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. 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...
  2. R

    Fermi energy of multiple electrons, infinite potential well

    Homework Statement [/B] Five free electrons exist in a three-dimensional infinite potential well with all three widths equal to a 12 angstroms. Determine the Fermi energy level at T 0 K. Homework Equations E = [(h_bar*pi)2/(2*m*a2)]*(nx2 + ny2 + nz2) The Attempt at a Solution Tried using EF...
  3. ohwilleke

    Understanding Fermi Contact forces

    Normally, you think about SM forces being conveyed by gluons, weak force gauge bosons, or photons (ignore that troublesome gravity thing for the moment) between point particles. There is also a property of fermions (particles with total angular momentum Q=1/2, 3/2, etc.) that they can't occupy...
  4. Lagraaaange

    How hard to get REU at Fermi Lab?

    Also is it better than doing research with professor in school? If you had to choose
  5. 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?"...
  6. 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?
  7. anorlunda

    Is the Fermi Gamma Ray Detector Capable of Detecting Individual Photons?

    Today's APOD shows an animated visualization of a gamma ray flare detected by The Fermi Space Telescope. The video says, "each circle represents one gamma ray" That language suggests single photon detection. Is that correct?
  8. seo_andromeda

    Transforming FERMI SMARTS data from magnitude to flux

    I'm using data from the FERMI SMARTS website, which gives the emissions of blazers. The data has been calibrated using differential photometry (dividing by the average magnitude of a number of reference stars.) "The raw photometry of comparison stars in the field of the blazar was calibrated...
  9. 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!
  10. majormuss

    Have trouble running the Fermi software on ubuntu terminal

    Hi all, I recently installed ubuntu on my pc and I am trying to run the Fermi software provided by NASA (http://fermi.gsfc.nasa.gov/ssc/data/analysis/software/). I believe I did all the installation steps right but I am having trouble starting the software. If you are familiar with this...
  11. 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...
  12. Spinnor

    Bose and Fermi statistics in 1+1 spacetime?

    Do we have Bose like and Fermi like particles (fields) in 1+1 dimensional spacetime, Fermi like particles (fields) that obey the Pauli Exclusion Principle? For what space dimensions does the Pauli Exclusion Principle operate? Thanks for any help!
  13. F

    Arithmetic mean Fermi Dirac & Bose Einstein

    Hi everybody, I was doing one asignment form class, I was tasked to prove that in one system, the arimetic mean of FD and BE distributions is equal to MB's distribution for undishtingable particles. After doing the numbers I found out that it actually was, but I don't know why this happens, can...
  14. 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...
  15. 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...
  16. August

    Fermi Energy's plausible, but why define Fermi Temperature?

    I get that in a single particle of a metal, Fermi energy is defined at T = 0 as the maximum energy that electrons can reach. I get that, but my book defines this concept called Fermi Temperature. Is Fermi Temperature the temperature where electrons can reach the next empty energy band in...
  17. 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...
  18. ugenetic

    Relations between workfunction, ionization, redox and fermi

    My understanding so far, critique appreciated: [1] workfunction closely relates to reduction potential Since workfunction is about boundaries and chemical reaction are mostly happening at the boundaries between bulk material, Workfunction should have a direct correlation with reduction...
  19. R

    Simple (?) question regarding the Fermi Surface

    We all see diagrams of the Fermi surface, the representation of the occupied states, but I can't seem to find a precise diagram of when an electric field is applied. Most diagrams show that the surface has moved, BUT they do not say in which direction relative to the electric field, and when...
  20. S

    Solid State Chemistry Question Regarding Fermi Energy

    Hi there, I am new to electron theory, and have a question regarding fermi energy. The book I am reading plots the Fermi energy distribuiton function vs Energy for T=0 ( upper right graph in pcture) and for T not equal to zero. The book says that, when T does not equal zero, the decrease in the...
  21. Q

    Unraveling the Fermi Paradox: Exploring the Mystery of Extraterrestrial Life

    What exactly is a Fermi Paradox, I am having trouble grasping this idea. Can you please keep it in simple language?
  22. U

    Quick question on Fermi Golden Rule

    Adopted from my lecture notes, found it a little fishy: Shouldn't ##\frac{dp}{dE} = \frac{E}{p}## given that ##p = \sqrt{E^2 - m^2}##. Then the relation should be instead: \frac{dp}{dE} = \frac{E}{p} = \frac{E}{\sqrt{E^2 - m^2}}
  23. A

    Fermi energy in metals approximately doubling

    Between Cs and Na, the fermi energy in metal approximately doubles. why doesn't the carrier concentration also double?
  24. 1

    Calculating The Fermi Energy - Condensed Matter Physics

    Homework Statement Calculate the Fermi energy, EF at 0K for potassium (atomic weight = 39, density = 860 kgm3). Homework Equations KF3 = 3π2n Fermi Momentum ρ = h(bar)KF The Attempt at a Solution :[/B] For the first part: Using: E = ρ2/ 2m Can substitute Fermi momentum into that to get: EF...
  25. U

    Fermi Golden Rule - Beta Decay

    We consider the following beta decay: ^A_ZX \rightarrow ^A_{Z+1} Y + e^{-} + \nu_e The Fermi golden rule is given by: \Gamma = \frac{2\pi}{\hbar} |A_{fi}|^2 \frac{dN}{dE_f} Reaction amplitude is given by ##A_{fi} = G_F M_{nucl} ## while density of states is given by ##dN = \frac{4 \pi...
  26. N

    Fermi distribution: Sum over states --> integral over states

    Homework Statement http://web.phys.ntnu.no/~kolausen/TFY4230/.oldExams/17_eksdes12.en.pdf solution: http://web.phys.ntnu.no/~kolausen/TFY4230/.oldExams/18_losdes12.en.pdf Look at problem 4a, formula (27) or the expression between (29) and (30). My professor keeps converting sums into...
  27. 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?
  28. N

    Fermi Energy in Intrinsic Si, Ge, and GaAs

    Homework Statement Using the values of the density of states effective masses me* and mh* in table 5.1, find the position of the Fermi energy in intrinsic Si, Ge, and GaAs with respect to the middle of the bandgap (Eg/2). Table 5.1 shows the following density of states effective masses me*/me...
  29. 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 ?
  30. S

    Fermi energy condensed matter exam problem

    Homework Statement Hello, I am preparing a condensed matter exam and I was wondering if I could get some help on the following question from a past exam paper: Show that for the free electron gas at zero temperature the Fermi energy is given by: ε_{F}=\frac{\hbar^{2}}{2m}(3π^{2}N)^{2/3} and...
  31. WannabeNewton

    Series expansion tetrad Fermi coordinates

    Hi all. I'm working on a project that requires me to perform calculations in Fermi normal coordinates to certain orders, mostly 2nd order in the distance along the central worldline orthogonal space-like geodesics. In particular I need a rotating tetrad propagated along the central worldline...
  32. C

    The application of of Fermi Dirac statistics in the white dwarf

    hi guys, I wonder if I have fully understood the Fermi Dirac statistics properly, but I have a question on it regarding its application in the white dwarf research. I read the Fermi energy is applicable for T=0, now if the core of a white dwarf is too hot then how can we apply the Fermi Dirac...
  33. S

    Fermi energy and Fermi momentum from first principles

    Hi everyone! I run the software ABINIT. It allows one to model solids as a plane-wave pseudopotential. Since it is based on first principles DFT, we are able to obtain the energies over many k-points. This would give us a band structure. Besides this, the calculation would print out a...
  34. T

    Bibliography to understand Fermi, Bose and Boltzmann statistics?

    I'm studying by Statistical Mechanics (Huang, page 180) but can't understand many things there, can anyone provide a good bibliography to study this? I don't understand what's an occupation number of a given momentum: if it's the number of particles with that given momentum, why can it only be 0...
  35. A

    Is is possible to find unoccupied states below fermi energy?

    Is is possible to find unoccupied states below fermi energy?? Or all states below fermi energy are always occupied?
  36. M

    Fermi Surface and Orthogonality Catastrophe

    I am reading section 8.5.1 of http://f3.tiera.ru/2/P_Physics/PS_Solid%20state/Giuliani%20G.,%20Vignale%20G.%20Quantum%20theory%20of%20the%20electron%20liquid%20%28CUP,%202005%29%28ISBN%200521821126%29%28799s%29_PS_.pdf (page 442 of the book, page 465 of the pdf). The author claims the...
  37. E

    Fermi energy of simple 3D gas

    Homework Statement Consider a 3D gas of N non-interacting fermions in a volume V at temperature T << Ef / k. Suppose that the particles in the energy range [0.25 Ef, 0.5 Ef] are suddenly removed. Calculate the Fermi energy of the remaining particles after the system reaches its new thermal...
  38. U

    How does the density of states change with temperature?

    Homework Statement Part (a): Plot fermi energy as a function of N Part (b): Derive the density of states and find its value Part (c): How many atoms reside at 20% of fermi energy? Estimate diameter of cloud Part (d): For the same atoms without spin, why is the cloud much smaller...
  39. B

    Interpretation to ARPES measured Fermi surface

    For any system, different experimental tools are able to measure the Fermi surface or electron dispersion. Then, are these Fermi surface or dispersion the ultimate outcome of the combined effects from the existing interactions? In other words, should the detected motion of electrons have been...
  40. 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?
  41. I

    What is the Fermi energy of (undoped) graphene?

    All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi level" (which is emphatically not what I'm looking for; I want the Fermi energy as defined in this Wikipedia article: http://en.wikipedia.org/wiki/Fermi_energy )...
  42. D

    Entropy of a Fermi dirac ideal gas

    Hello Homework Statement From the expression of the partition function of a fermi dirac ideal gas ln(Z)=αN + ∑ ln(1+exp(-α-βEr)) show that S= k ∑ [ <nr>ln(<nr>)+(1-<nr>)ln(1-<nr>) Homework Equations S=k( lnZ+β<E>) <nr>=-1/β ∂ln(Z)/∂Er <E>=-∂ln(Z)/∂β The Attempt at a Solution I...
  43. 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...
  44. A

    Tight binding fermi surface

    On the attached file the tight binding dispersion for a 2d square lattice is described. It is then assumed that the fermi surface is a square. My question is: How can it ever be a perfect square when the dispersion looks as it does. Also can someone explain: Why does the half filled case...
  45. D

    Obtain the Fermi function by comparing with the Bose-Einstein function

    Homework Statement Hey guys, So here's what we have: Bose-Einstein function g_{v}(z)=\frac{1}{\Gamma(z)}\int_{0}^{\infty}\frac{x^{v-1}dx}{z^{-1}e^{x}-1} Fermi function f_{v}(z)=\frac{1}{\Gamma(z)}\int_{0}^{\infty}\frac{x^{v-1}dx}{z^{-1}e^{x}+1} And we have the series version of...
  46. 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...
  47. H

    Fermi energy in semiconductors

    From thermodynamics we have dU=Tds-Pdv+\mu dN. So the chemical potential is the energy change due to adding an extra particle when S and V are constant. Now consider an intrinsic semiconductor at T=0 in which the valence band is all-occupied and conduction band is empty. If we add an extra...
  48. M

    What is the relationship between Fermi Energy and carbon nanotubes?

    What would be a good Internet link that would properly explain Fermi Energy or (Fermi Level)? How does the Fermi Energy of a material vary with external influence, such as doping of the material, and applied electric and magnetic fields for instance? What other factors can effect Fermi Energy...
  49. S

    Can you explain Fermi levels to me?

    I'm on my second year in college and I'm doing a lecture on Fermi levels. The descriptions on Wikipedia and other sites don't seem to have been made for my level of knowledge, as I have difficulty understanding it. How would you describe Fermi levels on an entry level?
  50. I

    Semiconductor and fermi energy

    hey guys i just wanted to confirm something; so, for systems of continuous energy states (or small separations of discrete energy states), we can plot a graph like this and call the fermi energy the middle point where Probability=1/2. like this where, if T=0K, the transition from...
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