journal article·2010-12-09Open access

Simulation of Hopping Transport Based on Charge Carrier Localization Times Derived for a Two-Level System

Aleksey A. Kocherzhenko, Ferdinand C. Grozema, Sergey A. Vyrko, Nikolai A. Poklonski, Laurens D. A. Siebbeles

The Journal of Physical Chemistry C· Volume 114· Issue 48

Abstract

Incoherent hopping models are commonly used to describe charge transport in many classes of electrically conducting materials. An important parameter in these models is the charge carrier hopping rate or its inverse, the charge carrier lifetime at a localization site. Among the most common approaches to calculating the charge hopping rate are those based on the hydrogen molecular ion (H 2 + ) theory and on the Marcus theory of electron transfer reactions. The former is typically used when describing doped inorganic crystalline semiconductors, while the latter is commonly employed for organic systems. In the present paper the limitations of these approaches are examined and a generalized expression for the charge carrier lifetime at a localization site is proposed, which includes the expressions found from H 2 + theory and Marcus theory as limiting cases. Charge transport simulations based on all three expressions are compared.
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Research context

OpenAlex topics: Conducting polymers and applications · Organic Electronics and Photovoltaics · Electrochemical Analysis and Applications

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Affiliations

Opto-Electronic Materials, Department of Chemical Engineering, Delft University of Technology, Julianalaan 126, 2628BL Delft, The Netherlands, and Department of Semiconductor Physics and Nanoelectronics, Physics Faculty, Belarusian State University, Pr. Nezavisimosti 4, 220030 Mink, Belarus

References (54)

Show source-provided references
1. Bässler H. · Phys. Stat. Sol. B · 1993 · 175 · 1510.1002/pssb.2221750102 ↗
2. Ambegaokar V. · Phys. Rev. B · 1971 · 4 · 261210.1103/PhysRevB.4.2612 ↗
3. Poklonski N. A. · Phys. Stat. Sol. B · 1983 · 117 · 9310.1002/pssb.2221170109 ↗
4. Lunkenheimer P. · Solid State Commun. · 1995 · 93 · 89110.1016/0038-1098(94)00895-7 ↗
5. Okutan M. · Physica B · 2005 · 355 · 17610.1016/j.physb.2004.10.101 ↗
6. Poklonski N. A. · Solid State Commun. · 2009 · 149 · 124810.1016/j.ssc.2009.05.031 ↗
7. Kirkpatrick J. · Phys. Rev. Lett. · 2007 · 98 · 22740210.1103/PhysRevLett.98.227402 ↗
8. Kohary K. · Phys. Stat. Sol. B · 2004 · 241 · 7610.1002/pssb.200303627 ↗
9. Lehmann M. · Chem.—Eur. J. · 2005 · 11 · 334910.1002/chem.200400586 ↗
10. van de Craats A. M. · J. Phys. Chem. B · 1998 · 102 · 962510.1021/jp9828989 ↗
11. Cornil J. · Adv. Mater. · 2002 · 14 · 72610.1002/1521-4095(20020517)14:10<726::AID-ADMA726>3.0.CO;2-D ↗
12. Choi S. H. · Science · 2008 · 320 · 148210.1126/science.1156538 ↗
13. Kocherzhenko A. A. · J. Am. Chem. Soc. · 2009 · 131 · 552210.1021/ja809174y ↗
14. Wilson T. M. · J. Am. Chem. Soc. · 2009 · 131 · 895210.1021/ja902258g ↗
15. Grozema F. C. · J. Am. Chem. Soc. · 2000 · 122 · 1090310.1021/ja001497f ↗
16. Senthilkumar K. · J. Am. Chem. Soc. · 2005 · 127 · 1489410.1021/ja054257e ↗
17. Bixon M. · Proc. Natl. Acad. Sci. · 1999 · 96 · 1171310.1073/pnas.96.21.11713 ↗
18. Giese B. · Acc. Chem. Res. · 2000 · 33 · 63110.1021/ar990040b ↗
19. Peyronneau J. · Nature · 1989 · 342 · 53710.1038/342537a0 ↗
20. Xu Y. · Science · 1998 · 282 · 92210.1126/science.282.5390.922 ↗
22. Mott N. F. · Phil. Mag. · 1969 · 19 · 83510.1080/14786436908216338 ↗
23. Marshall J. M. · J. Phys.: Condens. Matter. · 2008 · 20 · 285210
24. Kubo R. · J. Phys. Soc. Jpn. · 1957 · 12 · 57010.1143/JPSJ.12.570 ↗
25. Baranovskii S. D. · Phys. Stat. Sol. B · 1998 · 205 · 8710.1002/(SICI)1521-3951(199801)205:1<87::AID-PSSB87>3.0.CO;2-P ↗
26. According to ref3, in the three-dimensional case the ratio of the diffusion coefficient for the holes (that move by incoherent hopping) and their mobilityD/μdc=ξhkBT/ecan somewhat exceed the Nernst−Einstein relationkBT/e. Hereξh≥ 1 reflects the fact that with the increase of the root mean square fluctuations,U, of the electrostatic potential in a material, the hopping conductivity of the holes,μdc, decreases faster than their diffusion coefficientD. In particular, at low temperatures (U≫kBT) the ratioD/μhdepends on the bandwidth,U, of the band of quasilocalized states and on the degree to which it is filled with electrons, but only weakly depends onT. This conclusion correlates with the results of Monte Carlo simulations of theDe/μedependence on temperatute for electrons at the tail of the conduction band density of states in crystals, ref25. Also, according to ref13, in the presence of structural disorder eq3is not valid, and the charge carrier mobility must be calculated using eq2and the mean squared displacement ⟨r2(t)⟩ obtained from numerical simulations.
27. Davydov A. S. · 1976
28. Poklonski N. A. · Phys. Solid State · 2005 · 47 · 200510.1134/1.1992598 ↗
29. Holstein T. · Ann. Phys. · 1959 · 8 · 34310.1016/0003-4916(59)90003-X ↗
30. Marcus R. A. · Annu. Rev. Phys. Chem. · 1964 · 15 · 15510.1146/annurev.pc.15.100164.001103 ↗
31. Grozema F. C. · Int. Rev. Phys. Chem. · 2008 · 27 · 8710.1080/01442350701782776 ↗
32. Miller A. · Phys. Rev. · 1960 · 120 · 74510.1103/PhysRev.120.745 ↗
33. Kenkre V. M. · Phys. Rev. Lett. · 1974 · 33 · 80310.1103/PhysRevLett.33.803 ↗
34. Kenkre V. M. · Phys. Rev. B · 1975 · 11 · 174110.1103/PhysRevB.11.1741 ↗
35. Kenkre V. M. · 198210.1007/BFb0041435 ↗
36. Silbey R. · J. Chem. Phys. · 1980 · 72 · 276310.1063/1.439425 ↗
37. Pérez S. · Carbohydr. Res. · 1998 · 314 · 14110.1016/S0008-6215(98)00305-X ↗
38. Scott A. P. · J. Phys. Chem. · 1996 · 100 · 1650210.1021/jp960976r ↗
39. Hoofman R. J. O. M. · Nature · 1998 · 392 · 5410.1038/32118 ↗
40. Grozema F. C. · J. Phys. Chem. A · 2003 · 107 · 597610.1021/jp022379c ↗
41. Yang X. · Nanotechnology · 2007 · 18 · 42402910.1088/0957-4484/18/42/424029 ↗
42. Deng W.-Q. · J. Phys. Chem. B · 2004 · 108 · 861410.1021/jp0495848 ↗
43. Andrienko D. · Phys. Stat. Sol. B · 2008 · 245 · 83010.1002/pssb.200743435 ↗
44. Landau L. D. · 1981
45. Blumenfel’d L. A. · J. Struct. Chem. · 1967 · 8 · 77010.1007/BF00746490 ↗
46. Whittle P. · 200010.1007/978-1-4612-0509-8 ↗
47. Cox D. R. · 1991
48. Poklonski N. A. · Phys. Solid State · 2001 · 43 · 221910.1134/1.1427945 ↗
49. Cramer C. J. · 2002
50. Shklovskii B. I. · 198410.1007/978-3-662-02403-4 ↗
51. Prins P. · Phys. Stat. Sol. B · 2006 · 243 · 38210.1002/pssb.200562719 ↗
52. Senthilkumar K. · J. Chem. Phys. · 2003 · 119 · 980910.1063/1.1615476 ↗
53. Brédas J.-L. · Chem. Rev. · 2004 · 104 · 497110.1021/cr040084k ↗
54. Prins P. · J. Phys. Chem. B · 2006 · 110 · 1465910.1021/jp0626115 ↗