Calculator

Interconnect RC delay calculator (Cu, Co, Ru, Mo)

Plasma, vacuum, films and facilities. Everything is calculated in your browser; nothing you enter is sent to a server.

KEY POINTS

Interconnect delay is set by the product of resistance R and capacitance C. Copper's electron mean free path is long, about 40 nm, so as line width approaches it, surface and grain boundary scattering drive resistivity up sharply, and the barrier metal eats into the conductor cross-section. Below line widths of a dozen or so nanometers, the gap to ruthenium and molybdenum, with their higher bulk resistivity, narrows, while capacitance is lowered with low-k films and air gaps.

Wire geometry

Interconnect metalLine width W (nm)Aspect ratio H/WLine spacing S (nm)Barrier/liner thickness (nm)Interlayer dielectricWire length L (µm)

RC delay τ = 0.38RC65.51ps

Effective resistivity (conductor)6.01µΩ·cm

Bulk resistivity1.68µΩ·cm

Resistance per length98.8Ω/µm

Capacitance per length174.5aF/µm

Total wire resistance R9,880Ω

Total wire capacitance C17.45fF

Conductor cross-section (excluding barrier)16.0 × 38.0nm

The size effect is a simple sum of surface scattering (Fuchs–Sondheimer) and grain boundary scattering (Mayadas–Shatzkes), assuming fully diffuse scattering, a grain boundary reflection coefficient of 0.25 and grain size equal to conductor width. Real values change with deposition conditions and grain growth during annealing, so use this as an estimate for comparing trends. Driver resistance and load capacitance are not included.

Metals compared (same geometry)

Line width 20 nm, height 40 nm, spacing 20 nm, k = 2.7. Barrier thickness is a typical value for each metal.
Metal	Barrier	Effective ρ [µΩ·cm]	Resistance [Ω/µm]	Delay (L = 100 µm)	Resistance vs. Cu
Copper (Cu)	2 nm	6.0	99	65.5 ps	1.00×
Cobalt (Co)	1 nm	10.5	149	98.8 ps	1.51×
Ruthenium (Ru)	0 nm	9.6	120	79.5 ps	1.21×
Molybdenum (Mo)	0 nm	9.2	116	76.6 ps	1.17×
Tungsten (W)	1 nm	10.1	144	95.2 ps	1.45×

Line width and effective resistivity (averaged over the cross-section including barrier)

Copper (Cu)Cobalt (Co)Ruthenium (Ru)Molybdenum (Mo)

Resistivity averaged over the whole wire, including the barrier cross-section. As lines narrow, copper, with its long mean free path and need for a barrier, loses ground quickly and the gap to ruthenium and molybdenum closes.

Why copper loses out in fine interconnects

Copper has the lowest bulk resistivity of any practical metal, but its electron mean free path is long, about 40 nm, so as line width approaches that length, scattering at surfaces and grain boundaries drives resistivity up sharply. Copper also diffuses into dielectrics and needs a barrier a few nm thick; at a 20 nm line width, that alone takes more than 20% of the conductor cross-section.

Ruthenium and molybdenum have three to four times copper's bulk resistivity, but their short mean free paths mean a smaller size effect, and they can use thinner barriers or none. They are therefore being considered as copper replacements starting with the narrowest lower-level wires. Capacitance, by contrast, can only be reduced with low-k films or air gaps, so RC delay is attacked from both the resistance and the capacitance side.

FAQ

Why does copper resistivity rise in narrow lines?

Electrons scatter off surfaces and grain boundaries once the line width approaches copper's mean free path of about 40 nm, and the barrier needed to stop copper diffusion takes up part of the cross-section.

What does the 0.38 in τ = 0.38RC mean?

It is the factor for the 50% delay of a distributed RC line, where resistance and capacitance are spread along the wire rather than lumped.

Related equipment and companies

More calculators

Plasma, vacuum, films and facilities

Last updated: October 23, 2026