Semiconductors: charge neutrality

[marie2010]

hi,
can someone explain me what the charge neutrality level is in semiconductors. In particular, how do you define it with respect to the Fermi level? What about the Fermi level pinning? Is the branch point energy same as the charge neutrality level? How are these things related?
I appreciate your response.
Thank you.

 

[caffenta]

Like the name suggests, the charge neutrality level is the energy level at which the surface (or interface) is electrically neutral. If you have no surface states, the charge neutrality level would be the same as the Fermi-level (in equilibrium). If there are filled acceptor surface states, the Fermi level will be above the charge neutrality level. I think this picture illustrates it pretty well: http://academic.brooklyn.cuny.edu/physics/tung/Schottky/ele-aff1.jpg

Fermi level pinning occurs when the density of surface/interface states is so high that these states absorb any change in charge density. Applying a voltage would not move the Fermi level because the surface states get filled or emptied instead.

Btw, I often see textbooks that claim that surface states are always located within the band-gap, but this is not necessarily true. One good example of the opposite is InAs. It has donor surface states located above the conduction band edge which strongly pin the Fermi level. InAs has a natural accumulation layer, instead of a depletion layer which is most common. Another misconception I often see quoted is that the lack of band bending indicates the lack of Fermi level pinning. This is also not necessarily true. The surface states could be located at the Fermi level and application of a voltage would not be able to move the Fermi level if the density of those states is high.

 

[marie2010]

Thank you for the reply. I still have a question about how to determine where the neutrality level is for a given surface structure. That is, by looking at the density of states plots, where do we mark the charge neutrality level? I appreciate your help. Thank you.

 

[caffenta]

I don't think it is possible to pinpoint the CNL just by looking at the density of (surface) states plot. At least not as a general rule. But I may be wrong. I haven't done this type of work in over a decade. Sorry.

 

[marie2010]

Thank you for the reply. If one cannot (or maybe can) pinpoint the CNL by looking at the density of surface states plots, is there any another way of doing so? It seems that the knowledge of the CNL is very important for understanding the electronic structure of surfaces in general. Oh, one more thing, so for bulk systems, CLN=Fermi level, right?
Thanks for your help.

 

[caffenta]

There are multiple ways of determining the CNL. One is to model the charge and Fermi level position near the surface. The excess or missing charge can be used to find the CNL. There may be charge contributors other than surface states, so they must be accounted for as well. Experimentally, techniques like PES or BEEM can be used. Electrical measurements like CV or Hall are useful for buried interfaces.

I think the CNL discussed here should only be used with respect to surface/interface states. But I guess in equilibrium, since charge neutrality is a requirement, the bulk Fermi level could be considered a charge neutrality level.

 

[marie2010]

Thank you for the explanation.
I appreciate it.