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
Use of Capacitor in Technical Loss Reduction The use of capacitors to correct for poor power factor is a well-built and cost-effective means of reducing distribution system lo

Q. Figure gives the frequency-response graphs for a 709 op amp. Choose compensating components for the circuit to have a gain of 100 and a frequency response of up to 100 kHz.

how to calculate voltage when 3 voltage sources are given?

I''m trying to design ADC using MAX1198 and DAC using IDAC in Multisim 12 but none of them are working. I need some help in this regard

Q. Sketch the asymptotic Bode diagrams for the following functions:

Q. Diagram, explain the construction of a single stage RC coupled amplifier? An RC Coupled amplifier consists of a transistor connected in the emitter configuration with neces

For the amplifier circuit shown in Figure with R i ≅ ∞,R o ≅ 0,A = 10,R L = 100 , and v in = 1 V, calculate the power dissipated in the amplifier if the voltage at the power-s

The subsequent voltage-source multiplying DAC is to be utilized to convert the digital data stream "11" and "01" to an analog signal.  It has 2-bit inputs and hence is capable of c

How to calculate Electrical losses by transformation

a. write a report (at least  2 pages ) on various types of diodes( Show and explain  the theory, symbol, circuit, characteristics, data sheets and applications circuits using the d