Logistic characteristics of phonon transport in silicon thin film: the S-curve

The logistic characteristics of the averaged heat flux are investigated across the thin film incorporating the S-curve. Temporal behaviour of the heat flux vector is computed using the Boltzmann transport equation. The dispersion relations are introduced to account for the frequency dependent phonon transport across the film. The influence of film width on the characteristics of the averaged heat flux is also examined. It is found that temporal behaviour of the averaged heat flux follows the S-curve. The S-curve characteristics change for different film widths. The time to reach 95% steady value of the averaged heat flux is short for the film with small widths, which is attributed to the ballistic behaviour of phonons in the film.