Fermi Level
1. Definition
Fermi level, Ef = Ei + kT ln(Nd/ni), where Ef is the Fermi level, Ei is the center of the band gap, k is the Boltzmann constant, T is the temperature in Kelvin, Nd is the donor density assuming one donor can offer one electron, ni is the career density when Nd is zero.
- At this potential level, the electron occupation probability becomes 50%.
- It can be located at the level where the density of the state is zero.
- It goes up when Nd is increased.
Even when Ec-Ed (Ec is the level at the conduction band bottom, Ed is the donor level.) is larger than kT, the donor level can be ionized since,
- The electron trapped in the donor-atom is moving much more vigorously than electrons in the conduction band because of the uncertainty principle; thus, the trial for tunneling increases.
- Nc, which is the effective density of states, is much larger than Nd; thus, the electron is observed somewhere in Ec more often than at Ed.
- Note that with much wider range of motion somewhere in Ec, the kinetic energy of the electron becomes lower than at Nd because of uncertainty principle.
3. Transient response under the reversely biased Schottky contact.
E(imref, n) = Ei + kT ln (n/ni).
Under the reverse bias, carrier electrons move away from the semiconductor, but few electrons comes into the semiconductor because of the Schottky barrier; thus, E(imref, n) goes down.
When deep donor states exist in the bandgap, the deep donor states are ionized, leading to Narrow Depletion:
by T. H.
