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George Pau

Why does the potential show a singularity at the location where the boundary condition changes from Dirichlet to Neumann?

At the gate side, there is a change of boundary condition from Dirichlet to Neumann as we move from the gate to the insulator. Mathematically, this will lead to a singularity in the solution when we solve the poisson equation. Is there a reason why I am not seeing that in the solution generated by omenwire?

Thanks, George

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    Carlos Malheiro

    Hello!

    Well maybe just feed the polos with electrons I thing with a charge of 5 kilotons, and to reach to neumann just adjust the location and adjucation of the forces introducing an electromagnectic combustion with a ph of 30 positive and also ions of 900 megatons

    Greetings

    Cmalheiro

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    SungGeun Kim

    Sorry for the late answer. While I was asking people about this, nobody seems to have answer on this. However, to clarify the question, in what plot, would you expect to see the singularity? Because there is no cross-sectional plot for electro-static potential, it is very natural that you cannot see any singularity.

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      George Pau

      I am referring to the solution to the poisson equation, phi. The singularity I am referring to is explained in

      Sergey Repin, Stefan Sauter, Anton Smolianski, A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions, Journal of Computational and Applied Mathematics, Volumes 164-165, Proceedings of the 10th International Congress on Computational and Applied Mathematics, 1 March 2004, Pages 601-612, ISSN 0377-0427, DOI: 10.1016/S0377-0427(03)00491-6. (Section 5)

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        SungGeun Kim

        Ok, you mean that you cannot see singularities in 1D bandstructure plot? The 1D bandstructure plot has electrostatic potential(phi as you said) from source to drain. Therefore you cannot see any singularity. If you are mentioning 3D plot, you can see there is potential change when you go from the center of the nanowire to the oxide. However, if you want to see the sigularities there, you want to plot the 1D electrostatic potential plot from the center of the nanowire to the edge of oxide which needs more work. If you want that, we could try to do it in the next version of OMEN Nanowire, but we need very good and practical reasons why we should plot it.

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      George Pau

      A more physical explanation can be found in

      A. W. Smith, J. W. Parks, J. N. Haralson, K .F. Brennan, A smoothed Boundary Condition for Reducing Nonphysical Field Effects, IEE transactions on computer-aided design of integrated circuits and systems, 16(4):420-423, 1997

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    SungGeun Kim

    For this, I am not sure. I will get back to you after looking for a person who can answer.

    Thanks

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      George Pau

      Hi SungGeun,

      The question summary should have said \“Why doesn\‘t …..\” instead of \“Why does …\”. Sorry about that.

      George

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