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 – 624302. Tamilnadu.

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

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

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

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

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:

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

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

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.

|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.

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.

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