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Rui Li Journal Club, 02.04.08 Electrical Engineering Boston University

Generalized rate-equation analysis of excitation exchange between silicon nanoclusters and erbium ions. A. J. Kenyon, M. Wojdak, and I. Ahmad Department of Electronic and Electrical Engineering, University College London W. H. Loh and C. J. Oton

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Rui Li Journal Club, 02.04.08 Electrical Engineering Boston University

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  1. Generalized rate-equation analysis of excitation exchange between silicon nanoclusters and erbium ions A. J. Kenyon, M. Wojdak, and I. Ahmad Department of Electronic and Electrical Engineering, University College London W. H. Loh and C. J. Oton Optoelectronics Research Centre, University of Southampton Rui Li Journal Club, 02.04.08 Electrical Engineering Boston University Physics Review B 77, 035318 (2008)

  2. Outline • General form of coupled rate equations: two-level system • Effective excitation cross section • Stretched exponential rise/decay • Complicated rate equation model

  3. Si-ncs Er General form of coupled rate equations: two-level systems

  4. Effective excitationcross section Pacifici’s PhD thesis

  5. Effective excitation cross section is misleading? γis more robust (Weak pumping condition)

  6. Stretched exponential rise

  7. Stretched exponential decay • Auger nonradiative recombination. • Variations of size, shape and environment of Si-ncs. • Energy transfer between ncs. • Different decay channels (radiative and nonradiative recombinations). • Intrinsic property of Si-ncs as indirect-gap semiconductor nanocrystals.Delerue et al. Phys. Rev. B 73, 235318 (2006)

  8. Two energy transfer processes? Fujii et al. J. Appl. Phys. 95 1 (2004)

  9. Si-ncs in SRN decay: three effective decay parameters needed to fit the data We need to develop a rate equation model that includes 3 exponentials and coupling with Er ions

  10. A rate equation modelwith 3 exponentials is sufficiently accurate Weighting factors Fitting parameters: Population constraint Donor emission Si-ncs population is divided into three parts nb1, nb2 and nb3 with different decay times and weighted absorption cross sections.

  11. Origin of non-single exponential rise Gaussian Beam • Inhomogeneity may from • Coupling coefficient γ • Si-ncs decay time τA • Si-ncs absorption cross section σ • Excitation photon flux Φ

  12. Coupling Coefficient g In order to have stretched or multiexponential behavior, we need to have, for at least one class i with gi

  13. Saturation of rise rate • In homogeneity • Up-conversion

  14. Experiments: Si-ncs lifetime shortening Si 49% Underlying assumption: Er does not introduce significant non-radiative contributions Donor lifetime shortening A Gaussian beam is considered

  15. Conclusion • Coupled rate equation model • Validity of effective excitation cross section • Stretched (multiexponential) rise/decay (inhomogeneity τA γσ?Φ?) • Lifetime shortening • How complicated a simple model should we have to fit the experimental data?

  16. Gaussian Beam Energy coupling model with 3 “effective” decays • 2 coupling parameters (fast, slow) • 3 decay amplitudes Si-ncs Er

  17. Thank you !

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