Excitons in Multiple QWs

[phy127]

I have tried solving for the exciton energy in GaAs/AlAs QWs but my calculated results do not agree with published experimental results.

My model in the calculation is just a single GaAs well with AlAs barriers. Using the material parameters of both materials, and the well width, I calculated the heavy-hole exciton energy as

Ehh = E_gap_GaAs + EcQw + EhhQw - Ryd*4

where E_gap_GaAs is the GaAs band gap energy
EcQw and EhhQw are the first energy levels of the QW
Ryd is the 3D Rydberg energy accounting for the binding energy part

However, all my calculations are always smaller than the experimental results even if I remove the binding energy. Now, I'm beginning to wonder what is the effect of multiple QWs or embedding a single QW on a superlatice on the exciton energy.

By the way, I used the finite well model to calculate the quantized energy levels---those that involve the tangent something found in undergrad quantum physics.

QUESTIONS:
1. What is the effect of multiple quantum wells or embedding a single QW in a superlattice on the exciton energy? On the effective band gap (i mean without excitonic effects)?

2. Are there simple models (for multiple QWs) to calculate those energies?

Thanks

 

[Dr Transport]

A couple of comments:

AlAS is an indirect material, did you take that into account.

Your 4Rydberg term, are you taking into account that in a well, the exciton is 2-d in nature.

When you calculated the well energies, what did you assume for the split of the band gaps i.e. 60/40 or what?

other questions will follow. Look for a couple of papers by Madarasz and Szmulowicz from the late '80's to mid '90's.

 

[phy127]

Thanks for your reply Dr. Transport

I know, AlAs is an indirect material. But the well is anyway GaAs. So I just need the AlAs bandgap at the zone center for calculating the confinement energy in the GaAs well. (Am I right in doing this?)

Yes, I completely taken into account the 2D nature of QW excitons. That's why the binding energy is 4 times the 3D Rydberg energy.

I actually used 35/65 for the band offset following 2001 collection of band parameters by Vurgaftman et al.. I also used 60/40, still the same, my calculated energy is lower than the published results.