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Occupancies in sub bands of a quantum well

  1. Mar 19, 2017 #1
    1. The problem statement, all variables and given/known data
    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 occupancies of each sub-band in meV

    2. Relevant equations

    E_f=hbar2 * π / (m*)

    3. The attempt at a solution

    I tried to use the fermi energy equation to figure out where to go with it but just ended up solving for the electron density which I'm told is not the correct way. Other than that I'm pretty stuck on where to start.

    I know I need to use the 50meV value or it wouldnt have been in the question but not sure how.

  2. jcsd
  3. Mar 20, 2017 #2
    What do you understand by "occupancy"? I think your list of relevant equations is incomplete.
  4. Mar 21, 2017 #3
    Im taking a guess since I couldnt find any definition in the course materials but is it the number of occupied states within the band? Im not sure which other equations I need.
  5. Mar 21, 2017 #4
    I figure I need E= (hbar^2 * pi^2 * n^2) / (2*m_eff * d^2)

    but then I havent been given effective mass or well width so not sure where to go
  6. Mar 21, 2017 #5
    Do you know of a relation between the energy of the system and the number of levels that are occupied?
  7. Mar 21, 2017 #6
    is it the product of the fermi function to find probability and the density of states?
  8. Mar 21, 2017 #7
  9. Mar 22, 2017 #8
    I don't know either to be honest. So I'll use the fermi function and the 2D density of states. I know to use 50mev for the Fermi energy but what will E be? 30mev for both so theyhave equal occupancy?
  10. Mar 22, 2017 #9
    As I understand it, the total energy is the fermi energy you have the equation for, plus the potential energy referred to some chosen zero level. I think it might be useful to draw an energy-level diagram comparing the assumed quantum well with one sub-band and the real well with two sub-bands.
  11. Mar 22, 2017 #10
    Perhaps the way to think about this question is to imagine the hypothetical well with one sub-band as a kind of "bucket" that would have been filled with electrons to a "depth" of 50 meV. (This seems to explain why the occupancy is expressed in meV.) How would you picture the real well in those terms?
  12. Mar 23, 2017 #11
    This is to clarify the meV thing.

    "However let me clarify what occupancy in meV means. If you have a band or subband filled up to a Fermi energy, then the occupancy in meV means the energy from the bottom of the band up to the Fermi energy. In other words this is the range of states in meV which is occupied." So what you said makes sense.

    So I guess the way I was going to try and solve it won't work now. Is it just 50mev and 20mev?
  13. Mar 23, 2017 #12
    I think it may be. Depends what "it" is, of course.
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