Impact of Substrate Roughness on the Thermal Boundary Conductance in 2D Materials

Abstract

Heat dissipation and thermal management are key challenges for further adopting two-dimensional (2D) materials in nanoelectronics. Due to their large aspect ratio, most heat removal is through the substrate. Atomic-scale roughness at the surface of the substrate, together with the mechanical properties and the adhesion of 2D materials to the substrate, dictates how well 2D sheets conform and transfer heat to the substrate. However, a complete understanding of the combined impact of these factors on the thermal boundary conductance (TBC) of 2D/substrate interfaces is lacking. Here, we have used a numerical model to explore the TBC of interfaces between single layers of graphene, hBN, and MoS₂ and rough a-SiO₂ substrate. Our study shows that the effect of roughness on TBC depends on the average surface slope, defined as the ratio of rms roughness height and correlation length (Δ_rms/L_cor), rather than Δ_rms alone. We find that 2D materials conform well to a rough substrate when the surface slope is small and that the effective TBC remains unchanged. However, steep surface slope (Δ_rms/L_cor > 0.1), caused by large roughness or short lateral correlation length, makes the 2D material partially delaminate from the substrate, leading to variations in van der Waals (vdW) spring coupling constant (K_s). For interfaces with weak adhesion, outlier K_s values lead to an enhancement in the effective TBC by up to 12% compared to that of a flat interface, provided the in-plane thermal conductivity of the 2D sheet is sufficient (>1 Wm^1– K^–1) to spread the heat effectively. For interfaces with strong adhesion, we show that it is necessary that the slope remains below 0.1. Beyond this, the 2D material gets delaminated and coupling is weakened, resulting in a lower effective TBC. Therefore, our work provides essential information that will contribute to designing electronic devices with more efficient thermal management.