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Using a function in the expression field of a surface plot- quantum effects

Posted May 29, 2012, 11:27 a.m. EDT Materials Version 4.2a 5 Replies

Josh Lipsmeyer
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Greetings,
I am trying to model field emission from nano-structures. I want to do a surface plot of the current using the Fowler Nordheim equation. When i try to put the equation in the expression field of the surface plot i get an error. I believe it has to do with the fact that it is an exponential function. I am still very new to comsol and am not sure how to remedy this. Could anyone help out? Also, most of what I am modeling involves quantum effects. Does Comsol automatically figure in quantum effects, such as tunneling, or do i need to do something different in order to get an accurate model? Thanks in advance for you help

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5 Replies Last Post May 30, 2012, 2:28 p.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago May 29, 2012, 3:38 p.m. EDT
Hi

I suppose it's rather "exp(-B)" you wanted, or ?

Anyhow, I do not really see why just the plot of es.normE is good enough, if you use the Plot surface rage button you can enhance the color scheme nicely

One suggestion, your air domain is very big, its easier to mesh if you enclose your small structure in an air box (rectangle) perhaps 1 unit free around your device and mesh fine in there, then leave the external air part in normal mesh mode.

Be aware though that part of the field concentrations you obseve are due to numerical issues at the sharp corners, these form singularities, you could try to use very small fillets, and even higher mesh densities locally

--
Good luck
Ivar
Hi I suppose it's rather "exp(-B)" you wanted, or ? Anyhow, I do not really see why just the plot of es.normE is good enough, if you use the Plot surface rage button you can enhance the color scheme nicely One suggestion, your air domain is very big, its easier to mesh if you enclose your small structure in an air box (rectangle) perhaps 1 unit free around your device and mesh fine in there, then leave the external air part in normal mesh mode. Be aware though that part of the field concentrations you obseve are due to numerical issues at the sharp corners, these form singularities, you could try to use very small fillets, and even higher mesh densities locally -- Good luck Ivar
Josh Lipsmeyer
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Posted: 1 decade ago May 29, 2012, 6:08 p.m. EDT
What about quantum effects? If I refine the mesh locally at the tips, will the electric field observe take into account tunneling? The F-N equation is current density as a function of the electric field. The electric field is affected by the tip apex, and therefore affects the current density at the tips according to the F-N equation. There are certain behaviors that are expected with this phenomenon and I am not seeing them. For instance, the closer the structures are together, the lower the E-field should be. I am seeing the reverse of this. So, that is why I am wondering if this package takes into consideration quantum effects. Also, I was able to plot the F-N equation after I made this post. however, I am not sure what I did for it to start working. I just put the F-N equation in the expression field and updated the solution. Thanks for your response!!
What about quantum effects? If I refine the mesh locally at the tips, will the electric field observe take into account tunneling? The F-N equation is current density as a function of the electric field. The electric field is affected by the tip apex, and therefore affects the current density at the tips according to the F-N equation. There are certain behaviors that are expected with this phenomenon and I am not seeing them. For instance, the closer the structures are together, the lower the E-field should be. I am seeing the reverse of this. So, that is why I am wondering if this package takes into consideration quantum effects. Also, I was able to plot the F-N equation after I made this post. however, I am not sure what I did for it to start working. I just put the F-N equation in the expression field and updated the solution. Thanks for your response!!
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago May 30, 2012, 12:54 a.m. EDT
Hi

Well for me you should rather ask yourself which physical equations are describing tunnelling, and which are used by COMSOL by default in RF, what is missing ?.

I do not believe that refining the mesh can change the physics, the meshing is "just" a method to sample your calculations.

Quantum effects must be part of the model phyical description to be observed in the simulations. But you can extend COMSOL, the Model builder Schroedinger equation example is in the doc

--
Good luck
Ivar
Hi Well for me you should rather ask yourself which physical equations are describing tunnelling, and which are used by COMSOL by default in RF, what is missing ?. I do not believe that refining the mesh can change the physics, the meshing is "just" a method to sample your calculations. Quantum effects must be part of the model phyical description to be observed in the simulations. But you can extend COMSOL, the Model builder Schroedinger equation example is in the doc -- Good luck Ivar
Josh Lipsmeyer
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Posted: 1 decade ago May 30, 2012, 10:53 a.m. EDT
I am using the electrostatics package. Where can I find a list of all of the variables and all of the equations used in this package. I know that this package solves for potential and then goes from there. But where can I find the variables and equations?
I am using the electrostatics package. Where can I find a list of all of the variables and all of the equations used in this package. I know that this package solves for potential and then goes from there. But where can I find the variables and equations?
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago May 30, 2012, 2:28 p.m. EDT
Hi

I havent seen any exhaustive list yet for v4, so probably its in preparation, you have quite a lot squattered around in the doc, but also you have the lists under derived values global evaluation or integral ... you can get the ordered lists from the pull down menu.

Else you can turn on the Equation view and peek thereunder

--
Good luck
Ivar
Hi I havent seen any exhaustive list yet for v4, so probably its in preparation, you have quite a lot squattered around in the doc, but also you have the lists under derived values global evaluation or integral ... you can get the ordered lists from the pull down menu. Else you can turn on the Equation view and peek thereunder -- Good luck Ivar

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