Length-dependent thermal conductivity in suspended single-layer graphene

Abstract: Graphene exhibits extraordinary electronic and mechanical properties, and extremely high thermal conductivity. Being a very stable atomically thick membrane that can be suspended between two leads, graphene provides a perfect test platform for studying thermal conductivity in two-dimensional systems, which is of primary importance for phonon transport in low-dimensional materials. Here we report experimental measurements and non-equilibrium molecular dynamics simulations of thermal conduction in suspended single layer graphene as a function of both temperature and sample length. Interestingly and in contrast to bulk materials, when temperature at 300K, thermal conductivity keeps increasing and remains logarithmic divergence with sample length even for sample lengths much larger than the average phonon mean free path. This result is a consequence of the two-dimensional nature of phonons in graphene and provides fundamental understanding into thermal transport in two-dimensional materials.

• The paper presents a novel finding that thermal conductivity in graphene scales logarithmically with sample length, countering classical Fourier’s law in 2D materials.
• The authors combined experimental measurements with NEMD simulations to determine conductivity values between 1689 ±100 and 1813 ±111 Wm⁻¹K⁻¹ at 300 K.
• The study indicates that quasi-ballistic phonon transport in submicron graphene samples suggests new strategies for thermal management in nanoscale devices.

Length-Dependent Thermal Conductivity in Suspended Single Layer Graphene

The investigation of thermal conductivity in two-dimensional materials has yielded insightful results, particularly in the field of graphene. The paper "Length-dependent thermal conductivity in suspended single layer graphene" presents a comprehensive study that explores the relationship between sample length and thermal conductivity. The study spans both experimental measurements and non-equilibrium molecular dynamics (NEMD) simulations to address the novel thermal transport properties of graphene, particularly focusing on its two-dimensional nature.

In contrast to three-dimensional bulk materials where thermal conductivity is typically independent of size and geometry—as corroborated by Fourier’s Law—the study enunciates a distinct length dependency in two-dimensional systems, epitomized by graphene. Specifically, at room temperature (300 K), the thermal conductivity of graphene demonstrates a logarithmic divergence, scaling approximately as κ ~ logL with sample length (L). This behavior persists even when L exceeds the phonon mean free path (MFP) by an order of magnitude, underlying the significant role of the two-dimensional phononic architecture in graphene.

Empirical Findings and Methodology

The research meticulously details the methodology employed in the empirical and simulation phases. The single layer graphene (SLG) used in the study was grown via chemical vapor deposition on copper (Cu-CVD). The employed methodology effectively corroborates the length-dependent thermal conductivity through extensive experimental setups which include measurements of total thermal resistance and consideration of thermal contact resistance. The research delineates that the thermal conductivity of SLG exhibits values around (1689 ±100) Wm$^{-1}$K$^{-1}$ to (1813 ±111) Wm$^{-1}$K$^{-1}$ at 300 K in the longest sample studied (L = 9 μm). These values align well with those determined through Raman spectroscopy, strengthening the credibility of the findings.

In the field of quasi-ballistic phonon transport—a transport regime characterized by minimal phonon scattering—the study investigates submicron-range samples where phonons exhibit nearly ballistic behavior. Notably, the experimental observations indicating length-independent thermal conductance support theoretical anticipations of ballistic transport in graphene under appropriate conditions.

Simulation Insights

The NEMD simulations augmented the experimental investigation by allowing the probing of ideal, defect-free graphene structures. These simulations reaffirmed the empirical results, exhibiting a κ~logL scaling behavior at both 300 K and 1000 K. This sustained logarithmic divergence at varying temperatures underscores a fundamental characteristic of heat transport in suspended SLG under stationary non-equilibrium conditions. In the simulations, the decrease in thermal conductance for sizes extending beyond the ballistic transport regime, while still following logarithmic divergence, elucidates the complex phonon interactions in low-dimensional materials.

Implications and Future Directions

The insights gleaned from this study have significant implications for the theoretical understanding and practical application of graphene and similar low-dimensional materials. The observed length dependency of thermal conductivity challenges the conventional application of Fourier’s law to two-dimensional materials and calls for refined theoretical frameworks that incorporate the intrinsic properties of phonons in such media.

Practically, the recognition of length-dependent thermal transport opens avenues for optimizing thermal management in nanoscale devices using graphene, where precise control over heat conduction is critical. Considering the potential for extensive use in electronic and thermal devices, further studies exploring the contribution of phonons across different frequency domains and extending sample size to the macroscopic domain could enrich our understanding of thermal transport mechanisms in graphene. This would necessitate advancements in measurement techniques to manage the inherent challenges in studying larger graphene samples.

In conclusion, this paper presents a robust confirmation of the unusual thermal properties of graphene, dominated by phononic interactions in its two-dimensional framework. The consistent findings across both experimental and simulation domains provide a profound basis for future studies elucidating the broader implications of length-dependent thermal conductivity in low-dimensional materials.