Fermi energy Definition and 94 Threads

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...

I have made solutions a-d, but my fermi velocity seems too big.

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...

Attempt:

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...

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

Homework Statement Homework EquationsThe 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) So...

\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...

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 the...

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...

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

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...

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

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...

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...

what is 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...

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...

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...

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...

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...