What is Fermi level: Definition and 81 Discussions

The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by µ or EF
for brevity. The Fermi level does not include the work required to remove the electron from wherever it came from.
A precise understanding of the Fermi level—how it relates to electronic band structure in determining electronic properties, how it relates to the voltage and flow of charge in an electronic circuit—is essential to an understanding of solid-state physics.
In band structure theory, used in solid state physics to analyze the energy levels in a solid, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time.
The position of the Fermi level in relation to the band energy levels is a crucial factor in determining electrical properties.
The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure.
Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter.

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  1. B

    Calculating Fermi Level position in doped Silicon

    Estimate the Fermi level position EFn for a Si sample at room temperature that is doped with 1015 shallow donors cm-3. From coursework I've gatherred over the year I understand the equation needed is: EF=EC-kT ln(NC/n) n, being equal to the donor concentration EC is the conduction...
  2. O

    Flat band voltage, Fermi level

    Hi, I would like to get suggestions about the physical meaning of the (1) flat-band voltage and the (2) Fermi-level. Before being marked as newbie, I'd like to point out that I know how to calculate them and know that the (1) flat band voltage is the one which you apply, the energy band...
  3. S

    Fermi level de-pinning & Schottky barrier

    Hello. I was womdering does anyone know any good resources of information on Fermi level de-pinning & Schottky barriers? I have been hunting around online, with not much luck. I thought someone here might be able to suggest some things. Thanks. Seán
  4. L

    Fermi Level - clarification needed

    Fermi Level -- clarification needed Homework Statement Revered Members, Can i know what is meant by fermi level? I googled this, but i could not understand. One site says Fermi level as top of collection of electron energy levels at absolute zero. Homework Equations The Attempt...
  5. R

    Fermi level in semiconductors

    1. Fermi level is also defined as highest energy level at which electron can exist at 0K then it should be top of valence band but why is it in between conduction band and valence band ( in forbidden gap)? It should be in conduction band or valence band. How to explain this? 2. If density of...
  6. P

    Fermi level in extrinsic semiconductors

    Fermi level in an extrinsic semiconductor(after attaining thermal equilibrium) is said to be invariant (constant ) , and the proof uses the fact 'no current must flow thorough any cross-section'..But I don't think its true, charge will be transported due to diffusion and this is countered by...
  7. S

    Fermi level, band structure of solids, and effect on electrical conduction

    how is the relationship between fermi level and band structure of solids can effect electrical conduction properties of a material?
  8. H

    Equilibrium fermi level and carrier concentration

    Problem statement: Determine electron and hole concentrations in Si at room temperature given that the Fermi level is 0.20eV above the valence band energy. So my thoughts on this problem: First we draw the band diagram, and it's clear that this is P type. Then, p0 = Nv * exp((Ef - Ev)/KT)...
  9. T

    Fermi level and Fermi wavevector

    Note: I already asked this question ion the introductory physics forums but have had no replies. The question I'm being asked is: If the Fermi level of copper is 7eV calculate the magnitude of the Fermi wavevector?The formula I'm pretty sure it goes with is Kf=(3pi^2ne)^2/3 The reason I'm...
  10. N

    Exploring Fermi Level in Compound Semiconductors

    Aasslam u alaikum to all, i have confusion in knowing that " how fermi level form in a compound semiconductors e.g GaN, GaAs, etc. Thanks to all
  11. A

    Fermi Level Problem, help plssss

    Fermi Level Problem, help plssss ! Find the location of the fermi level with respect to intrinsic level if the probability that a state filled at the conduction band edge is equal to the probability that a state is empty at valence band edge. I am looking forward to your help.
  12. T

    Fermi-Dirac statistics at the Fermi level

    Hi all, I've search for my question and found no answer. I think it should be pretty simple... Fermi energy corresponds to the last occupied energy, as I understand it. So, energy levels in the Fermi gas are all filled with two electron of opposite spins, up to the Fermi energy. Saying it...
  13. J

    Why Do Spin Flips at Fermi Level Occur?

    Hi, I have come across a sentance in an article which I do not quite understand. H1 is just a perturbation Hamiltonian. Why will spin flips only occur at the Fermi level? Thank you
  14. S

    Potential energy vs. fermi level in metal-metal junction under applied field

    Hello, I have been lurking in the forum for a while. I have couple of questions that I cannot really find an answer to yet. If any of you have idea/suggestion/know of where to look at, I would greatly appreciate. First question: Let's put two different work function metal blocks to each...
  15. Z

    Location of Fermi level in semiconductors

    Hi Strictly from the definition of the Fermi level as the highest energy occupied at zero temperature, it seems that in the presence of a band gap the Fermi level (Ef) could be placed fairly arbitrarily anywhere between the conduction (Ec) and valence (Ev) bands, since the density of states is...
  16. C

    Calculating Fermi Level in Quantum Wells

    Hi. Does anyone know how to calculate the fermi level for the conduction band in a quantum well?
  17. P

    Vanishing fermi level and cut off value in self energy

    Guys, I have two questions: (1) what does a vanishing Fermi energy mean? (2) I have also calculated the phonon self energy for the electron phonon interaction in graphene. However in one of the papers, they state that one needs to subtract from this self energy the case of vanishing Fermi...
  18. M

    How Does the Fermi Level Influence Solar Cell Voltage?

    Hello, Im working on a paper on solar cells and i came across the term "Fermi level". What exactly is the Fermi level in this context: "The working voltage produced by the device is the difference between the chemical potential of the titanium dioxide (Fermi level) and the redox...
  19. S

    Fermi level simple explanation

    can any1 explain what fermi level is simple explanation also how are minority charge carriers formed and i can't understand the energy band diagram of pn junction that how both the fermi levels become equal WHAT IS MEANT BY THAT FERMI LEVEL i read in hyperphysics but i can't understand it...
  20. T

    Fermi level as a function of temperature

    Hello guys, very short question :), why does Fermi level go down with temperature? is there some physical explanation or discussion for this? apart from mathematics (well, some mathematics would be cool if necessary :)) Find attached some cool curve about this ;) Thanks guys :)
  21. W

    (Solid State) fraction of electrons within kT of fermi level

    Homework Statement Show that the fraction of electrons within kT of the fermi level is equal to 3kT/2Ef, if D(E) = E^1/2. Homework Equations f(E) = 1 / ( exp(E-Ef)/kT + 1 ) fermi distribution N = integral from 0 to inf of D(E)f(E)dE = total no. of electrons The Attempt at a...
  22. U

    At 0k, why is fermi level halfway in bandgap?

    At 0k, why is fermi level halfway in bandgap?? Fermi Level is defined as the maximum energy an electron posesses at 0k, which appears to be midway in the bandgap. I learned that in the bandgap, there are no available states (i.e. no wavefunctions of electrons) hence, no electrons can possibly...
  23. V

    Temperature effect on fermi level

    if fermi level is defined for 0K, then how does it vary in a semiconductor with temperature. also, why will the formation of holes affect the position of fermi level(by introducing acceptors). have i misunderstood something? please clear my doubt.
  24. M

    Fermi level rise up with raisng up the temperature

    Hi, Im just wondering, why the fermi level rise up with raisng up the temperature when donors are present in Extrinsic semiconductor? thanx
  25. V

    Question about Spectral Density at the Fermi level

    Hi everybody, I have the following homework assignment: 1. Derive the expression of density of state D(E) in free electron system. D(E) = \frac{m\sqrt{2m}}{{\hbar}^3\pi^2}V\sqrt{E}, (1) where m and V are electron mass and volume of the system, respectively. 2...
  26. N

    What Does It Mean When the Fermi Level is in the Band Gap?

    hello to everyone. It is normally said that in semiconductors the Fermi level is half way between the valence and the conduction band. I have the following question on that: what does it mean that the Fermi level is in the band gap? It should mean that the maximum energy of an electron in the...
  27. I

    What's so special about Cu, Ag, and Au? fermi level? band gap?

    i know this is a simple question, but i have been looking for a while (maybe 15 min) and i cannot find what is so special about Cu, Ag, and Au? i know there is something special about these 3 metals. something that none of the other metals have. i remember it having to do with fermi velocity /...
  28. A

    Calculating Fermi Level in Doped Silicon at Room Temperature and 0K

    Homework Statement (a)If a silicon crystal is doped with 10^15 cm−3 phosphorus atoms, find out the electron concentrations and hole concentrations in the silicon at room temperature. Find out the Fermi level. (b)Repeat at temperature = 0K Homework Equations n*p=ni^2...
  29. R

    Fermi level pinning in doped semiconductors

    I am reading 'Mesoscopic electronics in Solid State Nanostructures', second edition, by Thomas Heinzel. And I find it a bit too difficult from time to time. Especielly on the concept of Fermi level pinning in doped semiconductors. Does anyone know where to find a good explanation for this...
  30. dink

    Fermi Level in N-Type Semiconductors

    This is sort of a simple question. In a steady-state semiconductor doped n-type, is it possible for the quasi-Fermi level for the holes (F sub p) to be above the intrinsic level for the conductor (E sub i)? That is, E - F = (negative value)?
  31. Mk

    Fermi Level Explained: What is It?

    Hey, guys, what's a fermi level?
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