Fermi energy Definition and 94 Threads

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...

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?

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?

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...

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...

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...

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}...

Homework Statement The atom He^3 has spin 1/2 and is a fermion. The density of liquid He^3 is 0.081g/cm^3 near absolute zero. Calculate the Fermi energy \epsilon_F and the Fermi temperature T_F Homework Equations \epsilon_F = \frac{\hbar^2}{2m}(\frac{3 \pi^2 N}{V})^{2/3} T_F =...

Homework Statement Consider an electron gas with a density of states given by D(e) = ae2. Here a is a constant. The Fermi energy is eF. a) We first consider the system at zero temperature. Compute the total number of electrons N and the groundstate energy E. Show that the average energy per...

Homework Statement Here's what the question says. "Consider a cube of gold 1 mm on an edge. calculate the approximate number of conduction electrons in this cube whose energies lie in the range from 4.000 to 4.025 at 300k. Assume Ef(300K) = Ef(0)." Homework Equations Well, I know...

Hi all, In the solid state physics course I took a year ago we used the chemical potential μ which appeared inside the fermi-dirac distribution function to describe the energy that above it no electrons resides and below it they all reside as the temperature reaches 0 kelvin. Now, when I...

Homework Statement Calculate Efi with respect to the center of the bandgap in silicon for t= 200, 400, 600 kelvin. Homework Equations ni = Nc e^-((Ec- Ef)/(kt)) k = boltzman constant t= temperature in kelvin Ec = energy level of the conduction band ef= fermi energy level ni=...

I have taken several courses in semiconductors at the undergraduate level. Both the pure physics part (k vectors) and the more engineering parts (silicon processing, band diagrams) etc. So for all the junctions (Schottky, Ohmic, p-n) - I have never managed to imagine the idea of the Fermi...

To find the Fermi energy I need to find the electron density of the material and that I can do by finding the density of atoms in the material in some instances this same density. From what I gather it's not always that way Sometimes you have to multiply a certain number For example...

Quick Fermi Energy Question..Free electrons?? A quick question on the Fermi energy. From a 3D cubic well, one can derive an expression for the Fermi energy of a solid: Ef = h^2/2m . (3.pi^2.N/V)^2/3 Now, I have come across an expression where N/V, electrons per volume, is replaced by...

Homework Statement The degeneracy of the nth level above the ground state for a three dimensional harmonic oscillator is (n+1)(n+2)/2 where n takes values n=0,1,2,... A gas of N non-interacting identical lithium atoms (mass 6amu) each having spin1/2 is confined in a 3d harmonic potential...

Si is doped with 6 x 1015 cm-3 donors and 2 x 1015 cm-3 acceptors. Find the position of the Fermi level with respect to Ei at 300 K. i know the equations are (for n-type) EF = kT ln(ND/ni) + Ei (for p-type) EF = kT ln(ni/NA) + Ei however, since the problem gives me both donors and...

Homework Statement "The numerator of this fraction: \overline{E}=\frac{\int \! E N(E)D(E)dE}{\int \! N(E)D(E)dE} (N(E) is the number of particles in an energy state, D(E) is the density of states) is the total (as opposed to the average particle) energy, which we'll call U_{total} here...

Homework Statement a) Calculate the Fermi energy for copper. b) Calculate the ratio of the number of occupied levels at an energy of 8.5 eV to the number occupied levels at the Fermi energy at room temperature. c) Based on your answer to a) and b) above, show that at room temperature...

Hello, I have a question which has something to do with band structures etc: A two dimensional solid has two electrons per unit cell. The crystal potential is weak and the solid behaves like a free electron metal. Estimate the threshold for interband optical transitions in terms of the...

Hello, Im just an amateur physicsist and was interested in Fermi Energy. Found a page http://http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi2.html#c1" , that helped. However, I found the page and site a bit hard to understand in some places. Could someone please explain to me...

I was reading this website, and I don't understand this last statement. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html It reads: "Since only a tiny fraction of the electrons in a metal are within the thermal energy kT of the Fermi energy, they are "frozen out" of the heat...

I've tried to look this up online, but I can't find it anywhere. I'm just looking for the intrinsic fermi energy of silicon E_i ? Can someone maybe direct me towards a website where I could look it up? Either that, or is there a way to calculate it from the energy gap for intrinsic silicon...

Effect of Doping on Fermi Energy... I was wondering if anyone could give me a clear answer on why doping a semi conductor raises or lowers the fermi energy depending on n or p type semi conductors. There seem to be a few standard ways of explaining this, some to do with charge conservation or...

I know that when a metal is compressed its fermi energy is increased. I would attempt to explain this by saying, "as the volume has been decreased, so has the allowed number of particle in a 3D box states, thus as we have the same number of electrons and fewer allowed states, and the pauli...

As I know chemical potential of two reacting substances strongly depends on difference in Fermi energy between them. Fermi energy is inversely proportional to the mass of particles. Does that mean that Fermi energy of bare proton will be 2000 time smaller than that of electron? Usually...

Hi there, i've already read some topics in this forum about the fermi-energy/chemical potential. I've also read the article "The chemical potential of an ideal intrinsic semiconductor" from Mark R. A. Shegelski which made the whole thing a little bit more clear to me. but there are some...

Homework Statement We must calculate the Fermi energy of metallic potassium at 0K. We have aleady found the number of atoms per m cubed, we are told that each atom contributes one electron to the free electron gas. Homework Equations Fermi energy = ((hbar^2)/2m)(((3Pi^2)N)/V)^3/2 The...

Homework Statement I am wondering about something: Calculate the Fermi energy for the neutrons confined to a nucleus with 40 protons and 50 neutrons which roughly forms a sphere of radius 4.6 10^(-15) m. Homework Equations the formula of the fermi Energy is EF=...

I am wondering about something: Calculate the Fermi energy for the neutrons confined to a nucleus with 40 protons and 50 neutrons which roughly forms a sphere of radius 4.6 10^(-15) m. the formula of the fermi Energy is EF= ((h-bar)^2*(3*pi^2*n)^(2/3))/2m m:mass of electron, n = number...

relation of fermi energy in 3D is E=h(cut square)k(square)/2m, if i want a relation of fermi energy in 2D,what should i do?

Hi, Is this right: Fermi velocity is the velocity of electron-wave in a conductor. Why is it called Fermi velocity, i.e. what is its relation with Fermi energy, etc.. Thanks a lot. Cheers

Hi all, I'm studying on the current transfer at quantum level and I have a point that is not so much clear. While reading the Fermi sphere from the book "Current at the nanoscale", I could not understand the expression: The number of electrons in the conductor, N, is the ratio of the...

Homework Statement (I copy-pasted the question) Consider N non interacting electrons inside a 3D box similar to the one we saw in class, but this time it is not cubical, i.e. Lx = Ly \neq Lz. 1. Calculate the fermi energy as a function of N;Lx;Lz;me... 2. What happens if we take Lz --> 0...

In classical statistical mechanics, temperature of a system is the measure of its average kinetic energy. In quantum statistical mechanics, Fermi energy corresponds to last filled level at absolute zero and corresponding temperature is the Fermi temperature. Is the Fermi temperature also take...

fermi level?? is there any relation ( equation) that give the fermi energy level in terms of Na and Nd the concentration of dopant??

I feel dumb that I can't figure this out. I'm sure its something simple that I'm just not seeing, but its really frustrating. Homework Statement How many electrons (in percent of the total number of electrons per mole) lie KbT (ev) below the Fermi energy? Take Ef=5eV and T=300K...

please help me solve this... fermi energy of copper is 7eV. what is the fermi momentum of an electron in copper? what is the de Broglie wavelength of the electron? what is the fermi velocity?/// please help/////:cry:

I understand the principle behind p and n type doping, but I don't understand how such a small amount, 1ppm, can cause such a massive change in the fermi energy. as I understand it: for the intrinsic case the number of electrons exactly matches the number of holes and the fermi energy...

In metal, fermi energy is the highest energy states that electron occupied at T=0. And so, fermi energy of a particular metal is an intrinsic value, and won't be changed. Then for a semiconductor, What is fermi energy, is there any concrete interpretation as of metal? Why is it just in the...

Hey! When we say that the fermi energy of a certain metal is for example 2 eV what are the 2 eV measure relative to? The top of the valence band? If so, wouldn't the fermi energy of a semiconductor at 0 K be 0 eV? Thanks

we have non relativistic electrons at absolute zero. we need to show that the total energy is 3N*Ef/5 where Ef is the Fermi energy. this calculation I can do. we then need to show that the Pressure is equal to 2U/3V where U is the total energy. I did this by noting the dU=TdS - PdV and at...

Hi, Hope somebody can help - I seem to be missing the obvious and bonking my head on the wall. In Wong and also in Feshbach/deShalit, they calculate the Fermi momentum, Kf using the experimental value of Rho-0 and come up with Kf=1.3 fm-1 So far so good. Where I stumble is in...

Ok, so here's the basic idea. You have a refrigerator, with four walls each 6ft x 2ft x 4in. The walls are made out of copper(high thermal conductivity), with a silicon chip at the center. This chip is connected to an inductor and is essentially a L-C oscillating circuit. As the chip heats up...