We report the study of magnetotransport properties of regio-regular poly (3-hexyl thiophene) based organic diodes. The devices were fabricated using two different techniques of spin coating and inkjet printing. Positive magnetoresistance (MR) effect was observed at room temperature in all the devices. The highest MR magnitude reached up to 16% for some spin-coated devices and up to 10% in inkjet printed devices. The MR magnitude and line shapes were found to depend strongly on the measuring current. We observed deviation from the theoretically predicted Lorentzian or non-Lorentzian line shape of the MR traces, which is discussed in detail in the article. Although, the printed devices exhibit MR response as high as for the spin coated ones, they still need to be optimized in terms of performance and yield for large scale applications as magnetic sensors.
We investigate the charge-transfer interfaces between metal and redox arylamine molecular films through studying the current-voltage characteristics of single-layer organic diodes with the aid of anode interfacial engineering method. The diode turn-on voltage is shown to be highly sensitive to the arylamine/metal charge-transfer interfaces and thus can serve as a probe in detecting such organic/metal interfaces. We show that the diode electrical performance could be tuned through engineering the arylamine/metal interfaces via controlling the factors of anode work function, arylamine substitute…
The fabrication of single-carrier organic diodes from a series of sixteen molecular materials is reported. We experimentally demonstrate how the molecular structure affects the film morphology, and how the film morphology influences the diode performance. The compounds, with moderate molecular size and dendritic structures, are shown to be more favorable for good device performance than those small molecules with symmetry structures. The device turn-on voltage is found to be strongly dependent on the molecular first oxidation potentials. Independent of different anode materials, no obvious int…
p-Conjugated materials, including small molecules and polymers, are attracting substantial attention as novel gain media in semiconductor lasers; they offer many potential advantages not achievable with conventional inorganic semiconductors: simple processing, low cost, easy tuneability of the spectrum, and large-area integration on flexible substrates. Optically pumped lasing action in various small molecular and polymeric p-conjugated materials has been demonstrated using several resonator configurations. However, electrically pumped organic semiconductor lasers, i.e., organic injection or d…
The use of a thin mixed layer consisting of an inert diluent material and a light emitting material between the hole-transport layer and electron-transport layer of organic light-emitting diodes leads to an increase in the external quantum efficiency. The efficiency improvement is highly dependent on the thickness of the diluted light-emitting layer and driving current. Significant improvement seen at low current densities is explained in terms of effective hole confinement by the mixed layer while a modest decreases in efficiency at higher current densities may be attributed to luminescence q…
Organic Zener diodes with a precisely adjustable reverse breakdown from -3 V to -15 V without any influence on the forward current-voltage curve are realized. This is accomplished by controlling the width of the charge depletion zone in a pin-diode with an accuracy of one nanometer independently of the doping concentration and the thickness of the intrinsic layer. The breakdown effect with its exponential current voltage behavior and a weak temperature dependence is explained by a tunneling mechanism across the HOMO-LUMO gap of neigh- boring molecules. The experimental data are confirmed by a …
Based on the assumption that the contact barrier height determines the current flow in organic semiconductor-based electronic devices, charge injection at metal-organic (MO) interfaces has been extensively investigated, while space-charge conduction in organic bulk is generally overlooked. Recent theoretical modeling and simulation have pointed out that such a simplification is questionable due to the hopping nature of charge injection and hopping-related space-charge conduction. Here we show experimentally that charge transport in metal-organic diodes is complex interplay between injection-li…
Very thin (1.2-2.5nm) self-assembled organic dielectric monolayers have been integrated into organic thin-film diode to achieve electrical characteristics. These dielectrics are fabricated by self-assembling deposition, resulting in smooth, strongly adherent, thermally stable, organosiloxane thin films having interesting electrical capacitances (around 150 nF cm-2 at -3V) and insulating properties (leakage current densities around 10-5 A cm2 at -1V).
Electrically Detected Magnetic Resonance (EDMR) was used to study a series of multilayer organic devices based on aluminum (III) 8-hydroxyquinoline. These devices were designed to identify the micoscopic origin of different spin dependent process, i.e. hopping and exciton formation. EDMR is demonstrated to probe molecular orbitals of charge, and thus indirectly explore interfaces, exciton formation, charge accumalation and electric fields in operating organic based devices.
The application of solution-processable graphene oxide (GO) as hole injection layer in organic light-emitting diodes (OLEDs) is demonstrated. High luminance of over 53,000 cd m-2 is obtained at only 10 V. The results will unlock a route of applying GO in flexible OLEDs and other electrode applications.
A self-consistent, mean-field model of charge-carrier injection and unipolar transport in an organic semiconductor diode is developed utilizing the effective transport energy concept and taking into account a realistic density-of-states distribution as well as the presence of trap states in an organic material. The consequences resulting from the model are discussed exemplarily on the basis of an indium tin oxide/organic semiconductor/metallic conductor structure. A comparison of the theory to experimental data of a unipolar indium tin oxide/poly-3-hexyl-thiophene/Al device is presented.
Organic electrochemical transistors (OECTs) are currently being investigated for various applications, ranging from sensors to logics and neuromorphic hardware. The fabrication process must be compatible with flexible and scalable digital techniques to address this wide spectrum of applications. Here, we report a direct-write additive process to fabricate fully 3D printed OECTs. We developed 3D printable conducting, semiconducting, insulating, and electrolyte inks to achieve this. The 3D-printed OECTs, operating in the depletion mode, can be fabricated on thin and flexible substrates, yielding…
The present work is focused on theoretical and experimental study of localised levels in organic materials suitable for light-emitting devices and field effect transistors by means of thermal techniques. In our work we focused on low molecular compounds as well as on polymers, especially of two classes of materials: oxadiazoles and quinoxalines. Both organic compounds are well know as electron transport materials in OLEDs.
The use of natural or bioinspired materials to develop edible electronic devices is a potentially disruptive technology that can boost point-of-care testing. The technology exploits devices which can be safely ingested, along with pills or even food, and operated from within the gastrointestinal tract. Ingestible electronics could potentially target a significant number of biomedical applications, both as therapeutic and diagnostic tool, and this technology may also impact the food industry, by providing ingestible or food-compatible electronic tags that can smart track goods and monitor their…
We report high luminance organic light-emitting diodes by use of acid functionalized multi-walled carbon nanotube (o-MWCNTs) as efficient hole injector electrodes with a simple and solution processable device structure. At only 10 V, the luminance can reach nearly 50,000 cd/m2 with an external quantum efficiency over 2% and a current efficiency greater than 21 cd/A. The investigation of hole-only devices shows that the mechanism for hole injection is changed from injection limited to bulk limited because of the higher effective work function of the anode modified by the o-MWCNTs. We expect the…
Electroluminescence in organic light emitting diode (OLED) materials occurs via the recombination of excitonic electrons-hole pairs Only the singlet excitons of commonly used OLED materials, e.g., Aluminum trihydroxyquinoline (AlQ$_3$), decay radiatively, limiting the external quantum efficiency to a maximum 25%. Thus 75% of the energy is lost due to the triplet bottleneck for radiative recombination. We consider molecules derived from AlQ$_3$ which bypass the triplet bottleneck by designing structures which contain strong spin-orbit coupling. As a first stage of this work, groundstate energie…
The recombination of charges is an important process in organic photonic devices because the process influences the device characteristics such as the driving voltage, efficiency and lifetime. By combining the dipole trap theory with the drift-diffusion model, we report that the stationary dipole moment (μ0) of the dopant is a major factor determining the recombination mechanism in the dye-doped organic light emitting diodes when the trap depth (ΔEt) is larger than 0.3 eV where any de-trapping effect becomes negligible. Dopants with large μ0 (e.g., homoleptic Ir(III) dyes) induce large charge …
Quantifying the spin-spin interactions which influence electronic transitions in organic semiconductors is crucial for understanding their magneto-optoelectronic properties. By combining a theoretical model for three spin interactions in the coherent regime with pulsed electrically detected magnetic resonance experiments on MEH-PPV diodes, we quantify the spin-coupling within complexes comprising three spin-half particles. We determine that these particles form triplet-exciton:polaron pairs, where the polaron:exciton exchange is over 5 orders of magnitude weaker (less than 170 MHz) than that w…
Mobility-lifetime relation links photodegradation in spin-coated and gravure-printed organic solar cells
Technische Universität Chemnitz（开姆尼茨工业大学）；Friedrich-Alexander University Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；University of Bayreuth（拜罗伊特大学）；University of Potsdam（波茨坦大学）；Paul Drude Institute for Solid State Electronics（保罗·德鲁德固态电子研究所）
we investigated the magneto-electroluminescence (MEL) in tri-(8-hydroxyquinoline)-aluminum based organic light-emitting diodes (OLEDs) through the steady-state and transient method simultaneously. The MELs show the great different behaviors when we turn the driving condition from a constant voltage to a pulse voltage. For devices driven by the constant voltage, the MELs are similar with the literature data; for devices driven by the pulse voltage, the MELs are quite different, they firstly increase to a maximum then decrease as the magnetic field increases continuously. Negative MELs can be se…
The kinetics of the charge carrier recombination in dye molecule-doped multilayer organic light-emitting diodes (OLEDs) was quantified by transient electroluminescence (EL). Three sets of dye molecules, such as derivatives of naphthalimide and stilbene, were used as dopants in light-emission layer. Although the devices show almost the same EL spectra for each set of molecules, they show very different EL efficiency. The difference in EL efficiency was attributed to the difference in charge carrier recombination, as revealed by transient EL. The recombination coefficient (γ) was determined from…
White organic light-emitting diodes (OLEDs) are ultra-thin, large-area light sources made from organic semiconductor materials. Over the last decades, much research has been spent on finding the suitable materials to realize highly efficient monochrome and white OLEDs. With their high efficiency, color-tunability, and color-quality, white OLEDs are emerging to become one of the next generation light sources. In this review, we discuss the physics of a variety of device concepts that are introduced to realize white OLEDs based on both polymer and small molecule organic materi als. Owing to the …
This work reports our effort on understanding the efficiency roll-off in blue phosphorescent organic light-emitting diodes (OLEDs), based on a blue phosphorescence from bis(3,5-difluoro-2-(2-pyridyl)phenyl-(2-carboxypyridyl)- iridium (FIrpic) doped in 4,4-N,N-dicarbazole-biphenyl (CBP) host. The performance of a set of blue phosphorescent OLEDs with different FIrpic dopant concentrations was analyzed. Phosphorescent OLEDs, having a 30 nm thick pure FIrpic emissive layer, with a high luminous efficiency of 7.76 cd/A at 100 mA/cm2 was obtained. Theoretical calculation, based on the density funct…
Concentration quenching is a major impediment to efficient organic light-emitting devices. We herein report on Organic Light-Emitting Diodes (OLEDs) based on a fluorescent amorphous red-emitting starbust triarylamine molecule (4-di(4'-tert-butylbiphenyl-4-yl)amino-4'-dicyanovinylbenzene, named FVIN), exhibiting a very small sensitivity to concentration quenching. OLEDs are fabricated with various doping levels of FVIN into Alq3, and show a remarkably stable external quantum efficiency of 1.5% for doping rates ranging from 5% up to 40%, which strongly relaxes the technological constraints on th…
The semiconducting p-n junction is a simple device structure with great relevance for electronic and optoelectronic applications. The successful integration of low-dimensional materials in electronic circuits has opened the way forward for producing gate-tunable p-n junctions. In that context, here we present an organic (Cu-phthalocyanine)-2D layered material (MoS2) hybrid p-n junction with both gate-tunable diode characteristics and photovoltaic effect. Our proof-of-principle devices show multifunctional properties with diode rectifying factors of up to 10^4, while under light exposure they e…
Bridging the lab-to-fab gap in non-fullerene organic solar cells via gravure printing
Institute for Print and Media Technology, Chemnitz University of Technology（印刷与媒体技术研究所，开姆尼茨工业大学）；Institute of Physics, Chemnitz University of Technology（物理研究所，开姆尼茨工业大学）；Department of Engineering, Durham University（工程系，杜伦大学）
Singlet-polaron and triplet-polaron annihilation mechanisms are the most detrimental exciton quenching processes that lower the efficiency of organic light-emitting diodes (OLEDs) at high current densities, causing so-called efficiency roll-off in these devices. These exciton loss mechanisms are also the critical obstacles towards the realization of electrically pumped organic semiconductor lasers, which require very high current densities to reach threshold. Herein, under a relatively large external magnetic field, we demonstrate that the efficiency roll-off at high current densities in europ…
Organic light-emitting diodes (OLEDs) must be engineered to circumvent the efficiency limit imposed by the 3:1 ratio of triplet to singlet exciton formation following electron-hole capture. Here we show the spin nature of luminescent radicals such as TTM-3PCz allows direct energy harvesting from both singlet and triplet excitons through energy transfer, with subsequent rapid and efficient light emission from the doublet excitons. This is demonstrated with a model Thermally-Activated Delayed Fluorescence (TADF) organic semiconductor, 4CzIPN, where reverse intersystem crossing from triplets is c…
Devices which exploit the quantum properties of materials are widespread, with quantum information processors and quantum sensors showing significant progress. Organic devices offer interesting opportunities for quantum technologies owing to their engineerable spin properties, with spintronic operation and spin resonance magnetic-field sensing demonstrated in research grade devices, as well as proven compatibility with large scale fabrication techniques. Yet several important challenges remain as we move toward scaling these proof-of-principle quantum devices to larger integrated logic systems…
We use spectrally-resolved magneto-electroluminescence (EL) measurements to study the energy dependence of hyperfine interactions between polaron and nuclear spins in organic LEDs. Using layered devices based on Bphen/MTDATA -- a well-known exciplex emitter -- we show that the increase in EL emission intensity $I$ due to small applied magnetic fields of order 100 mT is markedly larger at the high-energy blue end of the EL spectrum (dI/I ~11%) than at the low-energy red end (~4%). Concurrently, the widths of the magneto-EL curves increase monotonically from blue to red, revealing an increasing …
The ability to accurately extract low-amplitude voltage signals is crucial in several fields, ranging from single-use diagnostics and medical technology to robotics and the Internet of Things. The organic electrochemical transistor, which features large transconductance values at low operation voltages, is ideal for monitoring small signals. Its large transconductance translates small gate voltage variations into significant changes in the drain current. However, a current-to-voltage conversion is further needed to allow proper data acquisition and signal processing. Low power consumption, hig…
Despite widespread interest, ultrathin and highly flexible light-emitting devices that can be seamlessly integrated and used for flexible displays, wearables, and as bioimplants remain elusive. Organic light-emitting diodes (OLEDs) with $μ$m-scale thickness and exceptional flexibility have been demonstrated but show insufficient stability in air and moist environments due to a lack of suitable encapsulation barriers. Here, we demonstrate an efficient and stable OLED with a total thickness of $\approx$12 $μ$m that can be fully immersed in water or cell nutrient media for weeks without suffering…
Carbene-metal-amide type photoemitters based on CF$_3$-substituted carbazolate ligands show sky-blue to deep-blue photoluminescence from charge-transfer excited states. They are suitable for incorporation into organic light-emitting diodes (OLEDs) by thermal vapour deposition techniques, either embedded within a high-triplet-energy host, or used host-free. We report high-efficiency OLEDs with emission ranging from yellow to blue (Commission Internationale de l'Éclairage (CIE) coordinates from [0.35, 0.53] to [0.17, 0.17]). The latter show a peak electroluminescence external quantum efficiency …
Spin-spin interactions in organic light-emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) are pivotal because radiative recombination is largely determined by triplet-to-singlet conversion, also called reverse intersystem crossing (RISC). To explore the underlying process, we apply a spin-resonance spectral hole-burning technique to probe electroluminescence. We find that the triplet exciplex states in OLEDs are highly spin-polarized and show that these states can be decoupled from the heterogeneous nuclear environment as a source of spin dephasing and can even b…
Novel thermally activated delayed fluorescence (TADF) material with diphenyl sulfone (DPS) as an electron acceptor and 3,6-dimethoxycarbazole (DMOC) and 1,3,6,8-Tetramethyl-9H-carbazole (TMC) as electron donors were investigated theoretically for a blue organic light emitting diode (OLED) emitter. We calculate the energies of the first singlet (S1) and first triplet (T1)-excited states of TADF materials by performing density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations on the ground state using a dependence on charge transfer amounts for the optimal Hartree-Fock percent…
We fabricate OLEDs using a stable neutral π radical, BDPA, as the emitter. There is only one electron in the singly occupied molecular orbital (SOMO) of this open-shell molecule. This feature makes the excited state of open-shell molecules be neither singlet nor triplet, but doublet. The key issue of how to harvest the triplet energy in an OLED is thus bypassed, due to the radiative decay of doublet is totally spin allowed. In the BDPA-based OLED, the emission was confirmed to be from the electronic transition from LUMO to SOMO, via the frontier molecular orbital analysis combined with the spe…
The performance of solution-processed organic light emitting diodes (OLEDs) is often limited by non-uniform contacts. In this work, we introduce Ni-containing solution-processed metal oxide (MO) interfacial layers inserted between indium tin oxide (ITO) and poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) to improve the bottom electrode contact for OLEDs using the poly(p-phenylene vinylene) (PPV) derivative Super-Yellow (SY) as an emission layer. For ITO/Ni-containing MO/PEDOT:PSS bottom electrode structures we show enhanced wetting properties that result in an improved OLE…
We present a comprehensive model to analyze, quantitatively, and predict the process of degradation of organic light-emitting diodes (OLEDs) considering all possible degradation mechanisms, i.e., polaron, exciton, exciton-polaron interactions, exciton-exciton interactions, and a newly proposed impurity effect. The loss of efficiency during degradation is presented as a function of quencher density, the density and generation mechanisms of which were extracted using a voltage rise model. The comprehensive model was applied to stable blue phosphorescent OLEDs (PhOLEDs), and the results showed th…
We develop a general theory of electron--hole recombination in organic light emitting diodes that leads to formation of emissive singlet excitons and nonemissive triplet excitons. We briefly review other existing theories and show how our approach is substantively different from these theories. Using an exact time-dependent approach to the interchain/intermolecular charge-transfer within a long-range interacting model we find that, (i) the relative yield of the singlet exciton in polymers is considerably larger than the 25% predicted from statistical considerations, (ii) the singlet exciton yi…
We present an exciton/lattice model of the electronic dynamics of primary photoexcitations in a polymeric semiconductor heterojunction which includes both polymer pi-stacking, energetic disorder, and phonon relaxation. Results from our model are consistent with a wide range of recent experimental evidence that excitons decay directly to well-defined polarons on a sub-100 fs timescale, which is substantially faster than exciton relaxation processes. Averaging over multiple samples, we find that as the interfacial offset is increased, a substantial fraction of the density of electronic states in…
Using d. functional theory (DFT) computations, the authors demonstrated a substantial skeletal relaxation when the structure of 2,5-bis-[4-anthracene-9-yl-phenyl]-1,1-dimethyl-3,4-diphenyl-silole (BAS) is optimized in the gas-phase comparing with the mol. structure detd. from monocrystal x-ray diffraction. The origin of such a relaxation is explained by a strong environmental strains induced by the presence of anthracene entities. Also, the estn. of the frontier orbital levels showed that this structural relaxation affects mainly the LUMO that is lowered of 190 meV in the gas phase. To check i…
We report observation of ferromagnetic (FM) ordering in organic semiconductors, namely regio-regular poly (3-hexyl thiophene) (RRP3HT) and 1-(3-methoxycarbonyl)propyl-1-phenyl-[6,6]-methanofullerene (PCBM), in the temperature range of 5-300 K in addition to magnetoresistance (OMAR) observed in the diodes made from the same materials. Particle induced x-ray emission spectroscopy confirms the presence of dilute magnetic impurities in the materials mainly as residues from the synthesis process. However, upon blending these two materials with FM signal, the FM ordering is suppressed by a huge para…
2D hybrid organic-inorganic semiconductors (HOIS) are low-cost, self-assembled semiconductors that have proven to be vital for novel optoelectronic devices due to their inherent stable excitons even at room temperature. 2D HOIS are chemically stable with respect to the 3D analogues, but their inherent anisotropy complicates their implementation in devices, including electroluminescence (EL) devices. We report on the synthesis, characterization, cathodoluminescence and EL of a new 2D HOIS, (4-fluoro phenethylamine-H)2PbBr4, and its defect variations (DVs). The latter, in contrast to the pristin…
We described an approach to achieve fine color control of fluorescent White Organic Light-Emitting Diodes (OLED), based on an Ultra-thin Premixed emitting Layer (UPL). The UPL consists of a mixture of two dyes (red-emitting 4-di(4'-tert-butylbiphenyl-4-yl)amino-4'-dicyanovinylbenzene or fvin and green-emitting 4-di(4'-tert-butylbiphenyl-4-yl)aminobenzaldehyde or fcho) premixed in a single evaporation cell: since these two molecules have comparable structures and similar melting temperatures, a blend can be evaporated, giving rise to thin films of identical and reproducible composition compared…
In this work we present an alternative to the use of PEDOT:PSS as hole transport and electron blocking layer in organic photodetectors processed by solution. As PEDOT:PSS is known to be sensitive to humidity, oxygen and UV, removing this layer is essential for lifetime improvements. As a first step to achieving this goal, we need to find an alternative layer that fulfills the same role in order to obtain a working diode with similar or better performance. As a replacement, a layer of Poly((4,8-bis-(2-ethylhexyloxy)-benzo(1,2-b:4,5-b)dithiophene)-2,6-diyl-alt-(4-(2-ethylhexanoyl)-thieno(3,4-b]t…
An electrode contact-related mechanism for the operational instability of organic electronic devices is proposed and confirmed via observation of a water-induced change in charge-injection barrier eights at the electrode/organic-semiconductor interfaces. Water molecules in air penetrate into the organic crystal via diffusion, and an external electric field orients the electric dipole of the water molecules at the electrode surfaces, leading to dipolar switching of the charge-injection barrier height. As a result of the switching, current-voltage curves of two-terminal Au-rubrene-Au devices cha…
In photovoltaic diodes recombination of photogenerated electrons and holes is a major loss process. Biological light harvesting complexes (LHCs) prevent recombination via the use of cascade structures, which lead to spatial separation of charge-carriers1. In contrast, the nanoscale morphology and high charge densities in organic photovoltaic cells (OPVs) give a high rate of electron-hole encounters, which should result in the formation of spin triplet excitons, as in organic light emitting diodes (OLEDs)2. OPVs would have poor quantum efficiencies if every encounter lead to recombination, but …
We review theories of phosphorescence in cyclometalated complexes. We focus primarily on pseudooctahedrally coordinated $t_{2g}^6$ metals (e.g., [Os(II)(bpy)$_3$]$^{2+}$, Ir(III)(ppy)$_3$ and Ir(III)(ptz)$_3$) as, for reasons that are explored in detail, these show particularly strong phosphorescence. We discuss both first principles approaches and semi-empirical models, e.g., ligand field theory. We show that together these provide a clear understanding of the photophysics and in particular the lowest energy triplet excitation, T$_1$. In order to build a good model relativistic effects need t…
We report the successful extraction of spin polarized current from the organic-based room temperature ferrimagnetic semiconductor V[TCNE]x (x~2, TCNE: tetracyanoethylene; TC ~ 400 K, EG ~ 0.5 eV, s ~ 10-2 S/cm) and its subsequent injection into a GaAs/AlGaAs light-emitting diode (LED). The spin current tracks the magnetization of V[TCNE]x~2, is weakly temperature dependent, and exhibits heavy hole / light hole asymmetry. This result has implications for room temperature spintronics and the use of inorganic materials to probe spin physics in organic and molecular systems.
Electron-hole (e-h) capture in luminescent conjugated polymers (LCPs) is modeled by the dissipative dynamics of a multilevel electronic system coupled to a phonon bath. Electroinjected e-h pairs are simulated by a mixed quantum state, which relaxes via phonon-driven internal conversions to low-lying charge-transfer (CT) and excitonic (XT) states. The underlying two-band polymer model reflects PPV and spans monoexcited configuration interaction singlets (S) and triplets (T), coupled to Franck-Condon active C=C stretches and ring-torsions. Focusing entirely upon long PPV chains, we consider the …
Measurements of the effect of a magnetic field on the light output and current through an organic light emitting diode made with deuterated aluminium tris(8-hydroxyquinoline) have shown that hyperfine coupling with protons is not the cause of the intrinsic organic magnetoresistance. We suggest that interactions with unpaired electrons in the device may be responsible.
We introduce an analytical model for ideal organic laser diodes based on the argument that their intrinsic active layers necessitate operation in the bipolar space charge-limited current regime. Expressions for the threshold current and voltage agree well with drift-diffusion modeling of complete p-i-n devices and an analytical bound is established for laser operation in the presence of annihilation and excited-state absorption losses. These results establish a foundation for the development of organic laser diode technology.
