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Electro statical actuation of a cantilever
Posted 06.11.2009, 13:41 GMT-5 3 Replies
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Hi all,
I'm new in using COMSOL, but I have already worked through a bunsh of tutorials. My aim is to model a micromirror membrane which consists of many layers (in the final type at least 25 layers) with different stress characteristics. This membrane additionaly consists of a conductive layer thus electrostatic actuation with an additional counterelectrode should be possible.
To get started with this problem I reduced the problem to a two layer cantilever in 2D. The cantilever deflects due to stress in one of the two layers. This works well up to values of about 100e6 Pa for Sigma_x (Material is GaAs) in one layer. If i further increase the stress, inverted mesh elements occur and I don't really understand what's the meaning of this and how I can get rid of this problem. Nevertheless I went on in modeling with 100e6 for which the problem could be solved. I set up all the boundary conditions for the Solid Stress & Strain, Moving Mesh and Electrostatics package. I just wanted to get a feeling of the dependency between the total displacement and the applied voltage (which I set up between a counter electrode and the top surface of the cantilever). I followed the given Models in the MEMS package "comb drive 2d" and "ale cantilever beam 2d". The difference to the latter is, that I now have two layers and my material is prestressed as i already mentioned.
The curious thing now is that an increase in voltage leads to an increase of the airgap between my cantilever and the counter electrode. I would assume them to attract each other. Another point is the order of magnitude which you need to see even small effects in a change of deflection (more than 1000 V at a spacing of only 2.5-5 µm of the two electrodes and a thickness of the cantilever of only 2 µm).
I think something must be definitely wrong with the boundary conditions, but I really don't know what could be wrong. I attached the model maybe someone can help me there by having a look on it.
If I forgot some important additional information let me know.
Thanks for your help!
I'm new in using COMSOL, but I have already worked through a bunsh of tutorials. My aim is to model a micromirror membrane which consists of many layers (in the final type at least 25 layers) with different stress characteristics. This membrane additionaly consists of a conductive layer thus electrostatic actuation with an additional counterelectrode should be possible.
To get started with this problem I reduced the problem to a two layer cantilever in 2D. The cantilever deflects due to stress in one of the two layers. This works well up to values of about 100e6 Pa for Sigma_x (Material is GaAs) in one layer. If i further increase the stress, inverted mesh elements occur and I don't really understand what's the meaning of this and how I can get rid of this problem. Nevertheless I went on in modeling with 100e6 for which the problem could be solved. I set up all the boundary conditions for the Solid Stress & Strain, Moving Mesh and Electrostatics package. I just wanted to get a feeling of the dependency between the total displacement and the applied voltage (which I set up between a counter electrode and the top surface of the cantilever). I followed the given Models in the MEMS package "comb drive 2d" and "ale cantilever beam 2d". The difference to the latter is, that I now have two layers and my material is prestressed as i already mentioned.
The curious thing now is that an increase in voltage leads to an increase of the airgap between my cantilever and the counter electrode. I would assume them to attract each other. Another point is the order of magnitude which you need to see even small effects in a change of deflection (more than 1000 V at a spacing of only 2.5-5 µm of the two electrodes and a thickness of the cantilever of only 2 µm).
I think something must be definitely wrong with the boundary conditions, but I really don't know what could be wrong. I attached the model maybe someone can help me there by having a look on it.
If I forgot some important additional information let me know.
Thanks for your help!
Attachments:
3 Replies Last Post 18.11.2009, 05:22 GMT-5
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Posted:
2 decades ago
No one who can help me with this problem?
Thanks - Christian
Thanks - Christian
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Posted:
2 decades ago
Hi Christian,
I gave a quick look to your model.
In attachment you see your model with some modifications that seem right to me.
Unfortunately now I do not have enough time to post all the explanations.
In any case, keep in mind that:
1) GaAs is an insulator, while in order to have a good actuation (and therefore an higher displacement of your by-layer structure) mechanism you have to set some conductivity (due to dopant) in these materials.
2) I think that 1000V as highest voltage is a too high value for such a structure. You will have pull-in in these conditions. This may be the cause of "inverted element" warning.
3) I have set the force on the boundary "in front of" the gap and to the "upper" one (check your model to understand what I'm saying)
4) the Au counterelectrode do not need any physical displacement. I suppose it is fixed. If I'm right, you can save computational cost and time by setting a "zero displacement" as subdomain condition in the ale module.
I hope this help.
Hi,
Alessandro Ricci
I gave a quick look to your model.
In attachment you see your model with some modifications that seem right to me.
Unfortunately now I do not have enough time to post all the explanations.
In any case, keep in mind that:
1) GaAs is an insulator, while in order to have a good actuation (and therefore an higher displacement of your by-layer structure) mechanism you have to set some conductivity (due to dopant) in these materials.
2) I think that 1000V as highest voltage is a too high value for such a structure. You will have pull-in in these conditions. This may be the cause of "inverted element" warning.
3) I have set the force on the boundary "in front of" the gap and to the "upper" one (check your model to understand what I'm saying)
4) the Au counterelectrode do not need any physical displacement. I suppose it is fixed. If I'm right, you can save computational cost and time by setting a "zero displacement" as subdomain condition in the ale module.
I hope this help.
Hi,
Alessandro Ricci
Attachments:
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Posted:
2 decades ago
Hi Alessandro,
first of all thanks a lot for your reply.
To 1):
actually this cantilever is just a very simple model for later simulations on a distributet bragg reflector membrane (3D with more than 30 layers each of a thickness of Lambda/4 with lambda=1.55µm optical wavelength)
Only the top layer will be conductive due to process techniques (PECVD layers are made of SiO_2 and SiN_x). The insulator characteristics of those layers should prevent a current flow from the upper to the bottom electrode in case of pull in. For the Force it should make only the difference that the capacity increases with those layers (epsilon_r) between the two electrodes and thus the electrostatical force increaes too with the factor epsilon_r which is quite nice (There is an applied voltage so V=const.) because it compensates slightly the larger spacing between the two electrodes (Force increases linearly with epsilon_r but decreases to 1/d^2 where d is the spacing / air gap).
To 2):
I set this high voltage because lower voltages didn't attract the cantilever (displacement was smaller than nm).
To 3):
Doesn't it make a big difference if you apply the force to the lower area of the cantilever instead to the top gold layer which the force is actually acting on? I mean the force at the bottom layer is much higher due to a smaller spacing between the two electrodes. Isn't it a completly different setup which is not compareable with mine? This would work only in the case of doped semi-conductive layers. But unfortunately it will be not possible doping them (for they will be replaced by SiO_2 and SiN_x. Doping for GaAs would be possible of course but is not preferred in the future).
To 4):
I completly agree with this point
I noticed that he is not able to find a solution for U = 0V have you any idea concerning this point? He neither can solve the model if I only solve the solid stress strain part. So I can not determine the bending of the cantilever in the rest position (caused by the different stress in the two layers).
Again: Thanks a lot Alessandro!
first of all thanks a lot for your reply.
To 1):
actually this cantilever is just a very simple model for later simulations on a distributet bragg reflector membrane (3D with more than 30 layers each of a thickness of Lambda/4 with lambda=1.55µm optical wavelength)
Only the top layer will be conductive due to process techniques (PECVD layers are made of SiO_2 and SiN_x). The insulator characteristics of those layers should prevent a current flow from the upper to the bottom electrode in case of pull in. For the Force it should make only the difference that the capacity increases with those layers (epsilon_r) between the two electrodes and thus the electrostatical force increaes too with the factor epsilon_r which is quite nice (There is an applied voltage so V=const.) because it compensates slightly the larger spacing between the two electrodes (Force increases linearly with epsilon_r but decreases to 1/d^2 where d is the spacing / air gap).
To 2):
I set this high voltage because lower voltages didn't attract the cantilever (displacement was smaller than nm).
To 3):
Doesn't it make a big difference if you apply the force to the lower area of the cantilever instead to the top gold layer which the force is actually acting on? I mean the force at the bottom layer is much higher due to a smaller spacing between the two electrodes. Isn't it a completly different setup which is not compareable with mine? This would work only in the case of doped semi-conductive layers. But unfortunately it will be not possible doping them (for they will be replaced by SiO_2 and SiN_x. Doping for GaAs would be possible of course but is not preferred in the future).
To 4):
I completly agree with this point
I noticed that he is not able to find a solution for U = 0V have you any idea concerning this point? He neither can solve the model if I only solve the solid stress strain part. So I can not determine the bending of the cantilever in the rest position (caused by the different stress in the two layers).
Again: Thanks a lot Alessandro!