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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How are resistivity and Density of States related?
I'm trying to understand the Shubnikov-de Haas oscillations, and even thouhg I understand that everytime a peak in the Density of States (DOS) related to a Landau level crosses the Fermi Level the ...
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Potential felt by an electron at the interface with a semiconductor
I was thinking about a very simple question. Imagine we have a semiconductor "embedded by vacuum". Regarding this situation, I was thinking what is the potential felt by the electron ...
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Can one infer that covalent bonds are directional from the band structure?
I've recently learnt about Wannier functions and changing basis from wave-like 'Bloch functions' to seemingly more localised 'Wannier functions' and how one can think of electrons equally as ...
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Painfully confused on free electron in an “empty” lattice
I'm trying to study some aspects of solid-state that have always bothered me and I am truly stuck on this conceptual boundary. We take the discrete spatial frequency Fourier Transform to arrive at the ...
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Calculating effective mass of electron from energy band diagram
How can I calculate the effective mass of electron in the conduction band of silicon with the approximation that they are free, from its energy band diagram by my hand - not software or something else?...
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Resistance of the form $(a-bT^2)$
In an experiment I did recently, I built a 2D spin-valve structure with FGT (materials like Fe3GeTe2, which reacts with air to create a thin insulating surface layer) and MoS2 layers. In testing, ...
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Why does the conduction band conduct in the SSH model?
I am reading "A short course on topological insulators" https://arxiv.org/abs/1509.02295. There is a basic point that I don't understand about conduction and the band structure. ...
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Does the Thomas-Fermi screening length formula only apply to metals?
Does the Thomas-Fermi screening length formula only apply to metals?
In my notes, the Thomas-Fermi screening length is:
$\lambda_{TF}^2 = \left(\frac{\pi}{6}\right)^{1/3} \frac{\epsilon(0) a_0}{4n^{1/...
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Why doesn't the work function being sensitive to surface not break the conservation of energy?
I understand that the work function is sensitive to the surface. But I don't understand how that doesn't violate energy conservation given the following scenario:
Suppose there are two electrons at ...
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About the degeneracy and the time reversal invariant point of Brillouin Zone
I'm confusing about some concept of the Band degeneracy in the band theory. As I know the Kramer Theorem guarantee that as long as your system is time reversal invariant and even the Spin orbial ...
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Is the electrical conductivity of a perfectly periodic crystal really infinite?
In a perfectly periodic solid and at absolute zero, where the electrons do not suffer any scattering, the electrical conductivity is infinite. However, pure periodic solids also display the curious ...
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The band structure of Weyl Semimetals
Weyl semimetals are topological quantum materials whose low energy excitations emerges as massles Weyl Fermions. They have a band touching point near the Fermi level called Weyl node.
What is ...
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How can we judge the topological property of a material by looking at it's band structure?
I am a beginner of studying topological insulator. I want to ask some general question in this area to clarify my understanding. May be I am asking wrong, hope you can point me out.
If certain ...
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Proof of necessity of Band Inversion in Topological Insulators
Is there any rigorous proof/argument for the necessity of Band Inversion in topological insulators? From a mathematical point of view, I am trying to find an answer in terms of the topology of the ...
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What is the electron effective mass value for a $\rm InSb$ lattice?
I'm trying to calculate the Thomas-Fermi screening length of the III-V semiconductor $\rm InSb$ with doping level $n = 5 \times 10^{18} \text{cm}^{-3}$ ($5 \times 10^{24} \text{m}^{-3} $ in SI units) ...
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Why energy levels of each atoms split in band theory of solid such that they are not degenerate?
I recently came across energy band theory in semiconductors and pauli's exclusion principle. But I'm not sure how energy level split and why, when the atoms are so much far from each other in solid. ...
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Why ferroelectric material needs to be insulating?
Is it necessary for a ferroelectric material to be insulating?
Is it possible for a metal to be ferroelectric?
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What is the cause of formation of indirect band gap in semiconductors?
Background: I am an electronics (device level) student who suddenly wished to understand semiconductor stuff from basics (at solid state level, without any background in that).
What I understood: From ...
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Group Velocity Formalism vs. Current Operator Formalism in band theory
There are at least two ways to argue about the velocity (or current) in band theory.
The first one is the group-velocity formalism
$$\mathbf v_g = \frac{1}{\hbar} \nabla_{\mathbf k} \epsilon_{\mathbf ...
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In Silicon, is visible light enough to excite most electrons from valence band to conduction band?
Valence band electrons in semiconductor may jump to conduction band if appropriate energy is applied in form of (I found the point from Samares' answer in this link and it also makes sense):
Thermal ...
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Quasi-Fermi levels, can this condition be false?
Let $E_{FV}$ be the Quasi-Fermi level of the valance band, $E_{FC}$ be the Quasi-Fermi level of the conduction band and $E_g$ be the band gap (the energy difference between valance and conduction band)...
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The calculation of effective mass for silicon
From what it was written, the calculation of effective mass in semiconductor had two different types, one is effective mass for density of states, through geometrical mean, the other one was the ...
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How does Oxygen influence band gap in Silicon Suboxides?
I just started to study about Mott’s Formalism and as I was going through some prerequisite material for Variable-Range Hopping Conduction I read the following paragraph,
" Theories on non-...
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Why does Ashcroft and Mermin say an acceptor level in a semiconductor cannot be empty, only singly or doubly occupied?
On page 581 of Ashcroft and Mermin, Solid State Physics:
Acceptor Level In contrast to a donor level, an acceptor level, when viewed as an
electronic level, can be singly or doubly occupied, but not ...
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Limits of integration on density of states in semiconductor
The density of electron states in a 3D semiconductor is given by $\rho(E)=\frac{1}{2\pi^2}\left(\frac{2 m^*}{\hbar^2}\right)^{3/2}\sqrt{E}$, derived commonly as shown here. I'm trying to understand ...
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Help. In tight binding 2d square lattice with two atoms basis
How we get the equations inside the box, which represent hopping between p and d orbital. I mean why we consider only two neighbouring.
Thanks in advance
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Finding a constant in nonparabolic dispersion relation in conduction band
The dispersion relation for a semiconductor is $$\frac{\hbar^2 k^2}{2m^*}=\sqrt{\alpha E+E_g^2}-E_g$$ where $E$ is the energy from the conduction band edge, $E_g$ is the bandgap energy, $m^*$ is the ...
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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 ...
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Effective density of states $N_c$ at different temperature for $\rm Si$
For Silicon at room temperature, Nc = 2.8x10^19 per unit volume. For 300K, m*/m = 1.81 for Silicon. Now Nc is proportional to 1.5th power of both temperature and m* (effective mass). So, at any other ...
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If a quantum state occupied by an electron has a $m^*_e>0$, will the same state if unoccupied have $m_h^*<0$ and vice-versa?
For electrons in a periodic potential, the effective mass of an electron in an energy band can be positive or negative depending on its quantum state specified by $n,k$ i.e. its energy $E_n(k)$ and ...
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What is the relation between effective mass and majority charge carrier
I am studying a semiconductor. My System has n-type dominating character.
I am getting effective mass for top of the valence band (VBM) as 5.04 while for bottom of conduction (CBM) band it is 0.20.
...
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High symmetry point formulas for energy bands in empirical tight binding
I have a question about some intriguing formulas that I found. I am following ...
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If an electron-hole pair is formed, where does the electron “go”?
I've seen the explanation before that holes are basically electron deficiencies in an atom and that the hole "moves around" by electrons from surrounding atoms shuffling to fill that spot ...
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How to interpret band structure of $\rm Si$?
I found it very instructive to see how the $E$-$k$ relationship of a free particle can be roughly identified from the extended band structure of a solid: The following is the outcome of the one ...
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The density of states for free electron in conduction band
In Introduction to Solid State Physics, eighth edition, by Kittel, page 141, eqs. (20,21), the density of states for electron in conduction in three dimensions is
$$D(\epsilon)\equiv \frac{dN}{d\...
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Why electronic band structure of any material wiggles in reciprocal space?
I have a doubt regarding, why changing of position in brillouin zone changes the energy levels?
This is because there is a change in the wave functions at every point in brillouin zone. But why is ...
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Dimensionality in Bistritzer MacDonald Hamiltonian
I was trying to understand the origin of flat bands for twisted bilayer graphene and had a basic misunderstanding.
The starting Hamiltonian is $$H = \begin{bmatrix} -iv_0 \sigma_{\theta/2}\nabla &&...
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Odd number of surface Fermi surfaces in strong Topological Insulators
I am now getting into topological insulators and I have read several times that a strong TI possesses always an odd number of Fermi surface bands crossing the Fermi level. However, this is not ...
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How to combine the band picture and dispersion in glass?
As far as I know, the band gap of glass is larger than the energy of visible light. Therefore visible light just pass through an IDEAL glass without any interaction. This band picture is how I ...
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How does band gap of a semiconductor affect its electrical conductivity?
From the relation for electrical conductivity
$$\sigma = ne\mu $$
We can clearly see that if carrier concentration ($n$) increases then $\sigma$ increases. When the band gap decreases, $n$ increases ...
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Electronic band structures
I am looking for step-by-step, clear, detailed and rigorous explanations of methodologies to calculate electronic bands of semiconductor, GaAs as an example, by solving the Schrödinger equation with ...
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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 ...
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Overlapping of Energy Bands in Metals
As per Energy Band Diagram of metals, the conduction band and valence bands overlap, But if we assume there is overlapping then the total number of energy bands will reduce as hence electron will have ...
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Energy gap in the nearly free electron
I am trying to understand the visualization of the energy gap in the nearly free electron approximation.
Context
The general equation to solve in a periodic potential $V=\sum_G V_G e^{i\mathbf{G} \...
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Energy bands motion in an npn transistor
How do electrons move in an npn transistor along their energy bands, in active mode?
How does the base current originate in this energy diagram?
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Band structure on different high symmetry points for the same structure
I apologise if this question is too easy for this community, but I couldn't find an answer to it. I see that for the same structure, band structures plotted differently. I mean in some examples band ...
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Energy Bands Question [closed]
When an electron passes into the valence band, is it no longer useful for conduction?
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Why does the $E$ vs $k$ curve disrupt at Bragg planes?
Interaction between 'nearly free' or 'bound' electrons is what leads to bands. I understand this but why specifically at Brillouin zone boundaries?
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Why doesn't the extra electron in n type semiconductor due to doping by a pentavalent impurity create a hole?
Isn't the pentavalent impurity atom positively charged and attracting the electron?
On receiving the energy why doesn't the electron create a hole in the valence band as it moves to the conduction ...
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Are there quantum states between the conduction band and the valence band?
Neamen's book states that the Fermi-Dirac distribution can be interpreted as the ratio of filled to total quantum states at any energy. For intrinsic materials, the value of Fermi-Dirac distribution ...
