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 comparison can be made out of two feature 1) Performance and 2) Integrity of Data Write through is better in integrity as it will flush for every writes. Write b


Normal 0 false false false EN-IN X-NONE X-NONE

Q. Describe some of the features hindering developing countries from growing faster. Answer: One of the features that are able to be hold developing countries from growing fas

Critical Rate of  Rise of Current The maximum  rate of  increase of current  during  on state  which  the SCR  can tolerate is called  the critical rate of rise  of current  f

RAL Rotate Accumulator Left Through Carry Instruction This  instruction rotates the content  of the accumulator  towards left by one bit. The D 0 bit moves to D 1   bit moves

Task a)    Investigate and describe the significance of the following: i.    Slenderness ratio and buckling in columns ii.    Effective length of columns b) Explain Eu


Q. Define the spectral resolution of satellite? Spectral resolution : The sensitivity to different features of earth is the most important aspects considered in the spectral

Certification of Energy Managers Certification of Energy Managers and Accreditation of Energy Auditing Firms One of the important provisions in the Act is to create a cad