Boltzmann equation modeling of thin-film quasiballistic phonon transport from a cylindrical electron beam heat source

Electron beams with sub-10 nm diameters can be used as nanoscale heaters or thermometers, enabling new techniques to probe heat transfer in nanostructures. However, since the electron beam diameter is often smaller than the energy carrier mean free path, using Fourier’s law will underpredict the temperature rise due to electron-beam induced heating. Here, we solve the Boltzmann transport equation (BTE) under the relaxation time approximation to quantify electron-beam induced heating in thin dielectric samples. In both thin and thick samples, the full BTE solution is in agreement with a simple “resistors in series model” that sums the ballistic resistance and the typical Fourier conduction resistance (considering the thin-film size effect). For nanoscale thermometry applications, the temperature rise under typical imaging conditions is predicted to remain negligibly small (<1 K), even when considering the dominant ballistic thermal resistance. Therefore, this BTE modeling indicates that nanoscale thermometry methods are not expected to display electron beam heating artifacts, but that the ballistic resistance can be important in experiments using nanoscale heat sources.

Ref: Wehmeyer, J. of Appl. Phys. 126, 124306 (2019).