1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Boundary conditions electrostatic potential

  1. Feb 29, 2016 #1
    I'm modelling a system with a nanosized semiconductor in 1d, inside which I want to find the electrostatic potential. Having found this I am unsure what boundary conditions to put on this, when it is connected to a metal on one side and to vacuum on the other. So far I have put that it is continuous at the metal interface (inside which it is a constant). But what about at the boundary to vacuum. I want to say that it should be simply continiuous which then gives that V(x) has a finite value, non constant, outside the semiconductor. But on the other hand this seems unphysical, since it would imply that there is a finite electric field outside the semiconductor. Should I simply put that V(x)=0 at the boundary to vacuum?
     
  2. jcsd
  3. Feb 29, 2016 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The potential continues into the vacuum the same as any potential does ... i.e. if you were modelling a sheet of charge with a metal on one side and a vacuum on the other how would you do it?

    A perfect metal just stamps it's own potential on everything where it is. You can get a step there... a lump of metal in a vacuum is often modelled as a finite square well.

    What level are you doing this at?
     
  4. Mar 2, 2016 #3
    I am modelling the band structure of a semiconductor-metal hetero junction, by solving the Schrödinger equation in the conduction band (in the effective mass approximation), calculating the electron density and then calculating the electrostatic potential in the semiconductor using Poissons equation. This is then plugged back into the Schrödinger equation and the procedure is reiterated until a self-consistent solution is found.
    When I calculate the electrostatic potential in the heterostructure I get a decay towards the vacuum edge of the semiconductor (on the right). I don't know if this is physical or if it comes from my numerical method failing. Physically I expect that if the semiconductor is large that the potential would approach a constant at the edge to vacuum. What do you think?
     

    Attached Files:

  5. Mar 3, 2016 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Decay of what?

    Sounds like the same calculation as my thesis except I did two semiconductors... I did the self-consistent calculation to include both materials.
    Charges are usually strongly confined to the material - this usually translates to a barrier at the material edges with the bending happening close to the junction.
    So you have vacc-metal-semi-vacc ... then I'd have modelled the outside boundaries as a step potential equal to the work function.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Boundary conditions electrostatic potential
  1. Boundary conditions (Replies: 3)

  2. Boundary conditions (Replies: 0)

  3. Boundary Conditions (Replies: 1)

Loading...