Depletion region and Schottky Barriers

[aaaa202]

I am having some trouble understanding the physics behind the formation of Schottky Barriers. According to the convential theory, the idea is that for an n-type semiconductor the electrons in the conduction band can lower their energy by filling empty states in the metal. This in turns creates a positively charged region in the vicinity of the interface for which you can solve Poissons equation and demand that the electrostatic potential compensates the offset between the Fermi level of the metal and the conduction band of the semiconductor. The effect of this is that you get a barrier near the interface that prevents anymore electrons from flowing into the metal. From an electrostatic point of view I have a hard time understanding this barrier. Since the depletion region has a positive charge, my intuition tells me that it should be energetically favourable for an electron in the bulk of the semiconductor to move to this region. Somehow this is not the case but I don't understand why. My feeling is that it is has something to do with screening from the metal and the fact that in reality there is not only the space charge region but also a negative sheet of charge at the surface of the metal creating a dipole potential.

 

[marcusl]

You can look at this as two opposing currents, one due to diffusion and the other due to electrostatic attraction. You have, in fact, mentioned both of these when you speak of electrons "moving." The net current across the contact region is zero at equilibrium, by definition, so the currents must be exactly balanced. You have accounted for the electric potential; you must add the other potential (diffusion) which is driven by the gradient of the chemical potential, just as it would be for atoms in a gas or ions in a liquid.

 

[Henryk]

the idea is that for an n-type semiconductor the electrons in the conduction band can lower their energy by filling empty states in the metal

That is correct

This in turns creates a positively charged region in the vicinity of the interface

That is correct to, but, keep in mind, the first quoted sentence: electrons moved to the metal !, that means the metal is charged negatively relative to the semiconductor. The negative charge of the metal is what repels the electrons from the interface and creates the positively charged region in the vicinity of the interface. The positively charged region just screens the field created by transfer of electrons from semiconductor to the metal.