Questions tagged [fermi-energy]

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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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32 views

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 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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59 views

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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Finding the Fermi surface given you have a set of solutions

I'm having trouble wrapping my head around how I'd do a certain calculation: finding the Fermi surface given I have a set of energies and a Ground state. Some background. I have a Hamiltonian which I ...
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42 views

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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Effect of Gate Voltage on conductivity - MOSFET [duplicate]

I have this formula for the current based on conductivity but I cannot see the influence when applying the gate voltage. What does it change ? My assumption is that I have to change the conductivity ...
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Fermi Energy and single particle state

I have a question about Fermi energy and the single particle state. I have it a bit hard, on how to formulate my question, for the below text, because I don't fully understand the concepts so well. ...
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44 views

Calculating Fermi Wavelength

I am trying to figure out what the Fermi wavelength of my system is. Specifically I am looking at simulation a graphene lattice in the tight binding model. For this, I know that the Fermi energy (...
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59 views

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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22 views

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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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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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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46 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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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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59 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
49 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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118 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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176 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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120 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
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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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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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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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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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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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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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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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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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238 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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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
149 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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54 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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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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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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120 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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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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204 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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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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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
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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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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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76 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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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 ...