Principal Role of Contact-Force Distribution in Determining the Thermal Conductivity of Supported Graphene

The thermal conductivity ($\kappa$) of graphene dramatically decreases once supported on a substrate, hindering its use for thermal management. To clarify the underlying mechanisms, we investigate the $\kappa$ of graphene on amorphous ${\mathrm{SiO}}_2$ by using molecular dynamics with particular attention to the graphene-substrate topography. Our analysis reveals that the suppression in $\kappa$ increases with the nonuniformity of the forces acting on graphene, which tends to increase as the substrate-surface roughness and graphene conformity increase. Our findings highlight the importance of the interfacial morphology on $\kappa$ and can provide guidance on the design of substrates to improve thermal transport through graphene.

Figure 1

Schematic demonstrating the evolution of the topography of graphene due to internal and external forces. Thermal perturbation of perfectly flat graphene induces local internal strain and thereby yields corrugated graphene; the internal strain can be described by the strain energy ($E_{\mathrm{st}}$) and strain force ($f_{\mathrm{st}}$). The presence of a substrate introduces vdW interactions at the interface which further influence the graphene morphology; the vdW coupling can be described by the vdW energy ($E_{\mathrm{vdW}}$) and vdW force ($f_{\mathrm{vdW}}$). The gray sheet represents graphene, while the yellow and red balls represent Si and O atoms, respectively, in amorphous ${\mathrm{SiO}}_2$ ($a\text{−}{\mathrm{SiO}}_2$).

Figure 2

Thermal conductivity ($\kappa$) as a function of surface roughness (${\sigma }_{\mathrm{z}}$); for freestanding graphene (red squares), ${\sigma }_z$ refers to the corrugation of graphene (${\sigma }_{z,\mathrm{gr}}$), while for supported graphene (green triangles and blue circles), ${\sigma }_z$ refers to the substrate surface roughness (${\sigma }_{z,\text{sub}}$). The inset compares ${\sigma }_{z,\mathrm{gr}}$ to that of ${\sigma }_{z,\text{sub}}$ for each supported graphene case; points far below the black diagonal line indicate poor conformity.

Figure 3

Relationship between the standard deviation of the applied vdW and strain force (${\sigma }_{\text{force}}$) and the thermal conductivity ($\kappa$).

Figure 4

Spatial distribution of eigenmodes with phonon participation ratio $<0.3$ ($|{\mathrm{\Phi }}_z|$) for the (a) graphe/quartz, (b) nonconformed $\text{graphene}/a\text{−}{\mathrm{SiO}}_2$, and (c) optimally conformed $\text{graphene}/a\text{−}{\mathrm{SiO}}_2$ cases. Color maps of the spatially resolved distance between graphene and the substrate for the (d) graphene/quartz, (e) nonconformed $\text{graphene}/a\text{−}{\mathrm{SiO}}_2$, and (f) optimally conformed $\text{graphene}/a\text{−}{\mathrm{SiO}}_2$ cases.