Understanding thermal boundary resistance (TBR) is becoming increasingly important for the thermal management of micro and optoelectronic devices. The current understanding of room temperature TBR is often not adequate for the thermal design of tomorrow’s complex micro and nano devices. Theories have been developed to explain the resistance to energy transport by phonons across interfaces. The acoustic mismatch model (AMM) [1, 2], which has had success at explaining low temperature TBR, does not account for the high frequency phonons and imperfect interfaces of real devices at room temperature. The diffuse mismatch model (DMM) was developed to account for real surfaces with higher energy phonons [3, 4]. DMM assumes that all phonons incident on the interface from both sides are elastically scattered and then emitted to either side of the interface. The probability that a phonon is emitted to a particular side is proportional to the phonon density of states of the two interface materials. Inherent to the DMM is that the transport is independent of the interface structure itself and is only dependent on the properties of the two materials. Recent works have shown that the DMM does not adequately capture all the energy transport mechanisms at the interface [5, 6]. In particular, the DMM under-predicts transport across interfaces between non Debye-like materials, such at Pb and diamond, by approximately an order of magnitude. The DMM also tends to over-predict transport for interfaces made with materials of similar acoustic properties, Debye-like materials. There have been several explanations and models developed to explain the discrepancies between the mismatch models and experimental data. Some of these models are based on modification of the AMM and DMM [7–9]. Other works have utilized lattice-dynamical modeling to calculate phonon transmission coefficients and thermal boundary conductivities for abrupt and disordered interfaces [3, 6, 10–13]. Recent efforts to better understand room temperature TBR have utilized molecular dynamics simulations to account for more realistic anharmonic materials and inelastic scattering [14–18]. Models have also been developed to account for electron-phonon scattering and its effect on the thermal boundary conductance for interfaces with one metal side [19–22]. Although there have been numerous thermal boundary resistance theoretical developments since the introduction of the AMM, there still is not an unifying theory that has been well validated for high temperature solid-solid interfaces. Most of the models attempt to explain some of the experimental outliers, such as Pb/diamond and TiN/MgO interfaces [6, 23], but have not been fully tested for a range of experimental data. Part of the problem lies in the fact that very little reliable data is available, especially data that is systematically taken to validate a particular model. To this end, preliminary measurements of TBR are being made on a series of metal on non-metal substrate interfaces using a non-destructive optical technique, transient thermal reflectance (TTR) described in Stevens et al. [5]. Initial testing examines the impact of different substrate preparation and deposition conditions on TBR for Debye-like interfaces for which TBR should be small for clean and abrupt interfaces. Variables considered include sputter etching power and duration, electron beam source clean, and substrate temperature control. The impact of alloying and non-abrupt interfaces on the TBR is examined by fabricating interfaces of both Debye-like and non Debye-like interfaces followed by systematically measuring TBR and altering the interfaces by annealing the samples to increase the diffusion depths at the interfaces. Inelastic electron scattering at the interface has been proposed by Hubermann et al. and Sergeev to decrease TBR at interfaces [19–21]. Two sets of samples are prepared to examine the electron-phonon connection to improved thermal boundary conductance. The first consists of thin Pt and Ag films on Si and sapphire substrates. Pt and Ag electron-phonon coupling factors are 60 and 3.1×1016 W/m3K respectively. Both Pt and Ag have similar Debye temperatures, so electron scattering rates can be examined without much change in acoustic effects. The second electron scattering sample series consist of multiple interfaces fabricated with Ni, Ge, and Si to separate the phonon and electron portions of thermal transport. The experimental data is compared to several of the proposed theories.
Electrical Contact Resistance, Thermal Contact Conductance and Elastic Incremental Stiffness for a Cluster of Microcontacts: Asymptotic Modelling