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!