Patent ID: 8731877

Claim:
A method of modeling surface impedance of an interconnect conductor of an integrated circuit design in which the conductor has a current flow in a z-direction, the method comprising: formulating a volumetric electric field integral equation with respect to an unknown volumetric current density j z of the current flow in a cross-section of the conductor due to a vector of excitation V p.u.l. by enforcing Ohm's law E z (ρ)=σ − j z (ρ) inside the conductor (ρ∈S) as follows: σ - 1 ⁢ j z ⁡ ( ρ ) + ⅈωμ 0 ⁢ ∫ S ⁢ G ⁡ ( ρ ❘ ρ ′ ) ⁢ j z ⁡ ( ρ ′ ) ⁢ ⅆ S ′ = - V p · u · l · ⁡ ( ρ ) ; representing the unknown volumetric current density in the volumetric electric field integral equation as a product of a current density of a peripheral surface of the conductor and an exponential factor describing a cross-sectional distribution of the current flow according to skin effect by approximating the unknown volumetric current density, represented as j z , across the conductor according to skin-effect of a plane-wave incident on a conducting plane with infinite extension as follows: j z ⁡ ( ρ ) ≅ ⅈ ⁢ ⁢ k σ ⁡ ( J z t ⁡ ( y ) ⁢ ⅇ - ⅈ ⁢ ⁢ k σ ⁡ ( X - x ) + J z b ⁡ ( y ) ⁢ ⅇ - ⅈ ⁢ ⁢ k σ ⁢ x ) 1 - ⅇ - ⅈ ⁢ ⁢ k σ ⁢ X + ⅈ ⁢ ⁢ k σ ⁡ ( J z l ⁡ ( x ) ⁢ ⅇ - ⅈ ⁢ ⁢ k σ ⁢ y + J z r ⁡ ( x ) ⁢ ⅇ - ⅈ ⁢ ⁢ k σ ⁡ ( Y - y ) ) 1 - ⅇ - ⅈ ⁢ ⁢ k σ ⁢ Y where J z t (y), J z b (y), J z l (x), J z r (x) are unknown surface current densities at points of radius-vector ρ projections onto respective top, bottom, left, and right walls of the conductor; adopting an approximation of Green's function across a cross-section of the conductor; and reducing the volumetric electric field integral equation including the unknown volumetric current density representation to a surface integral equation using the approximation of Green's function, resulting in a surface impedance model; and applying the surface impedance model to the integrated circuit design.