Resistance of a diode in different regime and the physics of recombination current I would like to ask question about the resistance of a diode under different regime. Surely, in reverse bias, it has a breakdown voltage, and in forward bias,it rises exponentially according to the exponential relationship according to the theory ( ideal Shockley diode equation ) . But what happens at the flat band situation? I do not understand why it should obey Ohm's law well when the fermi levels are split by  eV=eVo, where Vo is the barrier height (when applied bias V is zero). (see Fig.1.)
Any Justifications with the physics of the charge carriers or using formulas would be much appreciated.

Thanks
 A: I'll upgrade my comment to an answer.
You are thinking about this in the wrong way. 
If you operate a diode at a fixed point on the IV curve (that is by sourcing or sinking current as needed), then the device's resistance is constant. For example, you might want to do this with a PN junction solar cell; they are operated at the maximum power point.
However, this does not mean that the diode obeys Ohms Law, that is a property of the whole IV curve, not just a single point. 
Ohms Law states that for any applied bias the resistance is constant. This is clearly false for a diode because if the bias changes, even by a little bit, the resistance changes exponentially (in forward bias).
I think the confusion is arising from the fact that you are mentally equating the band structure of a forward bias diode (at the flat band point) to that of a simple resistor. And based on this fact, extrapolating to the statement that the diode must be Ohmic.
tl;dr Any device held at a particular point on it's IV curve has constant resistance, this doesn't mean that all electronic components are resistors.
