One-dimensional thin-film phonon transport with generation

The Boltzmann transport equation is often used for non-continuum transport when the mean free path of phonons is of the order of device sizes. One particular application involves heat generation in electronic devices. In a highly scaled MOSFET, for example, the majority of the heat is produced in a localized region immediately below the gate on the drain side. The size of this generation region is often smaller than the mean free path of phonons, which suggests the generation Knudsen number is large and non-continuum models are appropriate. Using a one-dimensional BTE and diffusion equation, a comparison between the continuum and non-continuum models is made. The focus of this comparative study is the behavior of each model for various Knudsen numbers for the device size and generation region. Results suggest that non-continuum distributions are similar to continuum distributions except at boundaries where the jump condition results in deviations from continuum distributions. Furthermore, the peak energy in a device predicted using the noncontinuum formulation is always less than that of the continuum model regardless of generation Knudsen number, which is in contrast to other prevailing studies.