Fermi Definition and 336 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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

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}}

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...

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...

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...

For the fermi dirac distribution function for temperatures higher than 0 K, how do we approximate the number of electrons available for conduction?

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...

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 ?

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 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...

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...

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...

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...

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

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...

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...

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...

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...

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?

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 )...

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...

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...

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...

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...

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...

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...

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?

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...

I understood that the fermi level is a hypothetical energy level given by the Fermi-Dirac distribution where the probability of finding an electron is exactly 50%. My question is: it always takes (Ec-Ev) energy to excite the electrons in the conduction band in an intrinsic semiconductor or...

All derivations of the Fermidistribution uses a canonical ensemble with a chemical potential, which is the same as to say that the ensemble can exchange particles with a resevoir. But are the derivations still valid for the canonical ensemble with a fixed number of particles and why isn't this...

There seems to be relation between Fermi surfaces and magnetoresistance, but I guess because I don't have a clear picture of fermi surfaces,I have problem understanding this relationship. Also I have heard about open and close fermi surfaces and saturation of magnetoresistance which I can't...

My book notes, that at a given temperature the ratio of the total number of particles in the fermi gas to the total number lying within (ε-kT,ε+kT) is given by: T/TF (1) And that each of these particles has an energy of ≈kT (2). I can't see where this comes from? :S Could anyone explain (1) and (2)?

Does this construction even make sense? By definition it is a surface of constant energy in k-space, so for the free electron it is a sphere. But for metals you have band structure so that a given k-vector can have several different energies associated with it. Which of these are to be chosen?

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?

I have posted questions similar to this over the past week, but I have never had a satisfactory answer. It is about the fermi distribution. From hyperphysics: "We picture all the levels up to the Fermi energy as filled, but no particle has a greater energy. This is entirely consistent with 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...

Recently a few friends and I were discussing the Fermi sea. One friend made the statement that if you could access the electrons from the Fermi Sea you could use the material you accessed them from as an electron source. Didn't make sense to me but it got me wondering. My question is, What...

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...

Does the (intrinsic) Fermi level of an insulator HAVE to lie very near the middle of the band gap? I know it might deviate slightly if electrons and holes have different effective masses, e.g. in Si. But can it be radically different? For example, are there insulators with 5 eV band gaps that...