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Outline Past Energy transfer Modelling energy transfer Present Spectral conversion for solar cells Up- and Downcon

Modelling Energy transfer using Monte Carlo simulations Andries Meijerink, Timon van Wijngaarden, Linda Aarts, Stefan Scheidelaar, Freddy Rabouw, Harold de Wijn, JuanMa Castillo, Thijs Vlugt Debye Institute, Utrecht University. Outline Past Energy transfer Modelling energy transfer

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Outline Past Energy transfer Modelling energy transfer Present Spectral conversion for solar cells Up- and Downcon

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  1. Modelling Energy transfer using Monte Carlo simulationsAndries Meijerink, Timon van Wijngaarden, Linda Aarts, Stefan Scheidelaar, Freddy Rabouw, Harold de Wijn, JuanMa Castillo, Thijs VlugtDebye Institute, Utrecht University

  2. Outline • Past • Energy transfer • Modellingenergy transfer • Present • Spectralconversionforsolarcells • Up- and Downconversion • ModellingusingMonte Carlo simulations • Examples: Tb-Yb, Pr-Yb, Nd-Yb • Future

  3. Past General equationenergy transfer Transfer rate = interaction D-A x spectral overlap integral

  4. Informationfrom donor decaycurves: Decay donor emissionfor different multipole-multipoleinteractionmechanisms. Distancedependence transfer rate: Dipole-Dipole: R-6 Dipole-Quadrupole: R-8 Quadrupole-Quadrupole: R-10 Angulardependenceusuallyneglected!

  5. Models to fit donor decay curves Inokuti-Hirayama for single-step energy transfer: Yokota-Tanimotofordiffusionlimitedenergy transfer: Problem: homogeneous distribution of acceptors is assumed, notgoodfor short range energy transfer in crystalwith discrete distance distribution between donors and acceptors

  6. Present The sun is hot HarvestingSolar Energy is the onlysolution to meet the worldwidedemand (need?) forenergy vs. Efficiency < 0.1% Efficiency > 10%

  7. Major loss mechanism solar cell • Thermalization loss • Transparancy loss Shockley-Queisser efficiency limit Si Solar Cell: 30% Figure taken from B.S. Richards, Solar Energy Materials & Solar Cells 90, 2329-2337 (2006)

  8. Solutions? Adapt the solar cell: • Tandem solar cells (up to 40% efficient) • Multiple exciton generation Adapt the solar spectrum: • Upconversion of IR to NIR (recovery of lost IR photons) • Downconversion of UV/VIS to NIR (doubling of e-h pairs, reduction of lost excess photon energy) S. Kurtz et al. J. Cryst. Growth 298 (2007) 748

  9. Adapt the solar spectrum • Transparency losses → Upconversion • Thermalisation losses → Downconversion

  10. Prime candidates for spectral conversion:

  11. Downconversion for Solar Cells: 1 VIS 2 IR Possible downconversion schemes: Brainstorm ECN 2003: Pr Yb Yb Er Yb Nd Yb Er

  12. Modellingenergy transfer Crucialforunderstanding up- and downconversion efficiency Cooperative downconversion in GdAl3(BO3)(4): RE3+,Yb3+ (RE=Pr, Tb, and Tm) Q.Y. Zhang, G.F. Yang, G. F.) and Z.H. Jiang, APPLIED PHYSICS LETTERS  91   (2007) 051903 Abstract: An efficient near-infrared (NIR) quantum cutting (QC) in GdAl3(BO3)(4):RE3+,Yb3+ (RE=Pr, Tb, and Tm) phosphors has been demonstrated, which involves the conversion of the visible photon into the NIR emission with an optimal quantum efficiency approaching 200%, by exploring the cooperative downconversion mechanism from RE3+ (RE=Pr, Tb, and Tm) excitons to the two activator ions, Yb3+. The development of NIR QC phosphors could open up a new approach in achieving high efficiency silicon-based solar cells by means of downconversion in the visible part of the solar spectrum to similar to 1000 nm photons with a twofold increase in the photon number. (c) 2007 American Institute of Physics. AnalysisdonewithYokoto-Tanimoto

  13. LUMITRANS http://homepage.tudelft.nl/v9k6y/LumiTrans/index.html • LumiTrans: a computer program to fit luminescencedecaycurves • LumiTrans is a computer program written in Java thancan fit experimentallyobtainedluminescencedecaycurvesusing a single transfer, cooperativeoraccretive model. Itcan account fordipole-dipole (r-6), dipole-quadrupole (r-8) and quadrupole-quadrupole (r-10) interactions. • The model to calculateluminescencedecaycurves is described in detail in: • Quantumcuttingbycooperativeenergy transfer in YbxY(1-x)PO4:Tb3+P. Vergeer, T.J.H. Vlugt, M.H.F. Kox, M.I. den Hertog, J.P.J.M. van der Eerden, A. MeijerinkPhys. Rev. B., 2005, 71, 014119 PDF. • Youcan download the program here (version 0.13, 15-6-2010). It is availableunder the GNU General Public License • Authors: • Juan Manuel CastilloSanchez, Thijs J.H. VlugtDelft University of TechnologyProcess & Energy LaboratoryLeeghwaterstraat 442628CA Delft, The Netherlands • Andries MeijerinkUtrecht UniversityCondensed Matter and InterfacesP.O.Box 80.0003508 TA Utrecht, The Netherlands Input: lattice parameters (a,b,c-α,β,γ) and uniquepositions in unit cell) + decaycurves Fit one curve (for donor concentration x) and simulate the rest.

  14. Tb-Yb Cooperativeenergy transfer: First predictedbyDexter (PRB, 1957) Tb-YbCooperative ET suggestedby Strek et al., J. Lumin. 92 (2001) 229

  15. Decaycurves τrad = 2.30 ms τtr+rad = 0.253 ms

  16. Interaction model: cooperative dipole-dipole Tb3+ is central ion R-6 Tb3+ R’-6 Yb3+ Yb3+

  17. The transfer rate for one configuration (2 shells) Cooperative Accretive

  18. Decaycurves: experiment + simulation: evidence for cooperative mechanism Elementary transfer rate (to 2 Yb nearest neighbours) = 260/s

  19. Pr-Yb • Energy Transfer MechanismPr-YbDownconversion: • 2-step, sequentialor • 1-step, cooperative ?? • Both claimed in the literature

  20. How to distinguish?Model decay curves with Monte Carlo simulations Pr Cooperative: Cross-relaxation: Averaging over 20 000 configs:

  21. Monte Carlo simulation for 20 000 configurations, Dots are data, Drawn lines are fits CR, broken lines Coop Model system: LiYF4:Pr1%,Ybx% Conclusion: CR fits very well (note: 1 fit parameter for all curves!), Coop does not fit at all. In line with expectation: if first order process is possible, it will be first order as second order is ~1000 x less probable

  22. Analyticalsolutions vs. Monte Carlo Fits with shell model, for 2, 4 and 7 nearest neighbor shells, dashed (2), dotted (4) dot-dash(7), MC simulation (drawn line) Fits for 7 NN shells similar to Monte Carlo simulations, but harder to model, especially for lower symmetry crystals and higher order transfer processes.

  23. Analyticalsolutions vs. Monte Carlo Fits with shell model, for 2, 4 and 7 nearest neighbor shells, dashed (2), dotted (4) dot-dash(7), MC simulation (drawn line) New? Notreally: Heber, Siebold and Dornauf: J. Lumin. 22 (1980) 1-16 J. Lumin. 22 (1981) 297-319 Shell model fits shown to workwell Fits for 7 NN shells similar to Monte Carlo simulations, but harder to model, especially for lower symmetry crystals and higher order transfer processes.

  24. Nd-Yb Simpleone- step energy transfer from4F3/2 level of Nd3+ to 2F5/2 level of Yb3+ (phononassisted) Illustration of Monte Carlo program

  25. Emission spectra: efficientenergy transfer

  26. Decaycurves and MC fits γr = 2.55·103 s-1 (τr= 390 µs) and Ctr = 7.07·108 Å6·s-1

  27. Conclusions and Future • Monte Carlo simulations can be used to accurately model energy transfer and distinguish between energy transfer mechanisms • Efficient resonant downconversion by the Tb-Yb couple through cooperative energy transfer and the Pr-Yb couple through sequential two-step ET • Future - More modelling to demonstrate e.g. quad-quad - Extending MC simulations to include energy migration over donor sublattice

  28. Future (2) Ptr>99% Ptr>50% Initialresultson Monte Carlo Modelling 2-step World Cup Transfer ?? Distancedependence??

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