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Exciton and Biexciton Energies in GaN / AlN Quantum Dots

Exciton and Biexciton Energies in GaN / AlN Quantum Dots. G. Hönig , A. Schliwa , D. Bimberg , A. Hoffmann Teilprojekt A5. Institut für Festkörperphysik Technische Universität Berlin. gerald.hoenig@physik.tu-berlin.de. c-plane GaN / AlN QDs. Vertical electron -hole separation

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Exciton and Biexciton Energies in GaN / AlN Quantum Dots

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  1. ExcitonandBiexcitonEnergies in GaN/AlN Quantum Dots G. Hönig, A. Schliwa, D. Bimberg, A. Hoffmann Teilprojekt A5 Institut für Festkörperphysik Technische Universität Berlin gerald.hoenig@physik.tu-berlin.de

  2. c-plane GaN/AlN QDs • Verticalelectron-hole separation • Redshiftof X • - X energy inverse proportional to QD-height

  3. Outline Exciton States BiexcitonComplex in Relation toExciton A New Approach: Wigner-crystals

  4. Electron Hole Interaction • Direct Coulomb Interaction • relatedtocharges • attractivebetweenelectronand hole • Exchange Interaction • relatedtospins • repulsivebetweenelectronand hole • ( ifspinsare antiparallel, if parallel = 0 ) • splitsupenergiesrelatedtospinorientation direct exchange

  5. Root of 4 Exciton States Diagonalizationofthe Hamilton-matrixleadstotheeigenstates: & Imaginetheparticlestatesstemfromtheconductionand heavy hole valence band, respectively. (neglectingtheintermixed band structure) The spinswouldbe: Total spinofexcitonstates: BRIGHT: ±1 DARK: ±2 Becauseofthe repulsive natureofexchangeinteractionbetweenelectronand hole, BRIGHT stateshavealwayshigherenergythan DARK states!

  6. ExcitonandBiexciton States 3,4 opticallyactive (BRIGHT) 1,2 opticallyinactive (DARK)

  7. Experimental Findings • full linear polarization • 180° periodicity • 90° phaseshiftbetweenstates • fine-structuresplitting on the order ofmeV C. Kindel, …, Y. Arakawa, G. Hönig, …, A. Hoffmann, D. Bimberg Phys. Rev. B 81, 241309(R) (2010)

  8. Investigationsof FSS Series arecalculatedwith 20% laterallyelongated QD structures. • comparativelyhuge FSS on the order ofmeV • heightincrease (withconstantaspectratio) causesdecreaseof FSS • diameterincrease (withconstantheight) causesdecreaseof FSS • agreementwith experimental findings (blacksquares) C. Kindel, …, Y. Arakawa, G. Hönig, …, A. Hoffmann, D. Bimberg Phys. Rev. B 81, 241309(R) (2010)

  9. Outline Exciton States BiexcitonComplex in Relation toExciton A New Approach: Wigner-crystals

  10. Biexciton Relative toExciton Ebind = 2 EX - EXX

  11. MeanfieldBiexciton Biexciton Exciton Spatialelectron hole separationleadstohigherenergyofthebiexciton! CorrelationEnergy & ConditionalProbabilities

  12. Nature ofCorrelationEnergy Weak lateral hole confinement => hole canmovefreelyat QD bottom => X: Hole cancorrelateitsdensitytotheelectronposition => XX: Hole cancorrelateitsdensitytothepositionsof e, e, h => repulsive interactionsstronglydecrease, => attractiveinteractionsstronglyincrease

  13. Height Dependence Exciton Biexciton

  14. Height Dependence • Ebindincreaseswithdecreasing QD height • Exciton DARK-BRIGHT splittingisimportant • Relative to BRIGHT statesEbindcanbecomepositve

  15. Height Dependence • Ebindincreaseswithdecreasing QD height • Exciton DARK-BRIGHT splittingisimportant • Relative to BRIGHT statesEbindcanbecomepositve Slopes: Theo. = (47 ± 6) meV/eV Exp. = (51 ± 6) meV/eV D. Simeonov, …,N. Grandjean, Phys. Rev. B 77, 075306 (2008)

  16. Outline Exciton States BiexcitonComplex in Relation toExciton A New Approach: Wigner-crystals

  17. Wigner Crystal Biexciton

  18. Wigner Crystal Biexciton Coulddeclareabsenceofsplittedbiexcitonemissionlines in QD sepctrawithvisibleexcitonsplitting.

  19. Experimental Findings Is oneoftheselinesthebiexciton?

  20. Experiment vs. Wigner-XX • Avoidingholes • Attractiveexchangeinteractionbetween parallel hole spins • ≈ 25 meVenergyreductionofbiexcitonstate

  21. Summary • Groundstateexciton: 4 possiblestates • BRIGHT statessplittingofmeV • DARK statessplittingofmEV • Biexcitonandexcitonemissionlinecrossing • New sortof Wigner crystallikebiexcitonspossible • Nosplitupbiexcitonemissionlines

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