Electrostatics problem: Metal coupled to a semiconductor

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Discussion Overview

The discussion revolves around the calculation of electrostatic potential in a system where a semiconductor with a charge distribution in the conduction band is coupled to a metal. Participants explore the application of Poisson's equation and the necessary boundary conditions for this scenario, particularly concerning the electrostatic potential at the metal boundary and at infinity.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes the need to solve Poisson's equation both inside and outside the semiconductor and expresses confusion about the appropriate boundary conditions, particularly the electrostatic potential at infinity.
  • Another participant suggests that if the conductor has no residual charge, it can be treated as having a constant potential far away, and recommends focusing on the electric field instead.
  • A different participant questions whether the scenario described relates to a Schottky diode, implying a specific context for the semiconductor-metal interaction.
  • Another participant argues that the problem should not be approached purely as a classical electromagnetism issue, emphasizing the importance of considering the difference in Fermi energy between the two materials and its implications at the junction.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the problem, particularly regarding boundary conditions and the relevance of Fermi energy differences, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

Participants highlight the need for specific boundary conditions and the implications of charge distributions, but do not resolve the assumptions about the electrostatic potential at infinity or the treatment of the electric field.

aaaa202
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I am simulating a system, where I have a semiconductor with a charge distribution in the conduction band coupled to a metal. I want to calculate the electrostatic potential due to this charge distribution but some things are confusing me. To calculate the electrostatic potential I solve Poissons equation inside and outside the semiconductor. To do so I need to supply it with some boundary conditions. Since the metal is a conductor the electrostatic potential should approach a constant at the metal boundary. Furthermore I should also specify the electrostatic potential in the vacuum region far away from the semiconductor, i.e. at infinity. But what should this value be? Obviously it should be a constant but I do not think it should be the same constant as in the metal. What are your thoughts on this?
 
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If conductor has no residual charge on its boundary then it can be considered as constant potential very far. It will be better to work with electric field instead. It should be zero inside and normal outward at the surface always!
 
aaaa202 said:
I am simulating a system, where I have a semiconductor with a charge distribution in the conduction band coupled to a metal.
So you are talking about a Schottky diode?
 
aaaa202 said:
I am simulating a system, where I have a semiconductor with a charge distribution in the conduction band coupled to a metal. I want to calculate the electrostatic potential due to this charge distribution but some things are confusing me. To calculate the electrostatic potential I solve Poissons equation inside and outside the semiconductor. To do so I need to supply it with some boundary conditions. Since the metal is a conductor the electrostatic potential should approach a constant at the metal boundary. Furthermore I should also specify the electrostatic potential in the vacuum region far away from the semiconductor, i.e. at infinity. But what should this value be? Obviously it should be a constant but I do not think it should be the same constant as in the metal. What are your thoughts on this?

I'm with svein. You're trying to do what has already been done and shown many times (mostly in textbooks).

Rather than approaching this as a classical E&M problem, you need to deal with the difference in the Fermi energy of each material and learn what happens when two materials of different Fermi energy at in contact with one another. The physics at the junction is no different than the physics at, say, a p-n junction that causes the depletion layer boundary.

Zz.
 

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