Interfacial Thermal Boundary Conductance

• Interfacial TBC is defined as the ratio of heat flux to temperature drop at material interfaces, quantifying energy transfer in MW·m⁻²·K⁻¹.
• Advanced experimental techniques and atomistic simulations reveal that phonon transmission and electron–phonon coupling critically modulate TBC.
• Enhanced TBC improves nanoscale thermal management, semiconductor device reliability, and performance in high-power electronics and 2D systems.

Interfacial Thermal Boundary Conductance (TBC) quantifies the ability of heat to flow across the interface of two dissimilar materials, playing a central role in nanoscale thermal management, semiconductor device reliability, and the engineering of multilayered and composite systems. TBC is fundamentally governed by the transmission and reflection of vibrational energy carriers—phonons (and, in the case of metals, electrons)—at the atomic junction where bonding, mixing, disorder, and electronic structure can all critically alter the microscopic heat flow. The field has evolved rapidly, with precise experimental measurements and advanced atomistic simulations revealing mechanisms well beyond the scope of classical, continuum-based models.

1. Fundamental Definition and Theoretical Frameworks

Thermal boundary conductance is rigorously defined as the ratio of the steady-state heat flux, $q$ (W·m⁻²), across an interface to the temperature discontinuity, $\Delta T$ (K), at the interface: $G = \frac{q}{\Delta T}$ This phenomenological description is extended microscopically using Landauer-type or diffuse mismatch formalisms, wherein the conductance is expressed in terms of phononic and electronic eigenmodes: $$G = \sum_p \int_0^{\omega_{\rm max}} \hbar \omega D_{1,p}(\omega) v_{1,p}(\omega) \alpha_{1\to 2,p}(\omega) \frac{\partial n(\omega,T)}{\partial T} d\omega$$ Here, $p$ denotes polarization, $D_{i,p}$ the phonon density of states (DOS), $v_{i,p}$ the group velocity, $n(\omega,T)$ the Bose–Einstein occupation, and $\alpha_{1\to 2,p}(\omega)$ the spectral transmission coefficient. The two dominant harmonic models for $\alpha$ are:

• Acoustic Mismatch Model (AMM): Specular, elastic transmission based on continuum acoustic impedance, $Z=\rho v$.
• Diffuse Mismatch Model (DMM): Diffuse, incoherent scattering governed by transmitted and available vibrational modes, with $\alpha$ given by ratios of DOS and velocities on each side.

For metals and certain nonmetals the electron–phonon channel must also be considered (see Section 4).

2. Phonon Transmission, Interfacial Structure, and Emergent Vibrational Modes

A central insight from atomic-scale simulations and high-resolution spectroscopies is that bulk-based theories (AMM/DMM) frequently fail to quantitatively predict room-temperature TBC, especially at amorphous, mixed, or highly epitaxial junctions. The discrepancy arises from:

• Interfacial localized phonon modes: Experimental EELS and Raman studies at Si–Ge interfaces have identified vibrational modes at $\sim12$ THz, confined within a $\sim1.2$ nm region, that do not exist in either bulk material. These contribute directly to TBC, comprising up to 5% of the measured conductance (Cheng et al., 2021).
• Disordered interfaces and defect engineering: Introduction of small-mass defects (i.e., atomic nitrogen) at the a-SiOC:H/a-SiC:H boundary increases the fraction of interfacial modes from $1.1\%$ to $4.0\%$, specifically populating the 20–40 THz range where amorphous thermal phonons dominate (Giri et al., 2017). This results in ultrahigh TBC values, approaching or exceeding $1$ GW·m⁻²·K⁻¹, unprecedented for diffusive, non-crystalline interfaces.

The emergence and control of such interface-specific vibrations—rather than perturbations of bulk states—establish new physical channels for energy transfer across otherwise resistive boundaries.

3. Quantitative TBC Values and Mechanistic Insights Across Materials Systems

TBC varies strongly with material choice, interfacial bonding, and structural quality. Salient results across representative classes include:

System	Measured/Simulated TBC (MW·m⁻²·K⁻¹)	Mechanistic Origin
a-SiOC:H/a-SiC:H (N defects)	$\gg 1,000$	High-frequency interfacial modes via mass defects
Epitaxial ZnO/GaN	490 +150, –110	Inelastic transport, zone-center, high overlap modes
Metal/diamond: Al, Zr, Mo, Au	316, 88, 52, 55 (sim)	Phonon spectrum matching, weak interfacial coupling
h-BN/FePt	$68 \pm 7$	vdW bonding, low c-axis phonon DOS
2D MoS₂/SiO₂, WS₂/SiO₂	13.5, 12.4 (diffuse theory/sim)	Dominated by diffuse flexural-phonon scattering
h-BN/graphene	35.1	Flexural ZA/c-axis LA mode transmission
Si/SiC (bonded+annealed)	293	Oxide-free, crystallized, specular transmission
GaN/diamond (bonded+annealed)	71–86	Crystallized Si interlayer, reduced interface mixing

For metal/diamond and ceramic interfaces, TBC is often limited by insufficient mode overlap and weak bonding, as established by machine-learning molecular dynamics (Adnan et al., 2024). In contrast, amorphous and chemically mixed semiconductor contacts are increasingly found to exhibit ultrahigh TBC, compatible with the formation of localized bridging modes (Giri et al., 2017, Cheng et al., 2021).

4. Multi-channel Energy Transfer: Electron–Phonon, Phonon–Phonon, and Interlayer Mediation

TBC in metal–dielectric and metal–semiconductor systems can be carried by:

• Phonon–phonon transmission at the interface
• Electron–phonon coupling at the interface (inelastic, non-bulk)
• Energy transfer via the sequence: electron–phonon (within metal) followed by phonon–phonon at the interface

An analytic series–parallel resistor network partitions the total conductance (Li et al., 2014): $$G_{\rm tot} = \left( R_e + R_{ep} \right)^{-1} + \left( R_p + R_{pp} \right)^{-1}$$ Where $R_e$ and $R_p$ arise from renormalized electronic and lattice conduction in the metal over a “Kapitza length”. $R_{ep}$ and $R_{pp}$ are the interfacial electron–phonon and phonon–phonon resistances, respectively.

Direct electron–phonon interfacial coupling ($\sigma_e$), sometimes exceeding the phononic channel ($\sigma_p$), can enhance TBC significantly in thick films with strong bulk electron–phonon coupling (Lombard et al., 2015). For ultra-thin films or weak coupling, the internal electron–phonon relaxation becomes rate-limiting.

Insertion of ultrathin metal interlayers (e.g., Ni, Ta) provides tunability of TBC via modulation of phonon spectrum overlap and electron–phonon strength. Strong coupling (Ta, $g\sim 3\times10^{19}$ W/(m³K)) results in sharp transitions; weak coupling (Ni, $g\sim 3.6\times10^{17}$ W/(m³K)) yields smoother modulation and local minima related to phonon dispersion matching (Oommen et al., 2019).

5. Environmental, Interlayer, and Topographical Effects

TBC and the apparent thermal conductivity of a layer are non-intrinsic properties; they are fundamentally influenced by neighboring materials, interface density, and interface geometry (Adnan et al., 2024, Merabia et al., 2015):

• Phonon-mode filtering: Proximate interfaces selectively transmit specific modes, leading to TBC enhancement (Si/Ge increases from 400 to 700 MW·m⁻²·K⁻¹ when interface separation $<$ phonon mean free path) and conductivity increase (Adnan et al., 2024).
• Interlayer impact: An Al$_{1-x}$Ga$_x$N “bridging” layer can degrade rather than enhance GaN/AlN TBC, with disorder and alloy scattering dominating over spectral bridging. Sigmoid alloy grading mitigates reflection loss, providing superior TBC to linear profiles (Adnan et al., 17 Jan 2026).
• Interfacial roughness: Regular asperities (triangular, sinusoidal) of height exceeding dominant phonon wavelength increase TBC proportionally to increased true area. Random small-scale roughness suppresses TBC to planar values due to incoherent phonon scattering (Merabia et al., 2015).

6. Experimental Methodologies and Mapping of TBC

Modern TBC measurement leverages both steady-state and transient techniques:

• Time-domain thermoreflectance (TDTR): Widely used for sub-nanometer sensitivity to TBC via multilayer heat-diffusion model fitting of in-phase and out-of-phase reflectance signals.
• Picosecond acoustics: Provides validation of layer thicknesses and acoustic impedance changes associated with bonding and annealing (Cheng et al., 2024).
• Three-omega and dual-frequency TDTR mapping: Enables wafer-scale visualization of TBC distributions, allowing diagnostic detection of weakly bonded or defective regions (Guo et al., 2024, Cheng et al., 2021).

Spatially resolved TBC mapping has revealed up to 17% variation after annealing in Si/SiC, and direct correlation with device temperature and thermal management capacity.

7. Applications, Device Implications, and Engineering Guidelines

High TBC at interfaces underpins advances in thermal barrier coatings, heat-assisted magnetic recording (e.g., FePt–h-BN), high-electron-mobility transistors (GaN/diamond, AlN/GaN), and 2D electronics. Design implications include:

• Maximizing mode overlap and bonding strength for enhanced TBC: Leverage small-mass defect engineering and controlled intermixing to activate interfacial modes in disordered/amorphous interfaces (Giri et al., 2017, Cheng et al., 2021).
• Minimizing disorder and maintaining smooth grading in critical multilayers: For AlN–GaN stacks, avoid unintended thick alloy layers and favor graded composition for optimal TBC (Adnan et al., 17 Jan 2026).
• Utilizing interface engineering (oxide-free, post-bonding annealing) for device integration: Realizing SiC/diamond and Si/SiC interfaces with TBC $\gtrsim 150-300$ MW·m⁻²·K⁻¹ opens pathways for high-power, thermally robust electronics (Cheng et al., 2024, Guo et al., 2024).

In summary, interfacial thermal boundary conductance is governed by a complex interplay of atomic-scale vibrational properties, structural engineering, and multichannel energy transfer mechanisms. Advances in spectroscopy, molecular dynamics, and interface design have established both the means to measure and the levers to control TBC, with fundamental and practical implications spanning thermal insulation, heat spreading, nanoscale device reliability, and emergent phononic engineering.