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Thermal Expansion Polycrystalline Silicon
Posted Apr 29, 2016, 4:55 p.m. EDT MEMS & Nanotechnology, MEMS & Piezoelectric Devices Version 5.2 6 Replies
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Hello,
I was trying to find a similar problem to mine but could not find it.
I am trying to find the stress gradient of a poly crystalline thin film layer deposited on silica and single crystal silicon.
To do so, I built the geometry and added a thermal expansion with a surrounding temperature of 800K and strain reference of 293K, with a fixed constraint at the bottom of the layer.
I am trying to find the steady state condition, so I am using the stationary solver.
The problem is that I can't seem to receive a gradient, the stress is constant along the whole layer, and therefore also the displacement.
I don't know what I'm doing wrong, I feel like it should be a simple simulation.
I would really appreciate your advice, and/or if you've seen or programmed similar simulations in the past, I would really appreciate it if you could share them.
Thanks!
Adam
I was trying to find a similar problem to mine but could not find it.
I am trying to find the stress gradient of a poly crystalline thin film layer deposited on silica and single crystal silicon.
To do so, I built the geometry and added a thermal expansion with a surrounding temperature of 800K and strain reference of 293K, with a fixed constraint at the bottom of the layer.
I am trying to find the steady state condition, so I am using the stationary solver.
The problem is that I can't seem to receive a gradient, the stress is constant along the whole layer, and therefore also the displacement.
I don't know what I'm doing wrong, I feel like it should be a simple simulation.
I would really appreciate your advice, and/or if you've seen or programmed similar simulations in the past, I would really appreciate it if you could share them.
Thanks!
Adam
6 Replies Last Post May 7, 2016, 2:43 a.m. EDT
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Posted:
9 years ago
What would cause the stress gradient? I think the simulator is giving the correct answer for the assumptions that went into the problem.
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Posted:
9 years ago
Hi Adam,
these issues are delicate to model, because you have more or less a topology change.
Lets take the case of a silicon wafer of fixed dimensions at T0=20°C=300[K], you heat it up to Thot=1200[K] or somewhere thereabout, in vacuum, the wafer remains more or less stress free- but grows in size due to the thermal expansion coefficient (that is in no way linear for such a temperature range, but lets forget that for the moment).
Then you add oxygen and you oxide the Si surfaces for a thin but significant layer of SiO2 on top of the Si (it could be nitrate or other layers, lets keep it simple SiO2 is a well known material). And you let it cool down, gently. Both the Young modulus and the thermal expansion of both Si and SiO2 changes over these temperatures hence the choice of Tref or the integral thereof has its importance, see the Solid/HT doc or www.comsol.com/community/forums/general/thread/50051/ and here: www.comsol.com/community/forums/structural-mechanics/thread/34508), all by all you come back with a part more or less at the original dimensions, and if you deposit/oxide only on one side of the wafer, definitively stressed are there as observed form the "plate" curvature of you wafer.
To simulate that you need to start from the Si initial size and heat it up to Thot to get the initial expansion, assuming its stress-less at this stage, then "add" a thin shell layer with the SiO2 material properties, also stress less at the Thot temperature, and then let it cool down having the cross coupling of the stiffness from the SiO2 shell layer and from the bulk Si part.
The difficulty is the "add a shell layer" at Thot, this is a topology change.
Simplest workaround: ignore the heating process and the size change, either you add in a known calculated value, or just forget about it.
Make a model with a bulk and a shell surface in Solid with thermal expansion. Set the Initial Temp to Thot, the Tref = Thot, add a dummy variable "T" defined as a parameter to step your solver down from Thot to T0, else add the full HT and a heat convection i.e. of 5[W/m^2/K] and run a steady state analysis.
A simple example is below.
Note the fact that one should use a shell implies to study the stress at the Shell boundary and in the Bulk, one can also ask if the shell neutral layer should be offset as the oxide layer grows also in thickness. Finally I have done a few "dirt trick" in my attached model, I model only a Pie section with a "point" fixed constraint (something to avoid, one also could use a soft Spring Foundation). Then, I renamed the dependent variable of the Shell to just "u" instead of the default "u2", this allows me to forget about the coupling, since the solid is not solved on the boundary where the Shell is defined I can use the same variable and do not need to explicitly write out any coupling between the two physics. This trick can be used, but must be used with caution, it's easy to forget a particular arrangement that might not accept such a shortcut. Finally I set the solver to "Fully Coupled" to have it solve a bit quicker, provided you have enough RAM.
But this is just the beginning, you need to implement the true cooling and alpha(T) relations, perhaps also E(T) relation for the material properties, and then decide if you use the secant or the more precise integration method for the thermal expansion calculations. And then how to add the initial heating without the surface layer, and then have it grown and participating to the cooling only process :)
A nice exercise to play with.
--
Have Fun COMSOLing
Ivar
these issues are delicate to model, because you have more or less a topology change.
Lets take the case of a silicon wafer of fixed dimensions at T0=20°C=300[K], you heat it up to Thot=1200[K] or somewhere thereabout, in vacuum, the wafer remains more or less stress free- but grows in size due to the thermal expansion coefficient (that is in no way linear for such a temperature range, but lets forget that for the moment).
Then you add oxygen and you oxide the Si surfaces for a thin but significant layer of SiO2 on top of the Si (it could be nitrate or other layers, lets keep it simple SiO2 is a well known material). And you let it cool down, gently. Both the Young modulus and the thermal expansion of both Si and SiO2 changes over these temperatures hence the choice of Tref or the integral thereof has its importance, see the Solid/HT doc or www.comsol.com/community/forums/general/thread/50051/ and here: www.comsol.com/community/forums/structural-mechanics/thread/34508), all by all you come back with a part more or less at the original dimensions, and if you deposit/oxide only on one side of the wafer, definitively stressed are there as observed form the "plate" curvature of you wafer.
To simulate that you need to start from the Si initial size and heat it up to Thot to get the initial expansion, assuming its stress-less at this stage, then "add" a thin shell layer with the SiO2 material properties, also stress less at the Thot temperature, and then let it cool down having the cross coupling of the stiffness from the SiO2 shell layer and from the bulk Si part.
The difficulty is the "add a shell layer" at Thot, this is a topology change.
Simplest workaround: ignore the heating process and the size change, either you add in a known calculated value, or just forget about it.
Make a model with a bulk and a shell surface in Solid with thermal expansion. Set the Initial Temp to Thot, the Tref = Thot, add a dummy variable "T" defined as a parameter to step your solver down from Thot to T0, else add the full HT and a heat convection i.e. of 5[W/m^2/K] and run a steady state analysis.
A simple example is below.
Note the fact that one should use a shell implies to study the stress at the Shell boundary and in the Bulk, one can also ask if the shell neutral layer should be offset as the oxide layer grows also in thickness. Finally I have done a few "dirt trick" in my attached model, I model only a Pie section with a "point" fixed constraint (something to avoid, one also could use a soft Spring Foundation). Then, I renamed the dependent variable of the Shell to just "u" instead of the default "u2", this allows me to forget about the coupling, since the solid is not solved on the boundary where the Shell is defined I can use the same variable and do not need to explicitly write out any coupling between the two physics. This trick can be used, but must be used with caution, it's easy to forget a particular arrangement that might not accept such a shortcut. Finally I set the solver to "Fully Coupled" to have it solve a bit quicker, provided you have enough RAM.
But this is just the beginning, you need to implement the true cooling and alpha(T) relations, perhaps also E(T) relation for the material properties, and then decide if you use the secant or the more precise integration method for the thermal expansion calculations. And then how to add the initial heating without the surface layer, and then have it grown and participating to the cooling only process :)
A nice exercise to play with.
--
Have Fun COMSOLing
Ivar
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Posted:
9 years ago
Follow on
Well one should always check a bit ;)
As this example above, slightly improved below.
As it is basically a 2D-axi model I tried to quickly reconstruct it in 2D-axi. But there, there are no "Shell" physics only membranes, so lets try that :)
=> looks nice until one studies the stress and strain or max displacements: we get only about HALF the deformations with a "membrane" in 2Daxi, so a fist lets state: a Membrane is not a Shell is not a Bulk solid ...
Always reread the doc and the hypothesis behind a given physics before clicking and selecting it :)
--
Good luck
Ivar
Well one should always check a bit ;)
As this example above, slightly improved below.
As it is basically a 2D-axi model I tried to quickly reconstruct it in 2D-axi. But there, there are no "Shell" physics only membranes, so lets try that :)
=> looks nice until one studies the stress and strain or max displacements: we get only about HALF the deformations with a "membrane" in 2Daxi, so a fist lets state: a Membrane is not a Shell is not a Bulk solid ...
Always reread the doc and the hypothesis behind a given physics before clicking and selecting it :)
--
Good luck
Ivar
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Posted:
9 years ago
Hi Adam, you are right this is a simple problem and you should see a stress gradient through the thickness, as well as at the edges of that layer. Maybe you did not fix the bottom layer in all directions as intended? Could also be that you have assigned the same temperature and thermal expansion coefficient to the whole model.
Nagi Elabbasi
Veryst Engineering
Nagi Elabbasi
Veryst Engineering
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Posted:
9 years ago
Hi Ivar, thank very much for your detailed response.
The models sure did give me some directions, and instructions on how to move forward when building and simulating COMSOL questions. I believe I received better results now, thank you!
The models sure did give me some directions, and instructions on how to move forward when building and simulating COMSOL questions. I believe I received better results now, thank you!
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Posted:
9 years ago
Hi Nagi, thank your for your reply. I did make sure to add fixed constraints at the bottom, and also on the sides. I defined a reference temperature of 298K and Heat Flux surrounding temperature of 800K.
I believe this is the solution I was suppose to receive. Thanks again!
I believe this is the solution I was suppose to receive. Thanks again!