Effects Of Energetic Disorder Research Articles

Relationship between Energetic Disorder and Reduced Recombination of Free Carriers in Organic Solar Cells

AbstractReducing non‐radiative recombination is key to achieve high fill factors (FFs) in organic solar cells. While it is generally accepted that recombination proceeds via charge transfer (CT) states at the donor:acceptor interface, the underlying principles that dictate the decay kinetics of these CT states are not yet well understood. Here, a study on the effect of energetic disorder is presented. Based on a data set of 10 representative donor:acceptor blends, clear correlations between disorder, the recombination coefficient of free charge carriers, and the non‐radiative voltage loss are found. It is suggested that a narrower distribution of CT energies leads to a longer CT decay time and thus reduces non‐radiative losses. This leads to a simultaneous improvement of the FF and open circuit voltage and highlights the importance of having materials with low energetic disorder on the way to the commercialisation of organic photovoltaics.

An analytical model for organic bulk heterojunction solar cells based on Saha equation for exciton dissociation.

The power conversion efficiencies of organic solar cells (OSCs) have been greatly improved in recent years. However, latest experimental data of high efficiency OSCs, the sublinear relationship between the short circuit current density (Jsc) and light intensity (Pin), and the effects of energetic disorder in bulk heterojunction organic solar cells have not been understood. An analytical model for high-efficiency OSCs is proposed, which takes most physical factors into account that have been ignored in most previous models, including practical solar spectra and absorption spectra, degeneracy effect, exciton effect, space charge limited current, and unified mobility expression dependent on temperature, electric field and density, etc. Three analytical iterative methods are proposed to solve the strong non-linear Poisson equation and the drift-diffusion equations. The method for the drift-diffusion equations involves introducing two constant coefficients and determining their values self-consistently by demanding the space averages of approximate drift and diffusion currents equal to the averages of accurate ones. The theoretical results for five high-efficiency OSCs are in good agreement with experimental data, including current-voltage curves, light intensity-dependent Jsc and open-circuit voltage (Voc) curves. The effects of energetic disorder in bulk heterojunction organic solar cells, and the sublinear relationship Jsc ∝ Pαin (α < 1) can be well explained. The Saha equation for exciton dissociation and the space-charge-limited-current (SCLC) effect are important for modelling high-efficiency OSCs. The Voc ∼ Pin relationship can be influenced by many factors. But, the Jsc ∼ Pin relationship can be mainly and slightly influenced by the exciton effect and energetic disorder, respectively. When aiming to realize higher performance OSCs, one should decrease six material parameters, including the energetic disorder, exciton mass, deep level impurity concentration, the ratios of electron and hole mobilities, densities of states for electrons and holes, and potential barriers at the anode and cathode. The performance parameters of 15 triad compounds are predicted by using ab initio Eg and absorption spectra from the literature along with other input parameters taken from previous optimized values, and the efficiency of two compounds was found to exceed 35%.

Effects of energetic disorder in bulk heterojunction organic solar cells

The energetic disorder can be reduced by developing new photovoltaic materials, especially non-fullerene acceptors, and significant progress in the PCEs of OSCs has been made.

Effect of energetic disorder on triplet-triplet annihilation in organic semiconductors

We present a model for the triplet-triplet annihilation in organic phosphorescent host-guest systems that considers the effect of the energetic disorder on the kinetics of the annihilation. Nonequilibrium (time-dependent) transport of the triplets that arises from the progressive relaxation of triplets in the energy landscape is taken into account in the model. Triplet excitons are considered to move between the guest sites (dye molecules) via the thermally activated tunneling mechanism; the annihilation step, however, takes place through the F\"orster mechanism. Based on the model developed, and by calculating the time evolution of the triplet concentration, we investigate the effect of the various parameters on the effective annihilation coefficient. At low dye concentrations, it is shown that relaxation of the triplets is not completed during their lifetimes, and therefore, the annihilation process occurs entirely in the nonequilibrium. We also address the competition between two pathways for the annihilation process: single-step, long-range annihilation, and diffusion-assisted annihilation. By a quantitative comparison with experimental data reported in the literature, we demonstrate certain conditions in which there is a considerable contribution from the diffusion to the total annihilation rate. The model presented in this work can also be used for the excitons that diffuse by the F\"orster mechanism.

A theoretical study of influence of charge carrier mobility in PTB7:PC71BM bulk heterojunction organic solar cells

In this study, an optoelectronic model is presented to simulate the structure of PTB7:PC71BM organic solar cells. This model is based on transfer matrix model for calculating optical processes and drift–diffusion model for computing both electrical and charge transport processes; the latter includes the effects of energetic disorder. In the presence of energetic disorder, the total recombination is calculated as the sum of Langevin recombination, recombination via charge transfer states, and recombination via exponential tail states. We investigate the influence of charge carrier mobility on photovoltaic parameters, charge transport, and recombination rate. Simulation results indicate that open circuit voltage is governed by the charge carrier mobility and power conversion efficiency as a function of charge carrier mobility has a maximum value at μ = 10−2 (cm2/Vs). Simulated current density–voltage curve reveals good agreement with published experimental results. The open circuit voltage is calculated as a function of generation rate. It is found that the slope of lines increases with decreasing the charge carrier mobility.

Monte Carlo Simulation of Geminate Pair Recombination Dynamics in Organic Photovoltaic Devices: Multi-Exponential, Field-Dependent Kinetics and Its Interpretation

Monte Carlo simulations are used to examine charge-transfer (CT) state recombination dynamics considering the effects of energetic disorder and bulk heterojunction morphology. Strongly biexponential recombination kinetics were observed, in agreement with spectroscopy. Data over a range of electric fields 106 ≤ F ≤ 108 V m–1 suggest that the slow component of recombination is due to energetic and spatial trapping of charges, as increasing the field reduces the magnitude of the slow decay. This behavior could not be described using a simple Onsager–Braun type model; hence, an alternative kinetic framework including an intermediate “quasi-free” state between the CT state and free charges is proposed and subsequently shown to fit the MC data very well. The predictive capability of the modified model was then tested by repeating MC simulations with an altered recombination rate. It is shown that more than just the recombination rate had to be changed in the modified kinetic model to retrieve good agreement with MC simulations. This suggests that the derived rates from the modified kinetic model do not have exact correspondence with physical processes in organic photovoltaic blends. We attribute the difficulty in fitting kinetic models to CT recombination data to the dispersive nature of hopping transport.

Effect of energetic disorder on the open-circuit voltage in organic bulk heterojunction composites

Under open-circuit condition, the current is not extracted and the photogenerated carriers in principle disappear only by recombination. We study the open-circuit voltage and transient photovoltage under the effect of bulk recombination in a medium with energetic disorder by using the multiple trapping (MT) model. The key parameter in the MT model is the dispersion parameter given by the ratio of thermal energy to the characteristic energy of trap states. We show that depends linearly on the logarithm of the light intensity and the slope depends on the of the MT model. Under the continuous irradiation of light, the photovoltage response to the weak perturbation by a pulsed light obeys pseudo-first-order decay. The rate as a function of is independent of the dispersion parameter. However, it obeys the power law as a function of light intensity, and the exponent is given by , which reduces to 1/2 in the absence of energetic disorder.

Effects of energetic disorder on the low-frequency differential capacitance of organic light emitting diodes

It has recently been shown how the injection barriers at the electrode interfaces and the built-in voltage (Vbi) of organic light emitting diodes can be obtained from measurements of the differential capacitance at low frequencies, using the voltage and height of a distinct peak in the capacitance-voltages curves. In this paper, we investigate the effects of Gaussian energetic disorder on the analysis, for single-carrier and double-carrier devices. We show how the disorder affects the peak position and height, and how from combined capacitance-voltage measurements and device modeling the injection barriers and Vbi can be determined. As examples, hole-only and double-carrier devices are investigated based on a blue-emitting polyfluorene-triarylamine copolymer.

Effects of Energetic Disorder and Mobility Anisotropy on Geminate Electron-hole Recombination in the Presence of a Donor-Acceptor Heterojunction

Geminate electron-hole recombination in organic solids in the presence of a donor-acceptor heterojunction is studied by computer simulations. We analyze how the charge-pair separation probability in such systems is affected by energetic disorder of the media, anisotropy of charge-carrier mobilities, and other factors. We show that in energetically disordered systems the effect of heterojunction on the charge-pair separation probability is stronger than that in idealized systems without disorder. We also show that a mismatch between electron and hole mobilities reduces the separation probability, although in energetically disordered systems this effect is weaker compared to the case of no energetic disorder. We demonstrate that the most important factor that determines the charge-pair separation probability is the ratio of the sum of electron and hole mobilities to the rate constant of recombination reaction. We also consider systems with mobility anisotropy and calculate the electric field dependence of the charge-pair separation probability for all possible orientations of high-mobility axes in the donor and acceptor phases. We theoretically show that it is possible to increase the charge-pair separation probability by controlling the mobility anisotropy in heterojunction systems and in consequence to achieve higher efficiencies of organic photovoltaic devices.

Relationship between energetic disorder and open-circuit voltage in bulk heterojunction organic solar cells

We simulate organic bulk heterojunction solar cells. The effects of energetic disorder are incorporated through a Gaussian or exponential model of density of states. Analytical models of open-circuit voltage (${V}_{\mathrm{OC}}$) are derived from the splitting of quasi-Fermi potentials. Their predictions are backed up by more complex numerical device simulations including effects such as carrier-density--dependent charge-carrier mobilities. It is predicted that the V${}_{\mathrm{OC}}$ depends on: (1) the donor-acceptor energy gap; (2) charge-carrier recombination rates; (3) illumination intensity; (4) the contact work functions (if not in the pinning regime); and (5) the amount of energetic disorder. A large degree of energetic disorder, or a high density of traps, is found to cause significant reductions in ${V}_{\mathrm{OC}}$. This can explain why ${V}_{\mathrm{OC}}$ is often less than expected in real devices. Energetic disorder also explains the nonideal temperature and intensity dependence of ${V}_{\mathrm{OC}}$ and the superbimolecular recombination rates observed in many real bulk heterojunction solar cells.

The effects of energetic disorder and polydispersity in conjugation length on the efficiency of polymer-based light-emitting diodes

Energetic disorder plays a critical role in governing the performance of organic light-emitting diodes (OLEDs). This is particularly true for polymer-based OLEDs in which disorder can be controlled but not eliminated. Contrary to the common assumption that energetic disorder has only a negative effect on performance, we provide experimental evidence of improved efficiency when the energetic disorder is increased upon deliberate addition of traps via an increase in polymer chain length distribution. We use numerical calculations to extract the mechanisms responsible for the observed improvements and discuss the general conditions under which traps can be introduced to increase device efficiency.

Theory of bulk electron-hole recombination in a medium with energetic disorder

The kinetics of bulk recombination between electrons and holes in semiconductors that have energetic disorder is studied theoretically. The effect of energetic disorder in the medium is taken into account by using a multiple trapping model in which charges repeat trapping into and detrapping from trap sites with different trapping energies. We assume that recombination between an electron and a hole can occur only when at least one of them is detrapped. The distribution of trap sites with different trapping energies $E$ is assumed to be exponential: $\ensuremath{\sim}\text{exp}(\ensuremath{-}E/{E}_{0})$. A general theory for the kinetics of bulk recombination between electrons and holes is formulated which is valid for an arbitrary ratio of the recombination rate constant ${k}_{r}$ and the trapping rate constant ${k}_{t}$. In the cases of ${k}_{r}={k}_{t}$ and ${k}_{r}⪡{k}_{t}$ the kinetics of bulk recombination is solved analytically. The analytical result for the case of ${k}_{r}={k}_{t}$ agrees with the simulation results by Nelson [Phys. Rev. B 67, 155209 (2003)] for the same case. Our theory predicts that the number density of charges decays as ${t}^{\ensuremath{-}\ensuremath{\alpha}}$ at long times, where $\ensuremath{\alpha}={k}_{B}T/{E}_{0}$ and $T$ is the temperature. This result explains recent experimental observations on bulk recombination between electrons and holes in organic solar cells.

Charge transfer at polymer-electrode interfaces: The effect of energetic disorder and thermal injection on band bending and open-circuit voltage

We investigate the band bending that occurs at the interface between a disordered organic semiconductor and a metal electrode. Ultraviolet photoemission spectroscopy measurements of thin organic layers on conducting substrates have revealed band bending within a few nanometers of the interface. It has been proposed that this is caused by the transfer of carriers from the substrate into empty states in the organic film. Here we numerically model this process by simulating a film with a given density of states in thermal equilibrium with a metallic substrate. Comparing the model with various published experiments, we demonstrate that the observed band bending can be explained equally well by either energetic relaxation of charge carriers on a timescale longer than photoemission (polaronic relaxation) or by a Gaussian density of states representing energetic disorder. In the former case, our results suggest that the thermal injection of carriers to higher-energy states has led observers to overestimate the relaxation energy by as much as several hundred meV. We also show that band-bending effects due to disorder are expected to significantly reduce the open-circuit voltage in organic photovoltaic devices, and we quantify the relationship between the amount of voltage loss and the degree of disorder.

Hopping Charge Transport in Disordered Organic Materials: Where Is the Disorder?

The effect of energetic disorder on charge carrier transport in organic materials has been reexamined. A reliable method for mobility calculation and subsequent evaluation of relevant disorder parameters has been discussed. This method is well suited for a direct calculation of the magnitude of dipolar disorder σdip in polar organic materials from the current transients. Calculation of σdip for several transport materials with varying concentration of polar dopants gives concentration dependences that are in reasonable agreement with theoretical predictions. A possible solution of the puzzle concerning the disorder effect on the mobility temperature dependence has been suggested.

Fine structure of the electrostatic energetic disorder at the interface between disordered organic material and metal electrode

AbstractThe physics of organic disordered materials is dominated by the effects of energetic disorder. We show that image forces reduce the electrostatic component of the total energetic disorder near an interface with a metal electrode. Typically, the standard deviation of energetic disorder is dramatically reduced at the first few layers of organic semiconductor molecules adjacent to the metal electrode and correlation properties of the disorder are different from the bulk properties. This means that the use of bulk disorder parameters (such as standard deviation of disorder) for description of the energetic disorder at the interface is poorly justified even in the case of identical spatial and chemical structure of the organic material at the interface and in the bulk of the transport layer. Implications for charge injection into organic semiconductors are discussed. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Energetic disorder at the metal-organic semiconductor interface

The physics of organic semiconductors is dominated by the effects of energetic disorder. We show that image forces reduce the electrostatic component of the total energetic disorder near an interface with a metal electrode. Typically, the variance of energetic disorder is dramatically reduced at the first few layers of organic semiconductor molecules adjacent to the metal electrode. Implications for charge injection into organic semiconductors are discussed.