Gaussian Disorder Model Research Articles

Analyzing Dynamical Disorder for Charge Transport in Organic Semiconductors via Machine Learning.

Organic semiconductors are indispensable for today's display technologies in the form of organic light-emitting diodes (OLEDs) and further optoelectronic applications. However, organic materials do not reach the same charge carrier mobility as inorganic semiconductors, limiting the efficiency of devices. To find or even design new organic semiconductors with higher charge carrier mobility, computational approaches, in particular multiscale models, are becoming increasingly important. However, such models are computationally very costly, especially when large systems and long timescales are required, which is the case to compute static and dynamic energy disorder, i.e., the dominant factor to determine charge transport. Here, we overcome this drawback by integrating machine learning models into multiscale simulations. This allows us to obtain unprecedented insight into relevant microscopic materials properties, in particular static and dynamic disorder contributions for a series of application-relevant molecules. We find that static disorder and thus the distribution of shallow traps are highly asymmetrical for many materials, impacting widely considered Gaussian disorder models. We furthermore analyze characteristic energy level fluctuation times and compare them to typical hopping rates to evaluate the importance of dynamic disorder for charge transport. We hope that our findings will significantly improve the accuracy of computational methods used to predict application-relevant materials properties of organic semiconductors and thus make these methods applicable for virtual materials design.

An effect of crystallographic distortion on carrier mobility in poly(3-hexylthiophene) thin films

The aggregation states and physical properties of polymers in thin films deviate from those found in the bulk. Although an effect of the thickness on the carrier mobility for thin films of poly(3-hexylthiophene) (P3HT) has been widely studied, there is a lack of discussion in terms of crystallographic distortion. Here, we demonstrate how the out-of-plane hole mobility in P3HT, which is a typical semiconducting polymer, changes with decreasing film thickness. Time-of-flight measurements with an analysis using the Gaussian disorder model revealed that the zero-field out-of-plane hole mobility decreased with decreasing thickness because of an increase in the energetical and spatial distribution of hopping sites. Grazing incidence wide-angle x-ray diffraction measurements revealed that such distributions of charge carriers were induced by the crystallographic distortion of P3HT in the thin films.

Electronic processes in organic–inorganic composite P3HT with silicon nanocrystals

The generation mechanisms and charge carrier transfer in a composite of polymer poly-3(hexylthiophene) (P3HT) and silicon nanoparticles (nc-Si) films are investigated using conductivity measurements at different temperatures and electric fields and photocurrent spectroscopy. It is shown that the widely used Gaussian disorder model for describing the electrical and optical properties of polymers is also valid for hybrid organic–inorganic materials consisting of polymer matrix with silicon nanoparticles addition. This indicates that the charge carrier transfer in such materials occurs over the localized states in the polymer part of composite material. It is shown that the nonmonotonic change in the conductivity arising upon the addition of silicon nanoparticles leads only to a change in the distribution of the density of localized states in the polymer, which determines the conductivity and photoconductivity of the hybrid material. It is demonstrated that the addition of nc-Si at lower concentrations to P3HT makes it possible to vary the conductivity and photoconductivity of the composite material over a wide range.

Alkyl chain length dependence of carrier transport in solution-processed phthalocyanine thin films evaluated via MIS-CELIV method

The carrier transport characteristics of 1,4,8,11,15,18,22,25-octaalkylphthalocyanine (CnPcH2) thin films have been investigated by utilizing metal–insulator–semiconductor charge extraction by the linearly increasing voltage method. As the alkyl chain length of CnPcH2 increased from n = 5 to 8, the estimated hole mobility decreased by almost one and a half order of magnitude in the range of 10−4 to 10−5 cm2 V−1 s−1. Furthermore, the relationship between the alkyl chain length and site energy distribution in solution-processed phthalocyanine thin films was investigated. The temperature and field dependences of the hole mobility were analyzed using the Gaussian disorder model, and the effect of the alkyl chain length was discussed by taking the enlargement of the energetic width of the hopping site and the distribution of the hopping distance into consideration.

Parametrization of the Gaussian Disorder Model to Account for the High Carrier Mobility in Disordered Organic Transistors

Correct parameterization of the Gaussian disorder model (GDM) on spatially random sites is necessary for a complete description of charge transport in disordered materials and concomitant device characteristics. Because the GDM on spatially random sites considers both energetic and spatial disorder, it is superior to the GDM on a cubic lattice. However, analytical arguments and experimental evidence are still lacking for correct parameterization of the model over a wide range of model parameters, energetic and spatial disorder, and electric fields. We show that the model requires a set of parameters to correctly account for high mobility and its charge density dependence, and we develop such a model. The model is implemented in a numerical simulation tool for comparison with the measured device characteristics. Accurate agreement with experimental data, particularly with the high mobility values in organic field-effect transistors, is achieved throughout a wide range of temperature by adjusting both the localization length and the attempt-to-escape frequency.

The impact of charge carrier relaxation, electron trapping and oxygen p-doping on the photocurrent transients of a conjugated polymer probed by the Time of Flight method

Most conjugated polymers have been considered so far to be primarily unipolar (hole or electron transporting) materials, even though there is no intrinsic reason why the mobility of holes and electrons should be different in organic semiconductors. We experimentally demonstrated by the Time of Flight method that a prototypical conjugated polymer, poly[2-methoxy-5-(2-ethylhexoxy)-1,4-p-phenylenevinylene], does not show any preference for the transport of electrons or holes, i.e. an ambipolar charge transport. Furthermore, the presence of traps and (unintentional) p-doping makes it difficult to address the intrinsic nature of the charge transport mechanism. However, by disentangling the dependence of the mobility from extrinsic factors, such as molecular oxygen, we were able to reveal a non-dispersive conduction for both holes and electrons. We also reveal a transition from trap-control to thermalization-control in the electrons’ charge transport mechanism. We used the Gaussian disorder model to analyze the experimental data, and we found that the positional disorder parameter is negligible for holes, and only the energetic disorder governs their charge transport, while the electrons’ conduction is governed by the interplay of both energetic and positional disorder.

Carrier transport properties in highly ordered smectic liquid crystal phase

AbstractWe have designed and synthesized a new liquid crystalline phenylbenzothienobenzothiphene derivative, Ph‐BTBT‐4S‐3, in order to investigate the carrier transport properties in highly ordered smectic liquid crystal phase at a wide temperature range lower than room temperature enough to analyze them. Ph‐BTBT‐4S‐3 exhibits smectic E (SmE) phase, which is the one of highly ordered smectic liquid crystal phases, at the wide temperature range from 200°C to under −130°C. Thanks to its wide temperature range of SmE phase, we could reveal the carrier transport properties in the low temperature range, which were well explained on the basis of Gaussian disorder model having a Gaussian width, σ, of 87 meV, which was larger than those of typical nonpolar liquid crystals of 40−60 meV and was attributed to additional dipole of a thioether group in the side chain.

Anisotropy of charge carrier transport in PCPDTBT field-effect transistor structures

In this paper we are analyzing anisotropy of hole mobility in the organic field-effect transistor structures with an active layer of PCPDTBT (poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta [2,1-b;3,4-b′]dithiophene)-alt-4,7(2,1,3-benzothiadiazole)]). Hole mobility and its dependence on the temperature was measured by i-CELIV and current transients methods. The combination of both techniques allowed us to obtain results of hole mobilities in perpendicular and parallel to the substrate directions. In the same temperature range differential scanning calorimetry (DSC) measurements were performed to detect morphological changes in the active layer of the field-effect transistor structure. From obtained results of mobility dependence on temperature, energetic disorder parameter of Bässler’s Gaussian Disorder Model (GDM) was estimated. DSC data and hole transport data demonstrated that the change in PCPDTBT’s morphology is responsible for the abrupt decrease of hole mobility on temperature in the field-effect transistor structure.

Experimentally Validated Hopping-Transport Model for Energetically Disordered Organic Semiconductors

Charge transport in disordered organic semiconductors occurs by hopping of charge carriers between localized sites that are randomly distributed in a strongly energy dependent density of states. Extracting disorder and hopping parameters from experimental data like temperature dependent current-voltage characteristics typically relies on parametrized mobility functionals that are integrated in a drift-diffusion solver. Surprisingly, the functional based on the extended Gaussian disorder model (eGDM) has been extremely successful at this, despite it being based on the assumption of nearest neighbor hopping (nnH) on a regular lattice. We here propose a variable range hopping (VRH) model that has been integrated in a freeware drift-diffusion solver. The mobility model has been calibrated using kinetic Monte Carlo calculations and shows good agreement with the Monte Carlo calculations over the experimentally relevant part of the parameter space. The model is applied to temperature-dependent space charge limited current (SCLC) measurements of different systems. In contrast to the eGDM, the VRH model provides a consistent description of both p-type and n-type devices. We find a critical ratio of aNN/$\alpha$ (mean inter-site distance / localization radius) of ~3 below which hopping to non-nearest neighbors becomes important around room temperature and the eGDM cannot be used for parameter extraction. Typical (Gaussian) disorder values in the range 45-120 meV are found, without any clear correlation with photovoltaic performance when the same active layer is used in an organic solar cell.

Carrier Transport Properties of Asymmetrically Substituted Calamitic Liquid Crystal in the Smectic A Phase of Dibenzo[c,h][2,6]naphthyridine Derivatives

Novel calamitic liquid crystals with asymmetrically substituted structure base on the dibenzo[c,h][2,6]naphthyridine (DBN) moiety as an electron-deficient core, 2-(4-decylphenyl)dibenzo[c,h][2,6]naphthyridine (C10-Ph-DBN), 2-chloro-8-decyl-DBN (Cl-DBN-C10) and 2-decyl-8-phenyl-DBN (Ph-DBN-C10), were synthesized and their carrier transport properties were investigated. The lower ordered smectic phase of SmA emerged in a very wide temperature range of 130 °C in all DBN derivatives, which allowed us to study the carrier transport properties in SmA phase in detail for the first time: we purified Cl-DBN-C10 enough to evaluate the carrier transport property in the SmA phase by time-of-flight method. It showed the temperature and electric field dependence of the mobility, indicating the energetic disorder of transport levels. We analyzed it within the framework of the Gaussian disorder model for electrons and obtained a Gaussian width of the density of states to 109 meV in the SmA. This is the first experimental result analyzed for the SmA phase in calamitic liquid crystals with non-negligible dipole moment.

Effects of Disorder on Thermoelectric Properties of Semiconducting Polymers

Organic materials have attracted recent interest as thermoelectric (TE) converters due to their low cost and ease of fabrication. We examine the effects of disorder on the TE properties of semiconducting polymers based on the Gaussian disorder model (GDM) for site energies while employing Pauli’s master equation approach to model hopping between localized sites. Our model is in good agreement with experimental results and a useful tool to study hopping transport. We show that stronger overlap between sites can improve the electrical conductivity without adversely affecting the Seebeck coefficient. We find that positional disorder aids the formation of new conduction paths with an increased probability of carriers in high energy sites, leading to an increase in electrical conductivity while leaving the Seebeck unchanged. On the other hand, energetic disorder leads to increased energy gaps between sites, hindering transport. This adversely affects conductivity while only slightly increasing Seebeck and results in lower TE power factors. Furthermore, positional correlation primarily affects conductivity, while correlation in site energies has no effect on TE properties of polymers. Our results also show that the Lorenz number increases with Seebeck coefficient, largely deviating from the Sommerfeld value, in agreement with experiments and in contrast to band conductors. We conclude that reducing energetic disorder and positional correlation, while increasing positional disorder can lead to higher TE power factors.

Identification of mechanical and damage parameters of composite laminates based on a CPAM method

A new method combining experimental and numerical data is proposed to simultaneously determine the mechanical properties and damage parameters in multilayered composite plates. Studied parameters are mechanical properties of each layer, width and length of delamination zone, location of damage’s center, and interface location of the damage. In this method, the PSO optimization procedure based on a CPAM algorithm uses vibration test data along with their corresponding numerical solution. Vibration data are the plates’ natural frequencies and mode shapes obtained in the modal laboratory. In order to efficiently investigate the studied parameters, the numerical solution is investigated by a commercial finite element package. The error function constitutes two parts, one part is included by the sum of the squared differences between experimental and numerical natural frequencies and the other is based on the mode shapes data. The mode shapes’ curvatures are also utilized to achieve high sensitivity to small faults. Moreover, by applying a Gaussian disorder model to the vibrational data, the sensitivity of the method is evaluated in the presence of unwanted noises. The results confirm the robustness of the proposed study for identifying both mechanical constants and damage parameters in composite plates.

Automated open-source software for charge transport analysis in single-carrier organic semiconductor diodes

Organic electronics is an emerging technology with numerous applications in which the active layer is composed of an organic semiconductor (OSC) or blends of multiple OSC. One of the key performance parameters for such devices is the charge carrier mobility which can be evaluated by different measurement techniques. Here, we review different formalisms for extraction and analysis of hole mobilities from temperature-dependent space-charge limited conductivity (SCLC) measurements for pristine OSC as well as for binary and ternary blends as used in e.g. photovoltaic applications. The model is also applicable to n-type materials. Possible sources of measurement errors, such as the presence of traps and series resistance, are discussed. We show that by a simple method of selecting a proper experimental data range these errors can be avoided. The Murgatroyd-Gill analytical model in combination with the Gaussian Disorder Model is used to extract zero-field hole mobilities as well as estimates of the Gaussian energetic disorder in the HOMO level from experimental data. The resulting mobilities are in excellent agreement with those found from more elaborate fits to a full drift-diffusion model that includes a temperature, field and density dependent charge carrier mobility; the same holds for the Gaussian disorder of pure materials and blends with low fullerene concentration. The zero-field mobilities are also analyzed according to an Arrhenius model that was previously argued to reveal a universal mobility law; for most –but not all– material systems in the present work this framework gave an equally good fit to the experimental data as the other models. An automated fitting freeware, incorporating the different models, is made openly available for download and minimizes error, user input and SCLC data analysis time; e.g. SCLC current-voltage curves at several different temperatures can be globally fitted in a few seconds.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole–Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log–log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Frequency Factor of the Semiempirical Model for the Radiation-Induced Conductivity in Spacecraft Polymers

We have extended the existing Rose–Fowler–Vaisberg model of the radiation-induced conductivity (RIC) in polymers by incorporating the latest ideas borrowed from theoretical and experimental results obtained in the field of electronic transport in molecularly doped polymers. These include the Poole–Frenkel-type field-dependent mobility and the arguments of the dipolar disorder formalism based on the Gaussian disorder model. Theory validation uses a new experimental technique based on the electron-gun technology allowing combined-induced conductivity and carrier mobility measurements in a typical molecularly doped polymer. Quasi-band and hopping theories of the carrier transport are critically discussed.

Fluorescent and charge transport properties of columnar phases made of mono and bi-phenazine derivatives.

Mesogenic dibenzophenazine derivatives have been synthesized and their liquid crystalline, fluorescent and electrochemical properties have been studied. All compounds form the Colhd phase, one of them (4-hydroxyphenyl 2,3,6,7-tetrakisoctyloxy-dibenzo[a,c]phenazine-11-carboxylate, 4) additionally shows an unusual columnar structure with p2mg symmetry, which is a partially lamellarized columnar phase. The emission spectra exhibit a huge Stokes shift that is due to the different molecular conformation in ground and excited states. The non-dispersive hole transport current under UV laser illumination was observed and the charge mobility in the range 10-4-10-3 cm2 V-1 s-1 was determined with the time of flight (ToF) method. The measurements have been interpreted according to the Gaussian disorder model, providing material parameters that reflect the energetic distribution of localized states (diagonal disorder, σ) and distribution of coupling parameters between transport sites (off-diagonal disorder, Σ).

Effect of Donor Building Blocks on the Charge-Transfer Characteristics of Diketopyrrolopyrrole-Based Donor-Acceptor-Type Semiconducting Copolymers.

We investigate the effect of donor (D) building blocks on the charge transportation characteristics of donor (D)-acceptor (A)-type semiconducting copolymers with alternating electron-donating and electron-accepting units to provide a basis for the rational design of high-performance semiconducting polymers. For this purpose, we studied three different diketopyrrolopyrrole (DPP)-based semiconducting copolymers comprising a common dithienyl-DPP [3,6-dithienyl-2,5-diketopyrrolo(3,4-c)pyrrole] and variable donor moieties: phenylene (P)-PDPPTPT, thiophene (T)-PDPP3T, and thienothiophene (TT)-PDPP2T-TT. Structural analysis using grazing incidence X-ray diffraction indicates that all three DPP-based copolymer films have edge-on phases but poor crystallinity of the films, except the PDPP2T-TT copolymer with branched alkyl side chains that are relatively long. The electrical measurements show that the DPP-based copolymer with a TT donor unit has the highest field-effect mobility value of 0.30 cm2/V s. To understand the role of the donor units in DPP-based D-A copolymers, further insight into the charge transportation behavior is realized by analyzing the temperature-dependent transfer curves of the DPP semiconducting copolymer-based field-effect transistors using the Gaussian disorder model. Compared to the DPP-based D-A-type semiconducting copolymer with a P-moiety and shorter-branched alkyl side chains that exhibit a broad distribution in the density of localized states (DOS) and a higher thermal-activated energy for charge hopping, the DPP copolymers with a TT-moiety and longer branched side chains have the narrowest DOS, the lowest activation energy, and thus the highest hole mobility. These results suggest that the higher mobilities obtained from PDPP2T-TT with a TT donor unit can be attributed to the suppressed DOS distribution near the transport level, which mainly originates from the narrowest energy band gap tuned with the orbital couplings of the DPP acceptor and TT donor units.

Comparative Monte-Carlo simulations of charge carrier transport in amorphous molecular solids as given by three most common models of disorder: The dipolar glass, the Gaussian disorder, and their mix.

We have performed Monte-Carlo simulations of the charge carrier transport in a model molecularly doped polymer using three most popular hopping theories (the dipolar glass model, the Gaussian disorder model, and an intermediate between them) in a wide range of applied electric fields and temperatures. Time of flight transients have been computed and analyzed in logarithmic coordinates to study the Poole-Frenkel field dependence, the non-Arrhenius mobility temperature dependence, and the nondispersive versus dispersive current shapes. We also have made an attempt to estimate the total disorder energy directly from simulation data at the lowest electric field thus checking the consistency of the model fitting. Computational results have been compared with the analytical and experimental information available in the literature.

Mobility modulation in low carrier concentration organic semiconducting thin films by varying disorder parameters

In the present work, an attempt has been made to modulate the carrier mobility in thermally evaporated, low carrier concentration organic thin films, with boron sub phthalocyanine chloride (sub pc) as a case study, by changing its various disorder parameters namely energetic disorder (σ), positional disorder (Σ2, Γ), and average inter-site hopping distance (a). The change in these disorder parameters was achieved by varying the substrate temperature of the films. All the films were electrically characterized under different temperature and bias conditions. An improvement of more than two orders in the mobility was achieved in the films with lower energetic and positional disorder. The transport mechanism exhibited a cross over from low frequency dispersion (high loss) regime to low loss regime with a decrease in disorder parameters. The average inter site hopping distance emerged as a key factor contributing to mobility enhancement. The zero field mobilities and other parameters were analyzed using Gaussian Disorder Model, Correlated Gaussian Disorder Model, and Murgatroyed equation. Variation in energetic disorder extracted from the analytical model was compared with the width of absorption tail obtained from UV-Vis spectra of the films.

Sensitivity Analysis of a CPAM Inverse Algorithm for Composite Laminates Characterization

Using experimental data and numerical simulations, a new combined technique is presented for characterization of thin and thick orthotropic composite laminates. Four or five elastic constants, as well as ply orientation angles, are considered as the unknown parameters. The material characterization is first examined for isotropic plates under different boundary conditions to evaluate the method’s accuracy. The proposed algorithm, so-called CPAM (Combined Programs of ABAQUS and MATLAB), utilizes an optimization procedure and makes simultaneous use of vibration test data together with their corresponding numerical solutions. The numerical solutions are based on a commercial finite element package for efficiently identifying the material properties. An inverse method based on particle swarm optimization algorithm is further provided using MATLAB software. The error function to be minimized is the sum of squared differences between experimental and simulated data of eigenfrequencies. To evaluate the robustness of the model’s results in the presence of uncertainty and unwanted noises, a sensitivity analysis that employs Gaussian disorder model is directly applied to the measured frequencies. The results with high accuracy confirm the validity and capability of the present method in simultaneous determination of mechanical constants and fiber orientation angles of composite laminates as compared to prior methods.