# fermi energy Definition and Topics - 20 Discussions

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.
In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.
The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level (also called electrochemical potential).
There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article:

The Fermi energy is only defined at absolute zero, while the Fermi level is defined for any temperature.
The Fermi energy is an energy difference (usually corresponding to a kinetic energy), whereas the Fermi level is a total energy level including kinetic energy and potential energy.
The Fermi energy can only be defined for non-interacting fermions (where the potential energy or band edge is a static, well defined quantity), whereas the Fermi level remains well defined even in complex interacting systems, at thermodynamic equilibrium.Since the Fermi level in a metal at absolute zero is the energy of the highest occupied single particle state,
then the Fermi energy in a metal is the energy difference between the Fermi level and lowest occupied single-particle state, at zero-temperature.

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1. ### Fermi energy for potassium

I have completed part a, from which I got the expression: Cv = 3KTn/(T_f) For part b, the first term is the electron contribution and the second term is the phonon contribution. I'm stuck on how to estimate the fermi energy for the potassium metal. I'm thinking I only need to consider the...

3. ### 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...
4. ### Calculate velocity of the fastest neutron inside a 96Mo nucl

Homework Statement Calculate the velocity of the fastest neutron in a 96Mo nucleus and, based on this, explain whether or not we are safe to consider such nucleons in a non-relativistic way. Hint: first calculate the Fermi energy. Homework Equations Fermi energy from Fermi gas model...
5. ### 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.
6. ### Conduction band, valence band and Fermi energy

Homework Statement Homework Equations The Attempt at a Solution The probability of getting a state with energy ## E_v## is ## \frac { N_v } { N_v +N_c } = \frac1{ e^{-(E_v – E_f)/k_BT} +1} ## ………….(1) Since, ## E_v < E_f, e^{-(E_v – E_f)/k_BT}>>1 ## as ## E_f – E_v>> k_BT ##……….(2)...
7. ### A Zero Energy Wavefunctions in 1D superconductor

\bf{Setup} Hi! I am trying to derive the wavefunctions of the zero energy solutions of the Schrodinger equation in a 1D p-wave superconductor (Kitaev model). I am starting with the Hamiltonian  H = \left[\begin{array}{cc} \epsilon_k & \Delta^{\ast}_k\\ \Delta_k & -\epsilon_k...
8. ### Fermi energy for two spin states equal in equilibrium?

Homework Statement Let's consider conduction electrons (at T=0K) that are put in a magnetic field. The electrons can have spin that is parallel or antiparallel to the magnetic field. Below is the density of occupied states for such a system (horizontally) as a function of energy (vertically)...
9. ### [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...
10. ### I Negative Magnetoresistance?

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...
11. ### I Differential number of particles in Fermi gas model

I'm practicing for the Physics GRE, and came across a question that has me stumped. "In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ0) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion...
12. ### A Fermi energy Ef changes with applied electric field?

Hi people, I dont understand why when we apply the electric field to the metal Ef remains the same. Ef as translation energy of electrons remains the same but we accelerate the electrons with applied electric field so the translation energy increases too? In other hand according the formula...
13. ### 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) ...
14. ### 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...
15. ### Energy gap between brillouin zones?

Homework Statement Consider a monovalent 2D crystal with a rectangular lattice constants ##a## and ##b##. Find expressions for the fermi energy and fermi wavevector in 2D. Show that the fermi surface extends beyond first zone if ## 2a > b\pi##. If the crystal is now divalent, estimate the...
16. ### 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. ### 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...
18. ### 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?
19. ### 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...
20. ### 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?