Understanding Fermi Level in Extrinsic Semiconductors

The Fermi level ($E_F$) in a semiconductor is a fundamental concept representing the energy level at which there is a 50% probability of finding an electron at absolute zero temperature. In intrinsic semiconductors, it lies near the middle of the band gap. However, when impurities are added (doping) to create extrinsic semiconductors, the Fermi level shifts.

Factors Influencing Fermi Level

The position of the Fermi level in an extrinsic semiconductor is determined by several factors related to the doping process and the material's properties:

• Donor Element Type: In n-type semiconductors, created by adding donor impurities (like Phosphorus in Silicon), the excess electrons make the Fermi level shift upwards, closer to the conduction band. Conversely, in p-type semiconductors, created by adding acceptor impurities (like Boron in Silicon), the deficiency of electrons (presence of holes) causes the Fermi level to shift downwards, closer to the valence band. The specific energy level of the donor or acceptor atoms also plays a role.
• Impurity Concentration: The concentration of dopant atoms significantly affects the Fermi level's position.
  • A higher concentration of donor impurities in an n-type semiconductor pushes the Fermi level ($E_F$) further up towards the conduction band edge ($E_C$).
  • A higher concentration of acceptor impurities in a p-type semiconductor pulls the Fermi level ($E_F$) further down towards the valence band edge ($E_V$).
  At very high doping levels, the Fermi level can even move into the conduction band (n-type) or valence band (p-type).
• Temperature: Temperature influences the thermal excitation of electrons across the band gap and the ionization of dopant atoms.
  • At higher temperatures, more electrons are thermally excited, increasing the intrinsic carrier concentration. This causes the Fermi level in both n-type and p-type semiconductors to move towards the intrinsic Fermi level ($E_i$), which is located near the middle of the band gap.
  • At absolute zero ($T = 0$ K), the Fermi level is determined solely by the doping concentration. As temperature increases, the influence of thermal generation becomes more significant.

Conclusion

Since the Fermi level's position is dependent on the type of impurity added (donor), the amount of impurity added (concentration), and the operating temperature, all the listed factors contribute to its final position. Therefore, the Fermi level for an extrinsic semiconductor depends on all these parameters.