Correlated Disorder Model Research Articles

Electron Transport in a Fluorine-Based Copolymer: Evidence for the Absence of Correlated Disorder

Spatial correlation between two unordered transmission site energies of semiconducting polymers applied to organic electronic devices can impact the charge carrier mobility (CCM). It has been uncertain if this spatial correlation exists in relevant polymers. This study focuses on electronic transmission in a fluorene-based copolymer called poly[(9,9-di-n-octylfluorenyl-2,7-diyl)-alt-(benzo[2,1,3]thiadiazol-4,8-diyl)](F8BT) commonly applied to polymer light-emitting diodes (PLEDs). In terms of the F8BT-based electron-only device (EOD), the layer thickness dependence (Ltd.) of the current density is analyzed. Two models are adopted, with the intention of depicting the electronic transmission: the improved extended Gaussian disorder model(IEGDM) and extended correlated disorder model (ECDM). The IEGDM considers the dependence of the CCM upon electric field, temperature, and carrier density, incorporating the influences of Arrhenius and non-Arrhenius temperature dependence. In addition, the ECDM includes or excludes the spatial correlations between two site energies. Current-voltage J – V features are analyzed using IEGDM and ECDM. The two models provide eminent fits. A contrast between the parameters of the models reveals a more practical intersite distance by IEGDM (1.3 nm) than the value by ECDM (0.4 nm). This suggests that correlations between the site energies may not be significant or may be absent. Therefore, through the analysis, the evidence is provided for the absence of correlated disorders.

Analysis of Charge Transport in Polymer: Non-Fullerene Blend: Evidence for the Absence of Correlated Disorder

Recently, rapid development of non-fullerene acceptors has attracted considerable attention to theirs charge transport. In this paper, charge transport and spatial correlations between the site energies in the blend of polymer PBDB-T derivative PM6 and non-fullerene acceptor Y6 are investigated. From an analysis of the temperature dependence of current density-voltage (J – V ) characteristics of hole-only and electron-only devices based on PM6:Y6 blend, it is found that consistent descriptions with equal quality are obtained using both the improved extended Gaussian disorder model (IEGDM) and the extended correlated disorder model (ECDM), within which spatial correlations between the transport site energies are absent and are included, respectively. By comparing model parameters with the typical values of organic materials, we view more realistic intersite distance obtained using the IEGDM compared to the value obtained using the ECDM as an indication that in PM6:Y6 blend correlations between the transport site energies are absent or play a minor role. Furthermore, it is found that energetic disorder is larger for hole than for electron in PM6:Y6 blend, and electron transport is intrinsically superior to hole transport.

Electron Transport in Donor-Acceptor Copolymer and Methanofullerene Derivative Organic Photovoltaic Blend

Recently, organic photovoltaics (OPVs) based on the blends of donor–acceptor (D–A) copolymers as efficient p-type materials and fullerene derivatives as acceptors have attracted considerable attention. In this paper, electron transport and electrical properties in a blend of D–A copolymer DTS-C0(F2) and methanofullerene derivative PC71BM are investigated. From an analysis of the temperature dependence of the current density–voltage (J − V) characteristics of electron-only device based on DTS-C0(F2):PC71BM blend, it is found that consistent descriptions for the experimental measurements are obtained using both the improved extended Gaussian disorder model (IEGDM) and the extended correlated disorder model (ECDM), within which spatial correlations between the transport site energies are absent and are included, respectively. By comparing the model parameters with the typical values of organic semiconductors, we view the more realistic intersite distance obtained using the IEGDM (1.9 nm) compared to the value obtained using the ECDM (0.48 nm) as an indication that in DTS-C0(F2):PC71BM blend correlations between the transport site energies are absent. Furthermore, it is shown that the effective mobility in DTS-C0(F2):PC71BM blend gradually increases with increasing temperature.

Entanglement contour in the disordered electronic systems

We investigate entanglement contour of a one-dimensional non-interacting electronic systems with two different models of the static disorder. We obtain the scaling behavior of entanglement contour for the standard Anderson model at zero temperature. We show that the exponential scaling of the entanglement contour leads a universal area law of entanglement entropy. On the other hand, the power-law scaling of entanglement contour reflects the logarithmic scaling law of entanglement entropy. Furthermore, we demonstrate entanglement contour as a theoretical tool for the characterization of quantum phase transition in condensed matter problems. More precisely, we numerically explore the scale-invariant feature of the scaled entanglement contour in the vicinity of metal–insulator transition for the power-law correlated disorder model. • We report the numerical calculations of the entanglement contour in the disordered electronic systems. • The decay of entanglement contour reflects the scaling law of entanglement entropy. • Entanglement contour is considered as a theoretical tool for the characterization of quantum phase transition in condensed matter problems.

Probing the Global Delocalization Transition in the de Moura-Lyra Model with the Kernel Polynomial Method

In this paper, we report numerical calculations of the localization length in a non-interacting one-dimensional tight-binding model at zero tem¬perature, holding a correlated disorder model with an algebraic power-spectrum (de Moura-Lyra model). Our calculations were based on a Kernel Polynomial implementation of the Thouless formula for the inverse localization length of a general nearest-neighbor 1D tight-binding model with open boundaries. Our results confirm the delocalization of all eigenstates in de Moura-Lyra model for α > 1 and a localization length which diverges as ξ ∝ (1 – α)–1 for α → 1–, at all energies in the weak disorder limit (as previously seen in [12]).

Optimization of the host–guest system within an OLED using different models of mobility

To optimize the host–guest system of organic light emitting devices (OLEDs), it were performed simulations by doping a small molecule organic semiconductor (acting as host) with the transition organometallic complex known as Ir(ppy)2(acac) (acting as a guest). The simulation was carried out using simOLED with different mobility models: the Pool–Frenkel Model (PFM), the Extended Gaussian Disorder Model (EGDM) and Extended Correlated Disorder Model (ECDM), with the aim to determine the magnitude of some parameters like temperature, applied electric field, film thickness and charge carrier density that improve the electrical and optical properties of OLEDs with a more simplified structure like ITO/CBP/CBP:Ir(ppy)2(acac)/TPBi/LiF/Al.

Charge Carrier Dynamics of Polymer:Fullerene Blends: From Geminate to Non‐Geminate Recombination

The charge carrier dynamics of a new polymer‐fullerene blend are examined on the femtosecond to the millisecond time scale. The full time range is globally fitted using a chemical reaction rate model that includes all key processes, charge generation, energy transfer, charge separation, and recombination, over the full 12 orders of magnitude in time and a factor of 33 in light intensity. Particular attention is paid to the charge recombination processes and it is found that they are highly material specific. Comparison of the dynamics to those of a previously studied polymer:fullerene blend reveals that while for one blend the recombination dynamics are mainly controlled by geminate recombination, the charge recombination in the presently studied polymer:fullerene blend are entirely controlled by non‐geminate electron‐hole recombination. Carrier density dependence of the non‐geminate recombination rate is analyzed and a correlated disorder model of site energies is proposed to explain the observed dependency.

Effects of Gaussian disorder on charge carrier transport and recombination in organic semiconductors

AbstractIn this review, we discuss recent advances in our understanding of charge transport and exciton generation in disordered organic semiconductors with a Gaussian DOS, with a focus on applications to organic light‐emitting diodes (OLEDs). Three‐dimensional (3D) modeling shows that the actual current density in OLEDs based on materials with a Gaussian electron and hole DOS is filamentary. However, it is possible to accurately calculate the average current density by solving a one‐dimensional (1D) drift‐diffusion equation, making use of compact expressions for the temperature, electric field, and carrier density dependent mobility which have been derived from 3D‐modeling. For the cases of spatially uncorrelated energetic disorder and spatially correlated disorder due to random dipole fields, these models are called the extended Gaussian disorder model (EGDM) and extended correlated disorder model (ECDM), respectively. We discuss how the effects of trapping on guest molecules can be included, and how exciton generation is described. The application of these models to hole and electron transporting polymer and small molecule materials is discussed, with an emphasis on the modeling of the transport and emission of blue‐emitting OLEDs based on a polyfluorene‐derivative.

Charge mobility and ZT in conducting organic thermoelectric

Charge dynamic in disordered organic semiconductors is often described in terms of transport sites and trap states. The process can be refined to include site energy distribution and hopping energetic. In turn, these will affect transport properties such as the carrier mobility and the thermal conductivity. As is well known, ZT in thermoelectric also depends on these parameters. This work attempts to analyze the relationship between site energy distribution and hopping mobility in oxidized Poly(3,4-ethylenedioxythiophene-tosylate) (PEDOT.Tos) (an organic thermoelectric known to have both high carrier density and low thermal conductivity). To understand the charge transport in oxidized PEDOT.Tos, we examined the thermoelectric data reported in the literature and used them to evaluate site parameters such as the escape frequency, the localization length and the width of the DOS (density of states). These results were used to compute the carrier mobility using the gaussian disorder model and the correlated disorder model We then used the computed parameters to assess the optimal value of ZT in PEDOT.Tos. Our simulations suggested that major improvement in ZT is achieved by increasing the localization length and to a lesser extent by reducing the bandwidth of the DOS. For the somewhat narrow bandwidth found in PEDOT.Tos (<kT), we are of the opinion that the transport site energy is strongly correlated.

Influence of Semiconductor Nanocrystal Concentration on Polymer Hole Transport in Hybrid Nanocomposites

This article investigates hole transport in poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV)/CdSe colloidal quantum dot (CQD) nanocomposites using a modified time-of-flight photoconductivity technique. The measured hole drift mobilities are analyzed in the context of Bässler’s Gaussian disorder model and the correlated disorder model in order to determine the polymer internal morphology of hybrid nanocomposite thin films. This work shows that increasing the CdSe CQD concentration decreases the polymer hole mobility from ~5.9 × 10−6 cm2/Vs in an MEH-PPV film to ~8.1 × 10−8 cm2/Vs in a 20:80 (wt%) MEH-PPV:CdSe CQD nanocomposite film (measured at 25 °C and ~2 × 105 V/cm). The corresponding disorder parameters indicate increasing disruption of interchain interaction with increasing CQD concentration. This work quantifies polymer chain morphology in hybrid nanocomposite thin films and provides useful information regarding the optimal use of semiconductor nanocrystals in conjugated polymer-based optoelectronics.

On the Use of Empirical Equation in Extracting Disorder Parameters in Inhomogeneous Organic Thin Films

Monte Carlo simulation of charge transport is employed to test the suitability of extensively used empirical equations, proposed by Gaussian disorder model (GDM)/correlated disorder model (CDM), for extracting disorder parameters from the field and temperature dependence of mobility in inhomogeneous organic thin films. Numerous observations suggests that the effective energetic disorder seen by the carrier in an inhomogeneous system decreases with increase in concentration of low disordered regions. However, the conventional analysis of field and temperature dependence of mobility obtained for such system, even with high concentration of low disordered regions, using the empirical equation provides the value of energetic disorder that is close to the value for regions of high disorder in the system rather than the effective energetic disorder. The study also shows that the inaccurate value of energetic disorder extracted using empirical equation in turn affect the extraction of positional disorder paramet...

Charge Transport in a Highly Phosphorescent Iridium(III) Complex‐Cored Dendrimer with Double Dendrons

AbstractThe charge transporting properties of a phosphorescent iridium(III) complex‐cored dendrimer, with two dendrons attached to each ligand of the core are reported. The results show that the high photoluminescence quantum yield of this material is obtained without compromising charge transport. The hole mobility values are reported over a wide range of temperatures and electric fields using the charge‐generation layer time‐of‐flight technique. The results are analysed using the Gaussian disorder model (GDM), the correlated disorder model, the polaronic correlated disorder model, and the short‐range correlated Gaussian disorder model. It is found that the GDM model gives the most comprehensive description of hole transport in this material. In spite of its larger size, the hole mobility of the doubly dendronised material compares favourably with that of a smaller singly dendronised material, and its spherical shape leads to low energetic disorder and clearly non‐dispersive charge transport. This shows how molecular shape can be used to combine favourable photoluminescence and charge‐transporting properties.

Charge Transport in Molecularly Doped Polymers: Tests of the Correlated Disorder Model

The correlated disorder model (CDM) has been proposed as a theory of charge transport in molecularly doped polymers (MDPs). Recently a test of the CDM was proposed: it was predicted that the dipolar disorder energy can be obtained from the slope of the log of the mobility versus square root of the electric field (the Poole-Frenkel or PF slope). We find that the dipolar disorder energy obtained from the experimental PF slopes are almost always larger than the theoretical predictions, especially for MDPs made from dopants with low dipole moments. In addition, the theory relates the dipolar disorder energy to the temperature T0 at which the electric field dependence of the mobility vanishes. We find that the observed T0 does appear to increase as the dipolar disorder increases but is in quantitative agreement (within 25 K) with the theoretical predictions for only a limited set of the measurements. We conclude that it appears that the CDM needs further development to be consistent with charge transport in or...

Influence of temperature-dependent mobilities on the nanosecond response of organic solar cells and photodetectors

We investigate the impact of temperature on the transient current density characteristics of organic solar cells and photodetectors. This is done by both experimental measurements and numerical simulations. In the process, we investigate the photoresponse of the device to an impinging laser pulse at different temperatures. By fitting the experimental results with the correlated disorder model we are able to quantify the influence of temperature on charge carrier mobilities in organic bulk heterojunction solar cells. We determine an almost doubling of the electron mobility on increasing the temperature from 11 to 50 °C.

Charge transport studies in fluorene – Dithieno[3,2- b:2′,3′- d]pyrrole oligomer using time-of-flight photoconductivity method

Charge mobility characteristics of a newly synthesised 2,6-bis[2-(9,9-dihexyl-9H-fluorene)]- N-(4-hexylphenyl)-dithieno[3,2- b:2′,3′- d]pyrrole oligomer ( DTP-FLU) was studied as a function of electric field and temperature using time-of-flight photoconductivity measurement. It is found that the DTP-FLU oligomer is a hole transporting material with a hole mobility of 7.7 × 10 −6 cm 2/Vs at an applied electric field of 2.9 × 10 5 V/cm at 298 K. The dependence of hole mobility with applied electric field and temperature is studied in detail by analyzing the experimental results using the Bassler’s Gaussian disorder model and Correlated disorder model. The energetic disorder parameter ( σ) = 100 meV, mobility pre-factor ( μ ∞) = 6.1 × 10 −4 cm 2/Vs and positional disorder parameter ( Σ) = 2.4 were extracted using Gaussian disorder model. The film morphology and photophysical properties of this new oligomer are also studied in detail.

Carrier-density and field-dependent charge-carrier mobility in organic semiconductors with correlated Gaussian disorder

Recently, it has been demonstrated that for organic semiconductors with a Gaussian density of states (DOS) and with on-site energies that are spatially uncorrelated the hopping mobility of charge-carriers can be strongly carrier-density-dependent (extended Gaussian disorder model, EGDM). In the literature, it has been argued that for some materials, the on-site energies are actually spatially correlated. In this paper, we develop a full description of the mobility in a correlated Gaussian DOS (extended correlated disorder model, ECDM), using a master-equation method. We show that the mobility is less strongly carrier-density-dependent than in the EGDM, but that the field dependence is more pronounced. The field dependence is found to be described by a Poole-Frenkel factor, as has been deduced from empirical analyses of experimental data, but only in a limited field range. As an example of an application, we present a comparison between analyses of the current–voltage–temperature J( V, T) characteristics of a poly-phenylene-vinylene (PPV) based hole-only device using the EGDM and the ECDM. For both cases, excellent fits can be obtained, but with the EGDM a more realistic value of the intersite distance is found than in the case of the ECDM. We view this as an indication that site-energy correlations do not play an important role in PPV.

Separate charge transport pathways determined by the time of flight method in bimodal polytriarylamine

Time of flight photocurrent transient studies on thin films of bimodal polytriarylamine (PTAA) show two distinct and separate arrival times for hole transport in the same sample at a single field. The corresponding mobilities differ by two orders of magnitude, typically μfast∼10−3 cm2 V−1 s−1 and μslow∼10−5 cm2 V−1 s−1 at room temperature, and are measured parametric in electric field and temperature. The mobility data are analyzed using the correlated disorder model by Novikov, yielding a fitting parameter set. The two conduction paths are believed to come about as a result of phase segregation between the shorter and longer polymer chains with the shorter chains giving rise to the faster conduction pathways (as confirmed by results obtained for monomodal, shorter, and longer chain PTAA, by sample thickness scaling of the photocurrents and by reversal of the illuminated electrode). Separate arrival times are also obtained in a blend of the two short and long chain monomodal polymers. The phase separation within the film is inferred by the appearance of two glass transition temperatures using dynamic mechanical thermal analysis.

Charge transport studies in electroluminescent biphenylyl substituted PPV derivatives using time‐of‐flight photoconductivity method

AbstractThe charge transport properties in a series of electroluminescent biphenylyl substituted PPV derivatives, poly[(2‐(3′‐(p‐2″‐ethylhexyloxyphenyl)phenyl)‐1,4‐phenylenevinylene) (MP‐PPV), poly[2‐(2′‐phenyl‐4′,5′‐bis(3″‐methylbutoxy))phenyl‐1,4‐phenylene vinylene] (BP‐PPV) and poly{[2‐(4′,5′‐bis(3″‐methylbutoxy)‐2′‐phenyl)phenyl‐1,4‐phenylene‐vinylene]‐co‐(9,9‐dioctyl‐2,7‐fluorenylene‐vinylene)} (BPPPV‐PF), have been studied using a time of flight (TOF) photoconductivity technique. The TOF transients for holes in these polymers were weakly dispersive in nature with a mobility of the order of ∼10−5cm2/V s at room temperature. The temperature and field dependence of charge mobility has been studied and analyzed using the disorder formalisms (Bässler's Gaussian disorder model (GDM) and correlated disorder model (CDM)). The charge transport parameters, such as mobility prefactor, energetic disorder, positional disorder, and the average intersite distance, were estimated from the fit and correlated to the molecular structure of the polymer. The microscopic charge transport parameters derived for these polymers indicate that these biphenylyl substituted PPV derivatives have very good chemical purity and structural regularity, which is similar to the reported values for structurally related fully conjugated polymers with high chemical purity. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1159–1166, 2008

Hole mobility within arylamine-containing polyfluorene copolymers: A time-of-flight transient-photocurrent study

We report a time-of-flight transient photocurrent study of the hole mobility, measured as a function of electric field and temperature, within (i) poly(9,9-dioctylfluorene), (ii) poly(9,9-dioctylfluorene-co-bis-$N,N$-(4-butylphenyl)-bis-$N,N$-phenyl-1,4-phenylenediamine) (PFB), and (iii) three copolymers that contain differing proportions of the moieties 9,9-dioctylfluorene, $N$-(4-butylphenyl)diphenylamine, and bis-$N,N$-(4-butylphenyl)-bis-$N,N$-phenyl-1,4-phenylenediamine. The results are analyzed using the Gaussian disorder model as proposed by H. B\"assler [Phys. Status Solidi B 175, 15 (1993)], the correlated disorder model as proposed by S. V. Novikov et al. [Phys. Rev. Lett. 81, 4472 (1998)], and finally, the polaronic correlated disorder model of R. E. Parris et al. [Phys. Rev. Lett. 87, 126601 (2001)]. We deduce values for the corresponding energetic and spatial disorder parameters, intersite hopping distance, wave-function decay constant, and polaronic activation energy, and consider how variations in chemical structure impact thereon.

Hole transporting properties of tris(8-hydroxyquinoline) aluminum (Alq3)

The hole transporting properties of tris (8-hydroxyquinoline) aluminum (Alq3) were investigated by time-of-flight (TOF) technique between 278 and 373K, and under an applied field range of 0.6–1.3MV∕cm. At room temperature, the hole mobility has a value between 10−9 and 10−8cm2V−1s−1. The hole mobility is at least two orders of magnitude less than electron under identical preparation and measurement conditions. Generally, all hole TOF transients of Alq3 exhibit a nondispersive behavior, with a clear plateau region and a dispersion tail. Two disorder transport models, namely, the Gaussian disorder model (GDM) and the correlated disorder model (CDM), were applied to analyze the temperature and field dependent hole mobility data. The GDM, however, is found to be invalid because it fails to produce a meaningful positional disorder parameter. The CDM gives a better fit to the data, yet the model is still not satisfactory.