1. Excitons in Excited States in a Quantum Well
Presented by
G. Vignesh
Research Scholar
Nanostructure Lab, Department of Physics,
Gandhigram Rural Institute – Deemed University,
Gandhigram –
Tamilnadu.

2. Outline Approximations Used: Assumptions: Procedure:
Effective Mass Approximation – Since it plays a Role in Density of States of QW !
Variation Technique – Due to Unknown Hamiltonian !
Assumptions:
Impurity States are Hydrogenic in Nature!
The bound Electron-Hole pair i.e Excitonic States has been treated as in its ground, First excited and Second Excited States. Wherein, Electron and Hole are in their Ground State.
It Deals with only Heavy-hole Excitons.
Procedure:
Effect of confining potential on binding energy and its interband transition energy
Two different confinements – SQUARE and PARABOLIC
Ground and few low lying excited states
Anisotropy in material parameters are involved

3. Motivation to the Present Work
Excitons in Nanoscale
Excitons towards Application
Excitons
Sustainable Tool
of Excitonics
Conquers Delay in Signal Processing
Rapid Photonic Processes
Hope of Foreseen Optical Chip
Effective Carrier-Photon inter conversion
Excitons
An Elementary Excitation
in Solids
Optically Active Source Even at
T >300K
Source with Inherent Magnetism
Condensable Source
of Electronics

4. Square Well Vs Parabolic Well
Excitonics: Importance of Square Quantum Well
Excitonics: Importance of Parabolic Quantum Well
Square Quantum Well
An Ideal Toy Model
Subband Energy Levels Spacing ~ n2
Confines the carrier even at narrow well widths
Provides Large Confinement to carrier
Parabolic Quantum Wells
A Realistic Model
Evenly Spaced Subband Levels
Confines a uniform charge densities
Parabolicity withstands Even at Higher Electric Fields
Directly Determines CB and VB Band offsets

5. Structure of Quantum Wells
Conduction
Band
Valance
AlxGa1-xAs
GaAs
Growth Axis Z
PARABOLIC QUANTUM WELL
Band Offset:
Vc= 60% ΔEg
Vv= 40% ΔEg Eg V
SQUARE QUANTUM WELL V

6. Theoretical Frame Work
Hamiltonian of exciton confined in GaAs/AlxGa­1-xAs quantum well is given by,
The individual Hamiltonian to define the quantized energy along confined and free directions is given by,
Solution to the above equation is where &
The trial wave function of the exciton in its ground, first and second excited states are given as,
Trial Wave Function The confining potential form Trial Wave Function
Subband Energy (Ee) Energy of the exciton can be calculated using Subband Energy (Eh)
The Binding energy values of the exciton:

7. Binding Energy of Excitons in Quantum Well
Lw<50Å:
PQWs An Unbound Exciton State due to Carriers Dispersion.
SQW-possibility of confinement
Larger binding at quasi 2D region
BE(1s)>BE(2p±) >BE(2s).
Exciton in 2p± state possesses symmetry lobes along x-y direction - prevents motion along x-y direction and hence enhances confinement.
At Bulk Limit: 2s and 2p state of SQW tend to merge.
Fig1. Binding Energy Variation of Exciton with Well width

8. Binding Energy Ratio of Excitons
Energy ratio decreases with increase of well width.
Spacing Between these curves is large in PQW -a significant change at larger widths.
The Quasi 2D behavior is observed only in SQW – Confirms Idealistic Nature

9. Interband Transition Energy
The subband structure in the respective wells is primly distinct - there would be significant change in the exciton binding energy!
The subband energy spectra are the essential factor to decide the structural influence on the exciton binding energy and its other physical properties.

10. |Ψ |2 of Excitons PQW SQW Lw=50Å Lw=200Å 1S 2S 2P±z x y
Lw=50Å
Lw=200Å
SQW 1S 2S
2P±
PQW
|Ψ |2 of Excitons
Symmetry of the Impurity Wavefunction get deformed due to quantum confinements - effectively alters the electron hole distance
The probability distribution is maximum for the ground state exciton at center of QW.
Wavefunction dispersion is more in the x-y plane as well width increases. There by reduces binding energy.

11. Conclusion
SQW
PQW
2 is Small
2 is Large
2 is Dispersion is high – Small Confinement
2 - Dispersion is Low – Large Confinement
Lower Transition Energy
Higher Transition Energy even at higher well widths
Bulk limit is approached at 500Å itself
Bulk limit is reached at Well width around 1000Å
The sharp peak of 2 and the observable change in the transition energy of exciton states at higher well widths reveal that PQW favors quantum confinement even at larger size.
As a result there is significant change in the impurity band.
Influences the optical and electrical properties of confined excitons for opto electronic applications.
The Effect of confinement profile on the carrier localization is Important.

12. Thank You