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Relationship between Density of States and the Fermi level

My understanding is that given the DOS of a material we find the fermi level by filling electrons into those energy levels and when we run out of electrons we reach close to the fermi level (or ...
Ajaykrishnan R's user avatar
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Fermi Level Shift in PN Junction

The image below shows the Fermi level shift of the PN junction when the potential of the N region is positive with respect to the P region. My textbook (Semiconductor physics and devices by Donald A. ...
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Chemical Potential of a Fermionic System

If the chemical potential of a fermionic system is $0$ at temperature $T=0$, will it be zero at any arbitrary finite temperature?
Snpr_Physics's user avatar
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Determining Fermi Energy for a specific $E(k)$ [closed]

I am currently taking an introductory course on solid state physics. One of the problems I came by while studying asks the following: Suppose we have a 1 dimensional solid of length L, with N ...
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Lindhard Function for Boson

We know the density-density response for a non-interacting system with electrons is given by \begin{equation} \chi(q,\omega)=\sum_{k} \dfrac{f_{k}-f_{k+q}}{\omega+\epsilon_{k}-\epsilon_{k+q}+i\eta} \...
Santanu Singh's user avatar
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Temperature dependence of chemical potential in a semiconductor

My professor just uploaded the following two foils: and Now I understand that if temperature increases we have some electrons in the conduction band and some holes in valence band, which would (I ...
bened's user avatar
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How does graphene Fermi velocity $v_F$ link to the envelope propagation

my questions stemmed from reading the article in Physica E. Vol. 86, 10-16. (https://www.sciencedirect.com/science/article/pii/S1386947716311365) Why does the graphene Fermi velocity $v_F$ appear in ...
Martin.s's user avatar
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Struggling with understanding two approximations in Statistical Physics [closed]

I am a student finishing my bachelors in Applied Physics, and whilst studying for Statistical Physics I came across 2 approximations I can't understand. These are the Quantum corrections for an Ideal ...
Im_Trying's user avatar
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Definition of Fermi level

In wikipedia article, there is following sentence. The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually ...
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Extremely strong peak around 10 eV energy of Aluminum crystal in an x-ray inelastic scattering experiment

I conducted an experiment where I measured Bragg reflection for two different atomic planes (200 and 400) of Aluminum crystal at an energy of 10 KeV. Then, in each of these two measurements I shifted ...
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Thermal Properties of the Free Electron Gas: Explanation of the $N$-particle systems and averaging over all $N$-particle stationary states

I have a master's degree in engineering and am trying to study more detailed topics in solid-state physics on my own. I have difficulties to understand the (2.38) $$P_{N}(E)=\cfrac{e^{-E/K_{B}T}}{\sum ...
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Depletion regime in MOS capacitor

(I originally asked this in Electronics SE, I was redirected here as this was a better place to post my question) I was watching a video lecture recorded by my Uni prof, where while dealing with the ...
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Apparent contradiction in the definition of Fermi-level

The fermi level in an intrinsic semiconductor is defined as $$E_F = (E_c + E_v)/2 + kT/q \ln (Nv/Nc).$$ From this equation, the position of fermi level is exactly at the center of the band gap at 0K. ...
prananna's user avatar
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3 answers
278 views

Is the Fermi level taken to be (approximately) constant, i.e. equal to the Fermi energy, in semiconductor physics?

I have been reading Neamen's "Semiconductor Physics and Devices" Chapter 3. He derives in Eq. (3.79) the Fermi-Dirac distribution function $$f_F(E) = \frac{1}{1 + \exp(\frac{E-E_F}{kT})}, $$ ...
shortwhile's user avatar
4 votes
2 answers
477 views

How to understand chemical potential?

I wonder how to understand the chemical potential in terms of the condensed matter physics. Let’s say without the thermodynamic terms. Let’s consider some example system that can conduct and its ...
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Chandrasekhar limit with relativistic electron gas

The problem In David Tong's lecture notes on statistical physics (pages 100-102), there's a chapter on Chandrasekhar limit in relativistic case, where he states that energy degeneracy is $$g(E)=\frac{...
zare023's user avatar
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How do I calculate the surface energy density from Fermi's energy?

I have the following question: Consider the free eletron model in 2D to answer: Calculate an expression for the fermi energy and for the surface energy density at T= 0 K, expressed in function of the ...
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What does the radius of Fermi-Surface or the wavevector says about the occupied electronic states?

I have the following task: Consider a simple cubic structure with a lattice constant of 0.3 nm and one atom per unit cell; the macroscopic crystal has a size of 1 cm³. Assume that each atom ...
Mario's user avatar
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2 answers
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Fermi-Energy for different cases

I Have been working on the fermi energy recently and understand where the fermi-energy equation comes from for the non-relativistic case but does the fermi energy change for the relativistic and ultra-...
Dyslexic Batnam's user avatar
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What’s the Fermi energy of a Dirac fermion?

Knowing that the energy of a Dirac fermion is $$ \varepsilon(\vec{k})= \pm \sqrt{\left(m c^2\right)^2+(\hbar c k)^2}, $$ Why is the chemical potential $0$ at $T=0$? Since the density of state is $0$ ...
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Are electrons bounded or unbounded to nuclei when they are degenerate?

I have a question about degenerate electrons in white dwarfs. So, as far as I know, when the gas contained in stars is compressed so much, the electrons start to fill the lowest energy level and then, ...
nervousdog's user avatar
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How can the fermi temperature of a fermi gas tell us about if it is degenerate or not? [duplicate]

I know that If $T≪TF$ then the gas can be considered completely degenerate. If $T∼TF$ then the gas is partially degenerate. If $T>TF$ then the gas is not degenerate. But I don't know how we can ...
Adrish Chatterjee's user avatar
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Chemical potential vs Electrostatic potential in semiconductors

In Semiconductor Physics, the bottom of conduction band $E_C$ is treated as the electrostatic potential. This energy level is typically used to express the carrier concentration in terms of the ...
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Can the Schrödinger equation only give eigenvalues greater than the Fermi level in a semiconductor potential well?

I'm an undergrad with no direct coursework dealing with solid state physics so please forgive misunderstandings. Say you have a well of semiconducting material surrounded by an infinite potential ...
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Lower-dimensional Bands in Higher-dimensional Band Structure

This is (at least for me) an entirely hypothetical question. How would a lower-dimensional band within a higher-dimensional band structure affect the overall conductive properties of a material? To ...
Fred's user avatar
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2 answers
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Intepretation of the Fermi Dirac distribution graph [closed]

Is there a significance or an important interpretation of the fact that the plots in the Fermi-Dirac distribtion graph, all intersect at the point with coordinates ($\epsilon_F$,$\frac {1}{2}$)? https:...
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Proof that Fermi level is constant throughout a system in thermal equilibrium

The explainations I saw: The one I was referring to in this question. I described why I find this explaination not satisfying in the question. Consider $2$ systems in contact. The rate of particles ...
Sgg8's user avatar
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1 answer
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How does the Fermi Surface relate to the band structure in alkali metal?

I have a question that surged when I was studying examples of the Fermi Surface (FS). Now, it is my understanding that both the FS and the band diagram are defined in the Brillouin Zone (BZ) and the ...
ruva17's user avatar
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Why does the bottom of the conduction band correspond to the potential energy of an electron?

While proving that Fermi level is constant throughout any system in thermal equilibrium, all the books I saw the proof in (for example, Sze and Shur) assume the following: the bottom of the ...
Sgg8's user avatar
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2 answers
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Where do the electrons that are filled up to the fermi level above the valence band go?

Many questions have been asked on this topic, but this has never been answered satisfactorily. Yet I want to give it a shot. Fermi Energy represents the energy level achieved when all the available ...
AshutoshGS's user avatar
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270 views

Chemical potential $\mu$ controls filling?

If total magnetization of a spin 1/2 system is zero, does it mean that system is at half filling? or chemical potential $\mu=0$? I was trying to show that chemical potential controls filling by taking ...
Barry's user avatar
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What is the physical explanation behind the softening of the Kohn anomaly mode associated with charge density waves?

From the literature I've read, Fermi-nesting is a mechanism that can lead to charge density wave (CDW) formation in which a gap is created in the Fermi surface (which correspons with a nesting ...
John's user avatar
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1 answer
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Do electrons really move on the conductor?

For my understanding: Maxwell's equations combined with Poynting's theorem give us a model where electricity is energy carried along with the electromagnetic field (energy is stored in the field, not ...
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1 answer
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Determining the Number of Points in the $n$-Space

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 ...
Dario Mirić's user avatar
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Fermi energy at zero temprature

If I have a beaker that is at zero temperature in thermal equilibrium with its surrounding. If I start filling fermions (say electrons) in it, then according to the Fermi-Dirac statistics, the energy ...
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Why is Fermi energy considered most probable energy that electron posses in solids?

It can be seen in graph that probability of electron occupying a energy level below $E_{f}$ is $>\frac{1}{2}$, then why it is said that Fermi energy is considered as most probable energy that ...
Puneet Jain's user avatar
5 votes
1 answer
400 views

Landau tubes and Fermi sphere

A question regarding Landau tubes: I cannot understand why pictures of the Landau tubes are in k space as the Fermi sphere, especially considering the fact that $k_y$ ceases to be a good quantum ...
Giovanni De Crescenzo's user avatar
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Fermi energy lying in the forbidden gap

So, according to the my textbook(Fundamentals of physics by Halliday & Resnick), the Fermi level is the highest occupied level at absolute temperature ($T=0 K$) and the energy corresponding to it ...
Mahmoud El-Nezely's user avatar
1 vote
1 answer
240 views

Relation between Fermi surface and Fermi velocity

Is there a direct relation between the Fermi velocity and the Fermi surface? Can one reconstruct the Fermi surface if the full angular distribution of the Fermi velocity is known?
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Rewrite the derivative of Fermi-Dirac distribution [closed]

I find the derivative to the Fermi-Dirac equation as via my textbook and this can be rewritten to using the identities $2cosh(x)=e^{x}+e^{-x}$ and $4cosh^{2}(x)=e^{2x}+e^{-2x}+2$ but I just can't ...
Eod Enaj's user avatar
2 votes
2 answers
81 views

How many $\rm eV$ near Fermi level are involved to the conduction of carriers? For metal and degernerated semiconductors?

How many $\rm eV$ near Fermi level are involved to the conduction of carriers? For metal and degernerated semiconductors? Someone say about ± 5 eV, but I cannot find any references to support.
Yo Yo's user avatar
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Making sense of negative $\mu$ in the Fermi-Dirac distribution

I'm trying to make sense of the fact that, in the Fermi-Dirac distribution, we have that the chemical potential can have any positive or negative value, that is $$ -\infty<\mu<\infty $$ But at $...
EigenAle's user avatar
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1 answer
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BCS energy gap in superconductivity: Microwave apsorption as proof

A quick question. The BCS theory predicts the existence of the energy gap below the Fermi level. The experimental proof is the absorption of the EM radiation in the microwave spectrum. Why/How? Could ...
Dominik Car's user avatar
1 vote
1 answer
185 views

Can the lifetime of an electron in the conduction band be calculated?

We know that in a semiconductor in every instant of time some electrons get excited from valence band to conduction band and some electrons are deexcited from conduction band to valence band. In this ...
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Why is the Fermi wavelength in a semiconductor larger than in a metal?

I am a high school student, trying to better understand quantum point contacts. Would appreciate a simple explanation if possible. Source: https://arxiv.org/abs/cond-mat/0512609 Since the conductance ...
Anonymous's user avatar
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0 answers
325 views

What are s-bands and d-bands in band structures?

Given a band structure diagrams I can understand whether there are band gaps and what the bands are but what are s-bands and d-bands and how do I tell them apart in these diagrams? Example: I ...
jessegerritsen's user avatar
2 votes
0 answers
113 views

Is Seebeck coefficient for a metal related to Fermi level as it is the case for contact potential?

When putting together two different metals a so called "contact potential" will be built up. So far I understand this is because the combined system wants to reach an equilibrium where free ...
MichaelW's user avatar
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Having more electrons than the Fermi energy allows

What happens when we have more electrons in a solid metal than the Fermi energy and Pauli exclusion allows? Let's say we reduce the temperature to a level where all the energy states are filled with ...
mim's user avatar
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Quasi-relativistic dispersion relation in solid state physics

I recently worked on a question where I was asked to find the fermi energy for a 2D solid by considering an electron gas with fermi-dirac statistics. It was based on content of chapter 4 of Steve ...
wavara5331's user avatar
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219 views

What is the chemical potential in case of semiconductors?

What the chemical potential physically means? In case of semiconductors how is it relevant? What is the difference between chemical potential and fermi energy in case of semiconductors? What is the ...
Neutralino's user avatar