Surface Impedance Modeling for 3D Conductor Current Flows
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Solution Overview
Problem
Current planar electromagnetic simulation technologies approximate three-dimensional conductors as zero-thickness sheets, which is inadequate for advanced semiconductor integrated circuits and on-chip interconnections, leading to inaccuracies in modeling current flows and losses due to finite conductor thickness and dielectric presence.
Innovation Solution
A method and apparatus that model current flows in three-dimensional conductive and dielectric bodies by defining planar surfaces, deriving surface impedance or admittance, and representing current flows using a notional electric surface current, allowing the retention of existing planar EM solver technology while accounting for finite thickness and dielectric effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If three-dimensional conductors are approximated as zero-thickness sheets in planar EM simulation, then computational complexity is reduced and existing planar solver technology can be used, but modeling accuracy deteriorates due to neglect of finite conductor thickness effects
Solution Approach 1:
The patent introduces a surface impedance concept that adds a dimensional parameter (surface impedance Zs) to the two-dimensional planar sheet model, effectively incorporating three-dimensional conductor thickness effects into a 2D simulation framework. The surface impedance relates the tangential electric field to the surface current density, capturing the impact of finite thickness without requiring full 3D modeling.
Solution Approach 2:
The patent modifies the planar sheet conductor model by introducing frequency-dependent surface impedance parameters that account for skin effect and proximity effect. The surface impedance Zs is expressed as a complex function of frequency, conductor thickness, and conductivity, allowing the 2D model to reflect 3D physical behavior through parameter transformation.
2Stability of the object's composition
If zero-thickness sheet conductor model is used, then the planar stratified nature of the background medium is maintained, but the skin effect and proximity effect in thick conductors cannot be accurately modeled
Solution Approach 1:
The patent introduces frequency-dependent surface impedance parameters that capture skin effect behavior. The surface impedance Zs is derived as a function of conductor thickness t, conductivity σ, and frequency ω, allowing the 2D planar model to accurately represent 3D skin effect phenomena through parameter transformation while preserving the planar stratified structure.
3Measurement precision
If full three-dimensional electromagnetic field simulation is used to model thick conductors, then modeling accuracy is improved, but computational complexity and solution time increase significantly
Solution Approach 1:
The patent extracts the essential three-dimensional effects (skin effect, proximity effect) from full 3D electromagnetic field simulation and formulates them as surface impedance boundary conditions for 2D planar solvers. This extraction process isolates the critical thickness-related phenomena and represents them through simplified impedance parameters, achieving 3D accuracy with 2D computational efficiency.
Solution Approach 2:
The patent creates an equivalent 2D planar model that copies the essential electrical behavior of 3D thick conductors through surface impedance parameters. The surface current density Js on the 2D sheet is related to the tangential electric field Et through the surface impedance Zs, which is derived from 3D field solutions but applied in a 2D framework, effectively copying 3D physics into a 2D computational model.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables accurate modeling of current flows and losses in thick conductors and dielectrics within a multilayered medium, maintaining the planar stratified nature of the background medium and reducing computational complexity, thus improving the prediction of circuit behavior in advanced electronic devices.
Implementation Method 1
At even higher frequencies, when the conductor becomes thick compared to the skin depth (t>δs), loss increases even more because the current is increasingly confined to the surface of the conductor. This is the so-called skin-effect region
Implementation Method 2
The internal field problem addresses the field problem inside the conductor and yields the surface impedance relation un×E(r)=Zs(un×Js(r)) between the tangential electric field at each point of the metal surface and the equivalent surface current at the same point
Data Source
AI summary
Current flows in a three-dimensional conductive or dielectric body embedded in a substrate of a different material are modelled in terms of surface currents induced in planar surfaces bounding the body and composed of the same material as the substrate, the surfaces having appropriate values for surface impedance.