What is Quantum well: Definition and 66 Discussions

A quantum well is a potential well with only discrete energy values.
The classic model used to demonstrate a quantum well is to confine particles, which were initially free to move in three dimensions, to two dimensions, by forcing them to occupy a planar region. The effects of quantum confinement take place when the quantum well thickness becomes comparable to the de Broglie wavelength of the carriers (generally electrons and holes), leading to energy levels called "energy subbands", i.e., the carriers can only have discrete energy values.
A wide variety of electronic quantum well devices have been developed based on the theory of quantum well systems. These devices have found applications in lasers, photodetectors, modulators, and switches for example. Compared to conventional devices, quantum well devices are much faster and operate much more economically and are a point of incredible importance to the technological and telecommunication industries. These quantum well devices are currently replacing many, if not all, conventional electrical components in many electronic devices.The concept of quantum well was proposed in 1963 independently by Herbert Kroemer and by Zhores Alferov and R.F. Kazarinov.

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  1. Janusz Bednarski

    How Does Voltage Affect LED Color Through Band Gap Adjustments?

    Hi! This question is translated so that's why it might sound a bit weird. I know that the answer should mention the band diagram of the LED, and I think that the answer is to introduce an electrical contact connected to a voltage source. Then when you increase the voltage, it should attract the...
  2. B

    A Carrier relaxation within a quantum well

    Hi Carriers injected in the conduction band of a bulk semiconductor, either by optical or by electrical injection, are relaxing to the lowest free states near the band edge by transmitting their excess energy and momentum to phonons before they recombine with holes in the valence band. This is...
  3. S

    A 1D Quantum Well - Different width "naming" gives different result ?

    Greetings everyone, Exactly as the title says. I am reaching to something strange and I do not know what I am missing. It must be something obvious... case 1: -L/2 to L/2 After taking the Schrodinger equation and considering potential equal to zero inside we reach at this...
  4. jisbon

    Quantum Physics (Electron in infinite deep quantum well)

    Hi all, below is my attempt. Pretty new at quantum so do correct me if I'm wrong. Thanks i) Since 1nm is the wavelength of the electron, Wavelength = 1nm, 1nm=2(2nm)/n , n=4? ii) - iii) From n=1 to n=4, Change in E = 15h^2/8mL where m is the mass of electron and L is 2nm? From the change in E...
  5. T

    Finite quantum well, multiple choice question

    Homework Statement:: Consider an electron trapped in a one-dimensional finite well of width L. What is the minimum possible kinetic energy of the electron? A) 0 B) Between 0 and h^2/8mL^2 C) ≈h^2/8mL^2, but it is not possible to find the exact value because of the uncertainty principle D)...
  6. T

    Quantum well, is this correct?

    Homework Statement:: An electron is in state n=2 in an infinite quantum well with width L. What is the probability to find the electron if you measure within the well's central third? Can someone cofirm whether or not my solution is correct Homework Equations:: Y=Asin(n*pi*x/L) I use the wave...
  7. Drone0

    Electron in a triangular quantum well with triangular barrier

    Hi, it's been so long since I learned quantum mechanics. So the only thing I can solve now is the square quantum well problem. But I need help because I have to solve this problem of quantum well. I tried some calculation but not far.I try to draw the capacitance-voltage profile by drawing the...
  8. D

    I Compute the optical gain of a quantum well

    Summary: Search to compute gain of a quantum well. Stuck with maths or programming. Hi everyone ! For a personal project, I search to compute the optical gain occurring on a semiconductor quantum well. I have based my calculations on a paper called Investigation and comparison of optical gain...
  9. M

    Fermi energy in a quantum well

    Problem Statement: See below Relevant Equations: 2D density of states ##g\left(E \right)=\frac{m^{*}}{\pi\hbar^2}## Fermi energy in a quantum cascade laser ##E_{F}=E_{i}+k_{B}Tln\left[exp\left(\frac{\pi\hbar^2n^{2D}}{k_{B}Tm^{*}} \right)-1\right]## I've been stuck on this problem for a few...
  10. C

    MATLAB_Quantum Well_Finite Difference Method

    Homework Statement Hi, I am new to MATLAB and have an assignment where I have to construct a Hamiltonian matrix, apply boundary conditions, then find corresponding eigenvalues and eigenvectors for the electron in a box problem. I am stumped where to start. From our class we learned that you...
  11. M

    Evolution of a particle in a well

    Homework Statement I posted a picture of the question https://imgur.com/a/8byywYL Homework Equations P = $$(<\psi_{n}|\psi_{o}>)^2$$ The Attempt at a Solution I am guessing that I compute(denote by ##\psi_{o}## the ground state of the old well and by ##\psi_{n}## the ground state of the new...
  12. G

    I Transition state of electrons in molecules

    Hi ! In my class we have an exercise that I technically understand but that I can't get conceptually. We have trois molecules (naphtalene, anthracene, tétracene). Considering each molecule as infinite quantum well of length 2L(naphtalene), 3L(anthracene) and 4L(tetracene), we would like to...
  13. E

    Occupancies in sub bands of a quantum well

    Homework Statement A quantum well is doped with electrons such that if it had one only one confined sub-band the Fermi energy would be 50meV. In reality the quantum well has two sub-bands with energy separation between the bottoms of the sub-bands of 30meV. Deduce what are the resultant...
  14. J

    A Optical gain peak, PL peak and EL peak: are they same/different

    I need to understand if Optical-gain peak, (Photoluminescence) PL peak and the Electroluminescence (EL) peak are they same or different. If they are the same/different what the corresponding conditions? Would be easier for me if bulk GaAs is used for the explanation (comparison at same...
  15. Y

    A Find Young's modulus of quantum well semiconductor

    Hi How to find young's modulus of quantum well semiconductor? For GaAs- young's modulus E=85 GPa and For Al0.3Ga0.7As- young's modulus E=84 GPa. For quantum well Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As Value of young's modulus is?
  16. F

    Quantum well, time evolution of probabilities

    hey, this thread might be a bit longer, but I have already calculated everything and I am quiet sure that it is right :) Just need someone who confirms me or not :) 1. Homework Statement Time evolution of probabilities. An electron inside a quantum well of length L is at time t = 0 in the...
  17. J

    How to Calculate the Ground Electron Level Energy in a Quantum Well?

    Homework Statement For a GaAs with bandgap Eg =1.4eV Effective electron mass is 0.07*me d=10nm Calculate the energy of the ground (lowest) electron level in the conduction band with respect to the bottom of the conduction band.Homework EquationsEa =Ec + h^2a^2 / 8*me*d^2 The Attempt at a...
  18. whatphysics

    Quantum Physics - Infinitely vs Finite depth quantum well

    Homework Statement Comment how the energy and wave functions of the electron would change in the case of a finite dept quantum well with the same width. Homework EquationsThe Attempt at a Solution I feel completely clueless as how to approach! :( * The full question can be found in the...
  19. K

    Charge Density in Quantum well Sub-bands.

    Homework Statement I am trying to calculate the charge density in the first subband (n=1) of the quantum well of length L as shown in the below figure. here is the electron wave function for the first sub-band and its value (from relevant equation 1) is given as Ψ12(x) = 2/L*sin2(πx/L) from...
  20. K

    Electric Field Effect on Quantum Well

    Hello everybody ! Recently i heard that, application of an electric field onto a quantum well tilts the quantum well and changes its 2-D density of states to 3-D bulk density. Is this true..? Can anybody give some more information or reference on this..? Thanks for any Help.
  21. C

    In an infinite quantum well, why Δn=0?

    I've been reading up a bit on semiconductor quantum wells, and came across a selection rule for an infinite quantum well that says that "Δn = n' - n = 0", where n' is the quantum well index of an excited electron state in the conduction band, and n is the index of the valence band state where...
  22. A

    How Can Effective Mass Discontinuity Be Managed in Quantum Well Simulations?

    I am making a finite elements simulation of electrons in the bottom of the conduction band of some material. To do so I assume that the electrons move in the bottom of a flat well with their original mass replaced by the effective mass. The idea is to calculate wave functions for electrons...
  23. Dirac62

    I Quantum well, Types of triangular ones

    Hello I want to ask, how many types of Triangular quantum well is there in quantum mechanics? how does the schrodinger eq. change? and also their eigenvalues. tnx.
  24. Dirac62

    Discover Eigenfunctions & Eigenvalues in Triangular Quantum Well

    Hello all, I need to understand how to find eigenfunctions and eigenvalues in a state of Triangular quantum well, It would consist of two triangle. Tnx a lot.
  25. GalileoGalilei

    Double asymmetric quantum well

    Hi, We know that for an infinite well of length a, eigenfunctions of the hamiltonian are : \psi_n(x)=\sqrt{\frac{2}{a}}sin(\frac{\pi n x}{a}) related to the eigenvalues E_n=n^2\frac{\hbar ^2 \pi^2}{2ma^2} Now, I would like to consider two infinite quantum wells of length a et b (not...
  26. D

    Quantum Well Lasing: Solve the Problem Now!

    Hi everybody, I want to solve this problem but I'm stucked with several equations all over the books, if anybody is expert in lasing please help me! We want to make a laser at ħω=Ec-Ev. Assume that the mirror reflectivity is [(n-1)^2] / [(n+1)^2] , where n=3.5 is the refractive index of...
  27. T

    How Do Parity and Potential Affect Quantum Well Solutions?

    Homework Statement The question is attached as a picture. Note: if someone would prefer I type it out I can. Homework Equations Schrodingers equation The Attempt at a Solution PART A I am pretty sure I got the well right. It looks like a finite well inside an infinite well. I...
  28. N

    Finding the fermi energy in doped quantum well

    Homework Statement Regular Doping: Let's say that we want to introduce some electrons into a quantum well, by adding dopant atoms (donors) to the semiconductor. The "regular" way to do this would be to deposit our semiconductor films, first a "barrier" layer with large band gap, then the...
  29. D

    How Small Can a Quantum Well Be for an Electron's Total Energy to Be Zero?

    1. Homework Statement -This is a problem on my practice final that I haven't been able to solve. Hoping someone out there can take a crack & clarify it for me. Quantum wells are devices which can be used to trap electrons in semiconductors. If the electron is in the well it has a lower...
  30. D

    Solving for DeltaX in a Quantum Well: Uncertainty Principle and Energy Analysis

    Homework Statement -This is a problem on my practice final that I haven't been able to solve. Hoping someone out there can take a crack & clarify it for me. Quantum wells are devices which can be used to trap electrons in semiconductors. If the electron is in the well it has a lower...
  31. B

    Quantum Well with Infinite Barriers

    Homework Statement An electron is in a one-dimensional rectangular potential well with barriers of infinite height. The width of the well is equal to L = 5 nm. Find the wavelengths of photons emitted during electronic transitions from the excited states with quantum numbers n = 2, λ21, and n =...
  32. M

    Quantum well laser diodes - Operation and design

    Quantum laser diodes. How does light escape? I recently became very interested on the functioning of these amazing devices and so I read online about the topic of quantum wells, semiconductors and lasers. After much reading I believe I can now understand the basics of lasers, resonant...
  33. K

    Finite Quantum Well: Wave Function when E>V{0}?

    Homework Statement If an electron is in a finite quantum well and it's E>V{0} what does the wave function look like? Homework Equations The Attempt at a Solution Wondering if anyone could help me out with this? I know that outside the well the electron will have the same...
  34. J

    What is the significance of k-values in a 2D quantum well system?

    It is a classic 2DE quantum well problem. I do not understand few things. I haven't seen the solution anywhere on the new, so this is why i ask here. It is a quantum well - Lx is it's dimension along x-axis Ly is it's dimension along the y-axis.There is a potential as in picture let's call it...
  35. E

    Absorption coefficient of quantum well

    we know that the quantum well absorption coefficient is calculated by summing over the electron-heavy hole and electron-light hole transitions: α_{w}(E) = \sum_{n}α_{e_{n}-hh_{n}}(E) + \sum_{n}α_{e_{n}-lh_{n}}(E) where n is the n^{th} transistion. but when the photon flux is incident...
  36. T

    Metal Contact Effect on 1-D particle in a box quantum well

    Dear All, When an electrical contact is made onto the quantum well, how would the energy states be affected ?
  37. R

    MATLAB Problem regarding Matlab code for n no of quantum well

    I have written a code which is something like that clc X = input('Molefraction of Al in system:'); n=input('no of well:'); width=zeros(1,50); for j=1:(2*n+1) width(j,:)=input('length of areas:'); end del_eg=1.247*X; V1=0.6*del_eg; V=zeros(1,100); for j=1:n...
  38. M

    Probability distribution in a quantum well

    Homework Statement Consider a mixed state comprising equal components of the first two energy levels in an infinite QW of width L. These have (normalised) wavefunctions ψ1 and ψ2. The wavefunction for the mixed state will be ψ(x,t)=(1/√2)ψ1e^(iw1t)+(1/√2)ψ2e^(iω2t) a) Calculate the...
  39. Z

    Finite square quantum well - depth

    Homework Statement Find the condition on the depth of the finite square well such that one finds two even and one odd bound state energy eigenstates, but no other bound state solutions exist. Your answer should appear as a range of allowed well depths, say ? < Vdepth of well < ? Homework...
  40. W

    About the semicondunctor quantum well

    consider the GaAs-AlGaAs semiconductor quantum well the gap of GaAs is situated inside the AlGaAs gap however, what is its precise position?
  41. J

    The quantum well density of states step function?

    I'm trying to get my head around the step function and the energy states of the quantum well. What I've got so far is this: The density of states for an electron confined in one direction by the potential barriers of the well, but free to move in the other two directions in the place of the...
  42. F

    Quantum dot, quantum wire, quantum well?

    Hello Forum, I understand that a quantum dot is a 3 dimensional confinement of an electron inside which the electron can only have quantized energy (quantized energy levels)...a quantum wire is a 2D trap, a well a 3D trap... What is so special about confining electrons in space? Why so many...
  43. S

    Electron-hole overlap integral for a quantum well

    Hi, I need some help to work out the electron-hole overlap integral Mnn' for a quantum well: Knowing that M'nn'=\int\varphi*en'(z).\varphihn(z).dz => How can I show that Mnn' is unity if n=n' and zero otherwise (in a quantum well with infinite barriers) ? => How can I show that Mnn' is zero...
  44. V

    Finite quantum well, factor of 2*pi seems necessary but why?

    Homework Statement Solve for the allowed energy values E of a finite square quantum well of depth U0 = 25eV, width a = 0.5nm that contains an electron of mass m (I'm presuming that m = 9.11*10^-31kg, the question doesn't indicate a specific value to use). I'm defining the interior potential to...
  45. J

    How Does a GaAs Quantum Well Influence Electron and Hole Energies?

    Here's the problem: A GaAs quantum well of thickness 10 nm is held in a cryostat at a low temperature and is excited with a powerful ultrashort laser pulse at time t = 0. The laser pulse injects 1 × 1015 m−2 electrons and holes per unit area of the quantum well into the conduction and valence...
  46. M

    Density of states in a quantum well

    Hi there, I'm a bit confused as to the meaning of the following figure, for the quantum well case: I understand that with the quantum dot, since the states are completely quantised you get the delta functions - states only exist at certain energies so the DOS at these energies is non zero...
  47. J

    Explaining the Unexpected Spikes in a Quantum Well Absorption Spectrum

    I'm looking in a textbook at a discussion of a semiconductor quantum well which is being irradiated and an absorption spectrum produced. Electrons are being promoted across the band gap and holes are being created. There are heavy hole and light hole transitions, and the spectrum shown rises in...
  48. R

    Calculate 1st 3 Energy Levels for Electron in Quantum Well

    Homework Statement Calculate the first three energy leveles for an electron in a quantum well of width 10Angstrom and infinite walls. Homework Equations En=\frac{n2pi2(hbar)2}{2mL2} The Attempt at a Solution m=9.109E-31Kg L=10E-10m hbar=1.055E-34 En=n2*6.032E-20 My problem...
  49. D

    Error in book? (derivation of quantum well)

    Hi, http://books.google.at/books?id=40rRzNbuhpAC&pg=PA146 Can anybody explain me why in the third bracket in 3.139 is suddenly a minus instead of a plus? In 3.136 it is a Plus! And it is pure substitution as far as I understand... And I checked everything before a few times: It should be...
  50. J

    2 particles in an infinite quantum well

    If we have 2 particles in ground state in an infinite quantum well of length L (one-dimetion). Suppose then that the unperturbed energy is two times the ground energy of only one particle in an infinite qunatum well of length L. Then I want to use first order perturbation theory to find the...