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Disorder induced e – h correlations in photo-transients in semiconductors

Disorder induced e – h correlations in photo-transients in semiconductors. A. Kalvov á, B. Velický Institute of Physics, Academy of Sciences of the Czech Republic GA ČR 20 2/04/0585. P rologue. last lecture : Photoexcited transients in disordered semiconductors. P rologue.

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Disorder induced e – h correlations in photo-transients in semiconductors

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  1. Disorder induced e – h correlations in photo-transients in semiconductors A. Kalvová, B. Velický Institute of Physics, Academy of Sciences of the Czech Republic GAČR 202/04/0585

  2. Prologue last lecture: Photoexcited transients in disordered semiconductors Seminar at the Theory Dpt. Disorder induced ...

  3. Prologue last lecture: Photoexcited transients in disordered semiconductors • off-diagonal elements only • c-band disordered opt. pulse Seminar at the Theory Dpt. Disorder induced ...

  4. Prologue last lecture: Photoexcited transients in disordered semiconductors • off-diagonal elements only • c-band disordered opt. pulse Seminar at the Theory Dpt. Disorder induced ...

  5. Prologue today's lecture: Photoexcited transients in disordered semiconductors …disorder induced e – h correlations off-diagonal elements only c-band disordered v-band disordered opt. pulse ? correlated disorder ? Seminar at the Theory Dpt. Disorder induced ...

  6. Reminiscence: optical transitions in crystalline semiconductors in dark in light sharp c-band empty sharp v-band full ideal bands vertical transition Seminar at the Theory Dpt. Disorder induced ...

  7. Reminiscence: optical transitions in crystalline semiconductors in dark in light sharp c-band empty sharp v-band full ideal bands vertical transition realistic bands polaron effect non-vertical transition smeared&renorm. c-band empty smeared&renorm. v-band full Seminar at the Theory Dpt. Disorder induced ...

  8. Reminiscence: optical transitions in crystalline semiconductors in dark in light sharp c-band empty sharp v-band full ideal bands vertical transition realistic bands polaron effect non-vertical transition smeared&renorm. c-band empty smeared&renorm. v-band full exciton effect Coulomb interaction within the photogen. e-h pair Seminar at the Theory Dpt. Disorder induced ...

  9. Reminiscence: optical transitions in crystalline semiconductors in dark in light sharp c-band empty sharp v-band full ideal bands vertical transition realistic bands polaron effect non-vertical transition smeared&renorm. c-band empty smeared&renorm. v-band full final state interaction … e and h interact as they fly away exciton effect Coulomb interaction within the photogen. e-h pair bound state … sharp optical lines in the optical gap scattering states … transition strength within the band of vertical e-h pairs is modified Seminar at the Theory Dpt. Disorder induced ...

  10. Reminiscence: optical transitions in crystalline semiconductors in dark in light sharp c-band empty sharp v-band full ideal bands vertical transition realistic bands polaron effect non-vertical transition smeared&renorm. c-band empty smeared&renorm. v-band full final state interaction … e and h interact as they fly away exciton effect Coulomb interaction within the photogen. e-h pair bound state … sharp optical lines in the optical gap scattering states … transition strength within the band Elliott factor of vertical e-h pairs is modified Seminar at the Theory Dpt. Disorder induced ...

  11. Optical transitions indisordered semiconductor True many – body effects … not considered Sufficiently strong alloy disorder Seminar at the Theory Dpt. Disorder induced ...

  12. Optical transitions in disordered semiconductor True many – body effects … not considered Sufficiently strong alloy disorder Disorder effects: Band mixing Random transition matrix Alloy scattering within each band Kinematic correlation between e and h Transfer of disorder due to optical hybridization Seminar at the Theory Dpt. Disorder induced ...

  13. Optical transitions in disordered semiconductor True many – body effects… not considered Sufficiently strong alloy disorder Disorder effects: Model of independent bands Bandmixing Model of independent bands Random transition matrix Alloy scattering within each band Kinematic correlation between e and h Transfer of disorder due to optical hybridization Seminar at the Theory Dpt. Disorder induced ...

  14. Optical transitions in disordered semiconductor True many – body effects… not considered Sufficiently strong alloy disorder Disorder effects: Model of independent bands Bandmixing Model of independent bands Random transition matrix linear Alloy scattering within each band Kinematic correlation between e and h non-linear Transfer of disorder due to optical hybridization Seminar at the Theory Dpt. Disorder induced ...

  15. Optical transitions in disordered semiconductor True many – body effects… not considered Sufficiently strong alloy disorder Disorder effects: Model of independent bands Polaron like effect band broaden.&renormal. Exciton like effect effective e – h attraction or repulsion Model of independent bands Alloy scattering within each band Kinematic correlation between e and h Transfer of disorder due to optical hybridization Seminar at the Theory Dpt. Disorder induced ...

  16. "Polaron" effects in random alloys periodic reference lattice random non-periodic potential V One configuration “no” wave vector k k-smeared band Seminar at the Theory Dpt. Disorder induced ...

  17. "Polaron" effects in random alloys periodic reference lattice random non-periodic potential V Periodicity restored Effective periodic potential Σ (E) One configuration Configuration average wave vector k restored E-smeared band Seminar at the Theory Dpt. Disorder induced ...

  18. "Exciton" effects in random alloys • One configuration: quasiclassical visualisation • For a smooth potential, use effective mass Hamiltonians: Seminar at the Theory Dpt. Disorder induced ...

  19. "Exciton" effects in random alloys • One configuration: quasiclassical visualisation • For a smooth potential, use effective mass Hamiltonians: Correlated case Anti-correlated case Seminar at the Theory Dpt. Disorder induced ...

  20. "Exciton" effects in random alloys • One configuration: quasiclassical visualisation • For a smooth potential, use effective mass Hamiltonians: Correlated case repulsion Anti-correlated case attraction Seminar at the Theory Dpt. Disorder induced ...

  21. "Exciton" effects in random alloys • One configuration: quasiclassical visualisation • For a smooth potential, use effective mass Hamiltonians: Correlated case repulsion Anti-correlated case attraction Seminar at the Theory Dpt. Disorder induced ...

  22. Model band structure two band semiconductor scattering (chaotization) …elastic collisions on static disorder potencial: correlated disorder: initial condition v-band full, c – band empty - non-random Seminar at the Theory Dpt. Disorder induced ...

  23. two band semiconductor scattering (chaotization) …elastic collisions on static disorder potencial: correlated disorder: initial condition v-band full, c – band empty - non-random Model band structure light pulse resonant … real transition strong … non-linear action, strength Pulse duration m … short compared to back scattering formation long compared to ground period Rabi phase … single pulse characteristic Seminar at the Theory Dpt. Disorder induced ...

  24. Alloy Hamiltonian with band-to-band correlation • completely random alloy with diagonal disorder Model of independent bands …formalized by band projectors non-random diagonal in both Bloch and Wannier basis One electron Hamiltonian for one configuration: Seminar at the Theory Dpt. Disorder induced ...

  25. Alloy Hamiltonian with band-to band correlation • completely random alloy with diagonal disorder Model of independent bands …formalized by band projectors non-random diagonal in both Bloch and Wannier basis band diagonal Bloch Hamiltonians random potencials obey the rule One electron Hamiltonian for one configuration: Seminar at the Theory Dpt. Disorder induced ...

  26. Alloy Hamiltonian with band-to band correlation • completely random alloy with diagonal disorder Model of independent bands …formalized by band projectors non-random diagonal in both Bloch and Wannier basis band diagonal Bloch Hamiltonians random potencials obey the rule Interaction with the pulse interband One electron Hamiltonian for one configuration: Seminar at the Theory Dpt. Disorder induced ...

  27. Alloy Hamiltonian with band-to band correlation • completely random alloy with diagonal disorder Model of independent bands …formalized by band projectors non-random diagonal in both Bloch and Wannier basis random part One electron Hamiltonian for one configuration: non-random part Seminar at the Theory Dpt. Disorder induced ...

  28. Alloy Hamiltonian with band-to-band correlation … continuation • Configuration average dark system: virtual crystal + static potential fluctuations “fully random diagonal disorder”… Wannier quasiatomic levels at a site fluctuate at random independently of other sites (the environment) Seminar at the Theory Dpt. Disorder induced ...

  29. pair correlation function … site diagonal elements only site independent matrix … ….. 2x2 scalar Alloy Hamiltonian with band-to-band correlation … continuation • Configuration average dark system: virtual crystal + static potential fluctuations Seminar at the Theory Dpt. Disorder induced ...

  30. Alloy Hamiltonian with band-to-band correlation … continuation • Configuration average dark system: virtual crystal + static potential fluctuations diagonals …intraband disorder off-diag. … cross-correlation Seminar at the Theory Dpt. Disorder induced ...

  31. Alloy Hamiltonian with band-to-band correlation … continuation • Configuration average dark system: virtual crystal + static potential fluctuations diagonals …intraband disorder off-diag. … cross-correlation Seminar at the Theory Dpt. Disorder induced ...

  32. ?? for general non-linear transient Non-equilibrium Green’s Functions (NGF) Langreth-Wilkins matrix of real-time NGF Seminar at the Theory Dpt. Disorder induced ...

  33. ?? for general non-linear transient Non-equilibrium Green’s Functions (NGF) Langreth-Wilkins matrix of real-time NGF Seminar at the Theory Dpt. Disorder induced ...

  34. ?? for general non-linear transient Non-equilibrium Green’s Functions (NGF) Langreth-Wilkins matrix of real-time NGF Seminar at the Theory Dpt. Disorder induced ...

  35. ?? for general non-linear transient Non-equilibrium Green’s Functions (NGF) Langreth-Wilkins matrix of real-time NGF Seminar at the Theory Dpt. Disorder induced ...

  36. ?? for general non-linear transient Non-equilibrium Green’s Functions (NGF) Langreth-Wilkins matrix of real-time NGF Self-energy … Dyson Equation with resp. to virtual crystal GF Seminar at the Theory Dpt. Disorder induced ...

  37. ?? for general non-linear transient Non-equilibrium Green’s Functions (NGF) Langreth-Wilkins matrix of real-time NGF Self-energy … Dyson Equation with resp. to virtual crystal GF virtual crystal Seminar at the Theory Dpt. Disorder induced ...

  38. ?? for general non-linear transient elastic alloy scatt. … propagators decouple from particle corr. function Non-equilibrium Green’s Functions (NGF) Langreth-Wilkins matrix of real-time NGF Self-energy … Dyson Equation with resp. to virtual crystal GF Seminar at the Theory Dpt. Disorder induced ...

  39. Virtual crystal and dark GF 1st step …elimination of … GF Seminar at the Theory Dpt. Disorder induced ...

  40. Virtual crystal and dark GF 1st step …elimination of … GF • better convergence • dynamical deviation from equilibrium • equilibrium is “dressed” by disorder (… dark polaron analogue) • band diagonal; • after ilumination … dynamical coupling both bands, • band-band statistical correlation Seminar at the Theory Dpt. Disorder induced ...

  41. Non-correlated and correlated GF Seminar at the Theory Dpt. Disorder induced ...

  42. Non-correlated and correlated GF 2nd step …relate correlated case vs. non –correl.case Seminar at the Theory Dpt. Disorder induced ...

  43. Non-correlated and correlated GF 2nd step …relate correlated case vs. non –correl.case • correlation part of the induced selfenergy • measure of correlation • , , Seminar at the Theory Dpt. Disorder induced ...

  44. propagators …closed DE Dyson equations for propagators, T-matrices Seminar at the Theory Dpt. Disorder induced ...

  45. propagators …closed DE Dyson equations for propagators, T-matrices Seminar at the Theory Dpt. Disorder induced ...

  46. Dyson equations for propagators, T-matrices propagators …closed DE symetric form • T-matrices… aditional scattering due to correlation Seminar at the Theory Dpt. Disorder induced ...

  47. Dyson equations for propagators, T-matrices propagators …closed DE symetric form • T-matrices… aditional scattering due to correlation Integral equation for T-matrices We define T-matrix … full non-equilibrium Seminar at the Theory Dpt. Disorder induced ...

  48. Dyson equations for particle correlation functions … play a central role notation for initial condition Compact forms of DEs Seminar at the Theory Dpt. Disorder induced ...

  49. Dyson equations for particle correlation functions … play a central role notation for initial condition Compact forms of DEs coherent part Seminar at the Theory Dpt. Disorder induced ...

  50. Dyson equations for particle correlation functions … play a central role notation for initial condition Compact forms of DEs non-coherent part Seminar at the Theory Dpt. Disorder induced ...

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