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Thermal Stress in 300 mm silicon Wafer Multi Layer Coating

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Hi all,

I try to solve a 2d, rotary symmetric model of a 300 mm silicon wafer which is coated with 3 layers in a thickness range of a view tens of nm. The first problem is the high aspect ratio that is canceling all coated layers if i enlarge the radius to 150 mm. So it´s not possible to connect the material nodes to the appr. layer. If i go back to the geometry node, the layers are all displayed. Is there any tollerance setting for visualization? But the thickness of the whole structure is also changed if i switch to real life 150 mm radius. If i set the radius to e.g. 1 mm it works. I don´t understand this problem, because it´s just a number. If 1mm or 150mm shouldn´t make a different at such a simple model.

Thanks for any comment,

Sven


8 Replies Last Post 16 août 2018, 11:45 UTC−4

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Posted: 6 years ago 7 août 2018, 06:25 UTC−4

I would recommend you to use the membrane physics for the thin films, if you have access to?

I would recommend you to use the membrane physics for the thin films, if you have access to?

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Posted: 6 years ago 7 août 2018, 11:33 UTC−4

Salut Etienne,

thanks for your prompt reply. Well, I also thought about membranes, shells or plates, but the problem is, that I need multiple "Membranes" or shells in a kind of laminate structure out of different materials. To implement one membrane to a 2d edge e.g. is possible, but not more, because how do you wanna distinguish between several membranes or shells if they are connected to same boundary or edge? You´re not able to specify different materials anymore. Also the layer feature in the geometry node doesn´t support this aspect ratio and requests a higher thickness of the single layers. It´s a bit disappointing.

Thanks, Sven

Salut Etienne, thanks for your prompt reply. Well, I also thought about membranes, shells or plates, but the problem is, that I need multiple "Membranes" or shells in a kind of laminate structure out of different materials. To implement one membrane to a 2d edge e.g. is possible, but not more, because how do you wanna distinguish between several membranes or shells if they are connected to same boundary or edge? You´re not able to specify different materials anymore. Also the layer feature in the geometry node doesn´t support this aspect ratio and requests a higher thickness of the single layers. It´s a bit disappointing. Thanks, Sven

Henrik Sönnerlind COMSOL Employee

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Posted: 6 years ago 8 août 2018, 03:55 UTC−4

Hi Sven,

You can add three Membrane interfaces to the same boundary. The material data can be given in the local Linear Elastic Material node, instead of taking it 'From material'. Since the layers are so thin, the actual stacking order should be irrelevant.

In order to couple the solid and the membranes, change the displacement degree of freedom in all Membrane interfaces to be the same as in Solid Mechanics ('u').

Regards,
Henrik

-------------------
Henrik Sönnerlind
COMSOL
Hi Sven, You can add three Membrane interfaces to the same boundary. The material data can be given in the local Linear Elastic Material node, instead of taking it 'From material'. Since the layers are so thin, the actual stacking order should be irrelevant. In order to couple the solid and the membranes, change the displacement degree of freedom in all Membrane interfaces to be the same as in Solid Mechanics ('u'). Regards, Henrik

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Posted: 6 years ago 8 août 2018, 12:18 UTC−4

Hi Henrik,

thanks for your proposal. Actually it seems to work. But there are some minor problems I still have.

1: If you look at the attached picture, you can see that the model is somehow fixed at the rotary axis. I already included the "rigid body movement suppession node". But...

2: I apply in several steps different temperature changes to the stack → i wanna simulate the depositing process to get the residual stress inside the layers. How is it possible to take the previous solution (stress or strain) as startpoint for the next sol. step? Using the "initial stress/strain" node, to be honest i don´t know which parameters I should put in the matrix. And the help bottom is not helpfull at all in this case.

3: Is it possible to display / get the stress values for the different layers/membranes? They are not visible, so I don´t find a way to visualize them.

Thanks and regards, Sven

Hi Henrik, thanks for your proposal. Actually it seems to work. But there are some minor problems I still have. 1: If you look at the attached picture, you can see that the model is somehow fixed at the rotary axis. I already included the "rigid body movement suppession node". But... 2: I apply in several steps different temperature changes to the stack → i wanna simulate the depositing process to get the residual stress inside the layers. How is it possible to take the previous solution (stress or strain) as startpoint for the next sol. step? Using the "initial stress/strain" node, to be honest i don´t know which parameters I should put in the matrix. And the help bottom is not helpfull at all in this case. 3: Is it possible to display / get the stress values for the different layers/membranes? They are not visible, so I don´t find a way to visualize them. Thanks and regards, Sven


Henrik Sönnerlind COMSOL Employee

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Posted: 6 years ago 9 août 2018, 02:08 UTC−4

Hi Sven,

  1. It is difficult to guess, but maybe you have added Rigid Motion Suppression to more than one of the physics interfaces.

  2. One way of activating the deposited material is to set a very low Young's modulus before it is deposited (E is then a function of a sweep parameter). Alternatively, you can run several sequential study steps, where you do not solve for the not yet deposited layers. In eihter case, the layer must be activated with zero stress, that is with initial strains. Since all layers share the same strain at the surface, you can use the strains in any of the aleady active layers (or the layer itself, if you are using the 'low E' approach). Use the 'withsol()' operator to pick the strains from a selected previous step.

This process can, by the way, be automated in the next version (5.4).

  1. Yes, you have the results for all layers available in the result menus.

Regards,
Henrik

-------------------
Henrik Sönnerlind
COMSOL
Hi Sven, 1. It is difficult to guess, but maybe you have added Rigid Motion Suppression to more than one of the physics interfaces. 2. One way of activating the deposited material is to set a very low Young's modulus before it is deposited (E is then a function of a sweep parameter). Alternatively, you can run several sequential study steps, where you do not solve for the not yet deposited layers. In eihter case, the layer must be activated with zero stress, that is with initial strains. Since all layers share the same strain at the surface, you can use the strains in any of the aleady active layers (or the layer itself, if you are using the 'low E' approach). Use the 'withsol()' operator to pick the strains from a selected previous step. This process can, by the way, be automated in the next version (5.4). 3. Yes, you have the results for all layers available in the result menus. Regards, Henrik

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Posted: 6 years ago 9 août 2018, 09:12 UTC−4

Hi Henrik,

thanks, your hints were great.

1: You was right. I had the "rigid motion suppr." node on every interface. This problem was solved very fast. Thanks for that.

2: I choose the way with the several studies for each depositing step, so that each studie run´s through all previous interfaces too. So I build up the model for each solution- and "depositing"- step + the new layer. To the "already existing" layers and the substrat I added an "initial stressund strain" node. Every existing layer and substrat I pointet to the same layer at the previous solution regarding the stress or strain. But at this point I´m still struggeling a bit with the right operator synthax. The "initial stressund strain" node for solid and membrane is different. Especially for the membrane it´s a bit confusing. I´ve attached 2 pictures for solid and membranes. Additionally I attached 2 pictures of possible strain and stress tensor components. There are several possible tensors, but which one is appropriating? Sure I could try them all and take the one which gives me the best results, but i would like to understand there meaning. Altogether, the model runs, even if the results are not matching the measurements. But i guess it´s also a matter of a lot of material property assumptions.

3: Yes your´re right, now that the model runs through, I see the plots for the membranes.

Thanks, Sven.

Hi Henrik, thanks, your hints were great. 1: You was right. I had the "rigid motion suppr." node on every interface. This problem was solved very fast. Thanks for that. 2: I choose the way with the several studies for each depositing step, so that each studie run´s through all previous interfaces too. So I build up the model for each solution- and "depositing"- step + the new layer. To the "already existing" layers and the substrat I added an "initial stressund strain" node. Every existing layer and substrat I pointet to the same layer at the previous solution regarding the stress or strain. But at this point I´m still struggeling a bit with the right operator synthax. The "initial stressund strain" node for solid and membrane is different. Especially for the membrane it´s a bit confusing. I´ve attached 2 pictures for solid and membranes. Additionally I attached 2 pictures of possible strain and stress tensor components. There are several possible tensors, but which one is appropriating? Sure I could try them all and take the one which gives me the best results, but i would like to understand there meaning. Altogether, the model runs, even if the results are not matching the measurements. But i guess it´s also a matter of a lot of material property assumptions. 3: Yes your´re right, now that the model runs through, I see the plots for the membranes. Thanks, Sven.


Mats Danielsson COMSOL Employee

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Posted: 6 years ago 16 août 2018, 05:43 UTC−4
Updated: 6 years ago 16 août 2018, 05:43 UTC−4

Hi Sven,

I think you are on the right track. With regard to the strains to use, I believe you should use the elastic strains (mbrn.eel11 etc.). It is the elastic strain that is producing stress, so by "offsetting" using the elastic strain, you ensure a stress-free activation of a layer.

Good luck!

Mats

Hi Sven, I think you are on the right track. With regard to the strains to use, I believe you should use the elastic strains (mbrn.eel11 etc.). It is the elastic strain that is producing stress, so by "offsetting" using the elastic strain, you ensure a stress-free activation of a layer. Good luck! Mats

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Posted: 6 years ago 16 août 2018, 11:45 UTC−4

Hi Mats,

thanks for the hint. It seems that this has the right effect on my model. The results are much more plausible and fitting to the real measurements now.

Thank you very much,

best regards

Sven

Hi Mats, thanks for the hint. It seems that this has the right effect on my model. The results are much more plausible and fitting to the real measurements now. Thank you very much, best regards Sven

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