B O O K R E v I E W S

Steed, Pamela A.

doi:10.1179/crn.2011.003

Cited by 10 publications

(20 citation statements)

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“…The result of Eqs. (51)- (57) agrees with this solution if the exponential DOS is inserted into this set of equations [61], as illustrated in Fig. 9.…”

Section: Transition From Dispersive To Non-dispersive Transport: Calcsupporting

confidence: 70%

“…They performed calculations in spirit of those by Grünewald and Thomas [44], concluding that they 'do not expect the results to be qualitatively different for a different choice of g(ε), as long as g(ε) increases strongly with ε'. Since then, numerous researchers used the exponential DOS for ODSs [15,38,39,[45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Furthermore, some researchers claim that the exponential DOS is an accurate approximation of the Gaussian DOS in the energy range in which transistors operate [38,39].…”

Section: Review Articlementioning

confidence: 99%

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Theoretical description of charge transport in disordered organic semiconductors

Baranovskiǐ

2014

Physica Status Solidi (b)

297

365

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Twenty years ago Heinz Bässler published in this journal the seminal review article on charge transport in disordered organic semiconductors [Phys. Status Solidi B 175, 15 (1993)], which has become one of the most popular references in this research field. Thanks to this paper, our understanding of charge transport in disordered organic materials has been essentially improved in the past two decades. New theoretical methods have been developed and new results on various phenomena related to charge transport in disordered organic materials have been obtained. The aim of the current review is to present these new theoretical methods and to highlight the most essential results obtained in their framework. While theoretical consideration in the article by Bässler was based on computer simulations, particular attention in the current review is given to the development of analytical theories. Dependences of charge carrier mobility and diffusivity on temperature, electric field, carrier concentration and on material and sample parameters are discussed in detail. Schematic behaviour of charge carriers within the Gaussian density of states (DOS)

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“…The result of Eqs. (51)- (57) agrees with this solution if the exponential DOS is inserted into this set of equations [61], as illustrated in Fig. 9.…”

Section: Transition From Dispersive To Non-dispersive Transport: Calcsupporting

confidence: 70%

Section: Review Articlementioning

confidence: 99%

Theoretical description of charge transport in disordered organic semiconductors

Baranovskiǐ

2014

Physica Status Solidi (b)

297

365

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“…The variance σ D energetic disorder can thus be extracted from temperaturedependent measurements of the CT absorption or related photoconductivity spectral response. [3,13,25,26] Very recently, Kahle et al [17] used an approach that goes beyond the semiclassical approximation to estimate the extent of static energetic disorder from an analysis of temperature-dependent CT emission spectra. However, an in-depth understanding of how energetic disorder is related to the geometric conformations of the donor and acceptor (macro)molecules and to the characteristics of the blend morphology, is still missing.…”

Section: Introductionmentioning

confidence: 99%

Charge‐Transfer States at Organic–Organic Interfaces: Impact of Static and Dynamic Disorders

Zheng

Tummala

Wang

et al. 2019

Advanced Energy Materials

105

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of this distribution in the semiclassical approximation is given by [15] 2 D 2 B k T σ λ =(1)where λ denotes the reorganization energy related to the electron transfer process between the CT state and the ground state; k B , the Boltzmann constant; and T, the temperature. The static disorder arises from the amorphous nature of the active layers and the positional inequivalency (even in the absence of vibrational motions) of the donor and acceptor (macro)molecules, which results in a time-independent distribution of the CT states with a standard deviation σ S . If both static and dynamic contributions have Gaussian distributions, the standard deviation of the overall (total) disorder σ T can be expressed as [12] T 2 S 2 D 2 σ σ σ = +The knowledge of the dynamic and static disorder contributions in D-A systems is important for an accurate determination of exciton dissociation rates, nonradiative recombination rates, charge transport, and charge-transfer optical transitions. In the semiclassical approximation, accounting for the impact of static disorder on the nonradiative recombination rate (k nr ) results in Equation (3), which is similar to the classical Marcus formula [16] except that the 2term appearing in the latter is replaced with T 2 σ [14,17,18] 2 1 2 exp 2 nr el 2 T 2 CT a 2 T 2 k V E  π σ λ σ ( ) = − −        where V el denotes the electronic coupling between the CT states and the ground state and CT a E , the adiabatic (relaxed) CT energy. Equation (3) underlines that both dynamic and static disorders can have a major impact on the nonradiative recombination rates and consequently on open-circuit voltage losses. Therefore, there is increasing interest, triggered in particular by the rapid advance in the efficiency of organic solar cells, in better understanding the role of disorder on device performance. [9,12,13,[17][18][19][20][21][22][23][24] In the semiclassical approximation used to derive Equation (3), the CT absorption band is also characterized by a Gaussian distribution with a variance given by Equation (2); [13] the static Molecular dynamics simulations are combined with density functional theory calculations to evaluate the impact of static and dynamic disorders on the energy distribution of charge-transfer (CT) states at donor-acceptor heterojunctions, such as those found in the active layers of organic solar cells. It is shown that each of these two disorder components can be partitioned into contributions related to the energetic disorder of the transport states and to the disorder associated with the hole-electron electrostatic interaction energies. The methodology is applied to evaluate the energy distributions of the CT states in representative bulk heterojunctions based on poly-3-hexyl-thiophene and phenyl-C 61 -butyric-acid methyl ester. The results indicate that the torsional fluctuations of the polymer backbones are the main source of both static and dynamic disorders for the CT states as well as for the transport levels. The impact of static and dynamic disorders on radia...

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“…If states above U c are delocalized, then it is natural to consider charge transport using the multiple trapping model [2], and in the opposite case a hopping transport is the more appropriate model. Recently it was suggested that in some amorphous organic semiconductors there is an exponential tail of the DOS [3][4][5][6][7][8][9][10][11][12]. Even in perfect organic crystals, where the bands are very narrow, charge transport at the room temperature is dominated by hopping due to thermally induced dynamic disorder and polaronic effects [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…This divergence indicates the invalidity of Eqs. (5)(6)(7)(8) connected with the transition to the non-equilibrium dispersive transport regime at κ > 1 where the average velocity goes to 0 for the infinite medium.…”

Section: Introductionmentioning

confidence: 99%

Diffusion of a particle in the spatially correlated exponential random energy landscape: Transition from normal to anomalous diffusion

Novikov

2018

The Journal of Chemical Physics

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Diffusive transport of a particle in a spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime for the 1D transport model and found that for slow decaying correlation functions the diffusivity becomes singular at some particular temperature higher than the temperature of the transition to the true non-equilibrium dispersive transport regime. It means that the diffusion becomes anomalous and does not follow the usual ∝ t law. In such situation, the fully developed non-equilibrium regime emerges in two stages: first, at some temperature there is the transition from the normal to anomalous diffusion, and then at lower temperature the average velocity for the infinite medium goes to zero, thus indicating the development of the true dispersive regime. Validity of the Einstein relation is discussed for the situation where the diffusivity does exist. We provide also some arguments in favor of conservation of the major features of the new transition scenario in higher dimensions.

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B O O K R E v I E W S

Abstract: P o P u l a t i o n a n d d e v e l o P m e n t R e v i e w 3 7 (1) : 1 9 1-2 1 0 (m a R c h 2 0 1 1)

Cited by 10 publications

References 0 publications

Theoretical description of charge transport in disordered organic semiconductors

Theoretical description of charge transport in disordered organic semiconductors

Charge‐Transfer States at Organic–Organic Interfaces: Impact of Static and Dynamic Disorders

Diffusion of a particle in the spatially correlated exponential random energy landscape: Transition from normal to anomalous diffusion

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