## 2 Theoretical Methods for TBR Prediction and Experimental Methods for TBR Measurement
### Theoretical and Computational Methods for TBR Prediction
More details about the thermal transport in single molecules, single molecule junctions, and self-assembled monolayers are available in some review articles [41; 42]. Figure 2: (**a**) Effects of surface roughness on the TBC of Al/Si interfaces. AFM 3D surface profiles for samples 1a (**left**) and 2 (**middle**) prepared using different pre-Al-deposition surface treatments. TDTR data comparison (**right**) shows that the TBC decreases with increasing Si surface roughness (reprinted from Ref. [30]. Reproduced with permission from the American Physical Society (APS). All rights reserved). (**b**) Bonding-induced TBC enhancement using organic nanomolecular monolayer (NML). TDTR data comparison (**left**) for Cu/SiO\({}_{2}\) interfaces without, and with, a CH\({}_{3}\)- or an SH-terminated NML. The TBC as a function of interfacial toughness (**middle**). Phonon DOS of the Cu, SiO\({}_{2}\), and SH-NML layers in Cu-NML-SiO\({}_{2}\) structures produced using MD simulations (**right**) (reprinted from Ref. [39]. Reproduced with permission from Springer Nature publishing. All rights reserved). (**c**) Effects of interfacial termination chemistries on the TBR between a transfer-printed gold film and a self-assembled monolayer (SAM). Depiction of the experimental system consisting of a Qz substrate, bifunctional SAM, and transfer-printed Au layer. List of all SAM chemistries studied and abbreviations used in the text. (**left**). TDTR data comparison for Au/CH\({}_{3}\)–C11–Si=Qz and Au/SH–C11–Si=Qz structures (**middle**). The TBC as a function of the methyl:thiol end-group ratio for 0%, 25%, 50%, 75%, and 100% thiol end groups (**right**) (reprinted from Ref. [40]. Reproduced with permission from Springer Nature publishing. All rights reserved). Molecular dynamics (MD) simulation is the predominant computational approach for predicting TBR [43; 44; 45]. Such simulations do not rely on assumptions about the nature of phonon scattering; instead, they require only a description of the atomic interactions as input. However, it remains challenging to establish an appropriate description of atomic interactions that can be applied to diverse systems. Consequently, Si and Ge are frequently chosen as study systems for investigating the TBR in MD simulations. This choice is driven primarily by the availability of reliable interatomic potentials that can accurately replicate the forces experienced by the actual atoms [17]. Figure 3a shows the temperature dependence and size effect of the TBR of Si/Ge interfaces calculated using MD simulations. The MD simulations, limited to the input of atomic interactions, do not allow for the investigation of the contributions of electrons or the effects of electron-phonon coupling on the TBR. In contrast, first-principles calculations can accurately capture the dynamics of various energy carriers, such as electrons, phonons, and magnons, as well as their interactions [46; 47]. However, the first-principles calculation method is computationally demanding and time consuming. In recent years, machine learning has emerged as a novel approach for TBR prediction [48; 49; 50; 51; 52; 53; 54; 55; 56; 57], and it has been demonstrated to achieve higher predictive accuracy than the conventionally used AMM and DMM methods [48]. Figure 3b shows the comparison of the correlation between the experimental values and the values predicted by the AMM, DMM, and machine learning method using Gaussian process regression (GPR). However, a lack of available experimental TBR results as training data limits the accuracy of the predictions of this method, as the size of a training dataset is a crucial aspect in determining the quality of the prediction performance in machine learning. Figure 3: (**a**) Calculation of TBR of Si/Ge interfaces using MD simulations. TBR calculation by least squares linear regression analysis of the temperature profile (**left**). Temperature dependence and size effect of the TBR of Si/Ge interfaces (**right**) (reprinted from Ref. [45]. Reproduced with permission from AIP publishing.