution in the film. The numerical code developed is validated through the thermal conductivity data reported in the open literature. It is found that the thermal conductivity predicted agrees well with the data obtained from the experiment. Temporal behavior of equivalent equilibrium temperature at the silicon film interface almost follows temperature variation at the edge of the aluminum dot. As the distance increases toward the film edge, where the low temperature is allocated, the contribution of quasi-ballistic and ballistic phonons to phonon intensity distribution becomes important in the film.