intrinsic semiconductor - metal junction

StarDam

I guess the title explains it all. I have skimmed through a bunch of websites and few on-line books about semiconductors, yet I did not find any description of this case (charge distribution, I/V characteristics). I also found too difficult to retrace the typical formulas for the intrinsic case, as the very basic assumptions are different and even the approximations used cannot apply to "my" case at all.
Now based on simple symmetry considerations, I do have a fairly good idea how the I/V characteristics should look like, i.e. I=I_{0}*sinh(qV/k_{B}T), but I am unable to derive it.
Any suggestions, references, links...?
Thanks in advance