Controlling thermal conductance through quantum dot roughening at interfaces

Abstract

We examine the fundamental phonon mechanisms affecting the interfacial thermal conductance across a single layer of quantum dots (QDs) on a planar substrate. We synthesize a series of Ge${}_{x}$Si${}_{1\ensuremath{-}x}$ QDs by heteroepitaxial self-assembly on Si surfaces and modify the growth conditions to provide QD layers with different root-mean-square (rms) roughness levels in order to quantify the effects of roughness on thermal transport. We measure the thermal boundary conductance (${h}_{\mathrm{K}}$) with time-domain thermoreflectance. The trends in thermal boundary conductance show that the effect of the QDs on ${h}_{\mathrm{K}}$ are more apparent at elevated temperatures, while at low temperatures, the QD patterning does not drastically affect ${h}_{\mathrm{K}}$. The functional dependence of ${h}_{\mathrm{K}}$ with rms surface roughness reveals a trend that suggests that both vibrational mismatch and changes in the localized phonon transport near the interface contribute to the reduction in ${h}_{\mathrm{K}}$. We find that QD structures with rms roughnesses greater than 4 nm decrease ${h}_{\mathrm{K}}$ at Si interfaces by a factor of 1.6. We develop an analytical model for phonon transport at rough interfaces based on a diffusive scattering assumption and phonon attenuation that describes the measured trends in ${h}_{\mathrm{K}}$. This indicates that the observed reduction in thermal conductivity in SiGe quantum dot superlattices is primarily due to the increased physical roughness at the interfaces, which creates additional phonon resistive processes beyond the interfacial vibrational mismatch.