Phonon scattering at kinks in suspended graphene

Abstract

Recent experiments have shown surprisingly large thermal time constants in suspended graphene ranging from 10 to 100 ns in drums with a diameter ranging from 2 to 7 microns. The large time constants and their scaling with diameter points towards a thermal resistance at the edge of the drum. However, an explanation of the microscopic origin of this resistance is lacking. Here, we show how phonon scattering at a kink in the graphene, e.g. formed by sidewall adhesion at the edge of the suspended membrane, can cause a large thermal time constant. This kink strongly limits the fraction of flexural phonons that cross the suspended graphene edge, which causes a thermal interface resistance at its boundary. Our model predicts thermal time constants that are of the same order of magnitude as experimental data, and shows a similar dependence on the circumference. Furthermore, the model predicts the relative in-plane and out-of-plane phonon contributions to graphene's thermal expansion force, in agreement with experiments. We thus show, that in contrast to conventional thermal (Kapitza) resistance which occurs between two different materials, in 2D materials another type of thermal interface resistance can be geometrically induced in a single material.

Dynamics of 2D Material Membranes

“…Since the time constants corresponding to in-plane phonons are estimated to be much smaller than that of the out-of-plane flexural phonons, the slow time-constant τ th measured in Ref. 19 is attributed to flexural phonons in combination with phonon boundary scattering effects at the boundary of the suspended drum 142 . Evidence for heat transport by fast in-plane phonons, with time-constants below the experimental detection limit, was obtained from observations of an experimental offset (see right panel of Fig.…”

“…At the edge of the drum the 2D material often makes a kink due to edge adhesion. Acoustic waves might travel across this kink from the suspended to the unsuspended part of the 2D material 142 , contributing to such acoustic radiation losses. In some cases the energy does not leave the resonance mode via the clamping points, but is transferred to other resonance modes of the same resonator via mode-coupling, which can lead to linear damping 143 but also to nonlinear damping as will be discussed in section V.…”

Tension tuning of sound and heat transport in graphene

“…We also assume kink angle β = 90 • at the edge of the membrane. Wrinkles and ripples in membrane surface can be regarded as kinks with a tiny β, of which contributions to the heat transport can be negligible since τ reduces dramatically as β decreases 27 .…”

“…The transmission probabilities for the different phonon modes (2j, j = l, t, z) at a given incident angle θ is given by Using the expression of wave amplitudes of the transmitted modes 2j (ref. 27 ), we further discuss the dependence of n and c z on u 2l , u 2l and u 2l , respectively (see Fig. S2).…”

“…To shed light on this observation, we use a phononic model to assess the transient thermal conduction in the membrane 13 . We assume in the model that the transport of flexural acoustic phonons in the membrane is ballistic, since their mean free paths are much longer than the radius r of membranes 26 , while using a scattering model 27 (see Methods and Fig. S1) to capture the tension dependent phonon transport across the kink at the edge of the membrane (Fig.…”