What is the DC analysis of shorting both ends of a diode?
A JUNCTION-POTENTIAL forms at the wire connections to the diode's silicon surface.  Not a depletion region, not a new diode.  It's called a &quot;non-rectifying junction&quot; (google search.)  Also see &quot;Ohmic Contact&quot; https://en.wikipedia.org/wiki/Ohmic_contact
A built-in junction-potential is not a depletion zone.  We can have  built-in potentials without depletion zones, but we can't have depletion zones without built-in potentials.
Remember, a junction-potential also forms whenever copper touches solder, or where iron touches nickel, or where Chromel touches Alumel.  These built-in potentials are also called Volta potentials, or Galvanic potentials.  Touching two different conductors together always causes them to become opposite-charged, as Alessandro Volta discovered, back in the &quot;static electricity&quot; era.  (This is not battery chemistry.  This is the metal-metal physics of thermocouples.  It was controversial during Volta's era, because Volta was certain that these built-in potentials appearing between differing metals were the long-sought perpetual-motion machine!  Heh.)
And back in the 1910 &quot;catswhisker diode&quot; days, it was a challenge to form diodes by touching sharp metal wires against Galena semiconductor.  Most of the time your little gold wire would just form a junction-potential, a short circuit but no diode.   You had to find a naturally low-doped region on the Lead-sulfide surface, since high-doped regions won't have a depletion zone.  (Hence it was a great discovery at Bell Labs to learn the trick of zone-refining of long semiconductor rods, where all the PPM parts-per-million contaminants could be swept out, producing low-doped semiconductors which don't normally occur in nature.)
Think:  if diodes always formed at every metal contact, then transistors would be impossible, because all three wire connections would always create inwards-pointing rectifiers on the semiconductor surface, and one of these would always be reverse-biased and turned off.  (These are EXTRA junctions, not part of the transistor's two base-junctions.)  Heh, even diodes themselves would be impossible, since diodes always have three separate junctions: the PN junction, plus two metal/semiconductor junctions where the wires are connected.
A good example of this effect is the TE module, the Peltier device.  It's made of 100 to 200 junctions, where all the junctions are metal/semiconductor, yet none of them act like diodes.  This happens whenever we use high-doped semiconductor, labeled as p++ or n++ materials.  They're also called &quot;metallic&quot; or &quot;degenerate&quot; semiconductor.  It becomes &quot;safe&quot; to make lead-connections against p++ or n++, since they only form thermocouples, not diodes.   To instead create metal-semiconductor diodes, or &quot;Shottky diodes,&quot; we must always use low-doped materials.
If you look closely at IC doping diagrams, or even transistor crystal diagrams, or read up on diode manufacturing, you'll see the p- and the n- regions which form the PN junction.  But out on the surface of the crystal block, we deposit small patches of n++ or p++ regions, and that's where the aluminum conductors are welded.   No diode is formed between a metal and a heavy-doped semiconductor.  (We call the heavy-doped material by the name &quot;metallic&quot; semiconductor, as if it had the electron-sea of metals, rather than the very sparse electron-gas of low-doped semiconductor.)
https://physics.stackexchange.com/questions/176547/how-does-annealing-improves-the-ohmic-contact
Official explanation:  heavy doping makes the depletion region contract to nearly zero thickness.  It becomes so thin that it's thinner than the DeBroglie quantum wavelength of electrons, and constantly produces quantum tunneling in both directions, even at extremely low voltage.   So, your metal contact is actually forming a tunnel-diode!  But if it always turns on at far below 0.1VDC, then we simply ignore it.  (Although maybe we shouldn't, at least when writing electronics textbooks.  I think we should be teaching about &quot;metallic&quot; doped semiconductors and their non-rectifying junctions right at the start, at the same time that we teach about PN junctions.  It would end much confusion.  Heh, also I think we should teach about transistors without PN junctions, as Bardeen and Brattain originally invented, before William Shockley strode in and took the project away, inventing PN junction theory and modern semiconductor physics in the process!)