in Fig. \[fig:TDTR\_sensitivity\] (b). The figure shows that they are nearly identical even though the two transmission coefficient profiles are completely different, demonstrating that in the diffusion regime the TDTR signal only depends on the magnitude of interface conductance.

On the other hand, in the quasiballistic regime the TDTR signal is sensitive to the shape of the transmission coefficient profile, enabling the coefficients to be obtained with tight constraints. We demonstrate this sensitivity in Fig. \[fig:TDTR\_sensitivity\] (c). For this calculation, the same transmission coefficient profiles are used but the bulk scattering rates of Si from Lindsay et al are used without modification. The longest MFP in silicon is on the order of micrometers, [@Broido2007; @Cuffe2014] and the characteristic length scale of a TDTR experiment with a modulation frequency around 1 MHz is also on the order of a micron. Therefore, the transport in the TDTR experiment for Al/Si is quasiballistic. In this case, the TDTR signals using two different transmission coefficient profiles are no longer identical as shown in Fig. \[fig:TDTR\_sensitivity\] (c), demonstrating that in the quasiballistic regime the TDTR signal is sensitive to both the magnitude of interface conductance and the spectral profile.

Fig. \[fig:TDTR\_sensitivity\] (c) plots a measured 