Geometrical quasi-ballistic effects on thermal transport in nanostructured devices

We employ thermoreflectance thermal imaging to directly measure the steady-state two-dimensional (2D) temperature field generated by nanostructured heat sources deposited on silicon substrate with different geometrical configurations and characteristic sizes down to 400nm. The analysis of the results using Fourier’s law not only breaks down as size scales down, but it also fails to capture the impact of the geometry of the heat source. The substrate effective Fourier thermal conductivities fitted to wire-shaped and circular-shaped structures with identical characteristic lengths are found to display up to 40% mismatch. Remarkably, a hydrodynamic heat transport model reproduces the observed temperature fields for all device sizes and shapes using just intrinsic Si parameters, i.e., a geometry and size-independent thermal conductivity and nonlocal length scale. The hydrodynamic model provides insight into the observed thermal response and of the contradictory Fourier predictions. We discuss the substantial Silicon hydrodynamic behavior at room temperature and contrast it to InGaAs, which shows less hydrodynamic effects due to dominant phonon-impurity scattering.