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Modeling thermal expansion of 2 bonded wafers - Boundary conditions und post-processing
Posted Jan 3, 2011, 6:37 p.m. EST Geometry, Materials, Modeling Tools & Definitions, Parameters, Variables, & Functions, Results & Visualization, Studies & Solvers, Structural Mechanics Version 4.0a 5 Replies
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Hello everybody,
I modeled thermal expansion of a silicon wafer with an etched cavity which is bonded to a glass wafer. I want to find out the influence of different gases inside the cavity on structural deformation of the whole structure. On the one hand there will be air inside, on the other hand non-perfect vacuum (air with very little pressure).
The bonded wafers cool down from 400°C to room temperature. They aren't fixed anywhere and only lie upon a plate.
So I worry about the boundary conditions I should use?! I attached my model, so anyone can see what I tried to do. I wonder about the resulting Mises-stress. It seems to be very high. Perhaps as a consequence of wrong boundary conditions? I only used tow points with prescribed displacement (taken from "capacitive pressure sensor" in Comsol's gallery).
So here my questions in short form:
1.) any suggestions for suitable boundary conditions?
Then in postprocessing I can't find an appropriate color-scale for showing the stress-distribution in both areas, glass and silicon. The differences because of different E-Modulus seem to bee too large. So
2.) Is it possible to assign different color-scales to both areas of the structure in one 2D-plot?
Next I want to consider the anisotropic E-Modulus of silicon, but didn't find a way to do so.
3.) Is it possible to enter E_x, E_y and E_z somewhere?
4.) And finally: when I want to use a non-perfect vacuum inside the cavity, say some mBar or so, how can I do this? Is it possible to change the pressure of the air in the linear-elastic-model?
Thanks a lot in advance
Chris
I modeled thermal expansion of a silicon wafer with an etched cavity which is bonded to a glass wafer. I want to find out the influence of different gases inside the cavity on structural deformation of the whole structure. On the one hand there will be air inside, on the other hand non-perfect vacuum (air with very little pressure).
The bonded wafers cool down from 400°C to room temperature. They aren't fixed anywhere and only lie upon a plate.
So I worry about the boundary conditions I should use?! I attached my model, so anyone can see what I tried to do. I wonder about the resulting Mises-stress. It seems to be very high. Perhaps as a consequence of wrong boundary conditions? I only used tow points with prescribed displacement (taken from "capacitive pressure sensor" in Comsol's gallery).
So here my questions in short form:
1.) any suggestions for suitable boundary conditions?
Then in postprocessing I can't find an appropriate color-scale for showing the stress-distribution in both areas, glass and silicon. The differences because of different E-Modulus seem to bee too large. So
2.) Is it possible to assign different color-scales to both areas of the structure in one 2D-plot?
Next I want to consider the anisotropic E-Modulus of silicon, but didn't find a way to do so.
3.) Is it possible to enter E_x, E_y and E_z somewhere?
4.) And finally: when I want to use a non-perfect vacuum inside the cavity, say some mBar or so, how can I do this? Is it possible to change the pressure of the air in the linear-elastic-model?
Thanks a lot in advance
Chris
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5 Replies Last Post Sep 27, 2011, 1:45 p.m. EDT
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Posted:
1 decade ago
Hi
there are several things to propose here
for the stress and heat related stress buildup/relaxation, check the Structural / thermal-structure interaction / Layered_plate model in the model library
The BC for the structural are th same in this model, so far I agree with your logic for your "iso-static" fixation
Note: in your model you can use ONE linear ealstic node and add SEVERAL thermal sub-nodes, per domain
For the crystaline Si, see the material library, there are two defined one amorphe and one crystalline.
You need also to set the lienar elastic node material properties use to anisotropic (in which case you have one of several anisotropic materials you need a speific lienar elastic node for the anisotropic and a separate one for the isotropic materials. you can either enter the material data specifically in the structural node, or referring to a material DB entry
I also see that you simulate the "air" as a structure (which is possible in 4.1 to avoid a simple ALE, as for this case, if you want to couple ACDC thereafter) but if you have a vacuum or low pressure then the bulk E modulus of the "air section should also be lower to avoid giving fale results, and the pressure you can simualte it by a surface pressure on the internal cavity. Reamins to define the pressure value, absolute (including outside surfaces) or differential (negative pressure inside ?), I'm not sure what to choose, should be thesame, but a test is worth to be performed as quick check.
--
Good luck
Ivar
there are several things to propose here
for the stress and heat related stress buildup/relaxation, check the Structural / thermal-structure interaction / Layered_plate model in the model library
The BC for the structural are th same in this model, so far I agree with your logic for your "iso-static" fixation
Note: in your model you can use ONE linear ealstic node and add SEVERAL thermal sub-nodes, per domain
For the crystaline Si, see the material library, there are two defined one amorphe and one crystalline.
You need also to set the lienar elastic node material properties use to anisotropic (in which case you have one of several anisotropic materials you need a speific lienar elastic node for the anisotropic and a separate one for the isotropic materials. you can either enter the material data specifically in the structural node, or referring to a material DB entry
I also see that you simulate the "air" as a structure (which is possible in 4.1 to avoid a simple ALE, as for this case, if you want to couple ACDC thereafter) but if you have a vacuum or low pressure then the bulk E modulus of the "air section should also be lower to avoid giving fale results, and the pressure you can simualte it by a surface pressure on the internal cavity. Reamins to define the pressure value, absolute (including outside surfaces) or differential (negative pressure inside ?), I'm not sure what to choose, should be thesame, but a test is worth to be performed as quick check.
--
Good luck
Ivar
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Posted:
1 decade ago
Once again, thanks a lot for your helpful reply!
For now, I assumed perfect vacuum in my model. Furthermore, going to 3D solved a lot of problems in my case :) So that's all for the moment...
Chris
For now, I assumed perfect vacuum in my model. Furthermore, going to 3D solved a lot of problems in my case :) So that's all for the moment...
Chris
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Posted:
1 decade ago
Dear Ivar,
Just following on what you say here, you mention that differential pressures in Comsol appear as negative pressure inside the structural element?
The reason being is I have a similar model where I apply a surface positive pressure (pushing outwards) from an internal cavity of a sphere, the cavity is filled with a low E material. The result of a slice of volume pressure plot gives me negative values of pressure when I click inside the cavity. If I apply 2000 Pa to the walls, the pressure inside goes to -1800 Pa, which seems a little weird to me.
I am not sure of the meaning of these negative pressures,
Many thanks again for your input,
Lina
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Posted:
1 decade ago
Hi
I'm not sure I catch you correctly there, but the sign of a pressure is w.r.t. the surface normal. For external boundaries this points outwards, by convention, for internal boundaries there is no convention, therefore one must take some care, comsol uses the up/down notation w.r.t. a specific domain.
Test it out on a simple case i.e. piston ina fixed cylinder, its easier to debug
--
Good luck
Ivar
I'm not sure I catch you correctly there, but the sign of a pressure is w.r.t. the surface normal. For external boundaries this points outwards, by convention, for internal boundaries there is no convention, therefore one must take some care, comsol uses the up/down notation w.r.t. a specific domain.
Test it out on a simple case i.e. piston ina fixed cylinder, its easier to debug
--
Good luck
Ivar
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Posted:
1 decade ago
Thanks a lot Ivar,
yes, the pressure is exerted over an internal boundary, the model entails a pressure being exerted outwards on the internal boundaries of a cavity (membrane). Kind of like what the pressure on the internal surface of a balloon shell would experiment.
The model actually shows that the soft shell expands, like a balloon, with positive applied pressure on the internal surface of the shell. However, the pressure inside the shell, that is, in the material that the shell encloses, i.e. like a balloon filled with gel, shows a negative pressure in the gel material.
I hope this gives a more clear view of the problem,
Thanks again,
(I will definitely try to debug with the piston cylinder, however, any comment you may have is welcome)