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 first-order copper interconnect resistivity increase from linewidth, mean free path, and a calibrated size-effect coefficient.
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.
When to use Copper Size Effect Calculator
- Estimate first-order copper interconnect resistivity increase from linewidth, mean free path, and a calibrated size-effect coefficient.
- Compare fabrication or device scenarios while holding coefficients and unit conventions constant.
- Check a hand calculation before moving to a higher-fidelity process, circuit, or TCAD model.
How the calculation works
The coefficient combines boundary-scattering assumptions; it is not a universal copper constant.
Δρ/ρ[%] = 100·k·λ/w Interpreting the result
The coefficient combines boundary-scattering assumptions; it is not a universal copper constant.
Assumptions and limitations
- The linear λ/w approximation is not a full surface-plus-grain-boundary transport solution and omits thickness, roughness, texture, and temperature dependence.
- Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.