Models intended to predict interfacial transport often rely on the principle of detailed balance when formulating the interfacial carrier transmission probability. However, assumptions invoked significantly impact predictions. Here, we present six derivations of the transmission probability, each subject to a different set of preliminary assumptions regarding the type of scattering at the interface. Application of each case to phonon flux and thermal boundary conductance allows for a final quantitative comparison. Depending on the preliminary assumptions, predictions for thermal boundary conductance span over two orders of magnitude, demonstrating the need for transparency when assessing the accuracy of any predictive model.

With the characteristic lengths of electronic and thermal devices approaching the mean free paths of the pertinent energy carriers, thermal transport across these devices must be characterized and understood, especially across interfaces. Thermal interface conductance can be strongly affected by the strength of the bond between the solids comprising the interface and the presence of an impurity mass between them. In this work, we investigate the effects of impurity masses and mechanical adhesion at molecular junctions on phonon transmission via non-equilibrium Green's functions (NEGF) formalisms. Using NEGF, we derived closed form solutions to the phonon transmission across an interface with an impurity mass and variable bonding. We find that the interface spring constant that yields the maximum transmission for all frequencies is the harmonic mean of the spring constants on either side of the interface, while for a mass impurity, the arithmetic average of the masses on either side of the interface yields the maximum transmission. However, the maximum transmission for each case is not equal. For the interface mass case, the maximum transmission is the transmission predicted by a frequency dependent form of the acoustic mismatch model, which we will refer to as the phonon mismatch model (PMM), which is valid for specular phonon scattering outside the continuum limit. However, in the interface spring case, the maximum transmission can be higher or lower than the transmission predicted by the PMM. V

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We explore the physics of thermal impedance matching at the interface between two dissimilar materials by controlling the properties of a single atomic mass or bond. The maximum thermal current is transmitted between the materials when we are able to decompose the entire heterostructure solely in terms of primitive building blocks of the individual materials. Using this approach, we show that the minimum interfacial thermal resistance arises when the interfacial atomic mass is the arithmetic mean, while the interfacial spring constant is the harmonic mean of its neighbors.The contact induced broadening matrix for the local vibronic spectrum, obtained from the selfenergy matrices, generalizes the concept of acoustic impedance to the nonlinear phonon dispersion or the short-wavelength (atomic) limit. * cap3fe@virginia.edu † ag7rq@virginia.edu Today's experimental techniques are opening up the possibility of tuning thermal conductivity of materials by engineering their thermal impedance at the nanoscale [1]. At these characteristic lengths (∼10nm), thermal boundary conductance (TBC) of interfaces provide a major contribution to the thermal conductance of the system, making critical the understanding of impedance matching at interfaces. Phonon transport across an interface is a convoluted process that involves the differing phonon modes, the short coherence lengths of the quantized vibrations and their broadband transport properties. Also, it involves complex and diverse interfacial atomic structures that depend strongly on materials and fabrication protocols. Several experiments [2-9] and simulations [10-15] have already shown the dependence of TBC with interfacial impurities, mixing, defects, chemistry or bond strength.Nevertheless, the standard models to calculate TBC, the acoustic mismatch model [16] and the diffuse mismatch model [17], completely neglect the properties of the interface. Although some work has been done to include those properties into a model [9,[18][19][20][21], a proper identification of the key physics determining TBC is still incomplete but it is crucial for impedance matching design at the nanoscale. This will lead the emerging field of phonon engineering to follow the successful steps of electronics and photonics, where engineering of nanoscale properties has endowed the fields with high degrees of tunability.While the overall goal of our study is to explore the physics of thermal impedance matching at interfaces covering the entire gamut from 1D to 3D, from linear to non linear dispersion and from coherent to incoherent transport, we will start building our intuition by studying coherent thermal impedance matching between two dissimilar 1D materials by controlling the properties of a single mass (Fig. 1a) or spring (Fig. 1b) in between. This toy model presents a starting point to understand ballistic contributions to TBC by important factors already identified in the literature, like interfacial impurities, mixing, defects, chemistry or bond strength [2-6, 8, 9, 19]. In fact, some authors...