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Computer simulation of photo induced phenomena

Computer simulation of photo induced phenomena. J ózsef Hegedüs Supervisor: Prof. S ándor Kugler (Budapest). Photo-induced expansion in amorphous Selenium thin-film. t hickness change [nm]. Y. Ikeda and K. Shimakawa: Journal of Non-Crystalline Solids 338–340 (2004) 539–542.

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Computer simulation of photo induced phenomena

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  1. Computer simulation of photo induced phenomena József HegedüsSupervisor:Prof. Sándor Kugler (Budapest)

  2. Photo-induced expansion in amorphous Selenium thin-film thickness change [nm] Y. Ikeda and K. Shimakawa: Journal of Non-Crystalline Solids 338–340 (2004) 539–542

  3. Photo-induced volume change in a-AsSe (expansion) and a-GeSe (contraction). Solid lines represent the changes in thickness. (A: after preparation, B: annealed, C: illuminated and D: annealed again.) a-As2Se3 a-GeSe2 Illumination Illumination Y. Kuzukawa et al.:Journal of Non-Crystalline Solids 227–230 1998 715–718

  4. Photo-induced expansion in amorphous Arsenic Selenide thickness change [nm] Y. Ikeda and K. Shimakawa: Journal of Non-Crystalline Solids 338–340 (2004) 539–542

  5. Selenium: model material of chalcogenide glasses In Greek mythology

  6. Selenium • Physical properties of Selenium: • The building units of Selenium in the condensed phases are chains and rings • Basically two-fold coordinated atoms • Band gap of a-Se: 1.8 eV • Melting temperature of c-Se: 217 OC

  7. Molecular dynamics simulation:Verlet algorithm + The time step (Δt) usually was 2 femtoseconds.

  8. Molecular dynamics simulation • Atomic interaction is handled by self-consistent tight-binding model1-4 • semiempirical method1, parameters are fitted to density functional calculations2-3 • the tight-binding model2-3 describes well the amorphous structure4 • We control the temperature in the simulations by rescaling the velocity of each atom [1] L. Goodwin, A.J. Skinner, and D. G. Pettifor, Europhys. Lett. 9, 701 (1989) [2] D. Molina, E. Lomba, G. Kahl, Phys. Rev. B 60, 6372 (1999). [3] E. Lomba, D. Molina, and M. Alvarez, Phys. Rev. B 61, 9314 (2000) [4] J. Hegedüs and S. Kugler, J. Phys. Condens. Matter 17 6459 (2005)

  9. Photo-excitation of Selenium molecules • Systems studied : • Selenium ring with 8 atoms • Selenium chain with 18 atoms • Modeling photo excitation: • one electron transfered from HOMO to LUMO J. Hegedüs, K. Kohary, S. Kugler, & K. Shimakawa, J. Non-Cryst. Solids, 338 557 (2004)

  10. before excitation after excitation

  11. before excitation after excitation

  12. Photo excitation in amorphous Selenium thin-films: 1) Structural model preparation2) Photo-excitation

  13. A structural model of amorphous Selenium thin-film open open

  14. 2D PBC 3D PBC

  15. Measuring the thickness of the sample thickness: difference between Z coordinates of center of masses of 10 surface atoms

  16. Light excitation electron-hole • Electrons and holes separate after photo excitation on a subpicosecond timescale due to the disorder. • Wecan neglect the Coulomb attraction between them. J. Hegedüs, K. Kohary, D. G.Pettifor, K. Shimakawa, and S. Kugler, Phys. Rev. Lett, 95206803 (2005)

  17. Light excitation electron-hole • We study photo-excited electrons and holes in two separate simulations: • We put one electron to the LUMO (photo-excited electron) • We remove one electron from the HOMO (photo-excited hole)

  18. before illumination (effect of photo excited electron)

  19. during illumination (effect of photo excited electron)

  20. Solid line: length of the breaking bond dotted line: thickness of the sample Light on Light off

  21. The photo-induced local expansion is transient. It can be repeated over and over again. Thickness of the sample

  22. Microscopic structural changes caused by photo-excited holes • We remove one electron from the Highest Occupied Molecular Orbital (HOMO)

  23. Two different kind of bonds: covalent bonds (black) and weak interchain bonds (gray)

  24. „black” bonds (covalent bonds) „gray” bonds (weak interchain covalent bonds)

  25. Before illumination

  26. During illumination

  27. Transient photo-induced weak interchain bond formation

  28. Transient photo-induced volume contraction Thickness of the sample

  29. Rate equation model to describe the macroscopic volume change

  30. The macroscopic volume change is the superposition of several local volume contractions and expansions • We introduce β+ andβ- which are the average volume change caused by oneelectron and by one hole

  31. Total expansion: d+ = β+ ne • Total contraction: d- = β-nh • Number of electrons (ne) = number of holes (nh) • Total volume change is: Δ(t) = ( β+ - β-) n(t) = βΔn(t)

  32. Rate equation for the time development of the number of photo excited electrons and holes after switching on the light: dn(t)/dt = G – C n(t) n(t)(using: ne(t) =nh(t) = n(t)) Rewritten as an equation for volume change:dΔ(t)/dt = G’ – C’ Δ2(t) (using: G’ = G βΔ; C’ = C/βΔ) Δ(t) = (G’/C’)1/2 tanh{(G’C’)1/2 t} (Solution)

  33. 8 Steady state case: t = • Δ(t = ) = (G’/C’)1/2= a Only one independent parameter to fit !!! 8

  34. Rate equation model with a fitting parameter describes the experiment in a-Se light on J. Hegedüs, K. Kohary, D. G.Pettifor, K. Shimakawa, and S. Kugler, Phys. Rev. Lett, 95206803 (2005)

  35. After the light is turned off: G=0 Differential equation for the volume change: dΔ(t)/dt = – C’ Δ2(t) Solution: Δ(t) = a/(aC’t + 1); a = Δ(t = ) 8

  36. Rate equation model with two parameters describes the experiment in a-Se light off

  37. Rate equation model for a-AsSe J. Hegedüs, K. Kohary, S. Kugler,Journal of Non-Crystalline Solids 352 (2006) 1587

  38. Photo-induced expansion in amorphous Arsenic Selenide transient expansion thickness change [nm] metastable expansion Y. Ikeda and K. Shimakawa: Journal of Non-Crystalline Solids 338–340 (2004) 539–542

  39. Rate equation model with two independent parameters describes the experiment in a-AsSe metastable part transient part time[s] time[s] light off light on J. Hegedüs, K. Kohary, S. Kugler,Journal of Non-Crystalline Solids 352(2006) 1587

  40. Summary • Photoexcited electrons  local volume expansion • bond breaking, wave-like structural change • Photoexcited holes  local volume contraction • weak interchain bond formation • Universal model of the macroscopic photo-induced volume change. • describes: photo induced expansion and contraction • Rate equation models describe the time development in the experiments: • in a-Se with one independent parameter (transient changes) • in a-AsSe with twoindependent parameters (transient+metastable changes)

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