Hydrodynamic thermal transport in suspended graphene ribbons

The steady-state behavior of thermal transport in bulk and nanostructured semiconductors has been widely studied, both theoretically [4] and experimentally [1], 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 giga- and terahertz applications of semiconductor devices. It has been theoretically predicted in 3-D materials that thermal conductivity in response to a time-varying temperature gradient starts decaying when the frequency of the applied heat source (Ω) exceeds a certain cut-off frequency uc, which was found to be related to the inverse of the average phonon relaxation time T C . The phonon relaxation time in bulk semiconductors such as silicon is short, on the order of 2–10 ps, leading to thermal conductivity that is independent of frequency up to very high ii c exceeding 10 GHz. In contrast, 2-D materials like graphene have much longer phonon relaxation times, especially below room temperature. Therefore, in suspended graphene and wide graphene ribbons, Ω c can be expected to be much lower than that of silicon. Moreover, the presence of strong momentum-conserving normal phonon-phonon processes, overshadowing the momentum-destroying umklapp processes in graphene results in hydrodynamic transport [2] where heat does not diffuse but rather propagates in a wavelike fashion, giving rise to the second sound phenomenon[7].