Thermal transport modeling of nanoscale graphene devices using a Peierls-Boltzmann treatment

In nonmagnetic insulators, phonons are the carriers of heat. If heat enters in a region and temperature is measured at a point within a phonon mean free paths of the heated region, ballistic propagation causes a nonlocal relation between local temperature and heat insertion. Our work focuses on the solution of the Peierls-Boltzmann equation (PBE) for nanoscale graphene devices. We use a realistic anharmonic scattering potential and examine different approximations such as the relaxation time approximation and the definition of local temperature. The results illustrate the expected local (diffusive) response for minimum phonon mean free path lambda_min<<L, and a diffusive to ballistic crossover as lamba_min increases toward the scale of the device size L.