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. E

    I How does diffusion of high energy electrons shift band structure?

    When an n-type material comes in contact with a p-type material to form pn-junction, electrons with the highest energy in the conduction band will diffuse to the p-side to reach equilibrium so the entire band structure on n-side will shift down relative to p-side as described in the following...
  2. chikchok

    I Chemical potential and Fermi level

    Does fermi level (in metals) depend on the density of states? I am asking this because from fermi-dirac distribution it seems like that fermi level is non-dependent of DOS, but there is chemical potential in fermi-dirac distribution, which is said to be dependent of DOS.
  3. Helena Wells

    I Fermi level change in semiconductors

    Suppose we have a crystal lattice of doped Si with dopant Boron atoms. The energy level of the holes of the Boron atoms are just some eV above the valence band of Si. My question: If we replace all the Si atoms with Ge atoms will the acceptor level change or not? I don't think it will change...
  4. B

    I Fermi level in a nonuniformly doped semiconductor

    Fermi level is known to be constant in a equilibrium state. It is also known to vary according to the number of donors/acceptors. In a nonuniformly doped semiconductor that has varying number of donors/acceptors at different position, how is the fermi level decided? Is it the average number of...
  5. M

    I Fermi Energy Calculations About Non Parabolic Dispersions

    Greetings! It is easy to understand that for a free electron, we can easily define the energy state density, and by doing the integration of the State density* Fermi-Dirac distribution we will be able to figure out the chemical potential at zero kelvin, which is the Fermi-Energy. Hence, we can...
  6. N

    I Valence band and Fermi level difference?

    I was wondering what the difference was between the valence band and fermi level? How do we distinguish between the two? Thanks in advance.
  7. B

    [PoM] Electrons Fermi level in a crystal

    Homework Statement The conduction band of a hypothetical crystal of one-dimensional Cesium reticular with step a=300 pm (1 atom per cell) is characterized by the ε dispersion law ##\epsilon (k) = V_0 + \frac{\hbar^2}{m_e}(\frac{1}{2}k^2 - \frac{a}{3\pi}|k|^3## where ##V_0 = -4 eV##, is set so...
  8. bluejay27

    I Where is the Fermi Level located?

    Where does the fermi level lie at? I have an understanding that at absolute zero it would be lying halfway the band gap. Shouldn't it be lying at the top part of the valence band?
  9. J

    B Fermi Level in Metals: Exploring Effects on Conductivity

    Hi, I have started looking at the fermi level and how it relates to the behaviour of conductors. It is my understanding from what I have read that the fermi level is the top of the fermi sea of filled energy states when the material is at T = 0K. 1) Is the fermi level inside the conduction...

    A Change in Fermi level with gradient of doping concentration

    In a degenerate n type semiconductor, when the doping concentration has a gradient(say -ve gradient), then how fermi energy level and intrinsic Fermi energy levels will depend upon the concentration gradient? ~If anyone knows anything about it, kindly help.
  11. G

    I Why Is Negative Magnetoresistance Possible in Dilute Magnetic Alloys?

    A free electron gas would have zero magnetoresistance; it takes two carrier types to get ordinary magnetoresistance, which is always positive in sign. Beal-Monod and Weiner explain the negative magnetoresistance found in very dilute magnetic alloys, in terms of the spin-flip scattering of...
  12. A

    I Density of states at Fermi level for metal vs semiconductor

    We are doing spectroscopy on some semiconductors covered by a layer of Aluminium. My professor says it might be a challenge for to see the valence band structure of the semiconductor because the metal has a high density of states at the fermi level. Does this make sense to you? Does a metal have...
  13. E

    I Double heterostructure junction in forward and zero bias

    Hi! When dealing with a pn homojunction, it is easy to see the features it has at equilibrium, and also the features it has with forward/reverse bias. Plots show the constant Fermi level at equilibrium and the different Fermi levels for a forward bias; moreover, examples show how much the bands...
  14. thund3rcz

    I Effect of SAM physisorbed on graphene - some questions

    Hello everyone! :) I'm sorry that I'm posting something that might be obvious, but I'm still struggling to capture all the concepts behind the fundamental physics of this model. Let's say, I have a 2D sheet of graphene, on which, there's a physisorbed layer of molecular dipoles (vdW bonding...
  15. Y

    I Quasi Fermi level and intrinsic Fermi energy

    Please explain me. I don't understand what is quasi fermi level f(E) and fermi energy Ef. For example (GaAs) at the room temperature (T=300K) Eg = 1.42 eV; (energy band gap) mc = 0.067 me; (effective mass of electron in conduction band) mv = 0.45 me; (effective mass of hole in valance band) kT =...
  16. M

    I Why is the work function measured from the Fermi level?

    why does work function measured from fermi level while work function is defined by lowest energy required to remove an electron from surface of materials and fermi level the level have 50% chance to occupation that's mean there is level above it have electron inside so why we don't measure...
  17. C

    Relation between electronic band structure and Fermi energy

    I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level). 1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...
  18. G

    Fermi level of n-type semiconductor Nd>Na>0

    Homework Statement This isn't actually a homework question, but in my semiconductors textbook, the following equation has been given: E_f = E_g - k_BTln(\frac{n_0}{N_d - N_a}) This is for the limiting case Nd>Na>0. I got a little confused as to where that equation has come from. Homework...
  19. K

    Fermi Level of intrinsic and extrinsic semiconductor

    (1) (2)(3) (4) (5) we can find Equation (5) by dividing po by n0, and write an equation with respect to Ei. However since equation (3) is a special form of (1) and (2), [when Ef=Ei] we can obtain equation (5) from any arbitrary Ef. However, since eq (5) consists of constants only, it will...
  20. K

    Semiconductor intrinsic Fermi Level? Bandgap Energy?

    http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_6.htm#2_6_2 equation (2.6.24) we have this equation for fermi level, but I wonder how this works though? In the lecture, we assumed Ec=Eg and Ev=0 to get E_gap/2. but I wonder how (Ec+Ev)/2 actually gives E_gap/2 instead of Ec-Ev=Eg
  21. A

    Finding the Fermi Level with Theoretical Modelling

    I'm making some theoretical modelling for a system, which is effectively 1d in the sense that it is much longer the wide. This means (like in model for quantized conductance) that the energy bands are parabolas with a spacing equal to the energy difference between the ground state, first excited...
  22. A

    What is the Fermi level in semiconductors?

    Can someone give me a clear, nonambiguous definition of the fermi level in a semiconductor? Is it the energy of the highest occupied state, the chemical potential at T=0 or what? I don't think it is the first since the fermi level is typically put midway between the conduction and valence band...
  23. A

    Is it possible to shift the fermi level?

    I know we can shift the fermi level by doping the material with other elements. In case of semiconductors doping with the pentavalent or trivalent will change the fermi level. But my question is ''can we shift the fermi level, without altering the position of valence band and conduction band?"...
  24. Arik Lin

    Uncrossing of Fermi level by d-electrons of Cu, Ag, Au

    I encounter contradictive informations about this issue which is supposed to define "real noble metals" is this statement correct at absolute zero or at any temperature? Does it include ds hybridizations?
  25. P

    Density of States of a metal at Fermi level

    Why can not the density of states of a metal at Fermi level be zero? Thanks!
  26. A

    Exploring the Physics of Fermi Level in Metals

    Hi, a question please: Do all metallic substances have an equal Fermi energy level (at a constant T) ? If not, what will happen (before equilibrium) if one "fuses" together two bulks of metal with different Fermi levels (as in a PN junction) ? Since there's an abundance of energy states...
  27. M

    Silicon NPN Transistor: Calculating Fermi-Level & Equilibrium Concentrations

    Homework Statement we look at a silicum n++ p+ n transistor. given: NE= 1,0×1018 cm–3; NB= 2,0×1016 cm–3; NC = 2,0×1015 cm–3; here E stands for the emitter, B for the basis and C for the collectorHomework Equations a. calculate the distance in eV from the fermi-level to EFi for the emitter...
  28. U

    Fermi Surface squashed by potentials

    Taken from my textbook: My understanding is that: One valence electron, 2 spin states -> Half-filled Brillouin zone Seeking inspiration from "Nearly Free Electron Model": gaps open up at zone boundaries States nearer to zone boundaries get pushed down in energy further Since a fermi...
  29. W

    Fermi Level and density of states

    Hi. Look at the picture on 1:28 and 1:37 in this video: How is it possible that the fermi-level is between two energy bands? The fermi level is defined as the highest energy level that contains an electron 50% of the time, so how is it possible for the fermi level being in an area that is...
  30. ugenetic

    [Semiconductor] Aluminum doped Silicon, valance band&holes

    From some literature, I read the following band structure of the Al doped Si. The explanation offered: "have vacant acceptor levels at energy Ea above the valence band. Electrons from the top of the valence band can be easily excited into these levels." I thought the above explanation is...
  31. Ahmad Kishki

    Fermi Level Concept: Probability & Forbidden Gap

    I was wondering if the fermi level lies in the centre of the forbidden energy gap on pure semiconductors, then how does it (by definition) have a probability 1/2 of being filled? Shouldnt the fact that the fermi level lies in the forbidden, forbid the fermi level from having any probability of...
  32. C

    Free electron concentration range between semiconductors and metals

    A structure with free electron density around 10^26 m^-3 is considered as a highly doped semiconductor or a metal? Or in other words, what is the lowest possible free electron concentration for a metal and what is the highest possible free electron concentration for a doped semiconductor?
  33. B

    Fraction of electrons excited above fermi level

    For the fermi dirac distribution function for temperatures higher than 0 K, how do we approximate the number of electrons available for conduction?
  34. L

    What Determines the Fermi Level of Semiconductors?

    Hi Guys, I read that the Fermi level of semiconductor, like germanium, is in-between the completely occupied upper band and conduction band, i.e. right in the gap. Why is that? shouldn't it have beed exactly the highest occupied level ?
  35. T

    Understanding Fermi Level in Silicon: Valence and Conduction Bands Explained

    what I've been told there is two groups of energy levels called the valence and the conduction band. what is the fermi level for silicon? how wide is the band gap for silicon?
  36. heycoa

    Questions regarding the Fermi level of a metal

    Hello, Are the electrons at the fermi level regarded as the "free electrons" of the metal? Also, how does one go about calculating the Fermi level? Is there an equation or is it experimentally determined? *Bonus question* Electrons that undergo phonon exchange and pair up are called...
  37. K

    How Can dI/dV Help Determine Fermi Level and Band Gap in Semiconductors?

    I'm supposed to be working with an STM in the coming weeks to determining the Fermi Level of some semiconductor diamond films. I was bombarded with a lot of information by my lab supervisor and the bit of my notes about the calculation just says "Differential of voltage vs current allows us...
  38. P

    Significance Of Fermi Level in Semiconductor

    I understood that the fermi level is a hypothetical energy level given by the Fermi-Dirac distribution where the probability of finding an electron is exactly 50%. My question is: it always takes (Ec-Ev) energy to excite the electrons in the conduction band in an intrinsic semiconductor or...
  39. W

    Why is the Fermi level a constant in thermal equilibrium?

    Why is the Fermi level a constant in thermal equilibrium? just like PN diode (P=material 1 ; N=material 2) the fermi levels are the same (Ef1=Ef2) in thermal equilibrium i confused that why there is no energy transfer so that can judge each energy E will obey rate from 1 to 2 ~...
  40. N

    Determining Energies of States Close to Fermi Level

    Homework Statement In class, we discussed metal quantum dots, and we argued that they’re not so useful for device applications since the separation between energy levels for energies near the Fermi energy is much less than a typical optical photon energy of 2 eV. Let’s consider that...
  41. H

    Calculate Minority Carrier Concentrations given the Fermi Level

    Homework Statement This question is based on a previous question in the same homework: The Problems deal with Silicon at 300K, using band gap energy Eg = 1.12 eV, electron density of states mass 0.327, hole mass 0.39, electron mobility 0.15 m2/Vs, hole mobility 0.05 m2/Vs and relative...
  42. E

    Exploring the Relationship Between Band Gaps and Fermi Level in Insulators

    Does the (intrinsic) Fermi level of an insulator HAVE to lie very near the middle of the band gap? I know it might deviate slightly if electrons and holes have different effective masses, e.g. in Si. But can it be radically different? For example, are there insulators with 5 eV band gaps that...
  43. C

    Fermi level in n-type or p-type semiconductors

    Hi, everyone. I'm learning basic theories about semiconductors but can't quite understand the concept of Fermi level. is this just a imaginary energy level or true existence? and why Fermi level is close to the conduction band of n-type semiconductor and valence band of p-type semiconductor...
  44. D

    Fermi Level of Electrons and Holes in Equilibrium and Non-Equilibrium

    Hi all, Why do the fermi level for electrons and holes coincide in equilibrium condition and why they separate as quasi fermi levels in non equilibrium situation?
  45. C

    Why is Fermi Level constant across pn junction?

    I know this is true under thermal equilibrium, but I am not sure why. Why can't the Fermi level be a function of position relative to the pn-junction? How does that follow from thermodynamics/statistical mechanics?
  46. E

    What is the physical meaning of the fermi level in semiconductors?

    I Know that the fermi level in an intrinsic semiconductor is found between the valency level and the conduction level in the energy gap , and I know that also when the semiconductor is doped the fermi level either move toward the conduction band or away from it.But actually I can not get the...
  47. P

    Fermi Energy and Fermi Level in Semiconductors

    I have searched a lot on the internet for a simple explanation of these two terms. As I have understood these things (quantum physics), after reading from a lot of sources, is that in an atom there are discrete energy levels and electrons occupy the levels according to the least energy of the...
  48. O

    Fermi level makes doped and undoped different?

    The intrinsic semiconductor Fermi level is the maximum energy level an electron can be in at 0K. Or Fermi level is a level where there is a probability of 50% to find electrons at any temperature. Conduction band is a range of energy where electrons freed from bonding stay. Valence band is...
  49. H

    How a fermi level can lies between valence and conduvtion band?

    As we know, in intrinsic semiconductors the fermi level is halfway between the valence and conduction band. and The fermi level is the level in which the most energetic electron settles at T=0. but my question: How can the fermi level be in a forbidden region in intrinsic semiconductors? or...
  50. M

    Newbie Questions on Band Gap and Fermi Level

    I am new to solid state physics, having been in computational chemistry (quantum mechanics) for the larger part of my career. Hence have a lot of newbie like questions that are not easily answered by google/wikipedia searching. 1)In viewing a 1-dimensional band gap diagram, crossing the...