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Impact of the Active Layer Morphology on Bimolecular Recombination Dynamics in Organic Solar Cells Veaceslav Coropceanu, Jean-Luc Bredas, and Shafigh Mehraeen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07768 • Publication Date (Web): 19 Oct 2017 Downloaded from http://pubs.acs.org on October 22, 2017

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The Journal of Physical Chemistry

Impact of The Active Layer Morphology on Bimolecular Recombination Dynamics in Organic Solar Cells Veaceslav Coropceanu, Jean-Luc Brédas, and Shafigh Mehraeen* Veaceslav Coropceanu School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics Georgia Institute of Technology Atlanta, Georgia 30332-0400 E-mail: [email protected] Jean-Luc Brédas School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics Georgia Institute of Technology Atlanta, Georgia 30332-0400 E-mail: [email protected] Shafigh Mehraeen, Department of Chemical Engineering, University of Illinois, Chicago, 810 S Clinton St, Chicago, IL 60607 Email: [email protected] *

Corresponding Author

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ABSTRACT Using kinetic Monte Carlo simulations, we present a reaction-diffusion model to describe the impact of the morphology of the active layer and charge-transfer lifetime on the bimolecular recombination kinetics in organic solar cells. The morphologies we consider range from bilayers to bulk heterojunctions with coarse and fine intercalated domains. We find that within the morphologies simulated by the potential model, it is the density of states that affects the order of bimolecular recombination kinetics. The results show that the morphology of the active layer, modeled by the potential model, only influences the average delay time between the exciton dissociation and the onset of bimolecular recombination. The results also indicate that the donor or acceptor domain size and the degree of Gaussian disorder have very similar effects on the charge recombination dynamics. Our findings suggest one possible way to explain (i) why bimolecular recombination deviates from second-order (Langevin) kinetics, and (ii) why Langevin theory overestimates the bimolecular rate constant.


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1. INTRODUCTION Over the past years, organic photovoltaics (OPV), as an active clean-energy harvesting technology, has drawn a lot of attention due to promising properties such as flexibility, light weight, and low-cost solution processability.1-4 Since the introduction of bulk-heterojunction (BHJ) architecture5-6 in the mid-1990’s, the performance of OPV cells increased significantly over time. With the development of fullerene-free acceptor, organic solar cells have now reached a power conversion efficiency exceeding 13%.7 However, further improvement in efficiency will be challenging, as OPV cells still suffer from significant energy losses. Indeed, recent data8-14 using high-resolution temporal techniques underline that excitons in high-performance devices can readily dissociate and charges separate within less than 100 fs. Thus, it is the competition between charge migration towards the electrodes and charge recombination15-17 appears to define the ultimate performance of OPV devices. In this context, a detailed understanding of the loss mechanisms is critical. There are increasing evidences8, 18-19 indeed that bimolecular recombination (BMR) represents the primary loss factor in thick bilayers20 and BHJ21-27 solar cells. Also, it has been shown that even after annealing, BMR still limits the device performance.28-29 Establishing the most relevant physical model of BMR has remained a challenge to date. A number of experimental data show that, depending on the nanomorphology30-31 and mobility of charge carriers,32-33 recombination evolves from a first-order (monomolecular) dynamics under short-circuit-current conditions to a second-order (bimolecular) kinetics under open-circuit-voltage conditions.8, 34-38 It is important to note here that according to conventional second-order kinetics, the charge carrier density ρ (t ) is given by:

= −( ) ,

(1)

where ( ) is the charge carrier density, is the time, and is the rate constant. In Langevin theory, the rate constant is given by = ( + )/, where and are the electron and hole mobilities, respectively, and is the effective dielectric constant of the blend.15 Deviations of experimental observations from Langevin theory were reported to occur in two ways: (i) deviation from second-order dependence on charge carrier density and (ii) discrepancy in the rate constant, each of which will be addressed below: (i) Indeed, in many polymer-fullerene based devices, the charge-decay dynamics probed by charge extraction technique29, 39 and transient absorption spectroscopy40-41 at open-circuit voltage42-43 was found to exhibit approximately a third-order dependence on ( ). Therefore, in order to be consistent with the experimental data, the rate constant () in the Langevin model has to depend on charge density (or, equivalently, on t).44-45 This third-order dependence of the BMR rate on charge density has been suggested to arise as a result of either a carrier lifetime dependence on charge density,46-47 recombination via an exponential tail of density of states (DoS),48-51 or carrier trapping in an inhomogeneous distribution of localized states.40-41, 51 Also, it



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was suggested that traps can sometimes enhance the dissociation of geminate pairs into free carriers,52 but can act as recombination centers as well, leading to a Shockley-Read-Hall (SRH) recombination dynamics.53-57 (ii) Several experimental observations39, 58-62 indicate that even when second-order kinetics is operative, the experimental rate constant ( ) is smaller than that estimated according to Langevin model, , by two to four orders of magnitude. Previous reports have attributed this overestimation to 2D recombination in the lamellar structure of conjugated polymer,60 charge carrier concentration gradient within the device,63 local dielectric constant difference,64 slow dynamics of charge carrier with smaller mobility,65-66 delocalization of opposite charges in an encounter complex,61 phase separation,67 domain purity,68 and back electron transfer to triplet excitons69 concurrent with redissociation of charge-transfer (CT) states back to free carriers.70-71 Despite extensive experimental efforts and extended theoretical descriptions of charge transport in disordered organic semiconductors,72-74 there are only a few theoretical studies to date51, 63, 70, 7577 that have been conducted to understand the characteristics of BMR as a primary charge carrier loss mechanism in organic solar cells. Particularly, the influence of 3D morphology on redissociation rate of populated CT states, and so BMR in the absence or presence of energetic disorder78-79 in the active layers of OPV devices is not well understood. Previous studies of BMR kinetics are limited to: (1) bilayer organic light-emitting diodes (OLEDs), using fixed holes and mobile electrons;80 (2) OLEDs, neglecting the effect of morphology on BMR;81 (3) BHJ OPV cell, assuming second-order kinetics;82 and (4) bilayer OPV cell, considering intermediate CT states.70 The purpose of the present work is not to use any prior assumption on the order of BMR kinetics or particular morphology, and go beyond these limitations. For that purpose, we investigate (1) the deviation of BMR kinetics from secondorder dependence on charge carrier density, and (2) the deviations of the BMR rate constant from that predicted by Langevin theory. We justify our findings with experimental evidence from previous reports.

2. METHODS To study the impact of morphology on BMR in an organic semiconductor at open-circuit voltage condition, we have developed a theoretical three-dimensional reaction-diffusion lattice model (see Appendix A in supplemental information). Notice that our model is different from the general theory of reaction-diffusion83 in two ways. (1) In the general theory of reactiondiffusion, reactions can occur anywhere in the domain (simulation box), whereas in our model, electrons and holes only recombine at the interface. (2) In the general theory of reactiondiffusion, particles and anti-particles are free to diffuse anywhere in the domain, whereas in our model, holes and electrons are restricted to diffuse in the donor and acceptor domains, respectively. Using this model, we performed Kinetic Monte Carlo (KMC) simulations. In these simulations, the charge carrier hopping rate from any site to one of the six nearest neighboring sites, is described according to Miller-Abrahams formalism:84


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= exp(−2) exp −(Δ! + |Δ!|)/(2#$ %),

(2)

where a = 1nm represents the lattice site spacing, denotes the intrinsic attempt frequency, indicates the inverse of localization radius, #$ is the Boltzmann constant, % is the temperature, and Δ! is the site energy difference between adjacent sites. During the simulation, when an electron and a hole occupy adjacent sites across the donor/acceptor (D/A) interface, they can hop to other vacant neighboring sites with the rates given by Equation 2 or recombine with a rate &' . For convenience, &' is also computed here using Equation 2 but with a modified attempt frequency, &' . We considered four different morphologies depicted in Figures 1A through 1D, where blue and hollow regions represent A and D domains, respectively, and red surfaces highlight the D/A interfaces. Figures 1A and 1B represent bilayers with flat and rough interfaces, respectively. The structures in Figures 1C and 1D are representative of BHJs, which are generated by the potential model,85-88 with large (25 nm) and small (5 nm) average domain sizes, respectively. To characterize the generated morphologies, we have calculated the interfacial area-to-volume ratio for Figure 1A to 1D, which are 0.010, 0.016, 0.049, and 0.250 nm-1, respectively.

A

E

E=0

B

C

E

DoS


D


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Figure 1. Panels A to D represent: a bilayer with flat interface (A), a bilayer with rough interface (B), a BHJ with coarse (C) and fine (D) D/A network. In these morphologies, hollow and blue regions illustrate donor and acceptor domains, respectively, and red highlights the interface regions. Panel E illustrates an energetic disorder described by a superposition of two distributions, a Gaussian DoS (black line), / (E), centered at ! = 0, and an exponential DoS (blue line), 0 (!), positioned below ! = 0. To investigate the effect of energetic disorder on the kinetics of BMR, we considered commonly used DoS,89 represented by: (i) a Gaussian distribution of states, centered at energy level ! = 0, with a total DoS concentration 1/ and a distribution width 2/ :

/ (!) =

34

8 5674

7>

0

9: ?7 @, ! ≤ 0, >

(4)

where the DoS concentration and distribution width are given by 10 and 20 , respectively; and (iii) a composite DoS, which has been found in some instances90 to better account for the energetic disorder. As illustrated in Figure 1E, this composite DoS is represented by a superposition of a Gaussian distribution for band (conducting) states and an exponential distribution of band-tail (trap) states.

3. RESULTS AND DISCUSSION The charge density decay with time using the morphologies in Figure 1 and the Gaussian or exponential DoS distributions (i and ii above) are shown in Figure 2. The DoS parameters used in the simulations (see Table 1) were chosen to be in the range of commonly used parameters for organic materials.90 The results obtained for a Gaussian DoS (Figure 2A) demonstrate that, irrespective of morphology, the charge-density decay at long time always scales as ρ ~ t −1 . This relation is indicative of second-order kinetics as illustrated by the long-time asymptotic dashed line in Figure 2A. Table 1. DoS parameters for data illustrated in Figure 2 DoS

σ/kBT

N (cm−3)

Gaussian

3

1021

Exponential

3

1021

However, an exponential energetic disorder leads to a further slow-down and dispersion of the BMR kinetics, compared to the Gaussian DoS. This is highlighted in Figure 2B, where the KMC


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simulation results (solid lines) agree with the theoretical long-time asymptotic predictions, ~

Impact of Active Layer Morphology on Bimolecular ... - ACS Publications

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