Table of Contents
What Is the Fermi Level?
The Fermi level (E_F) is the energy at which electron occupation probability is 50%. In semiconductors, its position relative to band edges determines carrier concentrations and electrical behavior. In intrinsic silicon, E_F lies mid-gap. N-type doping raises E_F toward the conduction band; p-type lowers it toward the valence band.
The Fermi level is the single most important parameter characterizing a semiconductor. It determines carrier concentrations, junction built-in voltages, and device characteristics. When two materials contact each other, electrons flow until Fermi levels equalize, creating the electric fields that enable transistors and diodes.
Formula
Where k = 8.617e-5 eV/K, T is temperature, n is electron concentration, n_i = 1.5e10 cm^-3 for Si at 300K.
Doping Effects
| Doping | E_F - E_i | Type |
|---|---|---|
| Intrinsic | 0 | Intrinsic |
| Nd=1e15 | +290 meV | n-type |
| Nd=1e18 | +467 meV | n-type (degenerate) |
| Na=1e16 | -349 meV | p-type |
FAQ
Why is Fermi level important?
It determines carrier concentrations via n = n_i * exp((E_F-E_i)/kT). When two materials with different Fermi levels touch, electrons flow to equalize them, creating built-in fields that are the basis for all semiconductor device operation.
What is degenerate doping?
When doping exceeds ~1e18 cm^-3, E_F enters the band. The semiconductor becomes metal-like with implications for tunneling, ohmic contacts, and quantum effects. This regime requires quantum mechanical treatment beyond the simple Boltzmann approximation.
How does temperature affect E_F?
Higher temperature generates more intrinsic carriers, pushing E_F toward mid-gap. At very high temperatures, intrinsic carriers dominate and the material becomes effectively intrinsic regardless of doping level.