Kinetic Monte Carlo Modelling of Organic Photovoltaic Devices

Organic photovoltaics (OPVs) is a rapidly growing low-cost PV technology sector that relies on multiple benefits of organic semiconductors viz. being environmental-friendly with a simplified processing/fabrication and tunable properties. While the performance of OPVs has gone up to over 19 % in the last 2 decades, it still lags behind the silicon-PV technology in terms of efficiency and stability. The performance of any solar cell is essentially a combination of three quantities: short circuit current density (jSC), fill- factor (FF), and open circuit voltage (VOC). Of these quantities, especially VOC still offers a scope of further improvement as it falls short of the theoretical achievable limit which requires a better understanding of the various loss channels in an actual device leading to a VOC reduction. Through this thesis, we have developed an understanding of VOC using non-equilibrium models and proposed ways leading to its enhancement. The first step in this study was to develop an understanding of the underlying charge transport mechanism, which relates to the efficiency with which the charges can be extracted at the terminals, or electrodes. Charge transport in any disordered organic semiconductor occurs by a process of hopping, in which charge carriers jump by thermally activated tunneling between localized sites that are randomly distributed in the energy dependent density of states. Thus, among other hopping parameters, the mobility of a charge carrier is crucially dependent on the disorder. We implemented a new semi-analytical hopping model that allows for a consistent extraction of these parameters from the space charge limited conductivity (SCLC) experiments. The model was calibrated against a numerical kinetic Monte Carlo (kMC) model and was used to analyze temperature-dependent SCLC curves for multiple systems used frequently as an active layer in organic solar cells. We observed that there exists a critical ratio between the inter-site distance and the localization length that decides the applicability, or not, of the much-used extended Gaussian disorder model (EGDM). The improved hopping model functions well for both fullerene and non-fullerene-based systems and can also describe the charge transport in electron-only devices, which so far have not been described successfully using EGDM. Having the charge dynamics and other hopping parameters in place, we subsequently developed and calibrated, by independent experiments, a robust and stochastic kMC model that can calculate a full j-V curve of a solar cell correctly. With the full calibration in place with respect to the morphology, recombination rate constant and injection barriers, the motivation was to have a model that can calculate both transients and steady-state j-V curves of a given device. So far, implementing kMC to analyze a full device has been a challenge, especially due to the numerical problems associated with the presence of Ohmic contacts. The calibrated model correctly predicts the device’s j-V and non-equilibrium hopping transport recombination dynamics. A crucial approximation that stems from inorganic solar cells and that is commonly made for organic solar cells as well, is the fast and complete thermalization of charge carriers in the density of states. However, the relaxation of charge carriers in case of organic semiconductors is not as straightforward as in inorganics, but rather a complex two-step process consisting of a fast on-site relaxation followed by a slower global relaxation occurring via hopping to increasingly deep sites. We have shown that the second slow thermalization does not complete within the charge carrier lifetime in the device and leads to a VOC that is 0.1 - 0.2 V higher than the equilibrium value. This is found for both fullerene and high-performing non-fullerene OPV systems. For a given OPV device, there is a significant difference between the upper limit for the efficiency set by theoretical considerations based on the assumption of near-equilibrium (the so-called Shockley-Queisser limit) and the actual measured efficiency. We numerically explored a new funnel-shaped morphology, which can lead to an impactful gain in VOC and efficiency of an organic solar cell. In contrast to the conventional blend morphology, which does not lead to a directed motion of the photogenerated charge carriers, the funnel morphology rectifies the otherwise undirected diffusive motion of ‘hot’ charges, which leads to a higher probability of extraction at the desired contact. We utilized the reciprocity analysis to calculate the gain in VOC and efficiency as compared to a hypothetical equilibrium system of the same material. We found that for an optimized funnel morphology, the efficiency can surpass the near-equilibrium limit. Mixing materials to form a high-performing ternary OPV has emerged as a possible route to improve performance. We performed a review of literature data and deduced that the relative gain in VOC is too small to contribute to a large gain in the efficiency. Instead, the major contribution to the efficiency enhancement is due to gains in the FF and/or jSC. Also, the VOC of the ternary system is found to be tunable relative to the ratio of the added species in the host system. These experimental findings were consistently described by extensive numerical simulations in which the active layer morphology was assumed to give rise to an energetic cascade for at least one of the charge carriers. In contrast, our explicit calculations show that the commonly employed parallel junction model cannot explain the experimental findings.Termen "organisk" avser något som huvudsakligen består av kol, och "organisk solcell" är helt enkelt en anordning för energiutvinning av ett sådant organiskt material som omvandlar solljus till elektrisk energi. Det är en snabbt växande teknik för energiutvinning till låg kostnad med många fördelar som låg vikt, miljövänlighet, giftfrihet osv. Även om prestandan hos dessa anordningar har ökat avsevärt, är det fortfarande ett pågående arbete att göra dem jämförbara med annan teknik. En typisk solcells prestanda bestäms av dess elektriska egenskaper, särskilt strömmen och spänningen vid exponering för solljus. Denna avhandling fokuserar på strategier för att förbättra utgångsspänningen hos organiska solceller. För att tillverka en organisk solcell används två typer av material; det ena fungerar som en donator, dvs. det kan lätt avge en elektron vid belysning, och det andra är en acceptor, dvs. ett material som kan ta upp denna elektron. Donatorn och acceptorn blandas för att bilda det aktiva skiktet i en cell, som deponeras mellan två strömuppsamlande elektroder. Dessa organiska material har inhomogeniteter i sin struktur, vilket leder till så kallad energetisk oordning, vilket innebär att inte alla platser där en laddning kan sitta har samma energi. Denna oordning påverkar hur lätt en elektron (eller ett hål - en positiv laddning) kan förflytta sig inom anordningen. Vi har studerat laddningstransportegenskaperna i en anordning med hjälp av en ny modell som ger en korrekt uppskattning av dessa egenskaper vid varje givet tillfälle. Vi har också utvecklat en numerisk modell som kan reproducera de experimentella ström- och spänningsegenskaperna hos en helt organisk solcell. När laddningar rör sig i en organisk solcellsenhet förlorar de en betydande mängd energi på grund av den ovan nämnda oordningen. Denna energiförlust kan minskas om en mer "riktad" eller forcerad rörelse sker så att elektronerna och hålen endast går till den önskade elektroden. Detta är möjligt genom att skapa en ny mikroskopisk struktur (morfologi) som underlättar en sådan riktad laddningsrörelse. Vi har föreslagit en ny trattformad morfologi som bildas genom ett lämpligt arrangemang av donator- och acceptor materialen och som leder till en betydande ökning av utgångsspänningen och därmed till en övergripande förbättring av solcellsutrustningens prestanda. Ett annat sätt att förbättra organiska solceller kan ske när en tredje organisk förening läggs till donator- och acceptor blandningen, som då kallas en ternär solcell. Det har visat sig att denna ytterligare art ger en förbättring av solcellens prestanda och gör det möjligt att göra ett tjockare aktivt skikt, vilket är fördelaktigt för att generera högre strömmar och därmed högre effekt. En litteraturgenomgång ger otillräcklig och icke-slutgiltig information om de ansvariga mikroskopiska strukturer som leder till högpresterande ternära enheter. Genom systematiska beräkningar och experiment har vi hittat den morfologi som konsekvent kan förklara dessa system. Författaren hoppas att detta arbete kommer att bidra till den forskning som är inriktad på att skapa förbättrade morfologier och system vilket kan leda till faktiska prestandaförbättringar i organiska solceller

Can Organic Solar Cells Beat the Near-Equilibrium Thermodynamic Limit?

Despite an impressive increase over the past decade, experimentally determined power conversion efficiencies of organic photovoltaic cells still fall considerably below the theoretical upper bound for near-equilibrium solar cells. Even in otherwise optimized devices, a prominent yet incompletely understood loss channel is the thermalization of photogenerated charge carriers in the density of states that is broadened by energetic disorder. Here, we demonstrate by extensive numerical modeling how this loss channel can be mitigated in carefully designed morphologies. Specifically, we show how funnel-shaped donor-and acceptor-rich domains in the phase-separated morphology that are characteristic of organic bulk heterojunction solar cells can promote directed transport of positive and negative charge carriers toward the anode and cathode, respectively. We demonstrate that in optimized funnel morphologies this kinetic, nonequilibrium effect, which is boosted by the slow thermalization of photogenerated charges, allows one to surpass the near-equilibrium limit for the same material in the absence of gradients.Funding Agencies|Swedish Research Counsil (Vetenskapsradet) [OPV2.0 2016-06146]; German Research Foundation under Germanys Excellence Strategy [2082/1-390761711]; Carl Zeiss Foundation</p

Slow Relaxation of Photogenerated Charge Carriers Boosts Open-Circuit Voltage of Organic Solar Cells

Among the parameters determining the efficiency of an organic solar cell, the open-circuit voltage (V-OC) is the one with most room for improvement. Existing models for the description of V-OC assume that photogenerated charge carriers are thermalized. Here, we demonstrate that quasi-equilibrium concepts cannot fully describe V-OC of disordered organic devices. For two representative donor:acceptor blends, it is shown that V-OC is actually 0.1-0.2 V higher than it would be if the system was in thermodynamic equilibrium. Extensive numerical modeling reveals that the excess energy is mainly due to incomplete relaxation in the disorder-broadened density of states. These findings indicate that organic solar cells work as nonequilibrium devices, in which part of the photon excess energy is harvested in the form of an enhanced V-OC.Funding Agencies|Swedish Research Council (project "OPV2.0")Swedish Research Council; European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grantSKA South Africa [799801]; Carl Zeiss Foundation</p

General rule for the energy of water-induced traps in organic semiconductors

Charge carrier traps are generally highly detrimental for the performance of semiconductor devices. Unlike the situation for inorganic semiconductors, detailed knowledge about the characteristics and causes of traps in organic semiconductors is still very limited. Here, we accurately determine hole and electron trap energies for a wide range of organic semiconductors in thin-film form. We find that electron and hole trap energies follow a similar empirical rule and lie similar to 0.3-0.4 eV above the highest occupied molecular orbital and below the lowest unoccupied molecular orbital, respectively. Combining experimental and theoretical methods, the origin of the traps is shown to be a dielectric effect of water penetrating nanovoids in the organic semiconductor thin film. We also propose a solvent-annealing method to remove water-related traps from the materials investigated, irrespective of their energy levels. These findings represent a step towards the realization of trap-free organic semiconductor thin films.Funding Agencies|Chinese Scholarship Council (CSC); SeRC (Swedish e-Science Research Center)</p

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, such as 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) is 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 is integrated in a freeware drift-diffusion solver. The mobility model is 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- and n-type devices. We find a critical ratio of a(NN)/alpha (mean intersite distance:localization radius) of about three, 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.Funding Agencies|Vetenskapsradet, project "OPV2.0"; European UnionEuropean Union (EU) [799477 - HyThermEl]</p

Carrier Mobility Dynamics under Actual Working Conditions of Organic Solar Cells

Although organic photovoltaics has made significant progress since its appearance decades ago, the underlying physics of charge transport in working cells is still under debate. Carrier mobility, determining the carrier extraction and recombination, is one of the most important but complex and still poorly understood parameters. Low-energy charge carrier states acting as traps play a particularly important role in carrier transport. Occupation of these states under real operation conditions of solar cells induces additional complexity. In this study, we use several transient methods and numerical modeling to address carrier transport under actual working conditions of bulk heterojunction organic solar cells based on fullerene and nonfullerene acceptors. We show that occupation of low-energy states strongly depends on the blend materials and the effective electric field. We define conditions when such occupation increases carrier mobility, making it less time-dependent on the microsecond time scale, and when its influence is only marginal. We also show that the initial mobility, determined by carrier relaxation within the high-energy part of the distributed density of states, strongly decreases with time independently of the low-energy state population.Funding Agencies|Vetenskapsradet, project "OPV2.0"; Carl Zeiss Foundation</p