How to find out DOS in Disordered Organic Semiconductors

1. TIDS15 September 1-5, 2013, Eden Roc Hotel, Sant Feliu de Guíxols (Spain) How to find out DOS in Disordered Organic Semiconductors Sergei Baranovski

2. Organic amorphous semiconductors https://www.google.de/search?q=Organic+semiconductors

3. Organic amorphous semiconductors

4. Computer simulations for a Gaussian DOS:: (G. Schönherr, H. Bässler, M. Silver, Phil. Mag. B 44, 369 (1981))

5. Temperature dependence of the mobility Santos Lemus and Hirsch, Phil. Mag. B 53, 25 (1986) ; Borsenberger, J. Appl. Phys. 68, 6263 (1990); Borsenberger et al., J. Chem. Phys. 94, 5447 (1991)

6. „Unfortunately, the Gaussian form of the DOS in random organic systems prevents closed form analytical solutions of the hopping transport problem.“ Review article[H. Bässler, phys. stat. sol. (b) 175, p.19 (1993)] „Due to the asymmetry of the exchange rates, the Gaussian form of the DOS precludes closed form analytical solutions to the generalized transport equation.“ Review article[P.M. Borsenberger et al., phys. stat. sol. (a) 140, p.11 (1993)] „Gaussian DOS cannot be cast into simple analytical solutions“ A.J. Mozer et al. Phys. Rev. B 71, 035214 (2005)

8. a-Se a-Si:H http://www.posterus.sk/?p=1247

9. M.C.J.M. Vissenberg and M. Matters, PRB 57, 12964 (1998) :

10. Mapping of 4d VRH onto 3d geometry:

11. pss (b), 1979 PRB, 1998 PRL, 2012

12. Organic disordered materials DOS: B. Hartenstein & B. Bässler, J. Non-Cryst. Solids 190, 112 (1995) R. Schmechel, Phys. Rev. B 66, 235206 (2002)

14. DOS: Gaussian or exponential?

15. DOS: Gaussian or exponential?

16. equal to ???

18. e Gaussian DOS versus exponential DOS Fundamental difference !

19. Our claim: DOS is evident by the concentration-dependent mobility  (n)

20. Thermal equilibrium Exponential DOS: most carriers are at the Fermi level cannot compete with

21. Thermal equilibrium Gaussian DOS: most carriers are at the energy cannot compete with

22. Organic disordered materials Gaussian DOS: Equilibrium energy level: H. Bässler, Phys. Stat. Sol. (b) 175, 15 (1993)

23. Enery relaxation in inorganicdisordered materials Exponential DOS: Transition rates:

24. Enery relaxation in inorganicdisordered materials Exponential DOS: Transition rates:

25. Enery relaxation in inorganic disordered materials Exponential DOS: Transition rates:

26. Enery relaxation in inorganic disordered materials Exponential DOS: Transition rates:

27. Enery relaxation in inorganic disordered materials Exponential DOS: Transition rates:

28. Enery relaxation in inorganic disordered materials Exponential DOS: Transition rates:

29. Enery relaxation in inorganic disordered materials Exponential DOS: Transition rates:

30. Enery relaxation in inorganic disordered materials Exponential DOS: Transition rates:

31. Enery relaxation in inorganic disordered materials Exponential DOS: Transition rates:

32. t1 t2>t1 t3>t2 t4>t3 Enery relaxation in inorganic disordered materials Exponential DOS: No stable one-particle picture Dispersive transport

33. Exponentuial DOS: charge carrier mobilityis not well defined (time-dependent! n-dependent!) ------------------------------------- Gaussian DOS: charge carrier mobilityis a well defined quantity even for a diluted system (n-independent!)

34. Exponential DOS Gaussian DOS Transport path  does not depends on n for  always depends on n

35. Exponential DOS Gaussian DOS Transport path  does not depends on n for  always depends on n

36. Exponential DOS x g(E) ~ exp[-E/E0] E E

37. Gaussian DOS x - σ2 / kT g(E) ~ exp[-E2 /2σ2] E E

38. t1 t2>t1 t3>t2 t4>t3 Enery relaxation in inorganic disordered materials Exponential DOS: No stable one-particle picture Dispersive transport

39.  (n) in organic amorphous materials

40. B-i et al., phys. stat. sol. (b) 230, 281 (2002); J. Non-Cryst. Solids 299-302, 416 (2002)

41. B-i et al., phys. stat. sol. (b) 230, 281 (2002); J. Non-Cryst. Solids 299-302, 416 (2002)

42. B-i et al., phys. stat. sol. (b) 230, 281 (2002); J. Non-Cryst. Solids 299-302, 416 (2002)

43. B-i et al., phys. stat. sol. (b) 230, 281 (2002); J. Non-Cryst. Solids 299-302, 416 (2002)

44. DOS in organic disordered materials is not (!) exponential B-i et al., phys. stat. sol. (b) 230, 281 (2002); J. Non-Cryst. Solids 299-302, 416 (2002)

45. Gaussian DOS: most carriers are at the energy Is there such an equilibration energy for DOS ? yes for p>1 Oelerich, Huemmer, B-i, PRL 108, 226403 (2012)

46. How to find p: Oelerich, Huemmer, B-i, PRL 108, 226403 (2012)

47. How to find p: DOS is close to Gaussian! Oelerich, Huemmer, B-i, PRL 108, 226403 (2012)

48. General theory for :

49. General theory for  (n): Oelerich, Huemmer, B-i, PRL 108, 226403 (2012)

50. Howto find p: DOS is close to Gaussian! Oelerich, Huemmer, B-i, PRL 108, 226403 (2012)