Questions tagged [electronic-band-theory]

Use this tag to ask about band-structure formation in solids, or about how electrons and holes behave inside them.

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Derivation of Optical Absorption Coefficient in Semiconductors

I have been researching how to derive an expression for the absorption coefficient in semiconductors. I know the absorption coefficient can be expressed as such $$\alpha = A(hf-E_g)^{n}$$ with $n = \...
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42 views

Why electron-holes interpretation can't be effective in metals?

Help me out here, If thought of as electron sea, there's is no need of holes in modeling conductivity in metals. But it's not that we can deny that there will be positive charge in the nucleus after ...
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22 views

Is “quaternary” adjective redundant while speaking of InGaAsP?

I'm reading an article. One sentence looks as following: The 500 nm thick waveguide layer consists of an InGaAsP quaternary layer But since InGaAsP is quaternary compound, why do they write ...
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1answer
29 views

How can the oscillating states of many atoms in a lattice combine to give even a larger number of possible states?

Basically, I was studying the band theory and there was that thing that I couldn't understand, and it appeared to be connected to another question: how is the blackbody radiation appear continuous ...
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39 views

Energy Band of pn junction in thermal equilibrium (Zero bias)

Consider the following diagrams: Question: Why in thermal equilibrium—the Fermi energy level is constant throughout the entire system? I know the following explanation A gradient in the Fermi level ...
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Why can't we choose a material with a low band gap to convert more photons into photo-electrons for a solar cell?

In Shockley–Queisser limit, how was the most efficient bandgap (1.5 eV) determined? Wouldn't you be able to generate more current with a lower bandgap since more photons are going to have enough ...
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55 views

Are there still no “simple analytical proofs” of Bloch's theorem in three dimensions?

Section 2.1.2 of Sydney G. Davison and Maria Stęślicka's 1992 Basic Theory of Surface States says: 2.1.2 Bloch theorem The generalization of the Bloch-Floquet theorem to three dimensions is ...
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37 views

Why is only bandgap-energy usable? (Thermal Relaxation)

I know from solar cell physics, that in a first approximation, the maximum energy from an exited electron is the energy of the bandgap, no matter how high the electron was excited by a photon in the ...
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Confusion with Fermi energy in Quantum Hall effect

It is well-known, that when someone turn on magnetic field, and if magnetic field large enough, only few Landau levels are filled: But I can't understand what going on with Fermi energy. Fermi ...
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3answers
92 views

Is there any relation between turn on voltage of LED and the colour emitted?

It is evident from the above V-I graph that longer the wavelength of the light emitted lower is the turn on voltage. I know that turn on voltage is voltage required to have significant current that ...
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1answer
53 views

Why a photon cannot change the crystal momentum of an electron?

We know that absorption of a photon excites an electron from the valence band to the conduction band without changing its crystal momentum $\vec{k}$. Why can't a photon change the crystal momentum of ...
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2answers
77 views

Why are there electron and hole currents in semiconductor, but only electron current in metal?

Why are there electron and hole current in semiconductor, but only electron current in metal ? I know that in metal there is an overlap between valence and conduction band, while for semiconductor, ...
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Can we understand the strong reflectivity of metals from band theory?

I know that solids, including metals, have electronic bands and bandgaps. If we consider some typical metal such as copper, we know that it strongly reflects visible light. From the point of view of ...
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42 views

Is it true that the Fermi-Dirac distribution is a probability?

Is it true that the Fermi-Dirac distribution is a probability ? I checked by doing the integral, and this does not give 1. Also, for $T=0 K$, since it is a step function, it is easy to see that the ...
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1answer
85 views

How to draw different zone schemes in the Kronig-Penney model?

Kronig-Penney model does not give us an equation of how the electron energy $E$ depends on its wavenumber $k$. Then how do they draw the $E-k$ curves in different zone schemes such as extended, ...
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63 views

Why Fermi energy is in between band gap?

It may seems like a copied question Question But It still didn't clear my doubt.Consider the following figure As you can see the fermi energy (Fermi energy) lies in between the bandgap and ...
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1answer
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Effective Mass structure outside first band minimum

I wanted to ask: if I would have the electron dispersion function of the first band, which is not parabolic can it be used/(inserted) with the effective mass function, for $\frac{d^2E(k)}{dk^2}$: $m^* ...
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Direct & Indirect (Kohn-Sham) band gap for $\rm MgS$

I recently performed a groundstate calculation for $\rm MgS$ using the self-consistent Kohn-Sham equation with LDA exchange-correlation. $\rm MgS$ has an FCC crystal structure with two atoms per (non-...
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1answer
36 views

Questions about Creation/Annhiliation Operators of electrons

I am trying to solve a question that asks me to find the two energy bands of a NaCl crystal, where "c" is the distance between Na and Cl where $a_{\vec{R}}^{\dagger}$ creates and electron centered on ...
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1answer
39 views

Wave function of $s$-band with odd parity

How does a wave function of a $s$-band state with odd parity looks like (in real space)? To keep it simple, the restriction to a linear chain and a state at the $\vec{k}=0$-point might be useful. My ...
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2answers
22 views

Comparing energy band diagram for metals, semiconductors and insulators

The energy band diagram is a model for describing why an insulator is not a good conductor compared to a semiconductor: in the first case, electrons would need to pass a very large band gap in order ...
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1answer
68 views

Interpretation of electronic band structure diagram

I want to understand the electronic band structure diagram of the following image, corresponding to $\text{MoS}_2$ (TMD): I read about DFT (density functional theory). DFT is based on solving the ...
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2answers
59 views

Electrons involved in bonding cannot be involved in conduction?

I am currently studying the textbook Physics of Photonics Devices, Second Edition, by Shun Lien Chuang. In a section discussing the basic concepts of semiconductor band and bonding diagrams, the ...
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Conduction, conduction and valence bands, and energy bands

I am currently studying the textbook Physics of Photonics Devices, Second Edition, by Shun Lien Chuang. In a section discussing the basic concepts of semiconductor band and bonding diagrams, I was ...
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Why is density functional theory unreliable for prediction of band gap [closed]

Why is density functional theory unreliable for calculation of band gap?
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After a diode start conducting, can you increase voltage across the diode without current change in the diode?

Personal Background: I am trying to reconcile my understanding of Fermi band diagram of diode with a diode's circuit behavior. I believe I have a point of misunderstanding somewhere that is causing me ...
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2answers
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Landau levels degeneracy

I'm studying the Landau quantization of free electron systems and a question comes to my mind when I arrive to the degeneracy of the levels. This is given by the following expression: $N=\frac{2e}{hc}...
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38 views

Flat bands in metals

When I look at the angular momentum resolved band structure of the sodium (Na), there are two flat band at very low energies (p at around -25 eV and s at around -50 eV). What should I understand from ...
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25 views

Semiconductor conduction band

What would happen in an hypothetical situation if we completely fill up the conduction band, will then also it will conduct? I know we can't fill that more than half. I think it will also not ...
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1answer
58 views

Effective mass as a consequence of energy band structure

The Wikipedia article on effective mass defines it as follows: In solid state physics, a particle's effective mass (often denoted ${\textstyle m^{*}}$) is the mass that it seems to have when ...
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Reconciling electron configuration and valence electron distribution over separate energy levels in energy band theory

This seemed like more of a chemistry question to me, but I was told by the people at chemistry.stackexchange that it might be more appropriate to post here, since "it was the physics guys that did all ...
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1answer
77 views

Filling of energy bands

In the context of electron energy bands for crystals, I have heard the phrase There are $x$ electrons per band, therefore the electrons fill $y$ bands. I am trying to understand the 'therefore' ...
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electronic band structure calculation using plane wave expansion: what are the diagonal matrix elements for a coulomb potential?

I'm trying to do a plane wave basis expansion calculation for the band structure / wavefunctions of electrons in a periodic solid, using a coulomb potential for the nuclei. I'm working from Ashcroft ...
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1answer
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Units in result for band gap photon momentum for GaAs

My textbook, Introductory Semiconductor Device Physics, by Parker, gives the following example: For GaAs, calculate the typical (band-gap) photon energy and momentum, and compare this with a ...
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1answer
49 views

Nearly free electron model: Pauli principle

If I look at the bandstructure in the nearly free electron model in a diagram with energy over wave vector $\bf{k}$, there are some parts of parabolas in my first Brillouin zone. I understand, why ...
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1answer
124 views

How do flat bands imply superconductivity?

I'm just doing a small ugrad assignment where I have to present a talk on twisted bilayer graphene. I'm having trouble understanding the meaning of a flat band. As far as I understand, a flat band ...
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3answers
170 views

Energy band theory: conduction of electrons and holes

My textbook, Introductory Semiconductor Device Physics, by Parker, says the following in a section on energy band theory: We are aware that conduction in most metals is by electrons but conduction ...
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2answers
55 views

Band structure of a nanoparticle

Considering a crystal at such a small size (for example, a sphere with diameter about 20 atoms) that the periodic boundary condition assumed in Bloch Theorem is not really a good estimation, I wonder ...
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2answers
55 views

Why does the concept of effective mass fail for linear dispersion relations?

I had a discussion about graphene and stumbled about a conceptual problem of myself about the effective mass of electrons close to the Dirac point in graphene or for any linear dispersion relation in ...
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1answer
31 views

How objects reflect green light?

I'm currently interested in energy levels and I've learned that there are energy gaps between molecular orbitals that makes things appear transparent (for visible light). Thus, objects like glass can ...
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1answer
40 views

Electron's excitement conditions for a Photon in conductors

Glass is a typical insulator: electrons inside their atoms has band gaps, which are setting limits for low-frequency photons and prohibits energy conveying for them. Therefore, light just passes ...
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Functional form for pseudopotential

I have found this resource quite good for a brief summary of pseudopotentials, of which I am trying to learn more about. The author shows that, once a functional form for the pseudo-wavefunctions has ...
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Hetero junction - similar work-functions

Why is it important that the two semiconductors in a hetero-junction, that is brought into contact, have similar work-functions? (If it is important). Obviously it's important for a metal-...
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60 views

Fermi level in a solid

I am confused as to how fermi level is defined within a crystal/ solid It is normally situated midway between valence band and conduction band, is this how it is defined or is there other reasons this ...
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49 views

Berry curvature of a two band lattice Hamiltonian

Consider a general two band lattice Hamiltonian, which can be expressed as a $2\times2$ matrix: $$\mathcal{H}=\vec{h}(\vec{k})\cdot \vec{\sigma}$$ where $\vec{\sigma}$ is the vector of Pauli matrices. ...
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Derivation of LCAO/Tight-binding method for energy bands

I'm having a bit of trouble properly understanding the LCAO/tight-binding method for calculating the band structure of metals. I'll try to go through the derivation/explanation given in our lecture ...
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1answer
61 views

What is the difference between HOMO-LUMO Energy gap and Forbidden (Energy) gap?

I have found a similar question on a different website upon searching on google but it didn't clear my confusion (which might be because I didn't understand the explanation). (PS: I am a 12th STD ...
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1answer
87 views

Flattened band in band structure

What does a flattened band in a band structure plot imply? I've been reading this paper https://doi.org/10.1016/j.apsusc.2012.06.092 and one of the primary results is the flattening of bands however ...
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Magnetic field dependence of resistance

Experimentally, under the application of an external perpendicular magnetic field, we observe a change in the longitudinal resistance. However, in the theoretical development starting from the Drude ...
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2answers
178 views

Fermi level and chemical potential in doped and pure semiconductors

Recently I was studying about band theory of semiconductors and I have some questions. I found two definitions of Fermi level $1)$ The quantum state which has a probability of occupancy of $0.5$ (...

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