Questions tagged [fermi-energy]

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Surface States and Fermi Level

In work Gelmont, B. L., Shur, M., & Stroscio, M. (1995). Polar optical-phonon scattering in three- and two-dimensional electron gases. Journal of Applied Physics, 77(2), 657–660 when author moving ...
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89 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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Validity of formula for density of states for free electron gas

I believe the formula for density of states given by $\frac{\hbar^2}{2m}{(\frac{3\pi^2N}{V})}^{\frac{2}{3}}$ is a good approximation to actual count only when $E_f$ is much larger than energies given ...
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32 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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13 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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58 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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22 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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34 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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33 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
57 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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61 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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28 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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34 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
36 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
24 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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30 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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39 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
57 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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52 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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96 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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62 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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19 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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61 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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3k 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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77 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
394 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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154 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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86 views

Meaning of Fermi Level in the context of many-body theory

I was wondering whether the concepts of Fermi Level or chemical potential make any sense in the context of many-body problems. I understand that when one is working with a one-electron hamiltonian, ...
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175 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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76 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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479 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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167 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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290 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
70 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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111 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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114 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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391 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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199 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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248 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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91 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
96 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
312 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
179 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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24 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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323 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
514 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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83 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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304 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 ...