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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Applying Slater-Koster tight binding method for Rhombohedral Bi
I am trying to build a tight-binding Hamiltonian for Bi which has the $D_{3d}$ point group and $R\bar{3}m$ space group. It has two inequivalent atoms in the unit-cell.
I understood the basics of the ...
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Why doesn't the number density of electrons increase with increase in temprature?
It is said that for some increase in temperature of a conductor there exists only some decrease in the average relaxation time of electrons in that conductor due to increase of their thermal ...
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Underdetermined system of equations in photon absorption in indirect semiconductors
Consider the photon absorption in indirect semiconductors. The relevant equations are
$$\textbf{Energy conservation:}\quad E_{photon} = E_g - E_{phonon}(q)$$
and
$$\textbf{Momentum conservation:}\quad ...
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Inversion asymmetric little representation in a Inversion symmetric large representation in brillouin zone
I am not am having trouble understanding the little representation which characterize high symmetry points in the brillouin zone of a crystal.
I understand this essentially mean that for some high ...
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Fermi level of oxide layer in MOS
At equilibrium, I know the Fermi level of metal needs to align with the Fermi level of semiconductor at equilibrium. But it is not clear to me whether the Fermi level of oxide layer needs to align ...
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Why is there a sharp divide between paramagnetism and diamagnets in the periodic table?
On the periodic table* basically everything to the right or the same group as copper is diamagnetic, whereas anything to the left is paramagnetic or magnetically ordered! Why is this?
It is definitely ...
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Bending of vacuum level in pn junction
The vacuum energy level is the same for both an isolated p-type and n-type materials means that the absolute energy of an electron that is just outside the p type material is the same as the absolute ...
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How does one use empirical pseudopotentials to model disordered random alloys?
How does one use empirical pseudopotentials to model disordered random alloys?
I am working on modeling random alloys and came across the following paper: https://link.aps.org/pdf/10.1103/PhysRevB.85....
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Gauge covariance vs gauge invariance
For Bloch electrons $\psi_{nk}=e^{ikr}u_{nk}$, with $k$ the crystal momentum and $n$ the band index, I would like to know if the integral ($m \neq n, k^\prime \neq k$)
$$
\langle u_{nk}|u_{nk^\prime}\...
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Division by zero when evaluating the limit
Assume Bloch electrons, governed by the Schrodinger equation $H\psi_k=E_k \psi_k$, where $\psi_k$ is the Bloch function with eigen energies $E_{k}$ and band velocity $v_{k}=\partial_k E_{k}$ with $k$ ...
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What is the relation between an electron moving among energy levels in an energy band and an electron moving in a solid?
I'm learning about the band theory of solids. I learned that if the valence band is not full, as in a P-type semiconductor, it can conduct electricity because in the valence band there are unoccupied ...
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Help in plotting the band structure of a maple leaf lattice
I was trying to plot the band structure of a maple leaf lattice. The Hamiltonian is given by:
$H = t_1 \sum_{ij} (c^\dagger_i c_j + c^\dagger_j c_i e^{\phi_{ij}}) + \sum_{ij} \sum^{4}_{n=2} t_n (c^\...
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Bloch oscillations and umklapp scattering induced by applied electric field
In Kittel's book chapter 8 there is a statement that says "The electron accelerates from
k = 0 toward the zone boundary; when it reaches k = pi/a it reappears (as by
an Umklapp process) at the ...
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How do you see that the Wannier functions are localized on ion sites?
In Condensed Matter Field Theory by Altland and Simons, when discussing the tight-binding approximation for a lattice system with a periodic potential, they define the Wannier states as follows:
$$
|\...
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Calculation of effective mass of electrons from energy dispersion relation for electrons [closed]
Given the energy dispersion relation for electrons, $ \epsilon_{k} = \beta(cosk_{x}a + cosk_ya + cosk_za)$ , I want to find out the effective mass of electrons at the boundary of the first Brilloin ...
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Why do dopant levels lie in the energy band gap of semiconductor?
Dopants create impurity levels in the band gap, this is what we were taught in semiconductor classes. And indeed that's what's seen in experiments (for example https://www.globalsino.com/EM/page2777....
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Second derivative of energy with $k$
In solid-state physics, we often encounter the velocity operator (e.g. this post) which the eigenvalues can be written as
$$
V^\mu(\vec{k}) = \frac{1}{\hbar} \frac{\partial E}{\partial k^\mu} \biggr|_{...
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What is the degeneracy of the free electron bands in a FCC lattice?
In Ashcroft and Mermin, the band structure diagram for free electrons in a FCC bravais lattice is provided. This diagram is shown at the end of this post.
For starters, each band shown has a trivial ...
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How do solar cells really work?
When I read articles on the workings of photovoltaics, the explanation tends to revolve around the idea of PN-junctions, and how an electric field separates charges (electrons and holes). In a Quora ...
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Why do we need to consider interaction for doping atom?
In semiconductors, the intrinsic carrier concentration is calculated by Fermi-Dirac distribution, but for the situation of doping, we need to consider the Coulomb interaction for doping atom, and the ...
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C$_{60}$ fullerene electronic structure, C$_{60}$ insulator
I read a post on Chemistry stackexchange, how to explain that C$_{60}$ is an insulator. The common ground seemed to be that -- in contrast to graphene -- a C$_{60}$ solid consists of separate ...
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Help with Parametrizing Path Through High-Symmetry Points in 2D Hexagonal Brillouin Zone
I'm currently working on a project involving the calculation of band structures for a 2D hexagonal lattice, and I need some guidance on how to properly parametrize a path that covers the high-symmetry ...
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Intrinsic band gap vs work function of doped semiconductors
I'm confused about this question on doped semiconductors:
Question: Photoelectrons with a maximum energy of $\ 0.5$ eV are observed when light of wavelength
$500$ nm is incident on a heavily n-doped ...
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Built-In Potential (Forward vs Thermal Equilibruim)
According to my book the built-in potential $V_{bi}$ for a PN junction under thermal equiliubrium is:
$$V_{bi}= \frac{KT}{q}In(\frac{n_{no}p_{po}}{{n_{i}}^2})$$
where $n_{no}$ and $p_{po}$ are the ...
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Why are zero-modes preserved on turning on coupling in twisted bilayer graphene model?
In the paper https://arxiv.org/abs/1808.05250 on page 3, they talk about how when the parameter $\alpha$ in the Hamiltonian in Eq. (5) equals $0$, we get zero modes at the Dirac points K and K’. This ...
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Reproduce band structure Kagome fermi-hubbard - Python
I am trying to reproduce figure 5c) of https://arxiv.org/pdf/2002.03116.pdf in Python.
So I would like to plot the band structure of a Fermi-hubbard defined in a Kagome lattice.
The eigenvalues are:
$\...
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Density of States, Photoemission and Integrating the Number of States
I'm reading Fowler's theory on photoemission. I'm stuck on a part which Fowler helpfully identifies as "obvious". Fowler sets up the free electron model, suggesting that electrons need a ...
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What causes bands to shift in energy or become narrow?
This is the density of states for pure palladium in bulk :
This is the density of states of palladium hydride :
clearly the d bands are shifting and becoming narrow. The narrowing of bands is said ...
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Einsteins Coefficient of Absorption in solid state
What solid state parameter determines the probability of absorption (Einsteins coefficient B) in a material? Is it material dependent?
I think, I cannot say bandgap. Because if I have a source having ...
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Is the Fermi level is same for the all solids?
If the solids at T=0k , the topmost energy level occupied by electrons in valence band is called Fermi level. Is this Fermi level is constant for all the materials? It is shown as same for metal, ...
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Confusion about the LCAO or tight binding model (nearest neighbors)
I'm using the book "Atomic and Electronic Structure of Solids" by Kaxiras. In chapter 4, the author introduces the tight binding or LCAO model for calculating electronic band structures. He ...
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What happens after bulk gold absorbs a photon with its energy at the band gap or higher (wavelength < 500 nm)?
As is explained in the answers of this question: Why are most metals gray/silver? nicely, the responsible transition occurs between the 5d orbital and the 6s orbital, which is relativistically shrunk ...
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Why is the band diagram of metals similar to that of an empty lattice?
The electrons at the bottom of a band diagram correspond to some of the most tightly bound electrons. Why is it the case that the bottom of the band structure of sodium, for instance, can be well ...
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How to determine the effective mass for multivariate dispersion relation? [duplicate]
Consider the 1D dispersion obtained by the tight-binding method:
$
E(k)=\epsilon_0-t\cos(ka)
$
$\epsilon_0$ is the on-site energy and $t$ is the hopping energy. To find the effective mass, you can ...
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Electron bands in solids and delocalized electrons
Most introductory textbooks introduce electron bands when discussing metal properties which gives the impression that electron bands are strictly affiliated with delocalized electrons.
However, bands ...
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Valence band in silicon (semiconductors)
I recently learnt that in a solid lattice there are many energy levels which are so continuous that they look like bands...
In silicon' valence band,there are those millions of 3p energy levels with 2 ...
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Can topologically non-trivial edge states exist without an energy gap?
I am relatively new to the field of topological materials, and I came across a paper that claims that they found topologically non-trivial states in a material. Basically, the authors found a type-I ...
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Matrix representation of Slater-Koster parameters
I'm coding a program to calculate electronic bandstructures using the Slater-Koster formalism (I am aware that such programs exist already- this is a pedagogical exercise). I notice that the $p-p$ ...
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For intrinsic semiconductors, is the gap Energy equals $E_c-E_v$ or $E_c+E_v$?
So I have a problem with the intrinsic Fermi Level because by definition it is in the middle of the gap energy, and knowing that Eg=(Ec-Ev), we should have Ei=(Ec-Ev)/2.
But when we follow the ...
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Can a DC voltage excite a pure semiconductor (or insulator) from the valence band to the conduction band?
I have a question I am sticking around and can't find a satisfying answer. Say I have an intrinsic semidonductor at zero Kelvin (no electrons in conduction band). I apply a DC voltage across it. Can ...
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Determining Fermi Energy for a specific $E(k)$ [closed]
I am currently taking an introductory course on solid state physics. One of the problems I came by while studying asks the following:
Suppose we have a 1 dimensional solid of length L, with N ...
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Periodic Zone Scheme - Bloch Theorem in Lattices
I am quite confused about the different representations of the dispersion relation in a lattice.
This image makes a lot of sense to me, since it only represents one dispersion curve and transforms it ...
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What do we actually mean by carrier lifetime in perovskite materials and where do charge carrier reside during that time?
During time-resolved photoluminescence studies in perovskite materials, one sometimes says that it has a microsecond carrier lifetime. What do we actually mean by that? Where does the excited electron ...
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Bloch functions and covalent bonds in some semiconductors
In a Group IV semiconductor (like Si, Ge), one atom makes 4 covalent bonds with its neighboring atoms. They create in this way the so-called a tetrahedral bond (that of the diamond structure). Each 2 ...
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References on obtaining experimental observables from band structure
I've recently been watching this lecture series in Condensed Matter physics. We have covered second quantization, used it to obtain the tight-binding model and then studied the band structure of ...
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One-dimensional tight-binding model with two different hoppings in the limit the hoppings are equal
I've recently been watching this lecture series on Condensed Matter. The part I'm currently on covers band theory for the tight-binding model in a few different scenarios. We covered two different ...
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What is the effect of spin-orbit interaction to the band structure?
I have a question regarding the spin-orbit interaction in zinc blend materials. As far as I understood, the split-off valence band (VB) forms as a result of this interaction, and it is a shift in ...
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How to determine the open circuit voltage of solar cells?
I am reading this paper which is about dye sensitized solar cell, but I do not understand its statement about the open circuit voltage of the cell (page 2242):
In page 2242, the paper says that:
The ...
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Electron dynamics in a periodic potential: Why wavepackets? Why $\vec{v}=(1/\hbar)\nabla_{\vec{k}}E_n$ is its group velocity?
Electrons in a periodic potential, $V(\vec{ r})$, satisfying $V(\vec{r}+\vec{R}) = V(\vec{ r})$, are described by Bloch states $$\psi_{n,\vec{k}}(\vec{r})=e^{i\vec{k}\cdot\vec{r}}u_{n,\vec{k}}(\vec{r}...
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If an atom loses electron, it becomes a cation; it does not form a hole. However, when electron is lost from a bond, it forms a hole and not a cation
If an atom loses an electron, it becomes a cation, and when an electron is lost from a bond, it forms a hole. This is what the professor told the class, but I am not able to find the reason for that ...
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