Carbon Nanotube Interconnect: Ballistic vs Diffusive Resistance

Interconnect Geometry

Length L 300 nm

Mean free path λ 600 nm

CNTs in bundle (M) 1

Live Readouts

Ballistic transport

Total resistance R

6.45 kΩ

L / λ ratio

0.50

Contact R (ballistic floor)

6.45 kΩ

Diffusive add-on

3.23 kΩ

Conductance G

0.155 mS

Channels N = 4M

How it works

A defect-free metallic single-wall carbon nanotube carries current through exactly 4 quantum-mechanical conduction channels (2 linear subbands × 2 spins). The Landauer-Büttiker formula gives the two-terminal resistance of a bundle of M parallel tubes, each of length L, as:

R(L) = (h / 4e²N) × (1 + L/λ)
N = 4M          h/4e² ≈ 6.453 kΩ  (quantum resistance per channel)
λ = electron mean free path (acoustic-phonon-limited, ~1 μm at 300 K)

When L ≪ λ, transport is ballistic: electrons cross the tube without scattering, and R collapses to a length-independent quantum contact resistance R_c = (h/4e²)/N — set entirely by the number of open channels, not by geometry. As L grows past λ, scattering events accumulate and transport turns diffusive: R grows linearly with L, exactly like an Ohmic wire, with slope (h/4e²)/(Nλ).

Length L — physical span of the interconnect between contacts.
Mean free path λ — average distance between phonon-scattering events; shrinks with more defects or higher temperature.
Bundle count M — parallel metallic tubes; each adds 4 channels, so contact resistance drops as 1/M.

Why it matters: this is exactly the tradeoff nanoelectronics interconnect design faces as wires shrink below a micron — copper's resistivity rises sharply from surface scattering at these dimensions, while a ballistic CNT bundle instead hits a resistance floor set by quantum contacts, which is why CNT and graphene interconnects are studied as copper's replacement for the shortest on-chip wires.

Ballistic electron (no scatter) Scattering event Nanotube / contact

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