# Violation of Fourier's law in homogeneous systems

## TL;DR

This paper investigates the physical mechanisms behind the formation of hotspots and graded thermal conductivity in homogeneous nanoscale systems, revealing that limited phonon scattering leads to these phenomena regardless of material or size.

## Contribution

It provides a detailed analysis of phonon scattering effects on thermal conductivity in homogeneous nanoscale systems using phonon Boltzmann transport equation.

## Key findings

- Graded thermal conductivity occurs with insufficient phonon scattering.
- The phenomenon is independent of material properties and system size.
- Insights aid understanding of heat dissipation in microelectronics.

## Abstract

Hotspot is a ubiquitous phenomenon in microdevices/chips. In homogeneous nanoscale graphene disk with a hotspot, a graded thermal conductivity is observed previously even when the system size is fixed. However, the underlying physical mechanism is not clear. In this work, the hotspots in homogeneous 2D disk/3D ball and graphene disk are studied based on phonon Boltzmann transport equation. The mechanisms of phonon scattering are analyzed. It is found that for a system with fixed size, the graded thermal conductivity is predictable as long as there is not sufficient phonon scattering, which is independent on material properties, dimensions or system size. This work may shed light on both theoretical and experimental studies on heat dissipation of microelectronics.