DaleSpam said:
Thanks for the interesting info. When you say "much larger than kT" how much larger do you mean?
I'd don't have an exact number but I think it would need to be at least 10 times larger to get anything close to a functional semiconductor junction. Essentially there can no P-type and no N-type, just a bland conductor unless E_g>>kT.
The following is a rough description of the physics involved, enough to give an overview. I’ll give the example of an n-type semiconductor but of course similar limitations apply to making a p-type as well.
Say we wanted to make a n-type semiconductor (Si for example), we’d have to dope it with a band-IV impurity at a level which is much greater than the intrinsic (undoped) electron concentration of the Si. There are limits however on just how large of an impurity concentration (dopant) we can use or else it will ruin the crystal structure of the primary semiconductor material. Typical dopant concentrations used in Si for example are in the range 10^13 to 10^18 atoms/cm3.
Now in addition to the free electrons created by the dopant there are also thermally generated electron-hole pairs, so unless the dopant level is much larger than this “intrinsic” carrier concentration we’ll never get a functional n-type semiconductor.
It turns out the number of thermally generated electrons is equal to N_c e^{-(E_c-E_f) / 2kT}, where N_c is the effective density of states in the conduction band and E_f is the Fermi Level. In practice the Fermi Level is typically about mid-way in the band-gap hence (E_c - E_f) \simeq E_g / 2.
N_c, the density of states, is given by some complicated quantum mechanics that I don’t fully understand, but the simple upshot is that it’s a very large number, only a few orders of magnitude smaller the actual density of the atoms themselves (N_c is about 3x10^19/cm^3 in Si). So unless e^{-E_g/2kT} is small (and I mean very small) we don’t have any chance of getting a functional doped semiconductor.
In Si for example, E_g=1.12 eV so at room temperature (300 Kelvin) e^{-E_g/2kT} is about 10^{-10}.
Hope that helps.