Two-channel model for nonequilibrium thermal transport in pump-probe experiments

We present an analytic solution for heat flow in a multilayer two-channel system for the interpretation of time-domain thermoreflectance (TDTR) experiments where nonequilibrium effects are important. The two-channel solution is used to analyze new room temperature TDTR measurements of Al/Cu and Al/Si sub(0.99)Ge sub(0.01) systems. Cu and Si sub(0.99)Ge sub(0.01) are examples of materials well suited for analysis with a two-channel model because thermal excitations responsible for the vast majority of the heat capacity in these solids contribute little to their thermal conductivity. Nonequilibrium effects are found to be unimportant for the interpretation of the Al/Cu TDTR data but dramatic for the Al/Si sub(0.99) Ge sub(0.01) TDTR data. The two-channel model predicts a significant reduction in the effective thermal conductivity of Si sub(0.99)Ge sub(0.01) in a region within 150 nm of the Al/Si sub(0.99)Ge sub(0.01) interface. The extra thermal resistance in this region is a result of the disparate heat flux boundary conditions for low- and high-frequency phonons in combination with weak coupling between low- and high-frequency phonons. When the experimental data are analyzed with a single-channel model, both the conductance and thermal conductivity appear to depend on pump-modulation frequency, consistent with the two-channel model's predictions. Finally, we compare the results of our diffusive two-channel model to a nonlocal description for steady-state heat flow near a boundary and show they yield nearly identical results.