Occupancies in sub bands of a quantum well

In summary, the question involves a quantum well with two sub-bands, each with a bottom energy separation of 30meV. The Fermi energy is given as 50meV for a hypothetical well with only one sub-band. The task is to determine the resultant occupancies of each sub-band in meV. The approach involves using the Fermi function and the 2D density of states, and picturing the real well as a "bucket" partially filled with electrons to a depth of 50meV. This leads to a possible solution of 50meV and 20meV for the occupancies of the two sub-bands.
  • #1
ElectricEel1
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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 occupancies of each sub-band in meV

Homework Equations



E_f=hbar2 * π / (m*)[/B]

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 wouldn't have been in the question but not sure how.

Thanks
 
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  • #2
What do you understand by "occupancy"? I think your list of relevant equations is incomplete.
 
  • #3
John Park said:
What do you understand by "occupancy"? I think your list of relevant equations is incomplete.

Im taking a guess since I couldn't find any definition in the course materials but is it the number of occupied states within the band? I am not sure which other equations I need.
 
  • #4
I figure I need E= (hbar^2 * pi^2 * n^2) / (2*m_eff * d^2)

but then I haven't been given effective mass or well width so not sure where to go
 
  • #5
Im taking a guess since I couldn't find any definition in the course materials but is it the number of occupied states within the band?

Do you know of a relation between the energy of the system and the number of levels that are occupied?
 
  • #6
is it the product of the fermi function to find probability and the density of states?
 
  • #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?
 
  • #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.
 
  • #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?
 
  • #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?
 
  • #12
Is it just 50mev and 20mev?

I think it may be. Depends what "it" is, of course.
 

1. What is a quantum well?

A quantum well is a type of semiconductor structure that is used in electronic devices, such as transistors and lasers. It consists of a thin layer of a material, typically a semiconductor, sandwiched between two layers of a different material. This creates a potential well that confines electrons to a two-dimensional region, allowing for unique quantum mechanical properties to emerge.

2. How do electrons occupy sub bands in a quantum well?

In a quantum well, electrons are confined to a two-dimensional region and can only occupy specific energy levels, known as sub bands. These sub bands are created by the quantum confinement of the electrons in the well. As the well becomes narrower, the energy levels become more discrete, and the number of sub bands increases.

3. What factors affect the occupancy of sub bands in a quantum well?

The occupancy of sub bands in a quantum well is affected by several factors, including the dimensions of the well, the materials used, and the temperature. The dimensions of the well determine the energy levels and the number of sub bands, while the materials used affect the electron density and the probability of scattering. Temperature also plays a role in determining the occupancy, as higher temperatures can lead to more thermal energy and a higher occupancy in higher energy sub bands.

4. How does the occupancy in sub bands affect the performance of a quantum well device?

The occupancy of sub bands in a quantum well can greatly impact the performance of a device. In electronic devices, such as transistors, the occupancy of sub bands can affect the conductivity and switching behavior. In lasers, the occupancy can impact the threshold current and the efficiency of light emission. Therefore, proper control and understanding of the occupancy in sub bands is crucial for the optimal performance of quantum well devices.

5. Can the occupancy in sub bands be manipulated?

Yes, the occupancy in sub bands of a quantum well can be manipulated through various techniques. One way is by changing the dimensions of the well, which alters the sub band energy levels. Another method is by applying an external electric field, which can shift the energy levels and affect the occupancy. Additionally, by controlling the temperature and the materials used, the occupancy in sub bands can also be modified. These manipulation techniques are important for tailoring the properties and performance of quantum well devices for specific applications.

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