1. Numerical Modeling of Photonic Nanostructures (and Organic Solar Cells) J osep Ferré i Borrull , Mohammad Mahbubur Rahman, Pedro Granero, Josep Pallarès, Lluis F. Marsal [email_address] Universitat Rovira i Virgili Universitat d’Estiu URV. July 2011. N a n o e l e c t r o n I c and P h o t o n I c S y s t e m s

2. Universitat d’Estiu URV. July 2011. Numerical Modeling

4. Introduction to Photonic Nanostructures Photonic Crystals ( More Properly: Photonic Band Gap Materials ) Universitat d’Estiu URV. July 2011.

5. Photonic Crystals Universitat d’Estiu URV. July 2011. ε ( r ) r a Band gap Band gap 0 k 2 π / a π / a -2 π / a - π / a ω - G G allowed allowed Dispersion relation for 1D photonic crystal h 

6. Photonic Crystals: The Band Structure TM TE Normalized Frequency!!! ω a/2πc=a/ λ Universitat d’Estiu URV. July 2011.

7. Introduction to Photonic Nanostructures Photonic Quasicrystals Ordered structures, but not periodic: Universitat d’Estiu URV. July 2011.

8. Introduction to Photonic Nanostructures Random Photonic Nanostructures Random Lasers Universitat d’Estiu URV. July 2011.

10. Photonic Properties of Quasi-random Nanostructures Nanoporous Anodic Alumina: a quasi-random strucuture Photonic Properties??? (e.g. photonic band gap) Universitat d’Estiu URV. July 2011.

11. Photonic Properties of Quasi-random Nanostructures Numerical Method Computational Domain FDTD L Variables: Pore (scatterer radius): r Domain Length: L Universitat d’Estiu URV. July 2011. Source Detector PML

12. Photonic Properties of Quasi-random Nanostructures Universitat d’Estiu URV. July 2011. Finite-Differnce Time-Domain Method (FDTD) Discretization of Maxwell Equations in Space and Time

13. Photonic Properties of Quasi-random Nanostructures Universitat d’Estiu URV. July 2011. Finite-Differnce Time-Domain Method (FDTD) Discretization of Maxwell Equations in Space and Time H 0 H 1 H 2 H 3 H 4 E 1/2 E 3/2 E 5/2 E 7/2 E 9/2 Important Aspect! Boundary Conditions at the Limits of The Computational Space

14. Photonic Properties of Quasi-random Nanostructures Universitat d’Estiu URV. July 2011. a  average interpore distance Averaging over N randomly chosen domains L = 12·a L = 16·a L = 20·a

15. Photonic Properties of Quasi-random Nanostructures Results: quasi-random structure on Si, r/a=0.35 TE Polarization Domain Length Universitat d’Estiu URV. July 2011.

16. Photonic Properties of Quasi-random Nanostructures Results: quasi-random structure on Si, r/a=0.35 TM Polarization Domain Length Universitat d’Estiu URV. July 2011.

17. Photonic Properties of Quasi-random Nanostructures Results: quasi-random structure on Si, L=19a Scatterer radius TE Polarization TM Polarization Universitat d’Estiu URV. July 2011.

18. Photonic Properties of Quasi-random Nanostructures Decreasing trend of the transmittance with  : Simulation of a fully random structure TE Polarization TM Polarization Universitat d’Estiu URV. July 2011.

19. Photonic Properties of Quasi-random Nanostructures Quasi-random crystals with metallic components. Au – Drude-Lorentz Model Good fit between λ=500nm-1000nm Vial et al., PRB 71, 085416 (2005) No scale invariance Universitat d’Estiu URV. July 2011.

20. Photonic Properties of Quasi-random Nanostructures Quasi-random crystals with metallic components. Triangular Lattice.  X Direction Quasi-random. r/a=0.05 Universitat d’Estiu URV. July 2011.

22. Light Trapping in Nanostructured Organic Solar Cells Planar Heterojunction Universitat d’Estiu URV. July 2011. Organic Solar Cells: Morphologies h + e - h + e - h + e - ? h + e - Bulk Heterojunction Nanostructured Heterojunction Donor Acceptor Ex Ex Ex

23. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Diffraction: a possible way for light trapping Incident Light Wavelength:  Diffracted Light Period: p p  

24. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Diffraction: a possible way for light trapping Incident Light Wavelength:  Trapped Light Period: p p <    >90º

25. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Nanostructuring Organic Solar Cells with Templates: Nanoporous Anodic Alumina 500nm 2µm

26. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Nanostructuring Organic Solar Cells with Templates: Nanoporous Anodic Alumina 1 µm

29. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Total Dissipated Power

30. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Reference Cells Bilayer – Planar Heterojunction Effective Medium: n, k: average of P3HT and PCBM 20nm 20nm 10nm 20nm 10nm

31. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Absorption Results. Features much smaller than wavelength. 100nm 1  m Effective Medium a=1.25nm a=12.5nm

32. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Absorption Results. Features smaller than wavelength.

33. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Absorption Results. Feature size the order of wavelength. 100nm 1  m a=200nm a=250nm a=125nm

34. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Absorption Results. Features bigger than wavelength. 100nm 1  m a=400nm a=2  m Bilayer

35. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Absorption Results

36. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Exciton Diffusion. Ex Ex How much absorbed light contributes to current? IPCE  Excitons reaching the D/A interface vs incident photons h  h  Ex Ex

37. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Exciton Diffusion. Planar Heterojunction (Reference) Exciton Concentration (  inc =540nm) 40nm 100nm

38. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Exciton Diffusion. Smallest features (a=12.5nm) Exciton Concentration (  inc =540nm) 40nm 100nm

39. Light Trapping in Nanostructured Organic Solar Cells Universitat d’Estiu URV. July 2011. Exciton Diffusion. Wavelength-order features (a=250 nm) Exciton Concentration (  inc =540nm) 40nm 200nm