What is Band theory: Definition and 44 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. E

    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...
  2. C

    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...
  3. DaTario

    I A problem with a figure related to band theory

    Hi, All. In searching for images related to the introduction of band theory in solid sate physics I found this one: I would like to ask you if I am correct in thinking the increase in the number of splittings (in b) is misleading to students. Thank you all DaTario
  4. chem_

    Band theory: effective mass and Hall's coefficient

    Consider the following scenario. A material has the E-k band scheme as shown in the figure (extended scheme of zones). Could anyone give me a suggestion regarding the following : Electrical character of the material with the temperature. Sign of the Hall coefficient. Sign of the effective mass...
  5. Philethan

    A Why do we need to know "two-bands" Hall coefficient and magn

    (Oh my god, why can't my post show normally? Some sentences just disappear, but I can still see them while editing. It's very weird. Can someone help me? I've reported.)I know only partially filled bands result in current density, and I think there must be not only 2 partially filled bands, but...
  6. Sagar Rawal

    A Mott insulators and electron-electron insulators

    I found this paragraph from one of wiki article, "Mott considers a lattice model with just one electron per site. Without taking the interaction into account, each site could be occupied by two electrons, one with spin up and one with spin down. Due to the interaction the electrons would then...
  7. Sagar Rawal

    A What is Mott Transition and its basic Priniciple?

    Hello Everyone, I was really curious to know what really is Mott Transition and How it works. I searched for hours but couldn't find any helpful answer. Somewhere it was suggested that it is a bridge between Quantum and Classical Mechanics and it is due to electron interaction where electron...
  8. learn.steadfast

    I Band theory and qualitative character of bands

    I'm interested in the the band theory of solids for semiconductor modeling. I haven't solved the Schrodinger equation for multiple atoms, but I'd like to know some details that experienced physicists might already know. Several texts show how the bands develop from molecular coupling of...
  9. M

    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.?
  10. M

    I Reciprocal lattice in connection with band theory

    I need details on this topic ,this is my assignment but my solid state physics is not so good,and don't know much about it but i have to do this assignment ,i have material on reciprocal lattice but for only including in assignment ,not for my understanding,so i directly need any material on...
  11. zoobyshoe

    The Rubber Band Theory of Bow Strings

    When I was 6 or 7 I decided to make a bow and arrow one day. I had never seen or handled one in real life, but it was intuitively obvious to me from TV that they way to do this was to tie the ends of a stretched rubber band to the ends of a stick. This would have worked, after a fashion...
  12. M

    I Opening of a band gap - Diffraction at the edge of BZ zones?

    I have a hazy idea that comes from a few video lectures (see below for example) where the following is stated: The condition for constructive interference (Bragg condition) in reciprocal space is that the wave vector should touch a Brillouin zone boundary. In this case, the standing wave that...
  13. P

    I Basic band theory question, free electron model

    Hello, I am trying to figure out the width of bands in a 1-dimensional lattice. Here is a short derivation from the book I am reading: if we approximate the free electrons as being in a square well then the energy levels are ## \frac{\pi^2 \hbar^2 n^2}{2mL^2}##. If there are ##N## ions...

    Band Theory of Solids: Electron Conduction & Current

    Do electrons in conduction band are only responsible for current? Don't the electrons in partially filled valence band capable of moving contribute to current? Material discussed-metals(conductors)
  15. N

    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...
  16. Benevito

    Conduction and valence bands in semiconductors

    Why is the conduction band state s-type and the corresponding valence band state p-type?
  17. T

    How Do Landau Levels Function in Solid State Band Theory?

    Landau level is the energy levels of free electron gas in a magnetic field. However, this term is also frequently used in solid state physics. I have the following questions: 1. what does this term exactly mean in band theory? After all, electrons are not free here. 2. why is de Haas-van Alphen...
  18. T

    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...
  19. T

    Wave packet description of electrons in solid state physics

    In solid state physics, I learned that the velocity of a bloch electron is ##\frac{\partial E(k)}{\partial k}##, where ##E(k)## is the energy dispersion. This formula is derived on the basis of the assumption that electrons is a wave packet of bloch state in solids. However, I have a question...
  20. N

    Why do holes not contribute to conduction in metals?

    It seems like when an electron moves to a higher energy level, even within the same band (conduction), the empty state should be a hole. But, we are told that in metals, electrons are the charge carriers. Do I just misunderstand what holes are? Or what is going on here?
  21. U

    Fermi Surface squashed by potentials

    Taken from my textbook: My understanding is that: One valence electron, 2 spin states -> Half-filled Brillouin zone Seeking inspiration from "Nearly Free Electron Model": gaps open up at zone boundaries States nearer to zone boundaries get pushed down in energy further Since a fermi...
  22. Q

    Explaining Band theory and Momentum Space to laymen?

    I didn't put this in the Education forum because I feel the level is probably too high. I have a physics degree and an education degree, but due to my inability to tolerate students who simply don't care about learning, I became an electrician instead. My colleagues and I were having a...
  23. P

    Understanding Band Theory: The Difference Between Conductors and Insulators

    My question is as follows: if you place an insulator into an applied field, the only thing that will happen is that the potential energy of each band will shift, according to the potential that it is in. Why is this exact same thing not what takes place in conductors? Why do the electrons at the...
  24. P

    Does each band have multiple allowed E-values for th same k?

    So every theoretical resource I've been able to find seems to map bands to lines for a 1D crystal, surfaces for a 2D crystal, and hypersurfaces for a 3D crystal. But then there are images like the ARPES data below (fig. 1a, 1b, 2) where the density of states is a lot higher within the valence...
  25. G

    Conservation of Energy with non-allowed states

    (This though came up while learning about band structure, so that is how I am going to explain it, but I think it applies equally well to a square well, for example). Say you have an electron at the Fermi level of an insulator. Then, you apply an electric field. No current flows, because all...
  26. S

    Band theory electron counting rules for metals/insulators

    I'm a little confused by the description I commonly hear about the electron "counting rule" in band theory. The general statement I find is that a solid with an "odd number of electrons per unit cell is a metal" (because this would imply a partially filled band), while an "even number of...
  27. W

    Help Understanding Qualitative Band Diagrams for F-Chain

    Homework Statement Hi everyone, I am trying to construct qualitative band diagrams and I think I have confused myself. I am not sure on how to figure out what the electron configurations are of the orbitals when k=0. I get that at k=π/2 it is the opposite state but I can't seem to figure out...
  28. M

    Understanding Band Theory: A Basic Guide

    Hi! I am having difficulty grasping what band theory actually is, especially what the bands are and the energy gap between them. Are they probabilities? Shared electrons between atoms such as in metallic bonding? What is the difference between the conductor band and the valence band? I think I...
  29. I

    The Effect of Diatomic Unit Cell on Polyacetylene Band Structure

    Question Statement Polyacetylene can be modeled naively as a one dimensional chain of carbon atoms each separated by a lattice constant 'a'. Taking the electrons in such a system to be nearly free and applying a weak periodic perturbation we can derive a dispersion relation giving a curve...
  30. aleksbooker

    What's a good primer of band theory (metals and semiconductors).

    Edit: I've made some progress on this one, and I now understand that the valence and conductance bands are composed of molecular orbitals contributed by each metallic atom joining the molecule. For example, three lithium atoms would contribute three total molecular orbitals, resulting in three...
  31. A

    Confused by band theory in a weak potential

    Apologies if this is rather trivial. I'm having a hard time wrapping my mind around the mathematics of energy bands and periodic potentials. I understand that an electron in a periodic potential will be of the form \phi_k(r) = e^{ik.r}u_k(r) . This wavefunction has periodicity of the...
  32. A

    Question about level splitting in band theory

    Hello , about the band theory I was confused some how seeing the attached image I ask :- 1- when the atoms are far away we take a single atom alone as a system , but when atoms get closer we identify them all as the system , right ?! 2- why do we use the word " splitting" , why...
  33. H

    Forbidden Electron Energies in Band Theory of Solids

    In band theory of solids, when an electron's wave vector lies at the first brillouin zone border, it satisfies the bragg condition and there is some forbidden region for that wave vector. I like to know what happens for such these electrons that they can not have some energies in the forbidden...
  34. T

    Understanding Energy Bands in Solids: A Quick Question on Band Theory

    Hello everyone, I have finished high school not long ago, and haven't start my uni. So I take this time to read some physics. I have no one teachs me, the only book I have is 'Giancoli's PHYSICS'. Its a good book (discriptive but not mathematical, which suits me as I haven't done much...
  35. C

    Band theory and Semiconductors

    Hello, I just watched this video, where Dr Brattain talk about semiconductor physics and I thought about what I learned in my solid state physics course, namely band theory. I have several questions : 1)The explanation in terms of chemical bonds given by Dr Brattain (around 10mins) seems a...
  36. P

    Trouble understanding band theory

    Hi, I have porblem in visualizing or imagining the formation conduction and valance band in basic semiconductor physics. Most of the books explains as ' when millions of atom combine together the outermost shell and subshells gets altered and form more energy levels for electrons to occupy. and...
  37. A

    Doubt on Band Theory of Solids: Can It Explain Electron Movement?

    I have a serious doubt about the concept of band theory of solids. While explaining the behaviour of semi conductors, the following explanation is given. "The valency bands are completely filled electron-bands, where as the conduction band is usually empty. The conduction takes place when a...
  38. I_am_learning

    Band theory of Conduction, what constititue resistance?

    In the band theory it is said that, in conductors, conduction bands are only half-filled. So, when Electric filed is applied, the electrons can easiliy jump into higher energy states of the same band and move freely. If the electrons a so free to move, what constitute the resistance of the...
  39. M

    Band Theory of Solids: Basic Concepts Explained

    I am reading the Band Theory of solids.Now, my question is on the basic concepts: {1}When energy is given to a solid, the electrons bound to the respective atoms move from the valence band to the conduction band and hence conductivity of material increases. {2}But we know that when we give...
  40. H

    Semiconductors and Band Theory

    I was taught this in school but my teacher could not explain why the band splits again with decreasing atomic distance. Also, then i wondered how do you explain the fact the it splits again nicely into 4N states for the valence band and 4N states for the conduction band? Could some one help...
  41. K

    Band Theory of Solids, Kittel CH 7

    Homework Statement I feel like I have a pretty good conceptual understanding of the origin of band theory, but these two problems were totally above my head. Kittel Ch7 #2 Consider the free electron bands of an fcc crystal lattice in the approximation of an empty lattice, but in the...
  42. S

    Energy Band Theory - Conduction & Valence Bands

    In the energy band theory, we are only concerned with two bands - the conduction band and the valance band. Electrons can only be found in one of these bands and they can't have any energy related to the band in the middle - the forbidden bad. My question is that how come there are only two...
  43. A

    Band Theory & Holes: Solving Electrical Conductivity Problem

    Can anybody solve me a problem about electrical conductivity in solid state? I think answer should be quite general: how do holes move within a certain band if they experience an external uniform electical field? I found some trouble when I think about current density, group velocity, crystal...
  44. S

    Exploring Band Theory & the Role of Even Cell Contributions in Insulators

    I have a question about insulator. The story starts from the fact that, taking a 1-D model, there are N possible values of wave vectors k within the first Brillouin zone [becasue number of possible k's = (2*Pi/a)/(2*Pi/L) = L/a = N where L is the length of the crystal, a is the distance...