Thermal Conductivity of Graphene in the Hydrodynamic Regime

Abstract

The steady-state behavior of thermal transport in bulk and nanostructured semiconductors has been widely studied, both theoretically and experimentally, with an intense focus on 2-dimensional materials such as graphene and graphene nanoribbons (GNRs) in recent years. The effect of ribbon size (width and length) and temperature on steady-state thermal conductivity is now well understood. On the other hand, fast transients and frequency response of thermal conduction, sometimes called dynamical thermal conductivity, has been given less attention. The response of thermal conductivity to rapidly varying heat sources may become more crucial in the future, especially with the constant growth in the clock frequencies in microprocessors and increase in gigahertz and terahertz applications of semiconductor devices. We observe that thermal conductivity, for any given ribbon size and temperature, reaches a constant d.c. value at low frequencies of the temperature gradient, characteristic of diffusive transport. In contrast, it rapidly decays when the applied frequency exceeds the average phonon scattering rate. Between these two, hydrodynamic transport occurs; in this regime, thermal conductivity remains near its steady-state value. Overall, the frequency response of thermal conductivity resembles low-pass thermal filter. The cut-off frequency where the transition occurs depends on temperature and size: lower temperature and larger samples lead to lower cut-offs, while even at room temperature, the cut-off frequency is approximately a few gigahertz, in the range of current CPU clock frequencies. We expect dynamical thermal conductivity to play a significant role in heat removal from devices based on graphene and related 2-dimensional materials.