Abstract
Recently, the dependence of exciton diffusion length \( (L_{D} ) \) on some photophysical parameters of organic solids has been experimentally demonstrated, however no systematic theoretical analysis of this phenomenon has been carried out. We have conducted a theoretical study by using the Förster resonance energy transfer and Dexter carrier transfer mechanisms together with the Einstein–Smoluchowski diffusion equation to derive analytical models for the diffusion lengths \( (L_{D} ) \) and diffusion coefficients \( (D) \) of singlet \( (S) \) and triplet \( (T) \) excitons in organic solids as functions of spectral overlap integral \( (J) \), photoluminescence (PL) quantum yield \( (\phi_{D} ) \), dipole moment \( (\mu_{T} ) \) and refractive index \( (n) \) of the photoactive material. The exciton diffusion lengths and diffusion coefficients in some selected organic solids were calculated, and we found that the singlet exciton diffusion length \( (L_{D}^{S} ) \) increases with \( \phi_{D} \) and J, and decreases with n. Also, the triplet exciton diffusion length \( (L_{D}^{T} ) \) increases with \( \phi_{D} \) and decreases with \( \mu_{T} \). These may be achieved through doping the organic solids into broad optical energy gap host materials as observed in previous experiments. The calculated exciton diffusion lengths are compared with experimental values and a reasonably good agreement is found between them. The results presented are expected to provide insight relevant to the synthesis of new organic solids for fabrication of bulk heterojunction organic solar cells characterized by better power conversion efficiency.
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H. Kang, G. Kim, J. Kim, S. Kwon, H. Kim, and K. Lee, Adv. Mater. 28, 7821 (2016).
M.C. Scharber and N.S. Sariciftci, Prog. Polym. Sci. 38, 1929 (2013).
R.F. Service, Science 332, 293 (2011).
T. Kietzke, Adv. Optoelectron. 2007, 1 (2007).
M.R. Narayan and J. Singh, Phys. Status Solidi C 9, 2386 (2012).
Y. Divayana and X.W. Sun, Org. Electron. 11, 67 (2010).
K. Feron, X. Zhou, W.J. Belcher, and P.C. Dastoor, J. Appl. Phys. 111, 044510 (2012).
B.P. Rand, J. Genoe, P. Heremans, and J. Poortmans, Prog. Photovolt. 15, 659 (2007).
B.C. Thompson and J.M.J. Fréchet, Angew. Chem. Int. Ed. 47, 58 (2008).
G. Dennler, M. Scharber, and C.J. Brabec, Adv. Mater. 21, 1323 (2009).
V. Stehr, B. Engels, C. Deibel, R.F.J. Fink, C. Deibel, and J. Pflaum, J. Chem. Theory Comput. 10, 1242 (2014).
R.C. Powell and Z.G. Soos, J. Lumin. 11, 1 (1975).
B.J. Mulder, Philips Res. Rep. 22, 142 (1967).
D. Kurrle and J. Pflaum, Appl. Phys. Lett. 92, 133306 (2008).
H. Tamura and Y. Matsuo, Chem. Phys. Lett. 598, 81 (2014).
R.R. Lunt, N.C. Giebink, A. Anna, J.B. Benziger, and S.R. Forrest, J. Appl. Phys. 105, 053711 (2009).
S.R. Scully and M.D. McGehee, J. Appl. Phys. 100, 034907 (2006).
S.R. Yost, E. Hontz, S. Yeganeh, and T. Van Voorhis, J. Phys. Chem. C 116, 17369 (2012).
Y. Terao, H. Sasabe, and C. Adachi, Appl. Phys. Lett. 90, 103515 (2007).
B. Movaghar, M. Grünewald, B. Ries, H. Bassler, and D. Würtz, Phys. Rev. B 33, 5545 (1986).
M.C. Heiber and A. Dhinojwala, J. Chem. Phys. 137, 014903 (2012).
S.M. Menke and R.J. Holmes, in 40th IEEE Photovoltaic Specialist Conference (2014), p. 51.
S. Raisys, K. Kazlauskas, M. Daskeviciene, T. Malinauskas, V. Getautis, and S. Jursenas, J. Mater. Chem. C 2, 4792 (2014).
A.K. Topczak, R. Tobias, B. Engels, W. Brütting, and J. Pflaum, Phys. Rev. B 89, 201203(R) (2014).
H.-Y. Hsu, J.H. Vella, J.D. Myers, J. Xue, and K.S. Schanze, J. Phys. Chem. C 118, 24282 (2014).
Y. Shao and Y. Yang, Adv. Mater. 17, 2841 (2005).
E. Engel, K. Leo, and M. Hoffmann, Chem. Phys. 325, 170 (2006).
V. Bulović and S.R. Forrest, Chem. Phys. 210, 13 (1996).
W.A. Luhman and R.J. Holmes, Adv. Funct. Mater. 21, 764 (2011).
J.K. Bergemann and S.R. Forrest, Appl. Phys. Lett. 99, 243303 (2011).
S.-B. Rim, R.F. Fink, J.C. Schöneboom, P. Erk, and P. Peumans, Appl. Phys. Lett. 91, 173504 (2007).
D.E. Markov, J.C. Hummelen, P.W.M. Blom, and A.B. Sieval, Phys. Rev. B 72, 045216 (2005).
S.R. Scully, P.B. Armstrong, C. Edder, J. Fréchet, and M.D. McGehee, Adv. Mater. 19, 2961 (2007).
R.R. Lunt, J.B. Benziger, and S.R. Forrest, Adv. Mater. 22, 1233 (2010).
B.P. Rand, D. Cheyns, K. Vasseur, N.C. Giebink, S. Mothy, Y. Yi, V. Coropceanu, D. Beljonne, J. Cornil, J.-L. Bredas, and J. Genoe, Adv. Funct. Mater. 22, 2987 (2012).
S. Cook, A. Furube, R. Katoh, and L. Han, Chem. Phys. Lett. 478, 33 (2009).
A.J. Lewis, A. Ruseckas, O.P.M. Gaudin, G.R. Webster, P.L. Burnand, and I.D.W. Samuel, Org. Electron. 7, 452 (2006).
P.E. Shaw, A. Ruseckas, and I.D.W. Samuel, Adv. Mater. 20, 3516 (2008).
Z. Masri, A. Ruseckas, E.V. Emelianova, L. Wang, A.K. Bansal, A. Matheson, H.T. Lemke, M.M. Nielsen, H. Nguyen, O. Coulembier, P. Dubois, D. Beljonne, and I.D.W. Samuel, Adv. Energy Mater. 3, 1445 (2013).
O.V. Mikhnenko, H. Azimi, M. Scharber, M. Morana, P.W.M. Blom, and M.A. Loi, Energy Environ. Sci. 5, 6960 (2012).
O. Mikhnenko, J. Lin, Y. Shu, J.E. Anthony, P.W.M. Blom, T.-Q. Nguyen, and M.A. Loi, Phys. Chem. Chem. Phys. 14, 14196 (2012).
F.S. Steinbacher, R. Krause, A. Hunze, and A. Winnacker, Phys. Status Solidi A 209, 340 (2012).
T. Förster, Discuss. Faraday Soc. 27, 7 (1959).
J.R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd ed. (Baltimore: Springer, 2006), pp. 1–475.
S.E. Braslavsky, E. Fron, H.B. Rodriguez, E.S. Roman, G.D. Scholes, G. Schweitzer, B. Valeur, and J. Wirz, Photochem. Photobiol. Sci. 7, 1444 (2008).
M. Pope and C.E. Swenberg, Electronic Processes in Organic Crystals (Oxford: Oxford Univ Press, 1982).
D.L. Dexter, J. Chem. Phys. 21, 836 (1953).
J.A. Freund and T. Pöschel (eds.), in Stochastic Processes in Physics, Chemistry, Biology, Lecture Notes in Physics, vol 557 (Springer, Berlin, 2000), pp. 85–107.
R.C. Hilborn, Am. J. Phys. 50, 982986 (1982).
A.C. Jacko and B.J. Powell, Chem. Phys. Lett. 508, 22 (2011).
A.K. Bansal, W. Holzer, A. Penzkofer, and T. Tsuboi, Chem. Phys. 330, 118 (2006).
Y. Kawamura, H. Sasabe, and C. Adachi, Jpn. J. Appl. Phys. 43, 7729 (2004).
A. Nollau, M. Hoffmann, K. Floreck, T. Fritz, and K. Leo, J. Appl. Phys. 87, 7802 (2000).
X. Cao, B. Hu, and P. Zhang, J. Phys. Chem. Lett. 4, 2334 (2013).
Y. Noh, C. Lee, and J. Kima, J. Chem. Phys. 118, 2853 (2003).
M. Tabachnyk, B. Ehrler, S. Bayliss, R.H. Friend, and N.C. Greenham, Appl. Phys. Lett. 103, 153302 (2013).
Y. Liu, M.A. Summers, S.R. Scully, and M.D. McGehee, J. Appl. Phys. 99, 093521 (2006).
Y. Tamai, H. Ohkita, H. Benten, and S. Ito, Chem. Mater. 26, 2733 (2014).
T. Fushimi, A. Oda, H. Ohkita, and S. Ito, J. Phys. Chem. B 108, 18897 (2004).
J.E. Kroeze, T.J. Savenije, L.P. Candeias, J.M. Warman, and L.D.A. Siebbeles, Sol. Energy Mater. Sol. Cells 85, 189 (2005).
E.B. Namdas, A. Ruseckas, I.D.W. Samuel, S.-C. Lo, and P.L. Burn, Appl. Phys. Lett. 86, 091104 (2005).
Y. Kawamura, K. Goushi, J. Brooks, J.J. Brown, H. Sasabe, and C. Adachi, Appl. Phys. Lett. 86, 071104 (2005).
G.P. Kushto, W.H. Kim, and Z.H. Kafafi, Appl. Phys. Lett. 86, 093502 (2005).
S. Ko, D.H. Kim, A.L. Ayzner, S.C.B. Mannsfeld, E. Verploegen, A.M. Nardes, N. Kopidakis, M.F. Toney, and Z. Bao, Chem. Mater. 27, 1223 (2015).
L.C. Groff, X. Wang, and J.D. McNeill, J. Phys. Chem. C 117, 25748 (2013).
A. Haugeneder, M. Neges, C. Kallinger, W. Spirkl, U. Lemmer, J. Feldmann, S.E. Harth, A. Gügel, and K. Müllen, Phys. Rev. B 59, 15346 (1999).
A. Holzhey, C. Uhrich, E. Brier, E. Reinhold, P. Bäuerle, K. Leo, and M. Hoffmann, J. Appl. Phys. 104, 064510 (2008).
J.J.M. Halls, K. Pichler, R.H. Friend, S.C. Moratti, and A.B. Holmes, Appl. Phys. Lett. 68, 3120 (1996).
M. Theander, A. Yartsev, D. Zigmantas, V. Sundström, W. Mammo, M.R. Andersson, and O. Inganäs, Phys. Rev. B 61, 12957 (2000).
J.E. Kroeze, T.J. Savenije, M.J.W. Vermeulen, and J.M. Warman, J. Phys. Chem. B 107, 7696 (2003).
L. Lu¨er, H.J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.H. Huisman, and D. de Leeuw, Org. Electron. 5, 83 (2004).
H. Choukri, A. Fischer, S. Forgeta, S. Chénais, and M. Castex, Appl. Phys. Lett. 89, 183513 (2006).
D.R. Kozub, K. Vakhshouri, S.V. Kesava, C. Wang, A. Hexemer, and E.D. Gomez, Chem. Commun. 48, 5859 (2012).
P. Peumans, A. Yakimov, and S.R. Forrest, J. Appl. Phys. 93, 3693 (2003).
M. Guide, J.D.A. Lin, C.M. Proctor, J. Chen, C. García-Cervera, and T.-Q. Nguyen, J. Mater. Chem. A 2, 7890 (2014).
H.R. Kerp and E.E. van Faassen, Nord. Hydrol. 1, 1761 (1999).
A. Huijser, T.J. Savenije, J.E. Kroeze, and L.D.A. Siebbeles, J. Phys. Chem. B 109, 20166 (2005).
J. Yang, F. Zhu, B. Yu, H. Wang, and D. Yan, Appl. Phys. Lett. 100, 103305 (2012).
M. Sim, J. Shin, C. Shim, M. Kim, S.B. Jo, J.-H. Kim, and K. Cho, J. Phys. Chem. C 118, 760 (2013).
J.D.A. Lin, O.V. Mikhnenko, T.S. van der Poll, G.C. Bazan, and T.-Q. Nguyen, Adv. Mater. 27, 2528 (2015).
W. Zhang, J. Yu, W. Wen, and Y. Jiang, J. Lumin. 131, 1260 (2011).
J. Wünsche, S. Reineke, B. Lüssem, and K. Leo, Phys. Rev. B 81, 245201 (2010).
M. Lebental, H. Choukri, S. Chenais, S. Forget, A. Siove, B. Geffroy, and E. Tutis, Phys. Rev. B 79, 165318 (2009).
W.A. Luhman and R.J. Holmes, Appl. Phys. Lett. 94, 153304 (2009).
N. Matsusue, S. Ikame, Y. Suzuki, and H. Naito, J. Appl. Phys. 97, 123512 (2005).
M. Samiullah, D. Moghe, U. Scherf, and S. Guha, Phys. Rev. B 82, 205211 (2010).
G.M. Akselrod, P.B. Deotare, N.J. Thompson, J. Lee, W.A. Tisdale, M.A. Baldo, V.M. Menon, and V. Bulovic´, Nat. Commun. 5, 3646 (2014).
A.D. Poletayev, J. Clark, M.W.B. Wilson, A. Rao, Y. Makino, S. Hotta, and R.H. Friend, Adv. Mater. 26, 919 (2014).
P. Irkhin and I. Biaggio, Phys. Rev. Lett. 107, 017402 (2011).
G. Schwartz, S. Reineke, T.C. Rosenow, K. Walzer, and K. Leo, Adv. Funct. Mater. 19, 1319 (2009).
N.C. Giebink, Y. Sun, and S.R. Forrest, Org. Electron. 7, 375 (2006).
V. Cleave, G. Yahioglu, P.L. Barny, R.H. Friend, and N. Tessler, Adv. Mater. 11, 285 (1999).
X. Li and M.L. Tang, Chem. Commun. 53, 4429 (2017).
X. Gong, S.-H. Lim, J.C. Ostrowski, D. Moses, C.J. Bardeen, and G.C. Bazan, J. Appl. Phys. 95, 948 (2004).
J. Kalinowski, W. Stampor, M. Cocchi, D. Virgili, V. Fattori, and P. Di Marco, Chem. Phys. 297, 39 (2004).
Y. Kawamura, J. Brooks, J.J. Brown, H. Sasabe, and C. Adachi, Phys. Rev. Lett. 96, 017404 (2006).
J. Singh, M.R. Narayan, and D. Ompong, J. Phys: Conf. Ser. 619, 012030 (2015).
X. Duan, Y. Huang, Y. Cui, J. Wang, and C.M. Leiber, Nat. 409, 66 (2001).
Y.A. Vlasov, N. Yao, and D.J. Norris, Adv. Mater. 11, 165 (1999).
A. Ryasnyanskiy and I. Biaggio, Phys. Rev. B. 84, 193203 (2011).
M.R. Narayan and J. Singh, J. Appl. Phys. 114, 073510 (2013).
Z. He, C. Zhong, S. Su, M. Xu, H. Wu, and Y. Cao, Nat. Photon. 6, 591 (2012).
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Yeboah, D., Singh, J. Dependence of Exciton Diffusion Length and Diffusion Coefficient on Photophysical Parameters in Bulk Heterojunction Organic Solar Cells. J. Electron. Mater. 46, 6451–6460 (2017). https://doi.org/10.1007/s11664-017-5679-2
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DOI: https://doi.org/10.1007/s11664-017-5679-2