Electrostatics problem: Metal coupled to a semiconductor

[aaaa202]

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?

 

[Let'sthink]

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!

 

[Svein]

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?

 

[ZapperZ]

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.