Questions tagged [fermi-energy]

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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
30 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
37 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
48 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 ...
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1answer
24 views

How do I find this relation between total energy and fermi energy?

I am currently studying the Sommerfeld model. I understand how to find the fermi energy $\epsilon_F$ by using the density of states function but I am unsure how to answer this question about the total ...
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29 views

Using Brillouin zones to write Hamiltonian and find momenta values

This is a homework problem that I have spent a large amount of time on..I will try my best to simplify the questions down to conceptual ones, but I will also write more or less that whole question ...
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1answer
33 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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1answer
17 views

Confusion about average KE in free electron model via Density of States (DOS)

Assume a low temperature regime in which levels up to the Fermi Level, $E_F$, are populated. I have evaluated the density of states in energy space as $$D(E)=\frac{L^3}{\pi^2\hbar^3}(2m_e^2E)^{1/2},$...
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27 views

The equality of fermi energy and chemical potential at high temperatures

Through the duration of my equilibrium statistical mechanics course, I came across a point in ideal Fermi systems where the Fermi energy was approximated as chemical potential when we derive the ...
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1answer
40 views

Why do semiconductor lasers become weaker after extended use (not due to battery)?

Why do semiconductor lasers become less bright as they are used for longer periods of time (assuming their battery is full)? Does it have something to do with the PN junction reaching some kind of ...
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0answers
33 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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1answer
55 views

Volume per $k$-state

We're talking about Fermi-energies for the first time, for $N$ spin $\frac{1}{2}$ particles in a 3D box, and she writes down that $$2 \times \frac{1}{8} \times \frac{4}{3} \pi k_f^3 = Nq \times \frac{\...
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41 views

Chemical potential in a simple semiconductor

I came across the following problem in my undegrad solid state physics book: Assume a semiconductor with two bands, the lower band is defined as $E(k)$ and the upper band is defined by $E_0 - E(k)$ ...
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1answer
64 views

Semiconductors/insulators: Why is the fermi energy between the valence and conduction band?

Ive asking myself a question on the fermi-energy. The fermi-energy is defined as the maximum energy which an electron, following the Pauli-rule, can have at T=0. In semiconductors and insulators the ...
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1answer
58 views

General formula for the variation of the chemical potential with temperature

For small temperatures $T$, such that $k_BT\ll \mu(T=0)\equiv \mu(0)$, the variation of chemical potential with temperature is given by $$\mu(T)=\mu(0)\Big[1-\frac{\pi^2}{12}\Big(\frac{k_BT}{\mu(0)}\...
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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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1answer
54 views

Is diamond able to conduct electricity given 5.5 eV of energy? How do we then identify insulators and semiconductors?

I have learnt that the band gap for diamond, an insulator, is $5.5\:\rm eV$. Does this mean that diamond is able to conduct electricity if we give it this immense amount of energy (let's assume we do ...
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2answers
2k views

Average energy for a free electron gas, at T=0K

For a free electron gas at $T=0K$, the average energy per electron is known to be $ \frac {3}{5} E_F$ where $E_F$ is the Fermi Energy. When first attempting to derive this, I thought that the average ...
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2answers
76 views

What is the significance of the time $\hbar/E_F$ where $E_F$ is the Fermi energy?

For free electrons in a metal, the Fermi energy $E_F$ (defined as the highest filled energy level at $T=0$). It represents a characteristic energy scale of the system as well as the energy of the ...
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1answer
265 views

Why is it not possible to dope semiconductors with elements with 6 or 2 valence electrons?

As far as I have learnt, semiconductors are often made using elements from the 4th group, and their properties are often enhanced by doping with either pentavalent or trivalent elements. Take the ...
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2answers
121 views

Is Fermi Level a property of the material?

I have gotten myself confused about the band structure explanation of semi-conductors vs insulators. The Wikipedia picture and the explanation surrounding it seem to suggest that Fermi Level is a ...
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2answers
1k views

Is Fermi level located above or below donor levels in n-type semiconductor?

I find contradicting information about this. Some resources says it's above donor levels Hyperphysics website: and other say it's below, eg. on this ResearchGate thread: in n-type semiconductor,...
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1answer
147 views

Why is there a difference between Fermi levels in metals and metal-oxide semiconductors (MOS)?

Why are Fermi levels in metals lower than the Fermi level of $\text{p}$-substrates in metal-oxide semiconductors (MOS)? Specifically, why is there a difference of $qV$? $\hspace{50px}$
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2answers
64 views

Is there a relation between Gap energy and Fermi energy?

Are Gap energy and Fermi energy in semi conductors co-dependent variables? If yes, what's the relationship between them?
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2answers
432 views

Why the Fermi temperature isn't zero?

The fermi temperature is defined as $$ k_BT_f = E_f$$ But the fermi energy is the energy at $T=0$, where the energy level is the highest occupied for electrons. So, why is the fermi temperature ...
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150 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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1answer
270 views

Fermi Gas - Number of Free Electrons at High Temperatures

What I am trying to do is to compute the specific heat of a free electron gas in a conducting metal. I am using Fermi-Dirac statistics as my framework to build off of. Importantly though, I want to ...
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1answer
61 views

Is it possible to locate the Fermi level (in a double doped semiconductor) without knowing the intrinsic Fermi level?

Suppose phosphorus ($\require{mhchem}\ce{P}$) is introduced into $\require{mhchem}\ce{p-Si}$. At a given temperature (say at room temperature $300K$) is it possible to find the location of the Fermi ...
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1answer
98 views

Electrons close to Fermi-Conductivity

As a student of electrical and computer engineering solid state physics is not my thing so I might have fundamental blanks here and there. I really like this course and I try to gain as much as ...
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2answers
108 views

What is the Bandgap energy of Rubidium?

Could anyone please tell me the bandgap energy for alkali metals like rubidium and cesium?
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188 views

Effect of temperature on the Fermi level in a semconductor

In intrinsic semiconductor, i have learned that fermi level is weakly dependent on temperature and it is sited between Ec and Ev. In this case, I have some questions. What could happen to fermi level ...
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0answers
187 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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2answers
235 views

Notion of anisotropic Fermi surface

I would like to check something. I know that the Fermi energy is the maximum energy occupied by a Fermion at $T=0$ (if I have $N$ fermion it will be the energy of the Fermion that has the highest ...
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86 views

electronic specific heat as a function of temperature AND fermi-level?

I don't really understand the above plot. I know that the specific heat depends on temperature..that is clear. But why are there multiple curves for different Fermi-Levels? I always thought that the ...
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1answer
86 views

$E_C$-$E_F$ in the equation for concentration of electrons at equilibrium

I'm trying to calculate the charge carrier concentration for silicon doped with phosphorous at a level of $10^{16}$ per cubic centimeter. I have the formula: $$n_0=n_ie^{-(E_C-E_F)/kT}$$ I found $...
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1answer
295 views

Fermi energy level

Definition of Fermi level: Fermi level is defined as the energy level in which the probability of OCCUPANCY of an electron is 1/2. My question: For semi-conductors, ...
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1answer
172 views

Density of states of electrons

The problem is as follows: Let the density of states of the electrons in some sample be assumed to be a constant D for $\epsilon > 0$ ($D=0$ for $\epsilon<0$) and the total number of electrons ...
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0answers
23 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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2answers
307 views

Semiconductors - Fermi energy and function

As I understand it, the Fermi function $$f(E) = \frac{1}{1+e^{(E-E_f)/(kT)}}$$ gives the probability of finding an electron at a particular energy in a material. It also has the following property : $...
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1answer
477 views

The concept of Fermi level

I have read and used the concept of Fermi level previously and this is simply an attempt on my side to better my understanding of it by asking myself various questions. I understand that the fermi ...
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0answers
77 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
277 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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1answer
123 views

How does fermion degeneracy affect elastic scattering in astrophysical compact objects?

As I currently understand it, absorption processes or inelastic scattering involving fermions in a degenerate gas are strongly inhibited, because to change the fermion energy (or create a new fermion) ...
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1answer
328 views

Why do insulators have “just enough” electrons to fill the valence band

This is the classic picture of the band structure for an insulator (or semi-conductor): The common explanation as to why this doesn't conduct is that the electrons fill the valence band perfectly ...
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2answers
462 views

How is it possible to have Fermi energy in the middle of bandgap for semiconductors?

Actually, I'm still a beginner for Fermi energy and its related band theory. Typically in an intrinsic semiconductor the Fermi energy or the highest occupied energy level of electrons at $0\, \mathrm ...
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1answer
2k views

The fermi gas model of a nucleus

In my nuclear physics lecture we learned about the "fermi gas modell" of a nucleus with which I have some problems. First the potential for the nucleons is shown in the picture below and it makes ...
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1answer
463 views

Electric field dependence of Fermi level, Fermi energy

I`m studying solid state physics and I have a question about this. I know that the Fermi energy is the energy which can be defined at $0K$. In $k$ space electrons occupy each k state from zero at 0K ...
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404 views

Calculating Fermi energy of free electron gas

I want to know if I'm understanding this right. I'm told to find the Fermi energy for a 2-D infinite square well of size $a$ (in both directions) with $N$ non-interacting particles using a Fermi ...
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1answer
1k views

When does the fermi-surface fit into the first brillouin zone?

Talking about the free electron approximation the Fermi-surface is a circle. However, sometimes it fits into the first BZ and sometimes it does not. I read that, in general, it does not fit into the ...
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1answer
80 views

reconcile transparency with energy band in solids

I am trying to reconcile the optics explanations (from “Why glass is transparent?”) with the bits I learnt about band gaps and fermi levels. It is hard to write down a single question for now, will ...