Non-local thermal transport modeling using the thermal distributor

Thermal transport in a quasi-ballistic regime is determined not only by the local temperature $T(r)$, or its gradient $\mathrm{\nabla }T(r)$, but also by temperature distribution at neighboring points. For an accurate description of non-local effects on thermal transport, we employ the thermal distributor, $\mathrm{\Theta }(r,r^{\mathrm{\prime }})$, which provides the temperature response of the system at point $r$ to the heat input at point $r^{\mathrm{\prime }}$. We determine the thermal distributors from the linearized Peierls-Boltzmann equation (LPBE) and the relaxation time approximation (RTA) of the Peierls-Boltzmann equation and employ them to describe thermal transport in quasi-ballistic graphene devices.