Example: Thin film resistance

Introduction

• This model shows the approach that can be used in COMSOL Multiphysics in order to model very thin films in diffusion and conductions problems.

• The example compares a high-fidelity model, where the physical extension of the film is taken into account, with a much less computationally demanding thin-film approximation.

• The example makes use of COMSOL Multiphysics’ ability to activate and deactivate dependent variables in different subdomains.

Thin films

Geometry and problem definition for the two cases

• This example treats the conduction of a direct current through a metallic conductor.

• The blue-colored layer is of a much poorer conductor.

• The thin layer creates a large number of elements and nodes.

• Analogous problems are found in diffusion and heat conduction models.

This films – Problem definition

High fidelity model

Approximation

Model Equations

Thin film – Problem Definition

0

01

01

02

12

1

zj

Implemented in the boundary conditions for both 1 and 2

Main flow of current

Main flow of current

Potential distribution, comparison

Thin films – Results

High fidelity model Approximation

Potential distribution, cross-section

Thin films – Results

High fidelity model Approximation

Concluding remarks

• The results from the high fidelity and the approximation are almost identical.

• The computational time for the approximation is an order of magnitude smaller than that of th detailed model.

• The modeling approach has been used for current conduction, diffusion, heat conduction, and porous media flow using Darcy’s law.

Thin films