Occupancies in sub bands of a quantum well

[ElectricEel1]

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

 

[John Park]

What do you understand by "occupancy"? I think your list of relevant equations is incomplete.

 

[ElectricEel1]

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.

 

[ElectricEel1]

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

 

[John Park]

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?

 

[ElectricEel1]

is it the product of the fermi function to find probability and the density of states?

 

[John Park]

is it the product of the fermi function to find probability and the density of states?

Reference https://www.physicsforums.com/threa...-bands-of-a-quantum-well.908220/#post-5722186

That sounds promising.

Do you understand why the occupancies are apparently measured in meV? I admit that's not clear to me.

 

[ElectricEel1]

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?

 

[John Park]

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.

 

[John Park]

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?

 

[ElectricEel1]

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?

 

[John Park]

Is it just 50mev and 20mev?

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