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PDE-interface, implementation of a 'jump' in the dependent variables at a boundary
Posted 19.05.2013, 10:43 GMT-4 Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.3a, Version 5.0 2 Replies
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Dear COMSOL-community,
currently I am trying to implement a model (in COMSOL 4.3a) in order to simulate the injection of spin currents from a ferromagnet into a semiconductor via a tunnel barrier.
The basic physical situation can be described be using the Valet-Fert-equation/drift-diffusion-equation for the spin-up and spin-down electrochemical potentials. Therefore, I used the PDE-interface with two dependent variables (to be precise, I made use of the ‘coefficient form’) and chose the different parameters in such a way, that I was able to implement the differential equation mentioned above.
In order to keep the model as simple as possible and to see if the model works properly, I neglected the tunnel barrier in a first step and reduced the model to a two-dimensional geometry. Therefore, the model restricts itself to two rectangles which are separated by a shared boundary.
Firstly, I implemented only a current source on the one side and on the other side a ground (Dirichlet boundary condition). The results are quite convincing and match the theoretical expectation, so therefore I am willing to assume that in principle the model is correct. Additionally, if expanded to three dimensions, everything seems to be fine as well.
Now, I would like to implement the tunnel barrier. It can ‘simply’ be described by having a jump at the boundary in the spin-up and spin-down electrochemical potentials mu_s, respectively. Unfortunately, at that point I am lost.
The conditions read (the tunnel barrier shall be located at z = z_0):
lim(epsilon -> 0)[(mu_s(z_0 + epsilon) – mu_s(z_0 – epsilon))] = constant * d(mu_s)/dz
with s = +,- for spin-up and spin-down, respectively. d(mu_s)/dz shall be the normal derivative of mu_s at z = z_0.
I assume that the solution of this problem requires the ‘weak form’ of the condition and the up/down-operator but after several hours/days of searching I am still not able to implement it properly (I tried Dirichlet boundary conditions but it turned out to be an unrewarding idea).
At this point, I’d like to thank you for reading my problem up to this point and I appreciate any suggestions and hints!
Kind regards
Matthias
currently I am trying to implement a model (in COMSOL 4.3a) in order to simulate the injection of spin currents from a ferromagnet into a semiconductor via a tunnel barrier.
The basic physical situation can be described be using the Valet-Fert-equation/drift-diffusion-equation for the spin-up and spin-down electrochemical potentials. Therefore, I used the PDE-interface with two dependent variables (to be precise, I made use of the ‘coefficient form’) and chose the different parameters in such a way, that I was able to implement the differential equation mentioned above.
In order to keep the model as simple as possible and to see if the model works properly, I neglected the tunnel barrier in a first step and reduced the model to a two-dimensional geometry. Therefore, the model restricts itself to two rectangles which are separated by a shared boundary.
Firstly, I implemented only a current source on the one side and on the other side a ground (Dirichlet boundary condition). The results are quite convincing and match the theoretical expectation, so therefore I am willing to assume that in principle the model is correct. Additionally, if expanded to three dimensions, everything seems to be fine as well.
Now, I would like to implement the tunnel barrier. It can ‘simply’ be described by having a jump at the boundary in the spin-up and spin-down electrochemical potentials mu_s, respectively. Unfortunately, at that point I am lost.
The conditions read (the tunnel barrier shall be located at z = z_0):
lim(epsilon -> 0)[(mu_s(z_0 + epsilon) – mu_s(z_0 – epsilon))] = constant * d(mu_s)/dz
with s = +,- for spin-up and spin-down, respectively. d(mu_s)/dz shall be the normal derivative of mu_s at z = z_0.
I assume that the solution of this problem requires the ‘weak form’ of the condition and the up/down-operator but after several hours/days of searching I am still not able to implement it properly (I tried Dirichlet boundary conditions but it turned out to be an unrewarding idea).
At this point, I’d like to thank you for reading my problem up to this point and I appreciate any suggestions and hints!
Kind regards
Matthias
2 Replies Last Post 05.09.2016, 23:42 GMT-4
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Posted:
1 decade ago
Appendix:
Please find attached the file 'cylindrical_geometry.mph' which contains the implemented Valet-Fert-equation WITHOUT the tunnel barrier. As mentioned above, this model seems to deliver reasonable results.
Please find attached the file 'cylindrical_geometry.mph' which contains the implemented Valet-Fert-equation WITHOUT the tunnel barrier. As mentioned above, this model seems to deliver reasonable results.
Attachments:
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Posted:
8 years ago
Hi, Matthias_FZJuelich
It's my great honour to find your post which would be helpful to my work. I want to make a simulation of the spin diffusion in QWs. But I am unfamiliar with the Comsol. I couldn't find relevant example in Semiconductor model library manual. It's easy for my purpose which achieve a 2D spin diffusion simulation as the function of position and time coordinates. I want to make the model in Comsol 5.0 semiconductor module. My idea is that electron dependent varieble "n" is replaced by spin variable "s", then set solution as "majority carriers, electrons",but this model doesn't run well due to change of the variebles. Could you give me some substantive advice in semiconductor module or PDE interface, thanks.
with best regards!
Bo Li
China
It's my great honour to find your post which would be helpful to my work. I want to make a simulation of the spin diffusion in QWs. But I am unfamiliar with the Comsol. I couldn't find relevant example in Semiconductor model library manual. It's easy for my purpose which achieve a 2D spin diffusion simulation as the function of position and time coordinates. I want to make the model in Comsol 5.0 semiconductor module. My idea is that electron dependent varieble "n" is replaced by spin variable "s", then set solution as "majority carriers, electrons",but this model doesn't run well due to change of the variebles. Could you give me some substantive advice in semiconductor module or PDE interface, thanks.
with best regards!
Bo Li
China