Questions tagged [fermi-energy]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
1answer
35 views

Can the lifetime of an electron in the conduction band be calculated?

We know that in a semiconductor in every instant of time some electrons get excited from valence band to conduction band and some electrons are deexcited from conduction band to valence band. In this ...
2
votes
1answer
36 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
1
vote
0answers
28 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 ...
1
vote
0answers
24 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 ...
0
votes
0answers
26 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 ...
1
vote
0answers
28 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 ...
0
votes
0answers
27 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 ...
0
votes
0answers
10 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 ...
1
vote
1answer
35 views

Intrinsic carrier concentration of a semiconductor without Boltzmann approximation [closed]

The carrier concentration of conduction band of a intrinsic semiconductor at a temperature $T$ is $$n_i=\frac{1}{2\pi^2}\left(\frac{ 2m_e^* }{ \hbar^2}\right)^{3/2}\int_{E_c}^{\infty}\sqrt{E-E_c}f_{FD}...
0
votes
1answer
30 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, ...
4
votes
1answer
339 views

Liquid mercury, relativistic effects and Fermi velocity

Reading this news article and some related references, I learned that mercury’s liquidity is due to relativistic effects in Hg, where "the electron approaches about 58% of the speed of light.&...
0
votes
0answers
25 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 ...
2
votes
0answers
59 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, ...
0
votes
0answers
48 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 ...
0
votes
1answer
25 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 ...
1
vote
2answers
106 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 ...
0
votes
0answers
29 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 ...
0
votes
0answers
9 views

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 ...
0
votes
0answers
58 views

Definition of Chemical potential [duplicate]

I am very confused with what actually the chemical potential (chemical potential energy should be the proper name, right?) is. As of right now, I know at least 3 or 4 different definitions of it, ...
0
votes
1answer
36 views

Carrier density and size of Fermi surface

I think I've heard that a large Fermi surface implies a large carrier concentration and a small Fermi surface implies a small carrier concentration. I am not really sure what the relationship is ...
1
vote
0answers
42 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 $\chi = 2.0 \cdot 10^{-5}$, ...
-1
votes
1answer
163 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 ...
4
votes
1answer
228 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 ...
2
votes
2answers
251 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 ...
0
votes
0answers
14 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 ...
0
votes
1answer
63 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 ...
1
vote
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 ...
0
votes
0answers
13 views

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 ...
0
votes
0answers
36 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. ...
0
votes
1answer
259 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 ...
0
votes
2answers
243 views

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 ...
0
votes
1answer
33 views

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 ...
0
votes
1answer
72 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 $k_bT$ ...
1
vote
1answer
28 views

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 ...
0
votes
0answers
257 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 $...
1
vote
0answers
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 ...
2
votes
1answer
61 views

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 ...
1
vote
1answer
78 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 ...
0
votes
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 ...
1
vote
0answers
104 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 ...
1
vote
1answer
67 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 ...
0
votes
0answers
36 views

Difference between Fermi energy and ionisation energy

At $T=0K$ what's the difference between Fermi energy and first ionisation energy?
1
vote
0answers
162 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 ...
1
vote
1answer
442 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 ...
0
votes
1answer
195 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 hopping ...
1
vote
1answer
61 views

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}{\...
1
vote
0answers
61 views

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 ...
1
vote
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 ...
0
votes
0answers
63 views

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 ...
3
votes
1answer
482 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 ...