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

While there is increasing effort to improve the efficiency of electronic devices made of 2D materials, thermal management remains a significant challenge. Due to their large aspect ratio, most of the heat dissipation is through the substrate. Roughness at the interface introduces sections of non-contact where the mechanical properties of 2D materials and the adhesion to substrate dictate how well they conform to the substrate. However, the impact of roughness to the TBC is not fully understood. Here, we explore the impact of roughness on TBC and demonstrate that by engineering surface slope, TBC can be significantly improved. We show that the fraction of delaminated material increases with increasing surface slope, where the slope of the rough substrates surface depends on the ratio of its rms roughness and lateral correlation length. On the ohter hand, the van der Waals coupling constants increases because of reduced distance near the peaks in the substrate roughness, driving up local TBC and resulting in higher effective TBC. We find that in-plane thermal conductivity helps spread heat along the sheet reducing the variation of temperature by up to 98.9 % when in-plane thermal conductivity is increased from 10 W/mK to 1000 W/mK. For TMDs, we find that roughness induces more variation in the substrate distance due to their larger bending rigidity compared to graphene. In addition, the low in-plane thermal conductivity hinders heat spreading along the sheets, which leads to lower effective TBC for MoS₂ on rough SiO₂ substrates.