Questions tagged [fermi-energy]

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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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Relation of fermi level with conductivity of monovalent metals

I read somewhere that monovalent metals have a high population density near their Fermi surface because they have partially filled bands. Can someone explain why this is so?
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Fermi gas model of nucleus, specifically when the numberof neutrons does not equal Z

I am studying for a final for an introductory course in particle physics.(Undergraduate course) and while working though old final problems I found one part question which I could not figure out how ...
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Average electron density of a Free electron gas

I'm trying to solve solving an exercise in quantum mechanics, and began facing some confusion regarding the definition of average electron density. For a 2D free electron gas, under an open boundary ...
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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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Can we say that the Fermi energy at 0 K lies exactly between the ground state energy and the surface barrier? Why/ why not?

In accordance with Pauli exclusion principle if there are N states only N/2 of them should be filled at 0 K in a 3D box having zero potential everywhere inside. For a box of dimensions ~ $10^{-2}$ m, ...
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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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How does field effect work on graphene?

I am trying to understand how the field effect from a gate works on graphene. Does the gate voltage affect the bands or the Fermi level? When studying how gate voltage affects a semiconductor, I ...
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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?

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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Determine Fermi Temperature from the experimental measurement of heat capacity $C_v$

In the lecture slide below I was introduced to the contribution of heat capacity of electron gas $C_{el}$ to the total heat capacity $C_v$. The textbook used is Kittel's Thermal Physics. From the ...
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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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Doubts about the microscopic derivation of Joule heating for degenerate fermi gases

The typical derivation of Joule heating: power = IV claims that each electron crossing the circuit losses an energy Ve (V=voltage difference, e=electron charge). If this energy is transformed into ...
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Definition of Chemical potential [duplicate]

I am very confused with what actually the chemical potential (chemical potential energy should be the proper name, right?) is. As of right now, I know at least 3 or 4 different definitions of it, ...
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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 contribtution 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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2 votes
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Why the electrons in a insulator fill up the valance band exactly?

The classic picture of the band structure for an insulator is a filled valance band below $E_F$ and empty conduction band above $E_F$. This picture seems to me that the electron density is fixed. For ...
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Meaning of fermi level related to distance to valence/conductance band

Is there any practical meaning of the Fermi level? In the below image we can see how it behaves when p and n-material connect: It basically holds a constant value(?). Can we draw any meaning out of ...
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Can a voltmeter itself disturb the electrochemical potential of battery?

I'm trying to understand the effect on a system when a voltage of a system is measured by connecting a voltmeter. For example let's say we are trying to measure the voltage of a Li-ion battery. The ...
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What would the Fermi level be if two different metals are in contact?

I know when two metals are in contact, the Fermi level must line up, somewhere between the two original metals for thermodynamic equilibrium. When this happens, I wonder how much does the Fermi level ...
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Confusing definition of thermodynamic pressure when calculating the electron degeneracy pressure

When dealing with statistical mechanics, one usually defines pressure as $$p(N,T,V,X):=-\frac{\partial F(N,T,V,X)}{\partial V}.$$ In engineering thermodynamics, I've often seen this definition ...
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Difference between Fermi energy and ionisation energy

At $T=0K$ what's the difference between Fermi energy and first ionisation energy?
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