Photogeneration of charge carriers in organic solar cells. The role of nonequilibrium states for electrons and holes

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Abstract

The aim of this study is to consider a photogeneration of charge carriers in nano-structured blends of the donor (D) and acceptor (A) materials. Upon optical excitation photons absorbed in one of these materials produce intramolecular excitons which can diffuse to the D–A interface and form at the interface the interfacial CT states. The interfacial CT state dissociates into a geminate pair of the non-equilibrium mobile electron and hole. In the present study, an empirical model describing thermalization of the non-equilibrium charges within the Coulomb well is proposed. Efficiency of the interfacial CT state dissociation into a pair of free charges is found as a function of the electric field applied, effective temperature and diffusion length of non-equilibrium electron-hole pairs.

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L. V. Lukin

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Author for correspondence.
Email: leonid.v.lukin@gmail.com
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Scheme of charge photoseparation processes involving interfacial CT states: E is the energy of the hot interfacial state CT(i), ECT0 is the energy of the cold state CT0, (e–, h+)neq is the nonequilibrium geminal electron-hole pair, (e–, h+)th is the geminal pair of thermalized electrons and holes.

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3. Fig. 2. The probability of formation of thermalized electron-hole pairs in the Coulomb field as a function of the diffusion length for different Tef and Z0: a – Tef = 600 K (solid lines, black circles) and Tef = 1000 K (dashed lines, white circles); b – Tef = 296 K (solid lines, black squares) and Tef = 400 K (dashed lines, white squares). The numbers next to the arrows are the Z0 values. The following parameter values ​​were used: e = 3.5, rinit = 2.5 nm.

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4. Fig. 3. Dependence of the parameter Y = r2w0exp(−rc/r) on the distance between thermalized electrons and holes at Tef = 600 K (solid lines) and Tef = T = 296 K (dashed lines). The numbers next to the curves are the values ​​of the diffusion length Lth (in nm). The dash-dotted curve shows the dependence of the “Onsager” factor exp(−rc /r) on r. The following parameter values ​​were used: Z0 = 500, T = 296 K, rc = 16.13 nm, ε = 3.5.

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5. Fig. 4. Dependence of the probability of dissociation of the cold interphase state CT0 on the strength of the applied electric field at R = 1 nm (solid lines) and at R = 1.3 nm (dashed lines). The numbers next to the curves are the values ​​of tct µ/η (measured in cm2 V–1).

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6. Fig. 5. Dependence of the probability Q1 on the strength of the applied electric field at Tef = 1000 K (solid lines, tct µ/η = 10–9 cm2 V–1) and Tef = 600 K (dashed lines, tct µ/η = 10–9 cm2 V–1). The dotted curves were obtained for tct µ/η = 10–12 cm2 V–1. The numbers next to the curves and next to the arrow are the values ​​of the diffusion length Lth (in nm). The following parameter values ​​were used: T = 296 K, ε = 3.5, rinit = 2.5 nm, Z0 = 500.

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7. Fig. 6. Dependence of the probability Q1 on the strength of the applied electric field at Tef = 800 K (solid lines, tct µ/η = 10–9 cm2 V–1) and Tef = 400 K (dashed lines, tct µ/η = 10–9 cm2 V–1). Dotted lines show the graphs of Q1(F ), obtained for tct µ/η = 10–12 cm2 V–1. The numbers next to the curves and next to the arrow are the values ​​of the diffusion length Lth (in nm). The following parameter values ​​were used: T = 296 K, ε = 3.5, rinit = 2.5 nm, Z0 = 500.

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8. Fig. 7. Rate constant of the reverse electron transfer as a function of the reaction energy. The values ​​of kET were calculated using equation (B.1) for λ = 0.4 eV (solid lines) and for λ = 0.2 eV (dashed lines). The numbers next to the curves are the values ​​of V0 (in meV); T = 296 K.

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9. Supplement A
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10. Supplement B
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11. Supplement C
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