Drift-diffusion solution wihtout using Plasma module

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Ahmad Islam

Ahmad Islam

December 26, 2013 5:26pm UTC

Drift-diffusion solution wihtout using Plasma module

I want to use comsol to solve drift-diffusion and Poisson equation in a coupled manner for a wire that has variable resistance (or charge density) across it. Charge density at each location depends on the potential that is present at that point. I need the solution in a 2D-axisymetric geometry. Currently, I can do the Poisson part easily using the comsol 4.3a that we have in our lab. However, our version does not have the Plasma module that I need for solving Drift-Diffusion.

In such case, please suggest me alternate ways of solving drift-diffusion without using the plasma module.

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Luke Gritter

Luke Gritter
Certified Consultant
AltaSim Technologies

December 27, 2013 2:29pm UTC in response to Ahmad Islam

Re: Drift-diffusion solution wihtout using Plasma module

Ahmad,

You can implement a drift-diffusion equation using the Transport of Diluted Species interface or one of the PDE interfaces. Drift-diffusion equations usually have to be solved in the time-dependent form to obtain a solution.

--
Luke Gritter
AltaSim Technologies

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Ahmad Islam

Ahmad Islam

December 27, 2013 3:32pm UTC in response to Luke Gritter

Re: Drift-diffusion solution wihtout using Plasma module

Luke,

Thanks for your comments. In the Transport of Diluted Species interface or Convection-Diffusion Module that you are suggesting, I am confused about how to incorporate position dependent velocity (u) within the model. Currently, the system takes either constant or uniform position dependence along r or z. But for my case, velocity variation is extremely non-uniform.

- Ahmad

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Luke Gritter

Luke Gritter
Certified Consultant
AltaSim Technologies

December 27, 2013 5:00pm UTC in response to Ahmad Islam

Re: Drift-diffusion solution wihtout using Plasma module

Ahmad,

If by “velocity” you mean the velocity of a neutral background fluid, then this is entered under the model inputs on the Convection and Diffusion node. You can enter any expression for the bulk fluid velocity or couple this interface to the results of one of the fluid flow interfaces.

If you have the Chemical Reaction Engineering Module, you can activate “Migration in electric field” to turn on the drift term. If you don’t have this module, you will have to modify the equation to properly account for the drift term, which can be done in a variety of ways (e.g. by using the conservative form and applying the drift term through the velocity input, modifying the equations in the Equation View, or adding a weak contribution).

Depending on the specific details of your problem, a PDE interface may be more suitable. This approach gives you the greatest flexibility and has the added benefit of allowing you to solve for the log of the species density, which can be more stable and accurate.

--
Luke Gritter
AltaSim Technologies

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Ahmad Islam

Ahmad Islam

December 27, 2013 5:25pm UTC in response to Luke Gritter

Re: Drift-diffusion solution without using Plasma module

Luke,

Thanks again for your mail and sorry for not clarifying my issues earlier.

The "velocity" that I need to use for my charged carriers comes from "Electric field" that I am obtaining by solving Poisson equation. Currently, convection-diffusion module has the term: velocity x derivative of carrier concentration (i.e., u*del C). But, I also need a C* del u term to take care of the non-uniform velocity or electric field within the simulated structure.

And, unfortunately, I do not have the Chemical Reaction Engineering module in my package.

- Ahmad

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Luke Gritter

Luke Gritter
Certified Consultant
AltaSim Technologies

December 27, 2013 7:08pm UTC in response to Ahmad Islam

Re: Drift-diffusion solution without using Plasma module

Ahmad,

To implement the drift term in the Transport of Diluted Species interface in the base package, you can change the convective term to "Conservative form" under Advanced Settings on the Transport of Diluted Species node (make sure you have Advanced Physics Options visible). This will properly account for the non-uniform electric field, and you can then use the velocity field inputs to specify the drift term.

--
Luke Gritter
AltaSim Technologies

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Ahmad Islam

Ahmad Islam

December 27, 2013 7:32pm UTC in response to Luke Gritter

Re: Drift-diffusion solution without using Plasma module

Got it. Thanks.

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Daniel Smith

Daniel Smith
COMSOL Employee
USA

January 2, 2014 9:45pm UTC in response to Ahmad Islam

Re: Drift-diffusion solution without using Plasma module

Hi, I'd just like to add that we have application specific implementations of the drift diffusion equations in the Plasma, Semiconductor and Electrochemical modules. The modules also have a set of appropriate boundary conditions for the physics in question. Manually implementing such boundary conditions by modifying the diluted species or using the general purpose PDE templates would be extremely difficult and time consuming. We always recommend using one of our add-on modules when appropriate.

Regards,
Dan

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