Fermi level, Electrical Engineering

Fermi Level

  • Electrons in solids obey Fermi-Dirac (FD) statistics.
  • This statistics accounts for the indistinguishability of the electrons, their wave nature, and the Pauli Exclusion Principle.
  • The Fermi-Dirac distribution function f(E) of electrons over a range of allowed energy levels at thermal equilibrium can be given by

F (E) = 1/ (1+e(E-EF)/KT)   (7)

where k is Boltzmann's constant (= 8.62 x   eV/K = 1.38 x 10-3 J/K)

  • This gives the probability that an available energy state at E will be occupied by an electron at an absolute temperature T.
  • EF is termed as the Fermi level and is a measure of the average energy of the electrons in the lattice => an extremely important quantity for analysis of device behavior.
  • Note: for (E - EF) > 3kT (known as Boltzmann approximation), f (E) ≈exp [- (E-EF)/kT] this is referred to as the Maxwell-Boltzmann (MB) distribution (followed by gas atoms).
  • The probability that an energy state at EFwill be occupied by an electron is 1/2 at all temperatures.
  • At 0 K, the distribution takes a simple rectangular form, with all states below EF occupied, and all states above EF empty.
  • At T > 0 K, there is a finite probability of states above EF to be occupied and states below EF to be empty.
  • The F-D distribution function is highly symmetric, i.e., the probability f (EF+ΔE) that a state E above EFis filled is the same as the probability [1- f (EF-ΔE)] that a state E below EFis empty.
  • This symmetry about EF makes the Fermi level a natural reference point for the calculation of electron and hole concentrations in the semiconductor.
  • Note: f (E) is the probability of occupancy of an available state at energy E, thus, if there is no available state at E (e.g., within the band gap of a semiconductor), there is no possibility of finding an electron there.
  • For intrinsic materials, the Fermi level lies close to the middle of the band gap (the difference between the effective masses of electrons and holes accounts for this small deviation from the mid gap).
  • In n-type material, the electrons in the conduction band outnumber the holes in the valence band, thus, the Fermi level lies closer to the conduction band.
  • Similarly, in p-type material, the holes in the valence band outnumber the electrons in the conduction band, thus, the Fermi level lies closer to the valence band.
  • The probability of occupation f(E) in the conduction band and the probability of vacancy [1- f(E)] in the valence band are quite small, however, the densities of available states in these bands are very large, thus a small change in f(E) can cause large changes in the carrier concentrations.

 

Posted Date: 1/11/2013 4:51:51 AM | Location : United States







Related Discussions:- Fermi level, Assignment Help, Ask Question on Fermi level, Get Answer, Expert's Help, Fermi level Discussions

Write discussion on Fermi level
Your posts are moderated
Related Questions

The increase in the current is building up the magnetic field surrounding the coil. Energy is stored in that field. Consider the energy supplied by the voltage source during the

can you differentiate the alpha,beta and gamma

Why do we use XRA A instruction The XRA A instruction is used to clear the contents of the Accumulator and keep the value 00H.

All semiconductors in their last orbit have (A)  8 electrons.  (B) 2 electrons. (C)  4 electrons. (D)  6 electrons. Ans:     All semiconductors in their

Q. Why CE configuration is widely used in amplifier circuits? The main ability of an transistor lies in amplifying weak signals. The transistor cannot alone perform this functi

How control and monitoring has be done - Sensors gather information from application being monitored or controlled. - The data being gathered is frequently analogue in natur

Q. An antenna has an aperture area of 10 m 2 ,an aperture ef?ciency of 0.6, and negligible losses. If it is used at 5 GHz, determine: (a) Its power gain. (b) The maximum pow

Q. What is a darlington pair?                             The Darlington circuit consists of two cascaded emitter followers with infinite emitter resistance in the first stage.

Q. Find the line current after the addition of capacitor bank? A 60-Hz, three-phase motor draws 25 kVA at 0.707 lagging power factor from a 220-V source. It is desired to impro