# What is Band structure: Definition and 95 Discussions

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands).
Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.).

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1. ### A Empirical tight-binding sp3s* band structure of semiconductors

I'm simulating on code the tight-binding sp3s* bandstructure of certain semiconductors, such as GaAs, AlP, InP, ZnSe, etc. with spin-orbit coupling at a temperature of T = 0 K but I'm having trouble at finding the corresponding spin-orbit splitting parameters. For example, I've found in this...
2. ### I Emission of light from incandescence of metals

a. We know metals emit EM radiation upon heating or electric current. I'd like to understand more fundamentally how this phenomenon takes place, on the basis of the basis of band structure, and which electrons are involved ? b. Classically, charges emit radiation when accelarating or...
3. ### I How does diffusion of high energy electrons shift band structure?

When an n-type material comes in contact with a p-type material to form pn-junction, electrons with the highest energy in the conduction band will diffuse to the p-side to reach equilibrium so the entire band structure on n-side will shift down relative to p-side as described in the following...
4. ### I Number of lines in Band Structure

The general idea is that, number of bands=number of lines. For instance, AlAs primitive cell (one of each atom per cell) has 13 bands; that is outer most shells have 13 distinct energy values. (Al: one 3s + three 3p, As: five 3d + one 4s + three 4p) But when I calculate Band Structure through...
5. ### A The main charge carrier in the ionic crystal is polaron or conduction?

Suppose I have a perfect crystal(e.g.TiO2-Rutile, band gap=3ev), under UV light, there should photoconductivity, according to the condensed matter theory, some of these excited conduction band electrons would form small polarons, I am wondering how many percent of the free conduction band...
6. ### I Question about Electronic Band Structure

According to this Wikipedia entry: https://en.wikipedia.org/wiki/Electronic_band_structure the discrete energy levels of an isolated atom split into N levels in a macroscopic crystalline lattice (N being the number of atoms in the lattice) forming essentially continuous bands from the discrete...
7. ### MATLAB Graphene band structure Matlab code

I have this code for 3D band structure of graphene but i can't understand why while graphene first brillouin zone is hexagonal but here a rectangle form of first brillouin zone is used?E0 = 0; % coloumb integral V = -2.7; % hopping integral [eV] acc = 1.41; % c-c bond length [Angstrom] lattice =...
8. ### I What kx/ky Values Are Used for Graphene Band Structure Plots?

Hello, https://www.researchgate.net/figure/Top-Graphene-nanoribbons-with-zigzag-left-and-armchair-right-edges-with-disordered_fig1_258105786 With what kx/ky values are these band structures plotted? The energy dispersion of graphene is given by this , yet I am confused to what kx/ky value...
9. ### Python Problem with coding the band structure of graphene nanoribbons

Hi, I have a Matlab code for calculating the band structure of graphene nanoribbon which is working fine, but I wanted to convert it to python and I've done it. I guess I made a mistake somewhere because the plot is totally wrong. Could someone check it for me, please?
10. ### A Electronic band structure of iron superconductor BaFe2As2

how can I determinate the electronic structure of a multiband system? for example in the case of the superconductor BaFe2As2 , the electronic properties are as known dominated by 5 Fe d states at the fermi energy, so 5 bands cross the Fermi level and form 5 Fermi surface sheets (if we consider...
11. ### Band structure of a 2deg including spin orbit coupling

first of all, I tried to obtain the energy eigenvalues of the Hamiltonian, by using the equation ##det(\hat H -\lambda \hat I)=0## ##\gamma V\delta(z)(\hat z \times \mathbf{p}) \cdot \sigma=\gamma V\delta(z)(p_x\hat j-p_y\hat i)\cdot(\sigma_x\hat i + \sigma _y \hat j)=\gamma...
12. ### I Free electron gas band structure?

How can I see, by looking at a band structure if the substance in question can be viewed as a free electron gas (FEG) or not? What characterizes a FEG in a bandstructure plot? Thanks in advance!
13. ### I Understanding Band Structure Diagrams

Hi! I never really understood band structure diagrams. I think they represent the energy of an electron, with the given circumstances, at a k vector. Are the electrons only allowed to be on the lines here? Or can they also be in areas enclosed under/between certain lines? What are some...
14. ### A Silicon band structure for both ibrav 0 and ibrav 2

Silicon Band Structure for both ibrav 0 and ibrav 2 I did scf and bands for silicon using both ibrav=0 and ibrav 2 After running the two bands separately I noticed that the band structures for the two (ibrav 0 and ibrav 2) were totally difference but in literature i read that the two (both ibrav...
15. ### I Bloch Waves within Tight Binding Approximation

So I thought I understood something well, and then I went to explain it to someone and it turns out I'm missing something, and I'd appreciate any insight you might have. If I think about Bloch's theorem, it states that ψk(r)=eik⋅ruk(r) where uk has the periodicity of the lattice. If u is...
16. ### A The hermicity of a k.p matrix?

I am trying to use the k.p method to study quantum well band structure. One example Hamiltonian look like this [J. Appl. Phys., 116, 033709(2014)] where ##{{\hat k}_ \pm } = {{\hat k}_x} \pm i{{\hat k}_y}## and the matrix elements are function of ##{{\hat k}_i}## and if quantum well is grown...
17. ### A The k direction in a k.p model ?

I am trying to do some calculation based on a k.p model of GaN proposed by S. Chuang [Phys. Rev. B, 54, 2491]. It is a 8 by 8 Kane model with basis functions: The 8 by 8 Hamiltonian contain first order of k is where ##{k_ \pm } = {k_x} \pm i{k_y}## the reciprocal space and high symmetry...
18. ### How to evaluate the effective mass tensor (band structure)

Homework Statement The energy-band dispersion for a 3D crystal is given by $$E(\mathbf k) = E_0 - Acos(k_xa) - Bcos(k_yb) - Ccos(k_zc)$$ What is the value of the effective mass tensor at ## \mathbf k = 0 ##? Homework Equations The effective mass tensor is given by  \left( \frac{1}{m^*}...
19. ### A Time reversal symmetry and Bloch states

Hello! The time reversal operator, ##\hat{\Theta}## transforms a Bloch state as follows: ##\hat{\Theta} \psi_{nk}=\psi^*_{nk}##. How does one proceed to prove the condition that ##\psi_{nk}## and ##\psi^*_{nk}## must satisfy in order for our system to be time reversal invariant? Thanks in advance!
20. ### Understanding solar cell band diagram

Hi everyone, I have been studying the physics of solar cells for a long time. The only thing that I can not completely understand is the physical operation of solar cell based on band diagram. Can anyone briefly explain the movements of carriers from one electrode to the another based on band...
21. ### Diamond/Silicon's band structure

Homework Statement I am asked to discuss the band structure of diamond. I saw the band structure of diamond has 4 filled valence bands and then 4 conduction bands. Silicon, the same. Homework Equations --- The Attempt at a Solution I'm feeling really silly because I don't understand why it is...
22. ### A Change in phonon dispersion with pressure

Hi, I'm looking into how phonon dispersion changes with pressure analytically and need to know how the atomic spacing in copper changes with pressure in order to model the crystal. I can't find any helpful papers online :( Any help would be appreciated thanks e
23. ### A Localized states and density of states

Hello, Let's suppose we have a two dimensional lattice which is periodic along certain direction, say x-direction, allowing us to define a quasi momentum k_x. The lattice is not periodic along the y-direction (perpendicular to x-direction). Therefore, we are able to obtain the band structure...
24. ### Impact of crystal defects on band diagram.?

I was studying about Crystal defects in crystals and came to know that it has huge effect on band diagram.I don't know about their specific impact on band diagram.So what are major impacts of crystal defects on band diagram.?
25. ### Electron distribution using tight binding band structure?

Hi everyone, I am just wondering how to calculate electron distribution using tight binding band structure for a system like graphene or any other solid. So the goal is to get |\psi(r)|^2 which \psi is the band state and it is the linear combination of Bloch sum...
26. ### I Fe Lattice: Band Structure & Fermi Surface Location

This is schematic band structure for the dxz and dyz orbitals using a 2D square Fe lattice. What is the location in the Brillouin zone of the hole-like Fermi surface and the electron-like Fermi surface?
27. ### A Band structure after compensation doping

As an electronic engineer I am not an expert on semiconductor physics but I think I understand the basics of energy band diagrams reasonably well. It all fits together fairly neatly with the normal textbook assumption that we are looking at pure N-type or P-type doping. The problem I have is...
28. ### A About band structure calculation

My question is more general but I explain it by a simple example i.e. graphene and tight binding method. I solved energy dispersion of graphene with tight binding by the two ways: First, I took graphene as a lattice with the two basis atoms A and B. In the second way, I took graphene as a...
29. ### A Band structure silicene nanoribbons

I've written the following program for drawing the band structure Silicene nanoribbons, but in a zero energy building is a straight line. Can help me to fixed problem. % tight binding calculations for zgnr clear; clc; close all; NU=14; % Number of atoms in unit cell Nbnd=4*NU; % number of...
30. ### A Band structure silicene using siesta software

I wants to plot band structure silicene with siesta software so that the K range is 0 to 1 but can not draw a graph in this rang. Can help me to fix the problem.
31. ### A Plotting Silicene Band Structure in Γ→M→K→Γ Path using Correct Equation

I want to plot band structure silicene in the following path: Γ→M→K→Γ Do the following equation for the above path is correct: close all clear all clc aa=2.28; a=3.86; a1=(a/2)*[sqrt(3),-1,0]; a2=(a/2)*[sqrt(3),1,0]; b1y=-(2*pi)/a; b1x=(2*pi)/(sqrt(3)*a); b2x=b1x; b2y=-b1y; %K-point pKx =...
32. ### I Band structure and valence electrons

The standard approach to explaining band structure is to assume that the electrons in a solid move in a potential from the ions, which is periodic leading to Blochs Theorem and the formation of band structure. But I am a bit confused at this point. Is the approach only valid for the valence...
33. ### I Double heterostructure junction in forward and zero bias

Hi! When dealing with a pn homojunction, it is easy to see the features it has at equilibrium, and also the features it has with forward/reverse bias. Plots show the constant Fermi level at equilibrium and the different Fermi levels for a forward bias; moreover, examples show how much the bands...
34. ### I Built-in potential in pn junction

Hello! The (potential) energy of an electron in a solid structure is always negative; also the E_c and E_v levels (conduction band and valence band limits) are negative, in the band diagram of a pn junction. When the junction is built and thermal equilibrium is reached, the depletion region...
35. ### I Pn junction to reach thermal equilibrium

Hello! Some of the processes caused by a pn junction are not clear for me. Just after the contact between the p and the n region, a migration of charges happens in a semiconductor junction in order to reach an equilibrium condition. A valence band and a conduction band are present in both...
36. ### A Break points in band structure

What do we mean by break points in band structure ? and what that sentence means : "if the band index were chosen in such a way that the energies are indexed in ascending order for any k then break points would appear in the εnk vs. k plot (with n fixed) wherever two lines intersect." ...
37. ### Mastering DFT: Calculating Band Structures for Heterostructures

I'm teaching myself how to do DFT for my master's project, where I want to use it for calculating band structures for different heterostructures. Now to learn DFT I am on one hand reading a book on the basic theory, on the other hand using different freeware packages to try and calculate the...
38. ### Relation between electronic band structure and Fermi energy

I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level). 1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...
39. ### CASTEP simulation for graphene band structure

Homework Statement I am running CASTEP DFT software to simulate pristine graphene, and am unsuccessful in obtaining the trademark zero band gap at the k-point as reported in numerous papers to date. Any assistance would be greatly appreciated as the subject is very new but I am keen to push...
40. ### Band structure silicon nanoribbons

Hi I have been drawing pi bands, silicon nanoribbons. But I can't draw sigma bands. Can help me for plotting sigma bands, silicon nanoribbons in Matlab.
41. ### How does band structure lead to metals/insulators?

I almost "get" it, but not quite. Can someone help? Here is my current understanding. Say you solve the Kronig-Penny model. You find that you get bands of N closely spaced energy levels, with large gaps between them. Under normal conditions, electrons fill the band to some level (let's say we...
42. ### Is band structure in semiconductors symmetrical with respect to k?

Do any band structure (in absence of any external field) in general, is symmetric with respect to k? In other words, do we always have E(k)=E(-k).
43. ### How to Calculate Hopping Parameters and Plot Band Structure in MATLAB?

Who can help me in writing the following program: phase(i) = exp(1i*dot(k(:,index),R(:,i))) This gives you the phase you're going to multiply with the hopping parameter. You'd have to write a loop that runs from i = 1:3 in order to multiply each contribution to the hopping parameter such that...
44. ### A question about band structure silicene

Dear forum people I consider four atomic orbitals of the silicon atom: s, px , py and pz , thus Hi,j is a 4*4 matrix. Hi,i is the expression of the diagonal matrix and Hi,j is the expression off-diagonal matrix where the expression for Hi,i and Hi,j is attached. But I can not calculate the...
45. ### A question about band structure silicene

Dear forum people I consider four atomic orbitals of the silicon atom: s, px , py and pz , thus Hi,j is a 4*4 matrix. Hi,i is the expression of the diagonal matrix and Hi,j is the expression off-diagonal matrix where the expression for Hi,i and Hi,j is attached. But I can not calculate the...
46. ### A question about band structure silicene by tight binding

Dear forum people, I know that electronic properties silicene is the same graphene but i can not figure out how can I plot band strcture silicene. I want to plot that in the following path: K→Γ→M→K
47. ### A question about band structure silicene

Homework Statement Dear forum people, I know that electronic properties silicene is the same graphene but i can not figure out how can I plot band structure silicene. I want to plot that in the following path: K→Γ→M→K
48. ### Dielectric function with band theory

As far as I am concerned, dielectric function can be computed by band structure. However, band structure is a global property of solids, while dielectric function is a local property. How a local property can be computed from a global property. Put it another way, if I want to calculate...
49. ### Plotting Band Structure in Graphene for Scientists

I just learned how to get a tight-binding dispersion for graphene. But i can not figure out how can I plot that. I want to plot that in the following path: Γ→K→M→Γ I would be appreciated if could some one give me a hand on my problem. thanks for alot.
50. ### Band Structure of a solid is not related to the size/doping?

Look at the diagram below, after all that doping, 2 blocks of Si have the same band structure? My understanding of band structure and fermi level is that: Given a block of solid (Please note, not a TYPE of solid, but this PARTICULAR block of solid) it will have its own unique band structure...