1. Example: Thin film resistance

2. Thin films
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.

3. Geometry and problem definition for the two cases
This films – Problem definition
Geometry and problem definition for the two cases
High fidelity model
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.
Approximation

4. Model Equations Thin film – Problem Definition Main flow of current
Implemented in the boundary conditions for both f1 and f2
Main flow of current

5. Potential distribution, comparison
Thin films – Results
Potential distribution, comparison
High fidelity model
Approximation

6. Potential distribution, cross-section
Thin films – Results
Potential distribution, cross-section
High fidelity model
Approximation

7. Thin films
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.