Home Knowledge Base The size effect is not a copper problem, it is a metal problem.

Molybdenum interconnect means using molybdenum as the conductor in the tightest wiring on a chip — the local metal levels, the contacts and vias beneath them, and the buried power rails under the transistors — in place of the copper dual-damascene stack that has carried every logic node since IBM put it into production in 1997. The claim that sells the switch is a crossover: below roughly 17.5 nm of drawn trench width, a barrierless molybdenum line carries current at lower resistance per micron than a copper line of the same drawn dimension. That number is real. The reason usually given for it is not, and the difference decides which half of the program deserves funding.

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fill="#c9d1d9" font-family="Georgia,serif" font-size="12.5">Cu + 2 nm TaN/Ta barrier</text><line x1="94" y1="129" x2="122" y2="129" stroke="#3fb950" stroke-width="2.5" /><text x="130" y="133" fill="#c9d1d9" font-family="Georgia,serif" font-size="12.5">Mo, barrierless</text><line x1="94" y1="150" x2="122" y2="150" stroke="#f97316" stroke-width="2.5" stroke-dasharray="5 4" /><text x="130" y="154" fill="#c9d1d9" font-family="Georgia,serif" font-size="12.5">Cu with no barrier (hypothetical)</text><text x="130" y="173" fill="#6e7681" font-family="Georgia,serif" font-size="11.5">the dashed line never crosses green, down to 2 nm</text><text x="522" y="92" fill="#e6edf3" font-family="Georgia,serif" font-size="13.5" font-weight="700">A 12 nm trench, in section</text><rect x="522" y="120" width="80" height="160" fill="#7c3a11" stroke="#f97316" stroke-width="1.5"/><rect x="535.3" y="120" width="53.3" height="146.7" fill="#f97316"/><text x="562" y="200" fill="#0d1117" font-family="ui-monospace,monospace" font-size="12" font-weight="700" text-anchor="middle">61%</text><rect x="634" y="120" width="80" height="160" fill="#3fb950" stroke="#3fb950" stroke-width="1.5"/><text x="674" y="200" fill="#0d1117" font-family="ui-monospace,monospace" font-size="12" font-weight="700" text-anchor="middle">100%</text><text x="562" y="300" fill="#f8b57a" font-family="Georgia,serif" font-size="12.5" text-anchor="middle">Cu + liner</text><text x="674" y="300" fill="#7ee787" font-family="Georgia,serif" font-size="12.5" text-anchor="middle">Mo alone</text><text x="522" y="324" fill="#c9d1d9" font-family="Georgia,serif" font-size="12.5">Same trench. 1.64× the conductor,</text><text x="522" y="341" fill="#c9d1d9" font-family="Georgia,serif" font-size="12.5">because nothing is spent on a liner.</text><text x="24" y="436" fill="#6e7681" font-family="Georgia,serif" font-size="12">Fuchs–Sondheimer plus Mayadas–Shatzkes, p = 0.5, R = 0.3, aspect ratio 2, grain size = line width.</text><text x="24" y="454" fill="#6e7681" font-family="Georgia,serif" font-size="12">The metal did not get better. The usable cross-section got worse.</text></svg>

The size effect is not a copper problem, it is a metal problem. Once a wire is narrower than the distance an electron travels between collisions, the surfaces and the grain boundaries start doing the scattering, and the Fuchs–Sondheimer and Mayadas–Shatzkes terms take over from the bulk value entirely:

$$\rho(w) = \rho_0\left[1 + \frac{3}{8}(1-p)\,\lambda\left(\frac{1}{w}+\frac{1}{h}\right) + \frac{3}{2}\cdot\frac{R}{1-R}\cdot\frac{\lambda}{D}\right]$$

Both correction terms are proportional to $\lambda/w$ and both are multiplied by $\rho_0$, so as the wire shrinks the ranking of metals stops depending on bulk resistivity and collapses onto a single figure of merit, the product $\rho_0\lambda$. That product is remarkably flat across the candidates. Copper sits at 6.67, molybdenum at 5.87, ruthenium at 4.76, tungsten at 8.18, cobalt at 7.36 and aluminium at 5.01, all in units of 10⁻¹⁶ Ω·m². Molybdenum's electronic advantage over copper in the asymptotic limit is therefore about 12%, and 12% is not a reason to re-qualify an industry's metallization. Every candidate metal is punished by the size effect; none of them escapes it.

MetalBulk ρ₀ (µΩ·cm)Mean free path λ (nm)ρ₀λ (10⁻¹⁶ Ω·m²)Diffusion barrierMelting point (°C)
Cu1.7139.06.67TaN/Ta plus liner, ≈2 nm1085
Al2.6518.95.01self-passivating oxide660
W5.2815.58.18TiN3422
Co6.2411.87.36thin liner1495
Mo5.3411.05.87none2623
Ru7.106.74.76none2334

Copper loses on geometry, and the geometry is entirely the barrier. Copper drifts through silicon and through low-k dielectric under bias, so every copper line is wrapped in a TaN/Ta barrier plus a cobalt or ruthenium liner, and that wrapper has not scaled with the pitch. Two nanometres of it on both sidewalls and the trench floor consumes 16% of a 30 nm trench, 24% at 20 nm, 30% at 16 nm, 39% at 12 nm and 46% at 10 nm. Molybdenum is refractory, has no fast diffusion path into oxide, and needs none of it, so 100% of the trench carries current — 1.64 times the conductor area at the 12 nm node for free. Run the same size-effect model with the barrier deleted and the celebrated crossover simply disappears: hypothetical barrierless copper stays below molybdenum all the way down to 2 nm, where the two curves finally meet. Halve the barrier to 1.0 nm instead of removing it and the crossover slides from 17.5 nm to 11.75 nm, which is a full node of runway bought with one nanometre of liner. The crossover is not a property of molybdenum. It is a property of the wrapper on copper.

Vias are where the same arithmetic turns violent. A trench loses barrier area on three sides and along one dimension; a via loses it on all four sides and along two, so the penalty is squared. At a 16 nm via the copper core is 144 nm² against molybdenum's full 256 nm², which works out to 16 Ω against 11 Ω, a 1.44× gap. At 12 nm the core collapses to 64 nm² against 144 nm², and the resistance gap widens to 38 Ω against 17 Ω, or 2.22×. At 10 nm the copper core is 36 nm² against 100 nm², 72 Ω against 23 Ω, a factor of 3.20×. A large accelerator die carries tens of billions of these in series with every signal path, which is why the first production insertions of alternative metals have been at contact and via level rather than in the long lines.

For an AI accelerator the payoff arrives as picoseconds on wires that never get longer. Local interconnect delay scales as the square of length because both resistance and capacitance grow with it, so the interesting comparison is a fixed short run at a fixed capacitance of about 0.2 fF/µm. At a 12 nm trench, a 10 µm local route costs 3.94 ps in copper and 2.58 ps in molybdenum, a 34% reduction; at 20 µm it is 15.77 ps against 10.33 ps. At a 16 nm trench the same comparison yields only 9%, because that width sits on the wrong side of the crossover. This is the shape of the whole argument in miniature: the benefit is worth nothing at one node and worth a third of the wire delay one node later, and it lands precisely on the structures that dominate a transformer accelerator — SRAM bitlines and wordlines, register-file access, and the short hops of an on-die network where wire delay, not gate delay, sets the cycle.

Molybdenum's decisive advantage has nothing to do with resistance at all. Electromigration and diffusion are governed by homologous temperature, the ratio of operating temperature to melting point, and at a 100 °C junction copper runs at 0.275 of its 1085 °C melting point while molybdenum runs at 0.129 of 2623 °C and tungsten at 0.101 of 3422 °C. That single ratio explains why tungsten has held the contact level for forty years and why copper has always needed a liner to suppress interface diffusion. It also decides the buried power rail, the structure that Intel ships as PowerVia at 18A and that TSMC and imec have described for A16-class backside power: the rail is patterned in or below the device layer and then has to survive source–drain activation anneals near 1000 °C. Copper is not beaten there, it is disqualified. Molybdenum's 4.8 ppm/K thermal expansion, against 2.6 for silicon and 16.5 for copper, is the second reason — a metal buried under the transistors has to move with the wafer, not against it.

Molybdenum can be etched, which makes damascene optional. Copper has no halide that is volatile at any temperature the back end can tolerate, and dual damascene exists precisely because of that fact: the industry adopted trench-first patterning, electroplating and chemical–mechanical polish as a way to route around a metal it could not etch. Molybdenum forms volatile oxychlorides such as MoO₂Cl₂, so it can be deposited as a blanket film, patterned, and etched subtractively, which changes the integration rather than just the conductor.

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The program is won or lost in the precursor, not in the periodic table. MoF₆ mirrors the WF₆ chemistry the industry already knows, but it brings the same fluorine attack on exposed silicon and low-k dielectric, which is why the fluorine-free routes matter: MoCl₅ and MoO₂Cl₂ chemical vapour deposition and atomic layer deposition at 400 to 600 °C, tooled by Applied Materials, Lam Research, Tokyo Electron and ASM International, at the cost of chlorine residue, corrosion risk and a higher thermal budget than a plated metal ever needed. The films that come out land near 8 to 12 µΩ·cm against a 5.34 µΩ·cm bulk value, because grains cannot grow wider than the line that contains them and because carbon, oxygen and chlorine impurities sit at those grain boundaries scattering exactly the electrons the whole exercise was meant to preserve. Nucleation delay on dielectric, adhesion without a liner to help, and the resistance of the Mo-to-Cu interface at the level where the stack transitions back to copper are the three items that actually appear on a qualification schedule, and none of them is a physics problem.

Read molybdenum through a process integration lens rather than a conductivity lens: the metal is 12% better than copper in the asymptotic limit and worse than copper by every classical measure, and it is winning anyway because it needs no barrier, survives a 1000 °C anneal and can be etched. Every hard problem here is a different instance of the same question — how much of the drawn trench actually carries current, and what did the rest of the process have to give up to put it there. The 39% barrier fraction at 12 nm, the 3.20× via gap at 10 nm, the 0.129 homologous temperature that qualifies a buried rail, and the 8 to 12 µΩ·cm gap between a deposited film and its own bulk value are four readings of that one question. Answer it first, and the choice between copper, cobalt, molybdenum and ruthenium stops being a materials argument and becomes an arithmetic one.

molybdenum interconnectmo interconnectalternative metal interconnectbarrier free metallizationbarrierless metallizationmolybdenum metallizationmo metallizationsubtractive metal patterninginterconnect resistivityelectron mean free path

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