Modeling of charge-transport processes for predictive simulation of OLEDs

Intensive research is taking place into alternative light sources to replace incandescent and fluorescent lamps. Organic light-emitting diodes (OLEDs) show great promise, with their main potential advantages being high energy efficiency, cheap roll-to-roll production, excellent color rendering and a unique form factor. However, significant challenges must still be overcome, particularly in the areas of luminous efficacy, lifetime and manufacturing. Several approaches to overcoming these challenges have been proposed, but it is difficult to design optimized devices around these approaches. This is because at present this design takes place through trial and error, which makes investigating the full parameter space of material choices and layer stack design virtually impossible. To improve this design process, a predictive OLED model is needed. A full predictive OLED model takes as input the layer stack design, deposition methods and chemical structures of the materials involved, and gives as output the angle-dependent emission spectrum and current-voltage characteristics of the device. This involves molecular dynamics, density functional theory, charge-transport modeling, excitonics and photonics. However, charge-transport modeling by itself already yields useful results, such as current-voltage characteristics and exciton generation locations. In such modeling one three-dimensionally (3D) simulates the charge transport in organic semiconductors, which takes place by hopping of charge carriers between localized sites. Since this 3D simulation is computationally expensive, the results must be translated to a fast one-dimensional drift-diffusion (1D-DD) approach to be of use in the OLED design process. In this translation, 3D simulation is used in two ways: to determine parameters like the charge-carrier mobility, and to validate the results of the 1D approach. Charge-transport modeling and the 3D-to-1D translation are the focus of this work. In this thesis, two 3D simulation methods are used, based on the master equation (3D-ME) and on Monte Carlo simulation (3D-MC). In the 3D-ME method, we determine for each site the probability that there is a charge carrier on this site. We use this method to determine the charge-carrier mobility in bulk systems. Advantages of this method are its speed and direct insight into the spatial distribution of charge carriers. An important disadvantage is that Coulomb interactions between individual charge carriers cannot be taken into account. In the 3D-MC method, we evaluate the full hopping model through explicit Monte Carlo simulation, including all Coulomb interactions. We use it to model charge transport in multilayer structures relevant for modern OLEDs. A first result is a new scaling theory which describes the dependence of the charge- carrier mobility on temperature and carrier density at zero electric field (chapter 3). This scaling theory is based on percolation theory, in which one critical bond determines the charge-transport properties of the entire system. We expand on percolation by considering not just this single critical bond but also the distribution of almost equally difficult bonds in the system. This leads to an accurate, closed-form expression for the mobility, containing three parameters which depend on the specific system considered (such as the type of lattice, the expression for the charge carrier hopping rate between two sites and the shape of the energy disorder). This theory makes it possible for the first time to analyze the effect of assumptions like the lattice and hopping rate. The second result is a description of the electric-field dependence of the mobility in host-guest systems (chapter 4). These are systems in which a small amount of sites act as charge-carrier traps, such as dopants, dyes or naturally occurring electron traps. At low guest concentration charge transport takes place only through the host. The effect of the guest sites is then purely to immobilize a number of carriers. At low electric field, this number can be determined from equilibrium Fermi-Dirac statistics. At finite fields this no longer applies because of field-induced detrapping: the field assists carriers in escaping the guest sites. We quantify this effect by generalizing the Fermi-Dirac distribution to a numerically determined occupation function. This allows an accurate prediction of the mobility, leading to improved simulation of OLEDs containing host-guest systems. The third result is a general description of charge transport at non-zero electric field (chapter 5). This result combines elements of the scaling and field-induced-detrapping theories described above. We show that the mobility factorizes into an ‘intrinsic’ factor and a ‘detrapping’ factor. These are physically separate effects, and we show that they affect the charge transport in devices in different ways. This means that the value of the mobility by itself does not fully describe charge transport at finite electric field. We present a new form of the 1D-DD method that explicitly splits these two factors of the field dependence instead of using the charge-carrier mobility. This method can be used to more accurately model devices in which high electric fields occur. The fourth and final result is a description of how to accurately implement internal organic-organic interfaces in the 1D-DD method (chapter 6). By comparing 3D-MC simulations to 1D-DD results, we determine and quantitatively describe three effects that must be taken into account. First, the charges at the interface are not in equilibrium, which must be taken into account in the boundary condition. Second, there is a discrete surface charge caused by charge carriers accumulating before the interface. Third, the Coulomb repulsion of this surface charge is reduced by Coulomb interactions between the carriers. All three effects can significantly influence the current in multilayer OLEDs and must be taken into account in an accurate 1D model. These charge-transport results have applications in the short, middle and long term (chapter 7). In the short term, the 1D-DD method can be used in characterization of organic semiconductors. Indeed, this approach (without the results in this thesis) has already been successfully used in several organic semiconductors to determine material parameters for a given choice of hopping model. By considering the time or frequency dependence of the mobility it may also be possible to determine which hopping model is appropriate. In the middle to long term, the 1D-DD method will be a valuable tool in OLED device simulation. The 3D-MC method has also proven to be useful in this kind of simulation. These methods are especially powerful when used to complement each other. Double-carrier charge transport and excitonics will have to be analyzed further to complete the 1D-DD method. In the long term, our most valuable result is most likely the insight we have gained into the physics underlying charge transport in organic semiconductors. This will allow us to truly understand OLED operation and come up with new concepts and designs. Some of our results, such as the scaling theory, may also be applicable to other fields of study

Converted phases from sharp 1000 km depth mid-mantle heterogeneity beneath Western Europe

Until recently, most of the lower mantle was generally considered to be well-mixed with strong heterogeneity restricted to the lowermost several hundred kilometres above the core–mantle boundary, known as the $\textbf{D}$″ layer. However several recent studies have started to hint at a potential change in Earth's structure at mid-mantle depths beneath the transition zone. Here we present a continental-wide search of Europe and the North Atlantic for mid-mantle P-to-s wave converted phases. Our data set consists of close to 50,000 high quality receiver functions. These are combined in slowness and depth stacks to identify seismic discontinuities in the range of 800–1400 km depth to determine at which depths and in which tectonic settings these features exist. Receiver functions are computed in different frequency bands to resolve the sharpness of the observed discontinuities. We find most seismic velocity jumps are observed between 975–1050 km depth, localised beneath western Europe and Iceland. The shear wave velocity jumps are roughly 1–2.5% velocity increase with depth occurring over less than 8 km in width. The most robust observations are coincident with areas of active upwelling (under Iceland) and an elongate lateral low velocity anomaly imaged in recent tomographic models which has been interpreted as diverted plume material at depth. The lack of any suggested phase change in a normal pyrolitic mantle composition at around 1000 km depth indicates the presence of regional chemical heterogeneity within the mid-mantle, potentially caused by diverted plume material. We hypothesise that our observations represent either a phase change within chemically distinct plume material itself, or are caused by small scale chemical heterogeneities entrained within the upwelling plume, either in the form of recycled basaltic material or deep sourced chemically distinct material from LLSVPs. Our observations, which cannot be directly linked to an area of either active or ancient subduction, along with observations in other hotspot regions, suggest that such mid-mantle seismic features are not unique to subduction zones despite the large number of observations that have previously been made in such settings.The facilities of IRIS Data Services, and specifically the IRIS Data Management Center, as well as the ORFEUS data centre were used for access to waveforms, related metadata, and/or derived products used in this study. IRIS Data Services are funded through the Seismological Facilities for the Advancement of Geoscience and EarthScope (SAGE) Proposal of the National Science Foundation under Cooperative Agreement EAR-1261681. For full citation list of all FDSN networks please see the Supplementary Material. Seismometers for the Cambridge seismic network in Iceland were borrowed from the Natural Environment Research Council (NERC) SEIS-UK (loans 857, 968 and 1022), and funded by research grants from the NERC and the European Community's Seventh Framework Programme Grant No. 308377 (Project FUTUREVOLC), to Robert S. White. J.J. was funded by a graduate studentship from NERC (LBAG/148 Task 5). S.C. is funded by the Drapers' Company Research Fellowship through Pembroke College, Cambridge. Thanks are also extended to the Icelandic Meteorological office for sharing data that were used in this study. A.D. and J.J. were funded by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007–2013/ERC grant agreement 204995) and by a Philip Leverhulme Prize. Data was downloaded from IRIS DMC and figures made using GMT (Wessel and Smith, 2001)

X-discontinuity and transition zone structure beneath Hawaii suggests a heterogeneous plume

The Hawaiian Island chain in the middle of the Pacific Ocean is a well-studied example of hotspot volcanism caused by an underlying upwelling mantle plume. The thermal and compositional nature of the plume alters the mantle phase transitions, which can be seen in the depth and amplitude of seismic discontinuities. This study utilises $>$ 5000 high quality receiver functions from Hawaiian island stations to detect P-to-s converted phases to image seismic discontinuities between 200 to 800 km depth. Common-conversion point stacks of the data are used to map out lateral variations in converted phase observations, while slowness stacks allow differentiation between true conversions from discontinuities and multiples. We find that the 410 discontinuity is depressed by 20 km throughout our study region, while the main 660 is around average depth throughout most of the area. To the southwest of the Big Island we observe splitting of the 660, with a major peak at 630 km, and a minor peak appearing at 675 km depth. This is inferred to represent the position of the hot plume at depth, with the upper discontinuity caused by an olivine phase transition and the lower by a garnet phase transition. In the upper mantle, a discontinuity is found across the region at depths varying between 290 to 350 km. Identifying multiples from this depth confirms the presence of a so-called X-discontinuity. To the east of the Big Island the X-discontinuity lies around 336 km and the associated multiple is particularly coherent and strong in amplitude. Strikingly, the discontinuity around 410 km disappears in this area. Synthetic modelling reveals that such observations can be explained by a silica phase transition from coesite to stishovite, consistent with widespread ponding of silica-saturated material at these depths around the plume. This material could represent eclogite enriched material, which is relatively silica-rich compared to pyrolite, spreading out from the plume to the east as a deep eclogite pool, a hypothesis which is consistent with dynamical models of thermochemical plumes. Therefore these results support the presence of a significant garnet and eclogite component within the Hawaiian mantle plume

Depressed mantle discontinuities beneath Iceland: Evidence of a garnet controlled 660 km discontinuity?

The presence of a mantle plume beneath Iceland has long been hypothesised to explain its high volumes of crustal volcanism. Practical constraints in seismic tomography mean that thin, slow velocity anomalies representative of a mantle plume signature are difficult to image. However it is possible to infer the presence of temperature anomalies at depth from the effect they have on phase transitions in surrounding mantle material. Phase changes in the olivine component of mantle rocks are thought to be responsible for global mantle seismic discontinuities at 410 and 660 km depth, though exact depths are dependent on surrounding temperature conditions. This study uses P to S seismic wave conversions at mantle discontinuities to investigate variation in topography allowing inference of temperature anomalies within the transition zone. We employ a large data set from a wide range of seismic stations across the North Atlantic region and a dense network in Iceland, including over 100 stations run by the University of Cambridge. Data are used to create over 6000 receiver functions. These are converted from time to depth including 3D corrections for variations in crustal thickness and upper mantle velocity heterogeneities, and then stacked based on common conversion points. We find that both the 410 and 660 km discontinuities are depressed under Iceland compared to normal depths in the surrounding region. The depression of 30km observed on the 410 km discontinuity could be artificially deepened by un-modelled slow anomalies in the correcting velocity model. Adding a slow velocity conduit of -1.44% reduces the depression to 18 km; in this scenario both the velocity reduction and discontinuity topography reflect a temperature anomaly of 210 K. We find that much larger velocity reductions would be required to remove all depression on the 660 km discontinuity, and therefore correlated discontinuity depressions appear to be a robust feature of the data. While it is not possible to definitively rule out the possibility of uncorrected velocity anomalies causing the observed correlated topography we show that this is unlikely. Instead our preferred interpretation is that the 660 km discontinuity is controlled by a garnet phase transition described by a positive Clapeyron slope, such that depression of the 660 is representative of a hot anomaly at depth.Seismometers for the Cambridge network in Iceland were borrowed from the Natural Environment Research Council (NERC) SEIS-UK (loans 857 and 968), and funded by research grants from the NERC to RSW. Thanks are also extended to the Icelandic Meteorological office for sharing data that were used in this study. A.D. and J.J. were funded by the European Research Council under the European Communitys Seventh Framework Programme (FP7/20072013/ERC grant agreement 204995) and by a Philip Leverhulme Prize. SC is funded by the Drapers’ Company Research Fellowship through Pembroke College, Cambridge, UK. Data was downloaded from IRIS DMC and figures made using GMT (Wessel and Smith, 2001). The authors would like to thank all the PhD students and technicians who aid in the running and maintenance of the University of Cambridge seismic network. Dept. Earth Sciences, Cambridge contribution no ESC.3452.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.epsl.2015.10.05

X-discontinuity and transition zone structure beneath Hawaii suggests a heterogeneous plume

The Hawaiian Island chain in the middle of the Pacific Ocean is a well-studied example of hotspot volcanism caused by an underlying upwelling mantle plume. The thermal and compositional nature of the plume alters the mantle phase transitions, which can be seen in the depth and amplitude of seismic discontinuities. This study utilises >5000 high quality receiver functions from Hawaiian island stations to detect P-to-s converted phases to image seismic discontinuities between 200 to 800 km depth. Common-conversion point stacks of the data are used to map out lateral variations in converted phase observations, while slowness stacks allow differentiation between true conversions from discontinuities and multiples. We find that the 410 discontinuity is depressed by 20 km throughout our study region, while the main 660 is around average depth throughout most of the area. To the southwest of the Big Island we observe splitting of the 660, with a major peak at 630 km, and a minor peak appearing at 675 km depth. This is inferred to represent the position of the hot plume at depth, with the upper discontinuity caused by an olivine phase transition and the lower by a garnet phase transition. In the upper mantle, a discontinuity is found across the region at depths varying between 290 to 350 km. Identifying multiples from this depth confirms the presence of a so-called X-discontinuity. To the east of the Big Island the X-discontinuity lies around 336 km and the associated multiple is particularly coherent and strong in amplitude. Strikingly, the discontinuity around 410 km disappears in this area. Synthetic modelling reveals that such observations can be explained by a silica phase transition from coesite to stishovite, consistent with widespread ponding of silica-saturated material at these depths around the plume. This material could represent eclogite enriched material, which is relatively silica-rich compared to pyrolite, spreading out from the plume to the east as a deep eclogite pool, a hypothesis which is consistent with dynamical models of thermochemical plumes. Therefore these results support the presence of a significant garnet and eclogite component within the Hawaiian mantle plume

The morphology, evolution and seismic visibility of partial melt at the core-mantle boundary: Implications for ULVZs

SUMMARY Seismic observations indicate that the lowermost mantle above the core–mantle boundary (CMB) is strongly heterogeneous. Body waves reveal a variety of ultra-low velocity zones (ULVZs), which extend not more than 100 km above the CMB and have shear velocity reductions of up to 30 per cent. While the nature and origin of these ULVZs remain uncertain, some have suggested they are evidence of partial melting at the base of mantle plumes. Here we use coupled geodynamic/thermodynamic modelling to explore the hypothesis that present-day deep mantle melting creates ULVZs and introduces compositional heterogeneity in the mantle. Our models explore the generation and migration of melt in a deforming and compacting host rock at the base of a plume in the lowermost mantle. We test whether the balance of gravitational and viscous forces can generate partially molten zones that are consistent with the seismic observations. We find that for a wide range of plausible melt densities, permeabilities and viscosities, lower mantle melt is too dense to be stirred into convective flow and instead sinks down to form a completely molten layer, which is inconsistent with observations of ULVZs. Only if melt is less dense or at most ca. 1 per cent more dense than the solid, or if melt pockets are trapped within the solid, can melt remain suspended in the partial melt zone. In these cases, seismic velocities would be reduced in a cone at the base of the plume. Generally, we find partial melt alone does not explain the observed ULVZ morphologies and solid-state compositional variation is required to explain the anomalies. Our findings provide a framework for testing whether seismically observed ULVZ shapes are consistent with a partial melt origin, which is an important step towards constraining the nature of the heterogeneities in the lowermost mantle and their influence on the thermal, compositional and dynamic evolution of the Earth.ER

Characterizing a cluster's dynamic state using a single epoch of radial velocities

Radial velocity measurements can be used to constrain the dynamical state of a stellar cluster. However, for clusters with velocity dispersions smaller than a few km/s the observed radial velocity distribution tends to be dominated by the orbital motions of binaries rather than the stellar motions through the potential well of the cluster. Our goal is to characterize the intrinsic velocity distribution of a cluster from a single epoch of radial velocity data, even for a cluster with a velocity dispersion of a fraction of a km/s, using a maximum likelihood procedure. Assuming a period, mass ratio, and eccentricity distribution for the binaries in the observed cluster this procedure fits a dynamical model describing the velocity distribution for the single stars and center of masses of the binaries, simultaneously with the radial velocities caused by binary orbital motions, using all the information available in the observed velocity distribution. We find that the fits to the intrinsic velocity distribution depend only weakly on the binary properties assumed, so the uncertainty in the fitted parameters tends to be dominated by statistical uncertainties. Based on Monte Carlo simulations we provide an estimate of how these statistical uncertainties vary with the velocity dispersion, binary fraction, and the number of observed stars, which can be used to estimate the sample size needed to reach a specific accuracy. Finally we test the method on the well-studied open cluster NGC 188, showing that it can reproduce a velocity dispersion of only 0.5 km/s using a single epoch of the multi-epoch radial velocity data. If the binary period, mass ratio, and eccentricity distribution of the observed stars are roughly known, this procedure can be used to correct for the effect of binary orbital motions on an observed velocity distribution. [Abridged]Comment: 11 pages, 6 figures, accepted by A&

Searching for differential addition chains

The literature sometimes uses slow algorithms to find minimum-length continued-fraction differential addition chains to speed up subsequent computations of multiples of points on elliptic curves. This paper introduces two faster algorithms to find these chains. The first algorithm prunes more effectively than previous algorithms. The second algorithm uses a meet-in-the-middle approach and appears to have a limiting cost exponent below 1