Simulating Residual Stress of Thin Films on Silicon Wafer by Thickness Changing
Posted Aug 8, 2025, 8:22 a.m. EDT MEMS & Piezoelectric Devices, Modeling Workflow, Physics Interfaces Version 5.3 0 Replies
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Hello!
I am trying to simulate the stress (or strain) that is obtained from
the fabrication process, and
the experimental process (temperature evaluation).
Initially, there is a silicon wafer. On top of it, there is a supporting SiO₂ layer. On this support layer, VO₂ is deposited using a sputtering system. I assume that all thin films inherently have an initial intrinsic stress from the deposition process. Based on previous studies, I have found that the magnitude of this stress depends on the difference in lattice parameters between the substrate and the film, as well as on the film thickness. The fabrication process is performed at room temperature.
Moreover, after deposition, the film is tested by measuring its resistance while the temperature is increased from 25 °C to 100 °C. I would like to observe how the stress/strain in the film changes as the temperature varies.
Currently, I am using COMSOL 5.3, and my procedure consists of the following steps:
- Fabrication Process (Goal: To show the initial stress distribution across the structure/geometry)
I assume that the wafer has negligible (zero) stress initially. After the second film is deposited, I use the Solid Mechanics module with a Stationary study.
I add another layer (m1) on top of the silicon wafer in the geometry.
I set the initial stress and initial strain in the silicon to zero.
I set the initial stress in the deposited layer to the given intrinsic stress, and the initial strain in the deposited layer to the calculated value from the lattice parameter difference:
(lattice parameter difference, such as strain=(a_m1 - a_film1)/(a_film1) ).
I would like to simulate cases where the top VO₂ layer has thicknesses of 10 nm, 30 nm, 50 nm, 70 nm, and 100 nm, and to show both:
the average stress applied over the entire surface area, and
the local stress distribution.
There is no temperature change and no external force or strain applied to the film. So, this simulation should ideally show the stress distribution that develops in the geometry due to the deposition process — specifically, the residual stress along with the initial intrinsic stress.
In addition, I would like to visualize stress vectors — arrows indicating the magnitude and direction of stress. I am not sure how to do this. I tried using an arrow array with (d.stress1x, d.stress1y), but the arrow directions did not match the expected theoretical results.
My questions for this step are:
Can the von Mises stress values obtained from this simulation be considered valid evidence of the residual stress formed in the thin film?
Are there any additional assumptions or considerations that should be added to make this simulation more realistic?
- Experimental Process (Temperature Increase) I use the Solid Mechanics and Thermal Stress modules with a Stationary study.
Assuming the same structure as in Step 1 (Si + SiO₂ + VO₂), I apply a temperature change from 25 °C to 100 °C to the thin-film system.
The boundary condition is set to room temperature.
The initial temperature is set to 100 °C.
For the same VO₂ thicknesses (10 nm, 30 nm, 50 nm, 70 nm, 100 nm), I want to observe the average stress over the surface area and the local stress distribution as the temperature changes.
I would like to know:
Is this the correct way to set the temperature change in COMSOL?
What exactly is the meaning of reference temperature and ambient temperature in COMSOL?
General Question I would like to know if this is the best approach to obtain the stresses in the layers after a fabrication process. Is it possible to automatically use the simulation results from one step as the initial conditions for the next process step? For example, after simulating the first fabrication step, could I then add a new layer to the geometry and assign it an initial intrinsic stress while preserving the stress state of the existing layers from the previous step?
Thank you!
If you’d like, I can also prepare a clean, concise version optimized for COMSOL’s discussion forum style so it’s both detailed and easy for others to respond with technical advice. That would make it much more likely to get expert replies.
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