Modeling quasiballistic phonon transport from a cylindrical electron beam heat source

Electron microscopy experiments use focused electron beams as nanoscale heat sources or thermometers. However, when the electron beam radius is smaller than the heat carrier mean free path, Fourier’s law will underpredict the electron-beam induced heating. Here, beam heating in nonmetallic samples is modeled by applying a general solution of the Boltzmann Transport Equation (BTE) under the relaxation time approximation [Hua and Minnich, PRB 90.21 (2014): 214306]. BTE results show that ballistic phonon effects in this radial heat spreading scenario are conveniently represented using a ballistic thermal resistance. Calculations of this ballistic resistance for Si, GaAs, and 3C-SiC show that ballistic effects dominate the total thermal resistance for typical beam radii (<10 nm), indicating that the ballistic resistance could be measured using electron beam heating experiments. However, the magnitude of the temperature rise remains small (<1 K), even when considering these ballistic effects. These BTE modeling results can be used to quantify electron-beam induced heating or to design experiments probing ballistic phonon transport using electron beam heat sources.

Ref.: Wehmeyer, Journal of Applied Physics 126, 124306 (2019).