What is Fermi energy: Definition and 104 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.
I ran across the following problem :
Statement:
Consider a gas of ## N ## fermions and suppose that each energy level ## \varepsilon_n## has a multiplicity of ## g_n = (n+1)^2 ##. What is the Fermi energy and the average energy of this gas when ## N \rightarrow \infty## ?
My attempt:
The...
Electron gas is a collection of non - interacting electrons. If these electrons are confined to certain volume (for example, cube of metal), their behavior can be described by the wavefunction which is a solution to the particle in a box problem in quantum mechanics. Allowed energy states for...
a) V=(4/3)pi(r^3)
N=M/m_n (M=mass of neutron star, m_n=mass of neutron)
Subbed into E_f = (hbar^2 / 2m) (3(pi^2)N / V)^(2/3).
T_F = E_F / k_B
b) dU = (dU/dS)_s dS + (dU/dV)_s dV
p = -(dU/dV)_s dV
V=(4/3)pi(r^3) -> r = cubedroot(3V/4pi)
subbed into U_g = -(3/5)(G M^2 / r)
take (dU/dV)
plug into...
1)In my book , there is a definition of fermi energy as topmost filled level in the ground state of an N electron system. This definition holds only for absolute zero,right? If it is not absolute zero,fermi energy is the energy at which the probability of a state being occupied is 50 percent...
The Fermi energy Ef is defined as the energy of the topmost filled level in the ground state of the N electron system. Ground state is n=1 level. And in the ground state there can be only one orbital right? One orbital can have only up to 2 electrons. Does this mean that fermy energy is the...
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...
Problem Statement: See below
Relevant Equations: 2D density of states ##g\left(E \right)=\frac{m^{*}}{\pi\hbar^2}##
Fermi energy in a quantum cascade laser ##E_{F}=E_{i}+k_{B}Tln\left[exp\left(\frac{\pi\hbar^2n^{2D}}{k_{B}Tm^{*}} \right)-1\right]##
I've been stuck on this problem for a few...
Hello ,evreyone.I have two questions about fermi energy.
1,Can I claim that 'fermi energy ' play the role of chemical potential?
2,I have learned from thermal physics that only electrons near fermi level can conduct in metals.How can electrons behave like this? I can't figure out why only...
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...
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...
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)...
\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
$$
\begin{equation}
H =
\left[\begin{array}{cc}
\epsilon_k & \Delta^{\ast}_k\\
\Delta_k & -\epsilon_k...
Here is a simplification of a problem given in my book. I don't get the simplification part.
Could you please help at this ? It seems book has done the calculation wrongly.
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)...
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...
The problem:
A simple cubic metal has an electron density such that the Fermi energy just touches the edge of the first Brillouin zone. Calculate the number of conduction electrons per atom for this condition to be fulfilled.
The attempt at a solution:
I know that the electron density for a...
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...
Homework Statement
This isn't really a homework question but I didn't know where to put it.
Homework Equations
##E_f = \frac{h^2 k_f^2}{2m}##
##k_f = (3 \pi^2n)^{\frac{1}{3}}##
The Attempt at a Solution
I'm going through a lot of examples and every time I punch the numbers in I get an...
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...
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 =...
what i mean exactly what is the position of Fermi energy for semi conductor materials
1- at the highest of valance band
2- at the mid-way in energy gap like Fermi level at 0 K
Hi people,
I don't 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...
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) ...
hi every body
question is :
Consider that 5.5E22 free electrons are confined in a potential barrier of length 3.2A . find its Fermi energy ?
the main point is that i was confident about the answer of question .. but the doctor said it is wrong .. he said i should use the relation between...
Homework Statement
Find the densities of states 0.08 eV above the conduction band edge and 0.08 eV below the valence band edge for germanium.
Find the volume density of states (i.e. number of states per unit volume) with energies between the conduction band edge and 0.4 eV above the conduction...
Homework Statement
Part 1) Use the fermi dirac probability function for t=150k, t=300k, and t=600k to fill in the table below.
Part 2) Also show a sample calculation for (e-ef)=0.06eV and T=300k.
Part 3)(Same as part 2?) Calculate the probabilities of a state at E -EF =0.06 eV being empty for...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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 )...
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...
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...
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...
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...
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...
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...