Questions tagged [fermi-energy]
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63
questions
0
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1answer
29 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:
$...
0
votes
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, ...
0
votes
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 ...
2
votes
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 ...
0
votes
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 ...
0
votes
0answers
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 ...
1
vote
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 ...
0
votes
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 $$D(E)=\frac{L^3}{\pi^2\hbar^3}(2m_e^2E)^{1/2},$...
0
votes
0answers
27 views
The equality of fermi energy and chemical potential at high temperatures
Through the duration of my equilibrium statistical mechanics course, I came across a point in ideal Fermi systems where the Fermi energy was approximated as chemical potential when we derive the ...
0
votes
1answer
40 views
Why do semiconductor lasers become weaker after extended use (not due to battery)?
Why do semiconductor lasers become less bright as they are used for longer periods of time (assuming their battery is full)? Does it have something to do with the PN junction reaching some kind of ...
1
vote
0answers
33 views
Fermi energy equilibration
A conventional example tells that when we bring two pieces of some materials with different work functions in contact electrons start to flow from material with lower work function into material with ...
2
votes
1answer
55 views
Volume per $k$-state
We're talking about Fermi-energies for the first time, for $N$ spin $\frac{1}{2}$ particles in a 3D box, and she writes down that $$2 \times \frac{1}{8} \times \frac{4}{3} \pi k_f^3 = Nq \times \frac{\...
0
votes
0answers
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 $E_0 - E(k)$ ...
4
votes
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 ...
0
votes
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 $$\mu(T)=\mu(0)\Big[1-\frac{\pi^2}{12}\Big(\frac{k_BT}{\mu(0)}\...
1
vote
0answers
16 views
Velocity normal to surface in thermionic emission
In the derivation of the Richard-Dushman law which relates the current density $J$ from thermionic emission in a filament of temperature $T$ and work function $\phi$
$$J = AT^2e^{-\frac{\phi}{kT}}$$
...
0
votes
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 ...
3
votes
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 ...
2
votes
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 ...
3
votes
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 ...
0
votes
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 ...
2
votes
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,...
1
vote
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}$
0
votes
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?
3
votes
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 ...
1
vote
0answers
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 &...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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?
0
votes
2answers
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 ...
1
vote
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 ...
3
votes
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 ...
0
votes
0answers
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 ...
1
vote
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}$$
I found $...
2
votes
1answer
295 views
Fermi energy level
Definition of Fermi level:
Fermi level is defined as the energy level in which the probability of OCCUPANCY of an electron is 1/2.
My question:
For semi-conductors, ...
0
votes
1answer
172 views
Density of states of electrons
The problem is as follows:
Let the density of states of the electrons in some sample be assumed to be a constant D for $\epsilon > 0$ ($D=0$ for $\epsilon<0$) and the total number of electrons ...
1
vote
0answers
23 views
Is it good approximation to use the Fermi theory in terms of proton and neutron for the given processes?
Suppose the processes
$$
p+\gamma \to n + \bar{l} + \nu_{l}, \quad p+\gamma \to p+\bar{\nu}_{l} + \nu_{l},
$$
where $p$ denotes a proton, $\gamma$ - a photon, $l$, $\nu_{l}$ - a lepton and ...
1
vote
2answers
307 views
Semiconductors - Fermi energy and function
As I understand it, the Fermi function $$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 : $...
1
vote
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 ...
1
vote
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 ...
1
vote
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 ...
6
votes
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) ...
3
votes
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 ...
5
votes
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
0answers
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 ...
0
votes
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 ...
1
vote
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 ...
