BTE-Barna: An extension of almaBTE for thermal simulation of devices based on 2D materials

Abstract

We present BTE-Barna (Boltzmann Transport Equation -Beyond the Rta for NAnosystems), a software package that extends the Monte Carlo (MC) module of the almaBTE solver of the Peierls-Boltzmann transport equation for phonons (PBTE) to work with nanosystems based on 2D materials with complex geometries. To properly capture how the phonon occupations evolve in momentum space as a result of scattering, we have supplemented the relaxation-time approximation with an implementation of the propagator for the full linearized version of the PBTE. The code can now find solutions for finite and extended devices under the effect of a thermal gradient, with isothermal reservoirs or with an arbitrary initial temperature distribution in space and time, writing out the temperature and heat flux distributions as well as their spectral decompositions. Besides the full deviational MC solver, a number of useful approximations for highly symmetric devices are also included.

Hydrodynamic signatures in thermal transport in devices based on 2D materials: an ab initio study

“…a bit longer than the non-local length, the true value of which is expected to be larger than the one in Table I [42]. The latter suggests that phosphorene is a highly hydrodynamic material at the nanoscale, as the phonon distribution is capable of keeping its inertia even under the effect of significant intrinsic scattering.…”

“…Heat flux and temperature profiles for several Levitov configurations are obtained through the PBTE solution. Owing to the high complexity of the Levitov geometry, we use an efficient, energy-based deviational Monte Carlo approach [37][38][39][40][41] to solve the PBTE under the RTA and beyond (bRTA), implemented in BTE-Barna [42] to solve the PBTE. Atomic positions, harmonic and anharmonic interatomic force constants (IFCs), needed to compute the basic phonon properties (i.e.…”

“…Atomic positions, harmonic and anharmonic interatomic force constants (IFCs), needed to compute the basic phonon properties (i.e. : group velocities, lifetimes, frequencies) and the propagator [40,42] required for the PBTE Monte Carlo solvers, were obtained from Refs. [43] for graphene and [44] for phosphorene.…”

“…Finally, to efficiently investigate some dimensional limits and other features as the existence of vortices with magnitudes well below statistical noise caused by the intrinsic scattering algorithms [39,42], we solved Eq. (1) using finite elements package FEniCS [47,48], with its parameters extracted from cumulative curves (see the fenics.py script in the Supplemental Material [49] for further details on those calculations).…”

“…It should be noted that the theoretical formulas used to obtain the RTA iso values are derived under the assumption of isotropy and are therefore expected to be useful only as approximations in the phosphorene case. Regarding values beyond the RTA, we expect them to be higher overall as in the RTA all processes are incorrectly deemed as directly resistive [27,42]. Notwithstanding this, in the case of graphene the dominance over RTA iso of low-frequency ZA-modes in the neighborhood of Γ with extremely large mean free paths (of the order of 4 mm)to the point that when suppressed the RTA iso gets reduced from 53.9 µm to 43.5 nm-makes the qualitative prediction of the beyond-RTA-behavior much more complicated, as the proper description of scattering operator would highly affect those ZA-modes.…”