Band bending versus band sloping

[yehokhenan]

I'm trying to reconcile how a built-in potential can form in a semiconductor heterojunction in which there is a significant band cliff to majority carrier diffusion from both sides of the junction i.e. there is a cliff which should block hole diffusion from the p-type as well as a cliff which block electron diffusion from the n-type. There ought to be a significant Fermi level offset and there are countless publications of such systems exhibiting rectifying behavior. The problem also extends to a scenario in which there may not be a band cliff but there are insufficient free carriers available for depletion e.g. an i-n or an i-p diode.

My assumption so far is that depletion need not necessarily occur for a built in potential to form and that band-sloping rather than band bending occurs instead - there is still a built in potential but there is no space-charge region (or, more generally, the space charge region does not wholly account for the built in potential) cf Fig 1b of this paper: http://pubs.acs.org/doi/abs/10.1021/jp300397f.
Contrary to this, most analytic derivations for built in potential, depletion width etc derive these quantities from the space charge density using Gauss' law. This is even the case for p-i-n junctions, in which a substantial part of the junction has sloped rather than bent bands.

My question is simply: Am I missing anything abvious? Is the idea of a band-slope built in potential physically sound?

Thanks!

 

[yehokhenan]

Thanks for the bump. I can try to word it more simply, my original post is a bit of a mouthful. Here goes...

p-n junctions form because electrons and holes diffuse across the junction, causing the regions either side to be depleted of charge. All the behavior associated with p-n diodes stems from this occurrence. So...what happens when there is a barrier/cliff/discontinuity in the bands that should block the electrons and holes diffusing? How does the junction still form?