Charge carrier recombination in amorphous organic semiconductors

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Abstract

Bimolecular recombination of charge carriers in amorphous organic semiconductors is considered. A common feature of these materials is the spatial correlation of the random energy landscape in which hopping transport of charge carriers occurs. The recombination rate constant for such materials was calculated including the case of locally ordered materials. It turns out that the spatial correlation of the random landscape causes violation of the Langevin relation between mobilities of charge carriers and the recombination rate constant. For different sources of energetic disorder the true rate constant can be either less or greater than the corresponding Langevin value. Promising classes of organic semiconductors are indicated where the recombination rate constant can exceed the Langevin value, leading to a potential increase in the efficiency of light generation in organic light-emitting diodes. Organic semiconductors with low recombination constants are promising for the use in solar cells. Features of two-dimensional bimolecular recombination in materials based on oligo- and polythiophenes, in which two-dimensional lamellae are formed, are considered. The formal recombination rate constant becomes dependent on the carrier concentration and effect of spatially correlated energetic disorder leads to the development of various rate constant dependences on the carrier concentration. Analysis of the current-voltage characteristics of organic devices gives the possibility to distinguish between two-dimensional and three-dimensional recombination.

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S. А. Novikov

A.N. Frumkin Institute of Physical Chemistry and Electrochemistry RAS; National Research University Higher School of Economics

Author for correspondence.
Email: novikov@elchem.ac.ru
Russian Federation, Moscow; Moscow

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Supplementary files

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2. Fig. 1. Temperature dependence of the γ/γL ratio for dipole-type disorder and different values ​​of σ (indicated near the corresponding curve in eV). The correlation function has the form c(r) = Aa/r with A = 0.76 (the value of the constant for a simple cubic lattice [27]), and a = 1 nm is the distance to the nearest neighbor; ε = 3.

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3. Fig. 2. Dependence of the ratio γ/γL on l for the attractive additional interaction and the exponential correlation function c(r) = exp(–r/l) for different values ​​of T, K: 150, 200, 250, 300 and 350 from the lower curve to the upper one, respectively; R = 1 nm, σ = 0.1 eV and ε = 3.

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4. Fig. 3. Dependence of the ratio γ/γR on the carrier concentration n/nR for two-dimensional recombination with a repulsive additional interaction and the dipole correlation function c(r) = 0.76a/r with a = 1 nm for different values ​​of σ, eV: 0.05, 0.07, 0.1, 0.13 and 0.15; T = 300 K, R = 1 nm, ε = 3, γR = 2πD. The dotted line with points corresponds to the case of the absence of disorder. Lines located closer to this dividing line correspond to smaller values ​​of σ.

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5. Fig. 4. Dependence of the ratio γ/γR on the carrier concentration n/nR for two-dimensional recombination with attractive (dashed lines) and repulsive (solid lines) additional interactions and the exponential correlation function c(r) = exp(–r/l) with l = 5 nm for different values ​​of σ, eV: 0.05, 0.07, 0.1, 0.13, and 0.15; T = 300 K, R = 1 nm, ε = 3. The dotted line with points shows the case of no disorder. The lines located closer to this dividing line correspond to smaller values ​​of σ. The dotted straight lines show the region where γ ∝ ns.

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6. Fig. 5. Dependence of the exponent s in the ratio γ ∝ ns on kT/σ at q = –1 and c(r) = exp(–r/l). Different curves are shown for l equal to 5 nm, 7 nm, and 10 nm (we use different symbols for different combinations of l and σ, but all the curves are quite close to each other, so we do not give more precise notations for individual curves). For smaller and larger l, the linear region in Fig. 4 is not sufficiently developed.

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7. Fig. 6. I-V characteristics for the case of equal mobilities and also γ = γ0 ns for s = 1 (dashed line) and s = 2 (dashed line). The solid curve corresponds to three-dimensional recombination. K = 1, Gs = 1, E0 = 1 × 105 V/cm and T = 300 K. For L = 1µ and typical values ​​of the corresponding parameters V0 = 1–10 V.

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8. Fig. 7. Dependence of the logarithmic derivative Ω = d(ln J )/d(ln V ) on lnV for different values ​​of s indicated next to the corresponding curve, K = 1 and Gs = 1; the upper curve is the three-dimensional recombination curve. The solid lines show the dependence for µ+ = µ–, the dashed lines show the dependence for µ+ = 2µ–.

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9. Fig. 8. Dependence of γ–/γL (crosses) and 2-γ+/γL (lines) on the charge carrier concentration for different temperatures (indicated near the curves) for the exponential density of states with E0 = 0.01 eV and the dipole correlation function with r0 = 1 nm.

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Note

The article was presented by a participant in the All-Russian Conference “Electrochemistry-2023”, held from October 23 to October 26, 2023 in Moscow at the Institute of Physical Chemistry and Electrochemistry named after A.N. Frumkin RAS.


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