Copper Size Effect Calculator
Estimate the first-order relative copper interconnect resistivity increase as Δρ/ρ = k·λ/w. The dimensionless coefficient k must be calibrated for the assumed surface and grain-boundary scattering; this compact model is not a full Fuchs-Sondheimer or Mayadas-Shatzkes calculation.
Description
Estimate the first-order relative copper interconnect resistivity increase as Δρ/ρ = k·λ/w. The dimensionless coefficient k must be calibrated for the assumed surface and grain-boundary scattering; this compact model is not a full Fuchs-Sondheimer or Mayadas-Shatzkes calculation.
Copper Size Effect Calculator is a focused tool for the following task. Estimate the first-order relative copper interconnect resistivity increase as Δρ/ρ = k·λ/w. The dimensionless coefficient k must be calibrated for the assumed surface and grain-boundary scattering; this compact model is not a full Fuchs-Sondheimer or Mayadas-Shatzkes calculation. It reports Resistivity increase from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Copper Size Effect
Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.
- Linewidth (nm)
- Required number in nm. Interconnect linewidth. Must be greater than 0 nm.
- Size effect coefficient
- Optional number. Dimensionless size effect coefficient. Must be at least 0; 0 yields 0 % increase.
- Electron mean free path (nm)
- Optional number in nm. Electron mean free path. Must be greater than 0 nm.
The cited overview of Electron mobility supplies background for the terminology and domain context used by this tool.1
How Copper Size Effect works
Estimate the first-order relative copper interconnect resistivity increase as Δρ/ρ = k·λ/w. The dimensionless coefficient k must be calibrated for the assumed surface and grain-boundary scattering; this compact model is not a full Fuchs-Sondheimer or Mayadas-Shatzkes calculation. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- Resistivity increase (%)
- Returned number in %. Relative resistivity increase over bulk copper. At least 0 %.
Limitations and assumptions
- Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
- Linewidth must be at least 5e-324.
- Size effect coefficient must be at least 0.
- Electron mean free path must be at least 5e-324.
- Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.
Alternative or Complementary approaches
Compare the estimate with measured process data, current device documentation, and a higher-fidelity circuit, field, thermal, quantum, or TCAD model when the decision requires it.
References
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Electron mobility — Wikipedia contributors
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