I have wondered myself why is that value fixed to around 0.7 V (0.3 Ge). I have researched about this topic over and over again, but I always find the same answer. They say "Because the voltage for Silicon Diodes is 0.7". That is just like saying that the sky is blue because blue is the color of the sky.
I am familiar with the Shockley diode equation, but I don't see the connection with the threshold voltage (I'm saying this because people have given me a link to its Wikipedia page).
I have also read something about the concentration of impurities near the junction being related to the voltage barrier (I am hoping to get an answer related to that, and the manufacture process).
Another answer I have been given is that that is silicons nature (I kind of hate this answer, because what I get from it is that the voltage is an intensive property, instead of extensive – which would make materials more "workable").
So the question per se is: Why 0.7 and not 0.4, 0.11, 1.2 (for Silicon)?
Best Answer
A slightly-more ELI5 answer:
When we touch any two different metals together, they charge up, one becoming positive, the other negative. They form a self-charging capacitor, or something like a low-voltage battery. This effect was detected in the early days of physics, discovered during sensitive measurements of electrostatic charge. It behaved much like contact-charging of silk rubbed against rubber. But with metals, no friction was needed. Later on it became clear that two different metals always produce the same voltage between them. (Well, same at room temp. The voltage changes slightly with temperature.)
But this voltage can never be detected by normal voltmeters. We can build our circuits out of copper, aluminum, iron, etc., and for every copper-aluminum junction, there will always be an aluminum-copper junction somewhere else. The metals-charging effect might be very large, yet it sums to exactly zero around a closed circuit. The neg terminal of one "battery" always faces the neg terminal of another. It's not an energy source (not the perpetual motion machine that Alessandro Volta thought he'd discovered!)
What if we bump a slab of p-type silicon against a slab of n-type silicon? That's a self-charging capacitor, and it produces roughly 0.7V between the silicon slabs. One slab steals electrons from the other, but just until the difference in orbit-energies of the mobile carriers is cancelled out. Note that diodes needn't be formed at the contact point. Instead we could use high-doped ++p and --n "metallic" silicon which cannot form diodes, yet when touched together, the slabs still produce that spontaneous charging and that same potential-diff. We could even solder the p and n silicon together (first silver-plate the ends, so solder will wet them,) and still that same 0.7V potential appears.
Why do diodes turn on at 0.7V, rather than at zero volts? It's because the depletion layer of the diode always contains that spontaneous "differing-metals-contact" 0.7 volts inside. The voltage keeps the diode turned off. On a disconnected diode this is not a measurable voltage (you'll never detect it directly, not unless you start measuring the e-fields surrounding the diode's terminals.) Heh, if we could form diodes from iron and copper, then instead of 0.7V, those diodes would turn on at the natural iron-copper potential-difference that all iron-copper junctions exhibit.
When we apply an external voltage to forward-bias the diode junction, the diode turns on when the external voltage cancels out the constant built-in invisible voltage. In other words, diodes only turn on when we've reduced the "invisible" junction-voltage to near zero: shorted it out by applying an opposing potential-diff.
All of this connects to many other physics effects. If we make a closed metal ring, a half-ring of copper connected to a half-ring of iron, then heat one of the junctions, many mA or perhaps amps will flow, since the two "invisible" voltages are no longer the same, and the small difference produces a large current in the circuit. In other words, thermocouple voltages are just a tiny remainder of this magical "invisible voltage," the thermo-voltage only arising because of an imbalance. We only detect the imbalance, but not the original potential-difference which always appears between two metals.
We can create a "source of cold:" a semiconductor refrigerator. If we solder any p-type silicon against n-type, then force a reverse current through the junction, where holes flow away from electrons, then the p-to-n connection becomes cold, and the metal contacts elsewhere become equally warm. Note that no diode was formed, since two separate silicon blocks were connected by solder. Swap the polarity and instead the metal contacts become cool, while the pn-solder junction heats up equally.
Also, this means that solar-cells don't work as most people imagine. Inside the dark solar cell, the pn junction has a natural 0.7V potential difference. Elsewhere in the circuit we find opposite differences (probably found mostly at the metal contacts to the semiconductor.) They all add up to the same 0.7V, which cancels the voltage of the pn junction. So, when the light hits the junction, carriers flood across it, and the junction-potential gets shorted out! Then, all the other potential-differences from other parts of the circuit will provide the e-fields which then force the charges to flow around the circuit. An illuminated pn junction in a solar cell doesn't provide the drive voltage. Weird! Instead, the metal contacts of the wires provide the drive voltage, and the illuminated pn junction provides a missing voltage which otherwise would halt the current. Missing junction-potentials are an oddity which isn't found in any normal circuit. When a voltmeter (made of copper, solder, silicon, etc.) is connected to an illuminated solar cell, the missing junction-potential of the pn junction lets us measure the total potential of all the other conductor junctions present. (Or, instead we could take the micro-view, and say that the absorbed photons are elevating the energy-level of mobile charges in the junction, allowing them to cross it, regardless of the strong e-field of the natural 0.7V trying to repel them back again.) The flood of high-energy mobile carriers have shorted out the junction, discharging the self-charged capacitor. But this also means that the Vout of a solar cell will NOT be related to the photon energy. Instead, the Vout is just the (now missing) potential-barrier of the pn junction.
But why do two different metals charge up when touched together?
It's because even two lone metal atoms also charge up when touched together. The energy-levels of different metal atom's orbitals are not the same. If touched together, one atom tends to steal electrons from the other ...but just enough to cancel the difference in orbital levels. Rather than single atoms, if instead we used two long chains of metal atoms, one of copper and one of iron, then when their ends touched, one chain would steal electrons from the other, until the magic invisible voltage-value appeared between the chains. It's a self-charging 2-plate capacitor. Works for metals, works for semiconductors. Search term: work-function of metals, and work-function difference of metal junctions (and Volta or Galvani potentials in electrochemistry.)
[Beware, this is a first-approximation gradeschool ELI5 answer. As mentioned elswhere here, diode turn-on potentials are only proportional to the work-function difference, not equal to it. Disconnected diodes don't actually have zero junction current, instead they have carrier-mobility effects, equal and opposite carrier diffusion currents, etc.]