Module 6 part B1

Fermi Energy Levels and Non-Equilibrium Conditions

Overview

Fermi energy levels are crucial in semiconductor physics, illustrating the energy state of electrons in materials. While previously discussed under equilibrium conditions, the behavior of Fermi energy levels changes under non-equilibrium conditions when excess carriers are introduced.

Equilibrium Conditions

• Energy Band Diagram for N-Type and P-Type MaterialsUnder equilibrium, the Fermi levels for n-type semiconductors are positioned close to the conduction band ( E_C), while for p-type semiconductors, it is nearer to the valence band ( E_V).

• Positioning of the Fermi LevelThe proximity of the Fermi level (E_F) to E_C or E_V depends on the concentration of electrons and holes:

  • Larger distance between E_F and E_C indicates higher electron concentration.

  • Larger distance between E_F and E_V signifies increased hole concentration.

• Mathematical RepresentationThe intrinsic concentration of carriers can be calculated using specific equations involving the Fermi levels, intrinsic Fermi level (E_FI), Boltzmann constant (k), and absolute temperature (T).

Non-Equilibrium Conditions

• Effect of Excess CarriersIntroducing excess carriers disrupts the equilibrium position of the Fermi level. The definition of Fermi level becomes ambiguous as excess electrons or holes lead to shifts in its position:

  • In n-type materials, when excess electrons are added, E_F moves up toward E_C.

  • In p-type materials, excess holes prompt E_F to shift toward E_V.

• Quasi Fermi LevelsDuring non-equilibrium conditions, we can still analyze the situation using quasi Fermi levels. This involves separating the overall electron concentration into contributions from thermal equilibrium and the excess carriers:

  • The total electron concentration can be calculated as the sum of standard electron concentration and excess electrons.

  • The quasi Fermi level for n-type (E_Fn) and p-type materials (E_Fp) can be determined under these conditions.

Practical Example with Silicon Semiconductors

• Silicon Band StructureFor silicon, which has a band gap of approximately 1.1 to 1.2 eV, the Fermi level can be explored by doping with donors at levels such as 10^15 per cubic centimeter.

• Fermi Level AdjustmentIncreasing the doping level moves the Fermi level closer to E_C, whereas reducing it results in a position farther away.

• Impact of Light ExposureAdding excess carriers, like 10^13 per cubic centimeter of electron-hole pairs through light application, further affects the Fermi levels:

  • For n-type, the Fermi level shifts upwards due to increased electron concentration.

  • For p-type, the calculation shows the Fermi level adjusting upwards considering the new concentration of holes.

Conclusion

Understanding the changes in Fermi levels under non-equilibrium conditions is vital for the effective application of semiconductors in technology. Supplementary notes will provide additional examples to clarify these concepts further.