Influence of Interfacial Mixing on Thermal Boundary Conductance Across a Chromium/Silicon Interface

The thermal conductance at solid-solid interfaces is becoming increasingly important in thermal considerations dealing with devices on nanometer length scales. Specifically, interdiffusion or mixing around the interface, which is generally ignored, must be taken into account when the characteristic lengths of the devices are on the order of the thickness of this mixing region. To study the effect of this interfacial mixing on thermal conductance, a series of Cr films is grown on Si substrates subject to various deposition conditions to control the growth around the $Cr∕Si$ boundary. The $Cr∕Si$ interfaces are characterized with Auger electron spectroscopy. The thermal boundary conductance $(hBD)$ is measured with the transient thermoreflectance technique. Values of $hBD$ are found to vary with both the thickness of the mixing region and the rate of compositional change in the mixing region. The effects of the varying mixing regions in each sample on $hBD$ are discussed, and the results are compared to the diffuse mismatch model (DMM) and the virtual crystal DMM (VCDMM), which takes into account the effects of a two-phase region of finite thickness around the interface on $hBD$⁠. An excellent agreement is shown between the measured $hBD$ and that predicted by the VCDMM for a change in thickness of the two-phase region around the interface.