Questions tagged [fermi-energy]
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Confusion about work function and Fermi energy
The work function $\Phi$ is the amount of energy required to move an electron from a state where it is at Fermi energy $E_f$ in the bulk of a metal to a state where it is at rest at a point just ...
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Derivation of the equation of state for degenerate electron gas
Ive been trying to calculate the equation of state of a degenerate electron gas (on the topic of stellar interiors), but there is a final step I’m missing.
I began by calculating the number of ...
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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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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 ...
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If $2p$ is the vorticity or vortex charge in a Fermi sea, what is just $p$?
Sorry in advance to ask such a simple question, but I promise I looked around and could not find a straight answer...
I think it might refer to pressure, or a form of pressure, but I am not sure...
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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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Question related to electronic thermal conductivity
I've been presented with the following question:
The atomic weight is of a monovalent metal is 197u and it’s density is $19.32 g cm^-3$.
Calculate the density of conduction electrons. Given that the ...
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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 ...
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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 ...
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Interpretation of Floquet Band Structure in Multi-band Models
Computing band structures inside Floquet formalism has become quite common, see e.g. [1]. While I think to fully understand it from a mathematical point of view, I'm lacking some physical ...
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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 ...
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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.
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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 $...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Intrinsic carrier concentration of a semiconductor without Boltzmann approximation [closed]
The carrier concentration of conduction band of a intrinsic semiconductor at a temperature $T$ is
$$n_i=\frac{1}{2\pi^2}\left(\frac{ 2m_e^* }{ \hbar^2}\right)^{3/2}\int_{E_c}^{\infty}\sqrt{E-E_c}f_{FD}...
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How can the total number of particles can be sum over all Density of states? [duplicate]
It is known that Density of states of a lattice structure is the probability distribution function of energy (for reference). This means that the sum/Integral of DOS over all energies is $1$. However, ...
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Liquid mercury, relativistic effects and Fermi velocity
Reading this news article and some related references, I learned that mercury’s liquidity is due to relativistic effects in Hg, where "the electron approaches about 58% of the speed of light.&...
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Why do we use a non-primitive unit cell for the brillouin zone of these metals?
I'm reading through a textbook and they defined a primitive unit cell as a unit cell with only one lattice point in it.
The Brillouin zone is defined as a primitive unit cell of the reciprocal lattice ...
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Do antiparticles have their own Fermi surface?
I am trying to understand Fig. 1 of this paper, which shows a quark-antiquark pair forming in a model of QCD with chemical potential:
Is the implication that antiquarks have their own Fermi surface, ...
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Shifting of Energy levels in PN junction under Equilibrium
My question is during equilibrium is achieved under no biasing, why it is that in fermi level diagram representation fermi levels are raised in p type nd lowered in n type. Is it not possible we ...
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What does the area under Fermi Distribution curve represent?
I am struggling to understand what does the area under the fermi distribution curve represent when plotted like this:
I know that area under the Maxwell Distribution curve when plotted for speeds of ...
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Unbiased PN junction Diode
I have certain doubts regarding the formation and movement of majority charge carriers when a p type and n type semiconductors are fused together.
When electrons and holes mover from p to n and n to ...
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Carrier density and size of Fermi surface
I think I've heard that a large Fermi surface implies a large carrier concentration and a small Fermi surface implies a small carrier concentration.
I am not really sure what the relationship is ...
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Why am I getting a large discrepancy between theoretical and experimental Fermi energies for aluminium?
I'm using a Gouy balance to try and experimentally determine the susceptibility and Fermi energy of an aluminium rod. For the susceptibility, the value I've arrived at is $\chi = 2.0 \cdot 10^{-5}$, ...
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Why is Fermi energy equal to chemical potential at absolute zero temperature
The probability that an orbital at energy $\epsilon$ will be occupied in an ideal electron gas at thermal equilibrium is given by
$$f(\epsilon)=\frac{1}{exp[(\epsilon-\mu)/k_bT]+1}$$
in kittel's book ...
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Tight-binding vs. nearly free electron (NFE) model predictions
I came across the following problem:
Suppose that a certain material consists of $N$ atoms that are ordered in a 2D lattice with a lattice constant $a$, and that each atom donates two conduction ...
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Fermi Energy for Semiconductor
I usually post question in bulleted form for convenience that does not mean I am asking more than one question.
Although Fermi energy and fermi Level is discussed many times on this website. Still, I ...
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How do I find the total electron energy for titanium?
I have a number of titanium atoms. I'm trying to find the total electron energy of this. I know that one formula is
Total Electron Energy = (3/5) * (Number of Electrons) * (Fermi Energy)
but I don't ...
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Seebeck Coefficient variation with Fermi Energy at different Temperartures for the Same Material
So we have been recently introduced to the Seebeck Coefficient in thermoelectrics, however, I had some questions on it, and I kept finding contrasting information online, maybe because I don't know ...
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Does the Fermi distribution also gives the probability of an energy level being full of electrons?
We started to learn about Fermi level and Fermi distribution function and I'm little confused .
From what I have understood , the Fermi distribution function gives the probability of a single state in ...
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Why does the Fermi-level decrease with temperature increase?
On temperature increase there should be an increased probability of finding an electron in the conduction band, this corresponds to the Fermi level rising up towards the conduction band so that there ...
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Fermi surface of a spherical nanoparticle
Assume to have a spherical nanoparticle of a metal whose Fermi surface in the crystal is a sphere (I think those are the metals having very symmetric crystals). Would then the Fermi surface be ...
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Electronic specific heat capacity using free electron theory
While considering the contribution of the electronic specific heat capacity, it is stated that, when the temperature increases from 0 K , only the electrons with energy range of the order of $k_bT$ ...
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Why can it be important to engineer band alignments/offsets (e.g. CdS buffer layer in CIGS)?
I would like to ask this question by the example of the CdS buffer layer in CIGS solar cells. One paper (https://pubs.rsc.org/en/content/articlelanding/2017/se/c7se00348j#!divAbstract) says that CdS ...
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Fermi-Surfaces of Alkali-Metals
I think I am a bit confused if I look at the following image of Fermi-surfaces for different metals:
Li, Na, K, Rb and Cs have only one valence electron. Hence, if one calculates the Fermi-vector $...
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Why is Fermi level the same in p type and n-type semi-conductor when they are connected?
In an energy band diagram the Fermi energy for both p-type and n-type are the same. Shouldn't the Fermi level be higher in the n-type because it holds the 5th electron very loosely therefore having ...
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