The role of short-ranged energetic correlations in the mobility field dependence of disordered organic materials

We studied the mobility of charge carriers in a model for disordered organic solids where the energies of the localized states are Gaussianly distributed with short-ranged correlations. We obtained an expression for the mobility as a function of electric field, temperature, energetic variance, and correlation radius. The temperature dependence obtained with short-ranged energetic correlations is different from that obtained with power-law decaying energetic correlations and suggests a possible way to distinguish the two types of correlations from the measured mobility. This work also presents a practical way of computing the mobility, applicable to any transport model based on a linear master equation, directly from the matrix of the hopping rates.     

Reformulated space-charge-limited current model and its application to disordered organic systems

We have reformulated a traditional model used to describe the current-voltage dependence of low mobility materials sandwiched between planar electrodes by using the quasi-electrochemical potential as the fundamental variable instead of the local electric field or the local charge carrier density. This allows the material density-of-states to enter explicitly in the equations and dispenses with the need to assume a particular type of contact. The diffusion current is included and as a consequence the current-voltage dependence obtained covers, with increasing bias, the diffusion limited current, the space-charge limited current, and the injection limited current regimes. The generalized Einstein relation and the field and density dependent mobility are naturally incorporated into the formalism; these two points being of particular relevance for disordered organic semiconductors. The reformulated model can be applied to any material where the carrier density and the mobility may be written as a function of the quasi-electrochemical potential. We applied it to the textbook example of a nondegenerate, constant mobility material and showed how a single dimensionless parameter determines the form of the I(V) curve. We obtained integral expressions for the carrier density and for the mobility as a function of the quasi-electrochemical potential for a Gaussianly disordered organic material and found the general form of the I(V) curve for such materials over the full range of bias, showing how the energetic disorder alone can give rise, in the space-charge limited current regime, to an I∝V(n) dependence with an exponent n larger than 2.     

Theoretical study of the transfer integral and density of states in spiro-linked triphenylamine derivatives

We present a method for calculating the parameters that control hopping transport in disordered molecular solids, i.e., the transfer integrals and the distribution of transport site energies. Average values of these parameters are obtained by performing quantum-chemical calculations on a large ensemble of bimolecular complexes in random relative orientations. The method is applied to triphenylamine (TPA) and three differently substituted spiro-linked phenylamine compounds, 2,2',7,7'-tetrakis-(N,N-di-4-methoxyphenylamino)-9,9'-spirobifluorene (spiro-MeOTAD), 2,2'7,7'-tetrakis-(N,N-diphenylhenylamino)-9,9'-spirobifluorene (spiro-TAD), and 2,2',7,7'-tetrakis-(N,N-di-m-methylphenylamino)-9,9'-spirobifluorene (spiro-m-TTB). In the case of TPA, the dependence of the root-mean-square hole transfer integral J on intermolecular separation r for the ensemble of relative orientations is compared with that obtained by performing the same calculations for a fixed, approximately cofacial, orientation of the two TPA molecules. The calculation for the disordered geometry predicts a larger localization radius r0, where J approximately exp(-r/r0), than the calculation for the fixed orientation and is in better agreement with experiment. In the case of the spiro-linked compounds, results from our method are compared with parameters extracted from time-of-flight mobility measurements analyzed with the Gaussian disorder model (GDM). We find that the highest occupied molecular-orbital (HOMO) energies of the bimolecular complexes are distributed on an asymmetric peak, whose width varies in qualitative agreement with the value of the energetic disorder sigma obtained from experimental data using the GDM. The mean-square hole transfer integral varies in accordance with the experimentally determined value of the mobility prefactor micro0. The differences between the differently substituted compounds are interpreted in terms of differences in the spatial extent of the wave function. Spiro-MeOTAD was found to have a greater localization radius, which leads to both a larger transfer integral and a broader distribution of HOMO energies than either of the other compounds. For these compounds, differences in energetic disorder could not be explained in terms of differences in the permanent dipole moment. Our method is proposed as an approximate means of predicting the effect of chemical structure on the values of transport parameters in disordered molecular films.     

Hopping charge transport in organic materials

General properties of the transport of charge carriers (electrons and holes) in disordered organic materials are discussed. It was demonstrated that the dominant part of the total energetic disorder in organic material is usually provided by the electrostatic disorder, generated by randomly located and oriented dipoles and quadrupoles. For this reason this disorder is strongly spatially correlated. Spatial correlation directly governs the field dependence of the carrier drift mobility. Shape of the current transients, which is of primary importance for a correct determination of the carrier mobility, is considered. A notable feature of the electro-static disorder is its modification in the vicinity of the electrode, and this modification takes place without modification of the structure of the material. It is shown how this phenomenon affects characteristics of the charge injection. We consider also effect of inter-charge interaction on charge transport.     

A quantitative analytical model for static dipolar disorder broadening of the density of states at organic heterointerfaces

Understanding the electronic structure of organic-organic heterointerfaces is crucial for many device applications of organic semiconductors. Here we have developed a simple analytical model to describe the effect of static dipolar disorder in a polymer dielectric on the density of states of an adjacent organic semiconductor. The degree of energetic disorder varies strongly with distance from the interface. Using a simple mobility model, we have been able to explain quantitatively both the magnitude as well as the gate voltage dependence of the field-effect mobility for polymer gate dielectrics with different dielectric constants.     

Liquid crystalline metal-free phthalocyanines designed for charge and exciton transport

A joint theoretical and experimental study of the electronic and structural properties of liquid crystalline metal-free phthalocyanines bearing a strong potential for charge and exciton transport has been performed. The synthesis of such compounds has been triggered by quantum chemical calculations showing that: (i) hole transport is favored in metal-free phthalocyanines by their extremely low reorganization energy (0.045 eV) and large electronic splittings; and (ii) the efficiency of energy transfer along the one-dimensional discotic stacks is weakly affected by rotational disorder due to the two-dimensional character of the molecules. We have synthesized two metal-free phthalocyanines with different branched aliphatic chains on the gram scale to allow for a full characterization of their solid-state properties. The two compounds self-organize in liquid crystalline mesophases, as evidenced by optical microscopy, differential scanning calorimetry, X-ray powder diffraction, and molecular dynamics simulations. They exhibit a columnar rectangular mesophase at room temperature and a columnar hexagonal mesophase at elevated temperature.     

The mobility in disordered molecular systems with energies given by a charge-induced dipoles interaction

We investigate the field dependence of the mobility in a model for a disordered molecular system containing spatial and energetic disorders. In this model we assign an isotropic polarizability to each site and take the site energies to be the site polarization energies, the interaction energy of a charge in the given site with the induced dipoles in the neighboring sites. This model was shown, in a previous publication, to contain short-ranged energetic correlations and we show in this work that this correlation produces a charge mobility proportional to the exponential of the square root of the applied field, the Poole-Frenkel dependence observed in various disordered organic materials, over a significant range of fields. We present an expression for the field dependence of the mobility in terms of the average intersite separation and of the isotropic polarizability of the electronic states, the two model parameters.     

Simulation of loss mechanisms in organic solar cells: A description of the mesoscopic Monte Carlo technique and an evaluation of the first reaction method

In this letter we evaluate the accuracy of the first reaction method (FRM) as commonly used to reduce the computational complexity of mesoscale Monte Carlo simulations of geminate recombination and the performance of organic photovoltaic devices. A wide range of carrier mobilities, degrees of energetic disorder, and applied electric field are considered. For the ranges of energetic disorder relevant for most polyfluorene, polythiophene, and alkoxy poly(phenylene vinylene) materials used in organic photovoltaics, the geminate separation efficiency predicted by the FRM agrees with the exact model to better than 2%. We additionally comment on the effects of equilibration on low-field geminate separation efficiency, and in doing so emphasize the importance of the energy at which geminate carriers are created upon their subsequent behavior.     

A room-temperature heptazine core discotic liquid crystal

Heptazine is the fundamental structural and functional unit of graphitic carbon nitrides and has a π-conjugated planar symmetry with semiconducting properties. Molecular self-assembly is one of the key factors to drive the electronic behaviour of π-conjugated organic molecules. To enhance the semiconductivity, heptazine is decorated at its active sites with 2,3,5-tris(dodecyloxy)aniline to get well-organised columnar packing. A novel heptazine-core room-temperature discotic liquid crystal (HDLC) with hexagonal columnar geometry is discovered. The molecular structure and mesomorphic properties of HDLC are investigated by ¹H-NMR, ¹³C-NMR, IR, polarised optical microscopy, differential scanning calorimetry and X-ray diffraction. Photophysical and electrochemical properties of HDLC are studied by UV–vis/fluorescence spectroscopy and cyclic voltammetry (CV), respectively. The energy band gap of HDLC estimated from CV at room temperature is 1.63 eV, which is much narrower than the previously reported band gap for heptazine derivatives. This decrease in the energy band can be attributed to the particular designing of HDLC for columnar packing. As a columnar liquid crystal providing a smooth path to the charge transport, HDLC with such a narrow energy band gap may find applications in organic electronics.     

The origin of charge localization observed in organic photovoltaic materials

Two of the primary hurdles facing organic electronics and photovoltaics are their low charge mobility and the inability to disentangle morphological and molecular effects on charge transport. Specific chemical groups such as alkyl side chains are often added to enable spin-casting and to improve overall power efficiency and morphologies, but their exact influence on mobility is poorly understood. Here, we use two-photon photoemission spectroscopy to study the charge transport properties of two organic semiconductors, one with and one without alkyl substituents (sexithiophene and dihexyl-sexithiophene). We show that the hydrocarbon side chains are responsible for charge localization within 230 fs. This implies that other chemical groups should be used instead of alkyl ligands to achieve the highest performance in organic photovoltaics and electronics.     

Theoretical comparative studies on transport properties of pentacene,pentathienoacene, and 6,13‐dichloropentacene

Pentacene derivative 6,13‐dichloropentacene (DCP) is one of the latest additions to the family of organic semiconductors with a great potential for use in transistors. We carry out a detailed theoretical calculation for DCP, with systematical comparison to pentacene, pentathienoacene (PTA, the thiophene equivalent of pentacene), to gain insights in the theoretical design of organic transport materials. The charge transport parameters and carrier mobilities are investigated from the first‐principles calculations, based on the widely used Marcus electron transfer theory and quantum nuclear tunneling model, coupled with random walk simulation. Molecular structure and the crystal packing type are essential to understand the differences in their transport behaviors. With the effect of molecule modification, significant one‐dimensional π‐stacks are found within the molecular layer in PTA and DCP crystals. The charge transport along the a‐axis plays a dominant role for the carrier mobilities in the DCP crystal due to the strong transfer integrals within the a‐axis. Pentacene shows a relatively large 3D mobility. This is attributed to the relatively uniform electronic couplings, which thus provides more transport pathways. PTA has a much smaller 3D mobility than pentacene and DCP for the obvious increase of the reorganization energy with the introduction of thiophene. It is found that PTA and DCP exhibit lower HOMO (highest occupied molecular orbital) levels and better environmental stability, indicating the potential applications in organic electronics. © 2015 Wiley Periodicals, Inc.     

LEED, STM, and TDS studies of ordered thin films of the rhombus-shaped polycondensed aromatic hydrocarbon C54H22, on MoS2, GeS, and graphite

Low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), and thermal desorption spectroscopy (TDS) are used to study vacuum vapor-deposited molecular thin films of the rhombus-shaped polycondensed aromatic hydrocarbon "rhombus-C54", C54H22, on MoS2 and graphite (0001) and on GeS (010) substrates. It is found that this compound forms well-ordered incommensurate superstructures of the closest packed flat-lying molecules in well-defined azimuthal orientations to the substrate. These films are thermally remarkably stable. By TDS, a monolayer binding energy on graphite of 2.3 eV was derived, whereas the molecules in the second layer were found to be less strongly bound (1.9 eV). This difference allows the preparation of monolayers by desorbing multilayers at the appropriate temperature. Apparently, this molecule is a promising candidate for further studies aiming at applications in organic electronics such as organic field effect transistors or light emitting displays.     

Hopping charge transport in amorphous organic and inorganic materials with spatially correlated random energy landscape

The general properties of the hopping transport of charge carriers in amorphous organic and inorganic materials are discussed. The case where the random energy landscape in the material is strongly spatially correlated is considered. This situation is typical of organic materials with the Gaussian density of states (DOS) and may also be realized in some materials with the exponential DOS. It is demonstrated that the different DOS types can lead to very different functional forms of the mobility field dependence even for the identical correlation function of random energy. Important arguments are provided in favor of the significant contribution of the local orientational order to the total magnitude of energetic disorder in organic materials. A simple but promising model of charge transport in highly anisotropic composites materials is proposed.     

Doping highly ordered organic semiconductors: experimental results and fits to a self-consistent model of excitonic processes, doping, and transport

An in-depth study of n-type doping in a crystalline perylene diimide organic semiconductor (PPEEB) reveals that electrostatic attractions between the dopant electron and its conjugate dopant cation cause the free carrier density to be much lower than the doping density. Measurements of the dark currents as a function of field, doping density, electrode spacing, and temperature are reported along with preliminary Hall-effect measurements. The activation energy of the current, E(aJ), decreases with increasing field and with increasing dopant density, n(d). It is the measured change in E(aJ) with n(d) that accounts primarily for the variations between PPEEB films; the two adjustable parameters employed to fit the current-voltage data proved to be almost constants, independent of n(d) and temperature. The free electron density and the electron mobility are nonlinearly coupled through their shared dependences on both field and temperature. The data are fit to a modified Poole-Frenkel-like model that is shown to be valid for three important electronic processes in organic (excitonic) semiconductors: excitonic effects, doping, and transport. At room temperature, the electron mobility in PPEEB films is estimated to be 0.3 cm(2)/Vs; the fitted value of the mobility for an ideal PPEEB crystal is 3.4 +/- 2.7 cm(2)/Vs. The modified Poole-Frenkel factor that describes the field dependence of the current is 2 +/- 1 x 10(-4) eV (cm/V)(1/2). The analytical model is surprisingly accurate for a system that would require a coupled set of nonlinear tensor equations to describe it precisely. Being based on general electrostatic considerations, our model can form the requisite foundation for treatments of more complex systems. Some analogies to adventitiously doped materials such as pi-conjugated polymers are proposed.     

Influences of molecular packing on the charge mobility of organic semiconductors: from quantum charge transfer rate theory beyond the first-order perturbation

The electronic coupling between adjacent molecules is an important parameter for the charge transport properties of organic semiconductors. In a previous paper, a semiclassical generalized nonadiabatic transition state theory was used to investigate the nonperturbative effect of the electronic coupling on the charge transport properties, but it is not applicable at low temperatures due to the presence of high-frequency modes from the intramolecular conjugated carbon-carbon stretching vibrations [G. J. Nan et al., J. Chem. Phys., 2009, 130, 024704]. In the present paper, we apply a quantum charge transfer rate formula based on the imaginary-time flux-flux correlation function without the weak electronic coupling approximation. The imaginary-time flux-flux correlation function is then expressed in terms of the vibrational-mode path average and is evaluated by the path integral approach. All parameters are computed by quantum chemical approaches, and the mobility is obtained by kinetic Monte-Carlo simulation. We evaluate the intra-layer mobility of sexithiophene crystal structures in high- and low-temperature phases for a wide range of temperatures. In the case of strong coupling, the quantum charge transfer rates were found to be significantly smaller than those calculated using the weak electronic coupling approximation, which leads to reduced mobility especially at low temperatures. As a consequence, the mobility becomes less dependent on temperature when the molecular packing leads to strong electronic coupling in some charge transport directions. The temperature-independent charge mobility in organic thin-film transistors from experimental measurements may be explained from the present model with the grain boundaries considered. In addition, we point out that the widely used Marcus equation is invalid in calculating charge carrier transfer rates in sexithiophene crystals.     

Amphiphilic hairy disks with branched hydrophilic tails and a hexa-peri-hexabenzocoronene core

Amphiphilic discotic molecules with hydrophilic side branches consisting of hexaphenyl hexa-peri-hexabenzocoronene and hexabiphenyl hexa-peri-hexabiphenylcoronene as the aromatic core and hexa-substituted oligoethers as the branched peripheral chains have been synthesized, and their microstructure has been characterized. The discotic molecules based on dibranched oligoether side chains have been observed to self-organize into a well-ordered hexagonal columnar structure within liquid crystalline phases, which possessed an exceptionally high thermal stability and an unusually wide temperature range over >300 degrees C. We suggest that a combination of the large lateral dimensions of the rigid cores and disordered structure of the oxygen-containing branches tails is a driving force to the formation of a highly ordered columnar structure in the bulk state with enhanced molecular segregation. In contrast to the thermotropic phase behavior that favors the formation of highly ordered columnar aggregates through a strong stacking interaction, the hexabenzocoronene cores are packed in a face-on arrangement at the air/water interface and on solid surfaces with surface domains composed of an array of 7 x 7 molecules. We suggest a crablike molecular conformation and cluster-segregated monolayers with 6-fold symmetry and unusual face-on packing on a solid surface. Preliminary spectroscopic studies in the bulk state have shown that the molecules based on a hexaaromatic-substituted core may serve as functional supramolecular materials with high energy transfer characteristic within the columns due to near-perfect columnar ordering, which is unchanged over a wide temperature range. We believe that an absence of the crystallization phenomenon of side-branched oligoether chains is critical for the formation of long-range columnar ordering with strong intracolumnar correlation of conjugated disks important for high carrier mobility.     

The role of exciton hopping and direct energy transfer in the efficient quenching of conjugated polyelectrolytes

The dynamics of fluorescence quenching of a conjugated polyelectrolyte by a cyanine dye are investigated by femtosecond fluorescence up-conversion and polarization resolved transient absorption. The data are analyzed with a model based on the random walk of the exciton within the polymer chain and a long-range direct energy transfer between polymer and dye. We find that rapid intrachain energy migration toward complex sites with the dye leads to the highly efficient energy transfer, whereas the contribution from direct, long-range energy transfer is negligible. We determine the actual density of complexes with the dye along the polymer chain. A clear deviation from calculations based on a constant complex association constant is found and explained by a reduced effective polymer concentration due to aggregation. Altogether, the quenching efficiency is found to be limited by (i) the energetic disorder within the polymer chain and (ii) the formation of loose polymer aggregates.     

Urbach rule in the optical spectra of crystalline and amorphous organic-solids

In this paper we explore the effects of microscopic structural disorder on the low energy optical absorption edges in some crystalline and amorphous organic solids. We advance a theoretical model which incorporates the simultaneous effects of static disorder and of exciton—phonon coupling on Frenkel exciton states. Explicit theoretical expressions were derived for the self energy and for the absorption lineshapes by the introduction of a two-step effective-field approximation, defining an effective exciton—phonon hamiltonian which was subsequently utilized within the framework of a single site average t-matrix approximation for disorder scattering. Numerical results for the low energy lineshapes over a broad temperature range demonstrate that exciton scattering by a static disorder field results in Urbach type low energy absorption tails, where the Urbach slope is temperature independent.     

Master equation approach to charge injection and transport in organic insulators

We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the ebeta square root E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode.