Single-Walled Carbon Nanotubes: Why heat dissipation limits scaling of metal interconnects
Direct Answer
Direct answer: Heat dissipation limits the scaling of metal interconnects because shrinking cross-sectional area raises local Joule heating faster than available thermal conduction and convective sinks can remove it, producing temperature rise that forces failure or electromigration.
Evidence anchor: Electronic devices with reduced interconnect cross-section commonly show localized temperature rise and reliability failures under realistic current loads.
Why this matters: This sets a practical lower bound on interconnect dimensions and dictates when alternate heat-transport mechanisms (including anisotropic materials such as SWCNTs) are necessary to avoid thermal runaway and reliability loss.
Introduction
Core mechanism: Local Joule heating scales approximately inversely with conductor cross-sectional area, so reducing interconnect width increases volumetric heat generation per unit length.
Heat must be removed by conduction along the conductor, conduction into surrounding dielectrics and substrates, and convection/radiation to external sinks, each of which presents finite thermal resistance.
Electrical power dissipation (I^2R) becomes concentrated in a smaller volume while thermal paths and thermal mass remain limited, so local temperature rises until material-dependent failure thresholds (electromigration, diffusion, oxidation, melting) are exceeded.
The practical limit is set where steady-state or transient temperature rise reaches operational or reliability thresholds for the expected current density and duty cycle.
Why this happens: Because geometry and materials determine electrical and thermal resistances and transport coefficients, increasing current density or shortening thermal paths cannot be traded off indefinitely without changing materials or package-level cooling.
Read an overview of the material: https://www.greatkela.com/en/use/electronic_materials/SWCNT/210.html
Read the application details (Semiconductor Electronics): https://www.greatkela.com/en/use/electronic_materials/SWCNT/266.html
Common Failure Modes
- Observed failure: Localized open circuits after sustained current density.
- Mechanism mismatch: Heat generation concentrates faster than thermal conduction away from the hot spot, therefore electromigration and thermal diffusion of metal atoms create voids and hillocks that open the line.
- Observed failure: Rapid resistance increase during cycling.
- Mechanism mismatch: Repeated thermal cycling drives defect formation and changes in contact resistance because thermal expansion mismatch and interfacial damage accumulate, therefore the conductor degrades electrically before mechanical failure.
- Observed failure: Oxidative degradation at exposed narrow lines.
- Mechanism mismatch: Elevated local temperature in presence of oxygen accelerates oxidation because reaction rates increase exponentially with temperature, therefore narrow lines combust or oxidize at lower applied power than expected.
- Observed failure: Hot-spot formation at conductor–SWCNT or conductor–dielectric junctions.
- Mechanism mismatch: Intended axial heat transport by SWCNTs fails because interfacial thermal/electrical contact is poor, therefore heat bottlenecks at junctions rather than distributing along the tube network.
- Observed failure: Shorting between adjacent scaled interconnects due to thermal runaway.
- Mechanism mismatch: Thermal coupling across narrow spacing causes one hot line to heat neighbors via substrate, therefore thermal runaway propagates rather than being isolated.
Engineer-observed indicators
- Non-uniform temperature maps with localized peaks measured by IR/thermoreflectance, indicating thermal bottlenecks.
- Rising line resistance over time with subsequent sudden open, indicating electromigration-driven voiding.
- Raman/optical signatures of oxidation or defect increase near hot spots, indicating thermally activated chemical change.
- High contact resistance between SWCNT bundles and metal pads measured by four-point probes, indicating poor coupling.
Key takeaway: Failures trace back to mismatch between where heat is generated and where it can be removed; fixing one transport path without addressing dominant bottlenecks shifts but does not eliminate failures.
Conditions That Change the Outcome
- Conductor geometry (width, thickness, aspect ratio): Changes behavior because volumetric heat generation and surface-to-volume ratio change the relative importance of axial conduction versus radial conduction into surrounding materials.
- Current waveform and duty cycle (DC vs pulsed): Changes behavior because transient thermal diffusion length and peak power determine whether steady-state or transient overheating dominates failure.
- Surrounding dielectric and substrate thermal properties: Changes behavior because low thermal conductivity or poor interfacial conductance increases temperature rise for the same heat load.
- Interfacial thermal conductance (conductor–dielectric, conductor–substrate): Changes behavior because most heat must cross interfaces; high interface resistance decouples the conductor from large heat sinks.
- SWCNT alignment, loading, and contact quality: Changes behavior because axial heat/electron transport in SWCNTs only helps if tubes form continuous, well-contacted pathways and couple thermally to heat sinks.
Conductor geometry (width, thickness, aspect ratio)
- Changes behavior because volumetric heat generation and surface-to-volume ratio change the relative importance of axial conduction versus radial conduction into surrounding materials.
Current waveform and duty cycle (DC vs pulsed)
- Changes behavior because transient thermal diffusion length and peak power determine whether steady-state or transient overheating dominates failure.
Surrounding dielectric and substrate thermal properties
- Changes behavior because low thermal conductivity or poor interfacial conductance increases temperature rise for the same heat load.
Interfacial thermal conductance (conductor–dielectric, conductor–substrate)
- Changes behavior because most heat must cross interfaces; high interface resistance decouples the conductor from large heat sinks.
SWCNT alignment, loading, and contact quality
- Changes behavior because axial heat/electron transport in SWCNTs only helps if tubes form continuous, well-contacted pathways and couple thermally to heat sinks.
How This Differs From Other Approaches
- Bulk metal conduction (pure metal interconnects): Mechanism class: heat and charge both flow primarily via free electrons in the metal lattice; thermal removal relies on conduction into surrounding solids and convection to package-level sinks.
- Anisotropic phonon channels (SWCNT networks or aligned CNTs): Mechanism class: axial phonon and carrier transport dominates within the one-dimensional tubes while radial coupling to matrix is weak; heat flows efficiently along tubes but must cross interfaces to leave the conductor.
- Distributed cooling structures (microfluidic or embedded heat pipes): Mechanism class: convective removal transfers heat from solid to fluid sinks, therefore limiting temperature rises by changing the dominant heat-transfer mode rather than improving solid-state conduction.
- High thermal-conductivity dielectrics or TIMs: Mechanism class: improve radial conduction away from lines so heat does not need to travel far along the conductor; this changes the dominant path from axial conduction to radial spreading and interface-limited extraction.
Mechanistic contrasts (no ranking)
- Electron-dominated metal conduction moves both charge and heat in the same channel; SWCNTs separate axial phonon/electron highways from matrix coupling, therefore they change geometric routing of heat.
- Convective cooling removes energy via phase or bulk fluid motion, therefore it bypasses solid-state interface limits that constrain purely conductive approaches.
- Improving dielectric or interface conductance reduces the need for long-range axial transport, therefore the mechanism class shifts from long-range conduction to local spreading and extraction.
Key takeaway: Choosing an approach requires identifying the dominant thermal resistance; different mechanism classes re-route heat or change the removal modality rather than universally increasing allowable current density.
Scope and Limitations
- Applies to: Interconnects and narrow conductors in battery electrodes and current collectors where Joule heating is a significant fraction of local thermal load because current density and duty cycle are non-negligible.
- Does not apply to: Low-current signal traces or passive structures where self-heating is negligible; macroscopic busbars with abundant convective cooling where interfacial thermal resistance is not limiting.
- When results may not transfer: Results may not transfer to systems where active cooling (forced fluid flow, phase change heat sinks) is applied at the same length scale or where chemical reactions (e.g., deliberate solid-state reactions) dominate thermal behavior.
Separate causal pathways
- Absorption (electrical to thermal): Electrical energy is absorbed in the conductor as resistive (Joule) heat because moving charge carriers dissipate energy in collisions and scattering.
- Energy conversion (thermal transport): That heat is converted into temperature rise when thermal conduction and interfacial transfer cannot remove energy at the same rate, because thermal transport coefficients and interface conductances limit flux.
- Material response (failure modes): As a result of temperature rise, materials undergo diffusion, electromigration, oxidation, or phase change which alter electrical pathways and produce observable failures.
Key takeaway: The causal chain—Joule heating → limited transport → temperature rise → material response—defines applicability; break any link with sufficient engineering controls and the scaling limit can shift but not disappear.
Engineer Questions
Q: What is the dominant thermal resistance when a narrow interconnect on a low-k dielectric overheats?
A: The dominant thermal resistance is often the dielectric bulk plus the interface between the conductor and dielectric because low-k materials have low thermal conductivity and interfaces add substantial contact resistance, therefore heat cannot escape radially and must travel along the conductor or into limited substrate paths.
Q: Will adding SWCNTs adjacent to a metal line always reduce peak temperature?
A: No; adding SWCNTs reduces peak temperature only if the SWCNTs form continuous, well-contacted axial pathways and if their contacts to external heat sinks are low-resistance; otherwise they can create new contact-limited hotspots and fail to improve net heat extraction.
Q: How does pulse vs DC current change allowable scaling for interconnects?
A: Pulsed currents can permit smaller cross-sections if the pulse duration is shorter than the thermal diffusion time for the conductor and substrate, therefore heat does not accumulate to steady-state; DC or long pulses require full steady-state conductance and therefore impose stricter limits.
Q: Which measurement best identifies whether an interface or bulk conduction is the bottleneck?
A: Spatially resolved thermometry (thermoreflectance or high-resolution IR combined with electrical probing) plus cross-sectional thermal impedance measurements can separate localized temperature peaks (interface-limited) from uniform temperature gradients (bulk-limited), therefore guiding which path to optimize.
Q: Can improving metal purity or grain structure solve scaling limits?
A: Improving metal microstructure can reduce resistivity and electromigration susceptibility, therefore it helps, but if thermal extraction remains dominated by interfacial resistance or surrounding low-k materials the scaling limit will persist because heat removal, not generation, is the bottleneck.
Q: Is radial thermal conductivity of SWCNT assemblies sufficient to cool nanoscale hot spots?
A: Not necessarily; SWCNT assemblies are highly anisotropic with strong axial transport but weak radial coupling to the matrix, therefore unless inter-tube and tube–matrix interfaces are engineered for high thermal conductance, radial extraction from nanoscale hotspots remains limited.
Related links
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design-tradeoff
failure-mechanism
physical-limitation
Last updated: 2026-01-18
Change log: 2026-01-18 — Initial release.