Questions tagged [fermi-energy]

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300 views

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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1answer
1k 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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4k 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
38 views

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
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0answers
61 views

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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0answers
421 views

Temperature dependent chemical potential

Chemical potential is determined by the number of electrons in the system and coincides with the Fermi energy at zero temperature. The chemical potential can shift as temperature changes if the ...
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0answers
33 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 ...
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0answers
27 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 ...
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0answers
31 views

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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2answers
120 views

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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0answers
44 views

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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0answers
25 views

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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27 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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115 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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172 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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0answers
18 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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0answers
25 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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0answers
50 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
83 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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0answers
220 views

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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0answers
329 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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51 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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1answer
99 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
80 views

Interchanging $\epsilon_F$ and $\epsilon$ when deriving Density of States (DOS) of Free Electron Fermi Gas (FEFG)

When deriving the Density of States for a Free Electron Fermi Gas, Kittel seems to flamboyantly interchange $\epsilon$ and $\epsilon_F$ when going between equations. I am specifically puzzled as to ...
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54 views

Fermi energy equilibration

A conventional example tells that when we bring two pieces of some materials with different work functions in contact electrons start to flow from material with lower work function into material with ...
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48 views

Velocity normal to surface in thermionic emission

In the derivation of the Richard-Dushman law which relates the current density $J$ from thermionic emission in a filament of temperature $T$ and work function $\phi$ $$J = AT^2e^{-\frac{\phi}{kT}}$$ ...
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0answers
321 views

Why the Fermi energy be approximated as the chemical potential at low temperature?

For the Fermi-Dirac distribution, $n(E)=\frac{1}{e^{\beta(E-\mu)}+1}$, why can we approximate the chemical potential, $\mu$, to be equal to the Fermi energy, $E_{f} = \mu(T=0) = k_{B} T_{f}$, when $T &...
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374 views

A question about Fermi surface in weak periodic potential

I am studying Solid State Physics by Ashcroft and Mermin. In Chapter 9, it is explained that the Fermi surface in weak periodic potential can be constructed from free electron Fermi sphere. The ...
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0answers
27 views

Is it good approximation to use the Fermi theory in terms of proton and neutron for the given processes?

Suppose the processes $$ p+\gamma \to n + \bar{l} + \nu_{l}, \quad p+\gamma \to p+\bar{\nu}_{l} + \nu_{l}, $$ where $p$ denotes a proton, $\gamma$ - a photon, $l$, $\nu_{l}$ - a lepton and ...
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103 views

How large can a fermi level get?

Long text. I wish to be corrected where I'm wrong, it's all about Fermi levels. The last thing I'm trying to figure out is what absolute Fermi level means to circuits. The difference in Fermi levels ...
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0answers
381 views

Why is the Fermi Dirac distribution defined between energy bands?

For a semiconductor charge distribution profile, I read that the only relevant areas for calculating charge concentrations are those coloured in the image (red for holes, blue for electrons), as ...
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0answers
8 views

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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10 views

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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23 views

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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0answers
35 views

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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0answers
14 views

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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28 views

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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0answers
33 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 ...
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0answers
15 views

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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1answer
31 views

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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27 views

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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65 views

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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1answer
27 views

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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30 views

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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15 views

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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0answers
37 views

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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0answers
271 views

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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1answer
37 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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0answers
39 views

Difference between Fermi energy and ionisation energy

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