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 alsofails 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 hydrcxjynamic 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.

The lattice Boltzmann Peierls Callaway equation for mesoscopic thermal transport modeling

The lattice Boltzmann Peierls Callaway(LBPC)method is a recent development of the versatile lattice Boltzmann formalism aimed at a numerical experiment on mesoscale thermal transport in a multiphase phonon gas.Two aspects of mesoscopic thermal trans-port are discussed:the finite phonon mean free path and the interface thermal resistance.Based on the phonon momentum screening length measured in the LBPC computa-tional apparatus,the validity of the Umklapp collision relaxation time in the Callaway collision operator is examined quantitatively.The discrete nature of the spatio-temporal domain in the LBPC method,along with the linear approximation of the exponential screening mechanism in the Callaway operator,reveals a large discrepancy between the effective phonon mean free path and the analytic phonon mean free path when the relaxation time is small.The link bounce back interface phonon collision rule is used to realize the interface thermal resistance between phonon gases with dissimilar dispersion relations.Consistent with the Callaway collision operator for the bulk phonon dynam-ics,the interface phonon collision process is regarded as a linear relaxation mechanism toward the local pseudo-equilibrium phonon distribution uniquely defined by the energy conservation principle.The interface thermal resistance is linearly proportional to the relaxation time of the proposed phonon interface collision rule.