What is Fermi: Definition and 383 Discussions

Enrico Fermi (Italian: [enˈriːko ˈfermi]; 29 September 1901 - 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics and experimental physics. Fermi was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements. With his colleagues, Fermi filed several patents related to the use of nuclear power, all of which were taken over by the US government. He made significant contributions to the development of statistical mechanics, quantum theory, and nuclear and particle physics.
Fermi's first major contribution involved the field of statistical mechanics. After Wolfgang Pauli formulated his exclusion principle in 1925, Fermi followed with a paper in which he applied the principle to an ideal gas, employing a statistical formulation now known as Fermi–Dirac statistics. Today, particles that obey the exclusion principle are called "fermions". Pauli later postulated the existence of an uncharged invisible particle emitted along with an electron during beta decay, to satisfy the law of conservation of energy. Fermi took up this idea, developing a model that incorporated the postulated particle, which he named the "neutrino". His theory, later referred to as Fermi's interaction and now called weak interaction, described one of the four fundamental interactions in nature. Through experiments inducing radioactivity with the recently discovered neutron, Fermi discovered that slow neutrons were more easily captured by atomic nuclei than fast ones, and he developed the Fermi age equation to describe this. After bombarding thorium and uranium with slow neutrons, he concluded that he had created new elements. Although he was awarded the Nobel Prize for this discovery, the new elements were later revealed to be nuclear fission products.
Fermi left Italy in 1938 to escape new Italian racial laws that affected his Jewish wife, Laura Capon. He emigrated to the United States, where he worked on the Manhattan Project during World War II. Fermi led the team that designed and built Chicago Pile-1, which went critical on 2 December 1942, demonstrating the first human-created, self-sustaining nuclear chain reaction. He was on hand when the X-10 Graphite Reactor at Oak Ridge, Tennessee, went critical in 1943, and when the B Reactor at the Hanford Site did so the next year. At Los Alamos, he headed F Division, part of which worked on Edward Teller's thermonuclear "Super" bomb. He was present at the Trinity test on 16 July 1945, where he used his Fermi method to estimate the bomb's yield.
After the war, Fermi served under J. Robert Oppenheimer on the General Advisory Committee, which advised the Atomic Energy Commission on nuclear matters. After the detonation of the first Soviet fission bomb in August 1949, he strongly opposed the development of a hydrogen bomb on both moral and technical grounds. He was among the scientists who testified on Oppenheimer's behalf at the 1954 hearing that resulted in the denial of Oppenheimer's security clearance. Fermi did important work in particle physics, especially related to pions and muons, and he speculated that cosmic rays arose when material was accelerated by magnetic fields in interstellar space. Many awards, concepts, and institutions are named after Fermi, including the Enrico Fermi Award, the Enrico Fermi Institute, the Fermi National Accelerator Laboratory (Fermilab), the Fermi Gamma-ray Space Telescope, and the synthetic element fermium, making him one of 16 scientists who have elements named after them. Fermi tutored or directly influenced no fewer than 8 young researchers who went on to win Nobel Prizes.

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  1. 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...
  2. A

    Deriving the Fermi Distribution: Fixed Particle Canonical Ensemble

    All derivations of the Fermidistribution uses a canonical ensemble with a chemical potential, which is the same as to say that the ensemble can exchange particles with a resevoir. But are the derivations still valid for the canonical ensemble with a fixed number of particles and why isn't this...
  3. ShayanJ

    Magnetoresistance and Fermi surfaces

    There seems to be relation between Fermi surfaces and magnetoresistance, but I guess because I don't have a clear picture of fermi surfaces,I have problem understanding this relationship. Also I have heard about open and close fermi surfaces and saturation of magnetoresistance which I can't...
  4. A

    Fermi Distribution: Explaining (1) & (2) in My Book Notes

    My book notes, that at a given temperature the ratio of the total number of particles in the fermi gas to the total number lying within (ε-kT,ε+kT) is given by: T/TF (1) And that each of these particles has an energy of ≈kT (2). I can't see where this comes from? :S Could anyone explain (1) and (2)?
  5. A

    Is the Fermi Surface Relevant for Metals with Band Structure?

    Does this construction even make sense? By definition it is a surface of constant energy in k-space, so for the free electron it is a sphere. But for metals you have band structure so that a given k-vector can have several different energies associated with it. Which of these are to be chosen?
  6. N

    Finding the fermi energy in doped quantum well

    Homework Statement Regular Doping: Let's say that we want to introduce some electrons into a quantum well, by adding dopant atoms (donors) to the semiconductor. The "regular" way to do this would be to deposit our semiconductor films, first a "barrier" layer with large band gap, then the...
  7. 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 ~...
  8. A

    Fermi Distribution: Explaining QM POV w/ Wave Functions

    I have posted questions similar to this over the past week, but I have never had a satisfactory answer. It is about the fermi distribution. From hyperphysics: "We picture all the levels up to the Fermi energy as filled, but no particle has a greater energy. This is entirely consistent with the...
  9. 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...
  10. 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...
  11. H

    What is band bending and how does it relate to Fermi Energy?

    Homework Statement Consider a pn junction in Si at 300K (other parameters given), with doping NA = 1021/m3 and ND = 1023/m3. Assume all impurities are ionized. On this basis find the Fermi level on each side. From this find the band bending VB and make a sketch of the pn junction. Homework...
  12. H

    Accessing electrons from the Fermi Sea?

    Recently a few friends and I were discussing the Fermi sea. One friend made the statement that if you could access the electrons from the Fermi Sea you could use the material you accessed them from as an electron source. Didn't make sense to me but it got me wondering. My question is, What...
  13. H

    How do I calculate the Fermi Energy of a compound?

    Homework Statement 1) This question has to do with pure InAs, with a bandgap 0.33 eV, electron mass 0.02, hole mass 0.41. (a) Evaluate the number of electrons/m3 int he conduction band at 300K. For this purpose you can assume the Fermi Energy is exactly at the center of the energy gap...
  14. M

    To calculate Fermi energy from arbitrary dispersion relation

    Homework Statement problem statement is attached as problem.pdf Homework Equations eqn are given in the pdf file The Attempt at a Solution I have tried in vain to connect Fermi energy with dispersion relation. I just don't have any clue ,I also tried to determine the effective...
  15. 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...
  16. J

    Photo of Enrico Fermi includes math/physics I do not understand

    The attached jpeg shows Enrico Fermi at the blackboard. There is a geometric drawing and some math I do not understand. Can you point me in the right direction? I have searched for a discussion of what he is presenting but cannot find one. The photo may be familiar because it was...
  17. 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...
  18. G

    Fermi energy approximation for white dwarfs

    Hello, I have read several articles/websites which talk about modelling white dwarfs, In all of these papers they state that it can be assumed the electrons have temperature zero, i.e. T<<T_fermi. I haven't been able to find a solid explanation of why this is approximation is possible...
  19. N

    Why symmetry breaking a paradigm whilst not describing Fermi liquid?

    Hi! So I'm a bit confused: first off, does Fermi liquid theory have "order". I suppose it depends on how you define order. But in case it does, is it described by symmetry breaking? From what I read, I think it does have order which is not described by symmetry breaking. But then I have...
  20. A

    Solid state physics fermi surface

    Homework Statement Some atoms in Cu crystal (Cu has a FCC lattice) are replaced by Zn atoms. Taking into account that Zn is bivalent, while Cu is monovalent, calculate the atomic ratio of Zn to Cu in ZnCu alloy at which the Fermi surface touches the first Brillouin zone faces. Use the...
  21. bayan

    Archived CMP. Probability of finding electron with E > fermi energy.

    Homework Statement what is the probability of finding an electron with energy between 5eV and 5.5eV at T=300k, given that the fermi energy of the metal is 4.2 eV. Homework Equations ##P(E,T)dE= \frac{3}{2} E_F^\frac {-3}{2} \frac{E^\frac{1}{2}}{e^\frac{E-E_F}{K_B T}+1}dE## The...
  22. C

    Suppose there is a semiconductor with Fermi energy

    Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states. I'd like to know why the mean number of excited electrons takes the form \bar n(T)={N\over \exp\beta(\mu-E_f)+1} where \mu is the chemical potential. ____ I can see that the Fermi...
  23. 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?
  24. G

    Fermi energy of nucleus

    How is it that the calculated Fermi energy of neutrons and protons in a heavy nucleus are different, but it's observed that they have the same energy? And how much is the Coulumb repulsion of the protons play a factor in that?
  25. 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?
  26. N

    Density of States at the Fermi Energy

    The density of states at the fermi energy is given by D(E_F)=(3/2)n/E_F I understand the density of states is the number of states per energy per unity volume, accounting for n/E_F. I don't understand how the 3/2 multiplying factor accounts for the volume?
  27. E

    A couple questions about energy bands and Fermi energy

    Hello, I'm studying digital integrated circuits and I'm new to solid state physics. I've studied PN junctions, drift and diffusion currents, now I'm trying to see these subjects in terms of energy bands and I'd really appreciate it you could explain to me a couple concepts. When two materials...
  28. C

    Are All States in a Free Fermi Gas Equal?

    edit* never mind figured it out thanks.
  29. N

    The Specific Heat of a Free-Electron gas calculated by using the Fermi

    Homework Statement Here g(ε_f) is the density of levels at the Fermi energy and T is the temperature. Calculate the specific heat of the electron gas in potassium (K) treating it as a free gas. For a free gas the density of electrons at ε_f is: g(ε_f)=(3/2)(n/E_f) where n is the electron...
  30. F

    Pions vs. Fermi Dirac Statistics and Bose-Einstein Statistics

    Hello! I have a small question, and I am not sure if I am missing something: Today I glanced at the wikipedia page for Pions, and saw this: Statistics: Bosonic Can anyone explain to me why a quark paired with a anti-quark obey Bose-Einstein Statistics? If quarks obey Fermi-Dirac statistics...
  31. S

    Calculating Fermi Energy of Cu

    Hey, My question is displayed below I have had a few questions like these and I just want to check my approach is correct, but I'm not sure - I know that the Fermi Energy of Cu is something like 7eV. Now we are told that there are 4 atoms per cube side - meaning 8 atoms but cubic...
  32. S

    How to Calculate Fermi Energy for a 1D Lattice with 2 Electrons per K-State

    Hey I have a question pictured below: I always seem to struggle with questions like these, my understanding is we know the spacing of K-states throughout the lattice is given by \frac{2\pi}{L} Such that the fermi wavevector divided by this spacing and multiplied by 2 due to the fact...
  33. Negi Magi

    Estimating the Number of Grains of Sand on Earth: A Fermi Approach

    1. How many sands on the earth? 2. Hints: Using the Fermi estimation 3.
  34. R

    Is the Fermi Coupling Constant Calculation from Oxygen Beta Decay Accurate?

    i'm reading through halzen and martin's chapter 12 on the weak interaction which they calculate the fermi coupling constant form oxygen beta decay using \Gamma = 1/\tau = G^2E_0^5/30\pi^3 with E_0 = 1.81MeV and \tau log 2 = 71 sec. they get G\approx 10^{-5}/m^2_N. where m_N is the nucleon mass...
  35. 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...
  36. 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...
  37. 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...
  38. R

    Calculating Fermi Energy for Gold Atoms

    Homework Statement The density of gold (atomic mass 197) is 19.32 g/cm3. Assuming each gold atom contributes one electron to the free electron Fermi gas, calculate the Fermi energy in eV. Homework Equations Fermi energy is given by: E_F=\frac{h^2}{8m_e} \left( \frac{3N}{\pi V} \right)^{2/3}...
  39. B

    Unlocking the Mystery of Fermi Energy in Accumulation-Mode FETs

    Greetings, I've been doing some literature research and can't seem to find any answers to my question. In an accumulation-mode FET (i.e. only relevant capacitance is that of the gate dielectric), how does one translate the applied gate-voltage to the Fermi energy of the active region? Say we...
  40. A

    Fermi Distribution Explained: Energy Levels in Metals

    Hello! I've just started reading about quantum mechanics, so my question may sound silly. I'm using the book of physics of Paul Tipler. It's says that inside the metals we have a lot of free electrons, like a electrons cloud (like when we learn in the School). These electrons follow the...
  41. C

    About fermi levels in extrensic semiconductors.

    Why does the Fermi level level drop with increase in temperature for a n type semiconductor.? What's the basic idea behind Fermi level? How does it get affected by temprature?
  42. P

    Is There a Simple Explanation for the Area Element in Fermi Normal Coordinates?

    Hi everyone, Defined the Fermi Normal Coordinates (which can be seen for example http://relativity.livingreviews.org/open?pubNo=lrr-2011-7&amp;page=articlese10.html" ) is there any heuristic argument to explain why the area element is something proportional to the element of solid angle? I...
  43. L

    Fermi Distribution of Energy Levels

    Based on Fermi distribution, if there are two electron energy levels with occupation possibility of ¼ and ¾, respectively, calculate energy difference between these two levels.
  44. T

    Error incurred from approximating fermi surfaces to be a sphere

    I read somewhere that the error incurred from approximating the Fermi surface to be a sphere in k-space goes as 1/N where N is the number of electrons. So, N is generally of the order 10^23. I couldn't figure out how they came up with the value. I was trying to say that the actual shape of the...
  45. Z

    De Broglie wavelength and Fermi wavelength

    As we know that the properties of nanoscale material are quite diffrent from the bulk's. But what's the threshold of the size, or what the upper limmit where significant difference can be observed? The De Broglie wavelength or the Fermi wavelength of the electron in material? How to understand that?
  46. arivero

    Fermi four point vs Higgs condensate: differences?

    The fermi four point interaction (consider its modern version, quark up to down plus electron plus antineutrino) is not renormalisable Then we introduce an intermediate boson W in the middle. Then we give mass to this W using the higgs mechanism. Then we produce the higgs via a fermion...
  47. fluidistic

    Calculating Fermi Energy in Graphite Using Free Electron Model

    Homework Statement Graphite has a structure of parallel planes weakly interacting with each others such that for many effects it can be considered as two dimensional. Each plane has a hexagonal (honeycomb) structure with a single C atom by site which gives 1 electron of conduction. Assume that...
  48. 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...
  49. 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...
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