Questions tagged [fermi-energy]

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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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1answer
20 views

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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25 views

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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Odd number of surface Fermi surfaces in strong Topological Insulators

I am now getting into topological insulators and I have read several times that a strong TI possesses always an odd number of Fermi surface bands crossing the Fermi level. However, this is not ...
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1answer
49 views

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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1answer
27 views

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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1answer
25 views

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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37 views

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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1answer
37 views

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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29 views

Fermi energy in Lithium

In Fermi-Dirac statistic the number of states with energy between $[\epsilon,\epsilon+d\epsilon]$ is $dN=g(\epsilon)d\epsilon$ if I want to know the total number of occupied states in an atom I do ...
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1answer
61 views

Temperature dependency of electron density in metals

I wanted to know how the electron density in metals behaves with temperature. I couldn't really find an answer online so I searched through my x-years old scripts and, surprisingly, I found a sentence ...
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1answer
35 views

What does it mean to say that the Fermi energy is equal to the hopping energy?

I have a conceptual question regarding the relation between hopping energy and Fermi Energy. In order for my question to make sense contextual background is needed: So the hopping integral or ...
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1answer
27 views

Fermi energy, occupation factor and number of particles

Using the grand canonical ensemble, we can show that the occupation factor of an energy level (when the temperature $T$ and chemical potential $\mu$ are fixed) is given by $$ f_E(T,\mu) = \frac{1}{\...
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29 views

Fermi Energy in Anisotropic Crystal

Suppose I have an anisotropic cristal, so it has, say, energy $$E=a(k_x)^2+b(k_y)^2$$ How would I calculate its Fermi energy? It doesn't depend only on the length of the vector $k$, so most of the ...
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37 views

Just another confusion on Fermi level and Fermi energy [duplicate]

I've heard it so many times: "At 0 K Fermi energy and Fermi level are the same." "The Fermi level for an intrinsic semiconductor lies at the middle of the band gap." And the definition of ...
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15 views

What is the correct definition for a Lifschitz transition?

The definition that was given to me by my professor said that a Lifschitz transition is when the topology of the Fermi surface changes. For example, if we have a one-dimensional Fermi surface, we ...
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53 views

Two dimensional semiconductor

I am dealing with a two dimensional intrinsic semiconductor with a 100meV band gap. I have the conduction and valence band equations which are parabolics. Also I have been given the electron and hole ...
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13 views

In a forward biased PN junction, is N region's fermi level the result of current or voltage?

Fermi level in the N region seems to dictate the amount of current that can flow thru the forward bias. Can this fermi level be manipulated with external voltage independent of amount of current flow? ...
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21 views

Fermi Gas model for the nucleus

I'm studying the nuclear model based on Fermi gas and in the part where there's the count of possible states giving the impulse the book says that the states, represented by dots because of the ...
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17 views

Why does the Fermi level lie at $k=\pi/2a$ , in polyacetylene?

Let $a$ be the equilibrium spacing between the $x$ coordinates of successive CH groups in the undimerized structure of polyacetylene. Why does the Fermi level lie at $k=\frac{\pi}{2a}$?
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1answer
76 views

Meaning of Fermi energy in semiconductor

We know from the band theory that in a semiconductor (of course for all metals, insulator) all energy states are not allowed. In a semiconductor there is a valence band and a conduction band, and in ...
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1answer
47 views

Can quarks in a proton be modeled as a Fermi gas?

I recently learned in one of my courses that a nucleus could be modeled as a Fermi gas. This led me to think about other fermions and whether or not I could mess around with them as well. Are the ...
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1answer
62 views

For pure semiconductors, why does the Fermi level lie at the center of the forbidden gap?

For an intrinsic semiconductor, the position of the Fermi level in the energy band diagram is half-way between the topmost level of the valence band and lowermost level of the conduction band i.e. ...
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1answer
48 views

Chemical potential of fermions [closed]

Hey guys I am trying to determine the chemical potential for electrons in metals. I have that: For the valance band, $\epsilon\lt\epsilon_\mathrm v$, $\rho(\epsilon)=g_\mathrm v$, while for the ...
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43 views

Why is the Fermi surface of a metal irregular at 0 K? And how does 'smearing' remedy the situation in DFT calculations?

I'm getting familiarized with DFT and was wondering why the Fermi surface of a metal is irregular at 0 K? It is for the same reason I believe, some 'smearing' needs to be done if the material in ...
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2answers
51 views

Why electron-holes interpretation can't be effective in metals?

Help me out here, If thought of as electron sea, there's is no need of holes in modeling conductivity in metals. But it's not that we can deny that there will be positive charge in the nucleus after ...
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1answer
55 views

Change in Fermi level Produces Electric field

I was reading book On Semiconductor Physics By Donald Neamen,In page 176 He discussed semiconductor that is nonuniformly doped with donor impurity atoms.Now Here The doping concentration decreases as ...
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1answer
48 views

Confusion with Fermi energy in Quantum Hall effect

It is well-known, that when someone turn on magnetic field, and if magnetic field large enough, only few Landau levels are filled: But I can't understand what going on with Fermi energy. Fermi ...
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3answers
102 views

Why Fermi energy is in between band gap?

It may seems like a copied question Question But It still didn't clear my doubt.Consider the following figure As you can see the fermi energy (Fermi energy) lies in between the bandgap and ...
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27 views

Fermi surface vs Fermi energy

Why we define Fermi surface only in metals; but we have Fermi energy in metals and non metals?? Thanks for your answers
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23 views

Determining the critical points of a $2D$ Fermi surface

Suppose I have a $2D$ Fermi surface like below: How would I discern where its critical points would be without looking at an image this? Here, since I know that, for instance, $X$ must be at the ...
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34 views

Why does the Fermi energy enter in this equation?

I am studying the book Solid state physics by Ashcroft & Merrin; in particular I am studying chapter 18: Surface effects. In this chapter, authors say that to remove an electron from the surface,...
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1answer
557 views

Fermi energy in conduction band while valence band and conduction band have no overlap

I often see band diagrams of of solids and in cases of semiconductors, I often see a band gap separating the valence band and conduction band while the Fermi energy lies in the conduction band like ...
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33 views

Fermi level position in doped semiconductor

Physically by increasing temperature, the semiconductor tends to be intrinsic as the number of free electrons genereted by thermal generation becomes comparable to free electrons due to doping till it ...
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1answer
69 views

Fermi energy as an energy difference?

I was traveling down the Wikipedia rabbit hole when I ran across something that caught me off guard. On the Fermi energy page, it says that the Fermi energy is: ...the energy difference between the ...
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2answers
128 views

Fermi Energy Definition

Ok, so I'm having a hard time understanding the definition of Fermi Energy. Several sites basically repeat each other, saying that it is the energy difference between the highest and lowest occupied ...
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92 views

Fermi level in a solid

I am confused as to how fermi level is defined within a crystal/ solid It is normally situated midway between valence band and conduction band, is this how it is defined or is there other reasons this ...
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1answer
176 views

Electron and holes in tight binding Hamiltonian on two sublattices

Background Say that I have a tight binding Hamiltonian (with spinless fermions) of the form $$H = - 2t \sum_{ij} (c_i^{\dagger} c_j + h.c) - 2\mu \sum_i c^{\dagger}_i c_i$$ where we only sum over ...
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What is Fermi Surface of superconductors?

It is known that, in superconductors, at the Fermi level, electrons are paired(Cooper pairs) and there is a gap (see figure). However, there are lots of ARPES experiments showing the "Fermi surface" ...
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133 views

Is Fermi energy the same as chemical potential?

In all of the textbooks , the Fermi Energy was interpreted as the energy level below which all possible energy states are filled. However with a Fermi-Dirac type of distribution, which has asymptotes ...
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90 views

Number of electrons within Fermi Surface

This question is regarding problem 9.5 in Ashcroft and Mermin where we have to calculate the radius of the Fermi circle in a 2D square lattice with lattice constant $a$ and $m$ electrons per primitive ...
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32 views

What is the effects on the electrical conductivity of a crystal structure if the Fermi sphere fits inside the first Brillouin zone

My explanation: If the Fermi sphere fits inside the first Brillouin zone then there are empty states between the 1st and 2nd Brillouin zone which electron can be excited into. Hence, the crystal ...
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1k views

Why is the Fermi level (energy) shfited in doped semiconductors?

According to the Fermi level is shifted due to doping: Upwards in case of n-type and downwards in case of p-type. Why is this? The Fermi level is the level where the probability that an electron ...
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1answer
66 views

Understanding Fermi gas number density

According to Wikipedia, the number density of a 3D Fermi gas is given by: $$\dfrac{N}{V}=\dfrac{1}{3\pi^2} \left( \dfrac{2 E_F m}{\hbar^2} \right)^{3/2}$$ This means that if the mass of the ...
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1answer
43 views

Density of levels in Fermi-Dirac statistics

We know that $$ u=\int_{-\infty}^{+\infty} D(\mathcal{E})\mathcal{E}f(\mathcal{E})d\mathcal{E} $$ where $D(\mathcal{E})$ is called density of levels per unit volume. My textbook (Kittel) says that: $...
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1answer
187 views

Does an insulator always contain the Fermi surface in the 1st BZ

I'm looking for a clarification about the classification of metals and insulators; is it correct to state that if the Fermi surface is contained into the first BZ, then the material is an insulator, ...
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3answers
305 views

Fermi level in metals and semicoductors

As we read about Fermi energy, it is the energy of the highest occupied electrons. But if we look at the energy level diagram of semiconductor the Fermi level is situated somewhere between the valence ...
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1answer
190 views

Show that the Fermi surface is perpendicular to the Brillouin zone boundary in the nearly free electron approximation

How can one show that the Fermi surface is perpendicular to the Brillouin zone boundary in the nearly free electron approximation? Similar question without an answer: Why does the Fermi Surface cross ...