Dielectric Screening Meets Optimally Tuned Density Functionals

Kronik, Leeor; Kümmel, Stephan

doi:10.1002/adma.201706560

Cited by 137 publications

(151 citation statements)

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“…The range-separation parameter was optimized using a nonempirical procedure [43] in the presence of a dielectric medium in order to mimic the impact of the solid solid-state environment [44][45][46] (see the discussion in refs. [44][45][46] and the Supporting Information for details). In order to reduce the computational time, in all excited-state calculations, P3HT was modeled by pentamers and the hexyl groups (C 6 H 13 ) were replaced with methyl groups (CH 3 ).…”

Section: Resultsmentioning

confidence: 99%

Charge‐Transfer States at Organic–Organic Interfaces: Impact of Static and Dynamic Disorders

Zheng

Tummala

Wang

et al. 2019

Advanced Energy Materials

105

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of this distribution in the semiclassical approximation is given by [15] 2 D 2 B k T σ λ =(1)where λ denotes the reorganization energy related to the electron transfer process between the CT state and the ground state; k B , the Boltzmann constant; and T, the temperature. The static disorder arises from the amorphous nature of the active layers and the positional inequivalency (even in the absence of vibrational motions) of the donor and acceptor (macro)molecules, which results in a time-independent distribution of the CT states with a standard deviation σ S . If both static and dynamic contributions have Gaussian distributions, the standard deviation of the overall (total) disorder σ T can be expressed as [12] T 2 S 2 D 2 σ σ σ = +The knowledge of the dynamic and static disorder contributions in D-A systems is important for an accurate determination of exciton dissociation rates, nonradiative recombination rates, charge transport, and charge-transfer optical transitions. In the semiclassical approximation, accounting for the impact of static disorder on the nonradiative recombination rate (k nr ) results in Equation (3), which is similar to the classical Marcus formula [16] except that the 2term appearing in the latter is replaced with T 2 σ [14,17,18] 2 1 2 exp 2 nr el 2 T 2 CT a 2 T 2 k V E  π σ λ σ ( ) = − −        where V el denotes the electronic coupling between the CT states and the ground state and CT a E , the adiabatic (relaxed) CT energy. Equation (3) underlines that both dynamic and static disorders can have a major impact on the nonradiative recombination rates and consequently on open-circuit voltage losses. Therefore, there is increasing interest, triggered in particular by the rapid advance in the efficiency of organic solar cells, in better understanding the role of disorder on device performance. [9,12,13,[17][18][19][20][21][22][23][24] In the semiclassical approximation used to derive Equation (3), the CT absorption band is also characterized by a Gaussian distribution with a variance given by Equation (2); [13] the static Molecular dynamics simulations are combined with density functional theory calculations to evaluate the impact of static and dynamic disorders on the energy distribution of charge-transfer (CT) states at donor-acceptor heterojunctions, such as those found in the active layers of organic solar cells. It is shown that each of these two disorder components can be partitioned into contributions related to the energetic disorder of the transport states and to the disorder associated with the hole-electron electrostatic interaction energies. The methodology is applied to evaluate the energy distributions of the CT states in representative bulk heterojunctions based on poly-3-hexyl-thiophene and phenyl-C 61 -butyric-acid methyl ester. The results indicate that the torsional fluctuations of the polymer backbones are the main source of both static and dynamic disorders for the CT states as well as for the transport levels. The impact of static and dynamic disorders on radia...

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Section: Resultsmentioning

confidence: 99%

Charge‐Transfer States at Organic–Organic Interfaces: Impact of Static and Dynamic Disorders

Zheng

Tummala

Wang

et al. 2019

Advanced Energy Materials

105

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“…Nevertheless periodic DFT calculations with hybrid functionals and PW basis sets remain substantially heavier, from a computational standpoint, than local or semi-local DFT calculations. The functionals PBE0 [42] and HSE [43][44][45] are among the most popular hybrid functionals used for condensed systems, and lately dielectric dependent hybrid functionals [46][47][48][49] have been increasingly used to predict structural and electronic properties of solids [46,47,[49][50][51][52][53][54][55][56][57] and liquid [58][59][60] and of several molecules [47,48,61]. Another category of orbital dependent functionals recently proposed is that of Koopmans-compliant functionals, used for both molecules and solids [62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Dielectric-dependent hybrid functionals for heterogeneous materials

Zheng

Govoni

Galli

2019

Phys. Rev. Materials

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We derive a dielectric-dependent hybrid functional which accurately describes the electronic properties of heterogeneous interfaces and surfaces, as well as those of three-and two-dimensional bulk solids. The functional, which does not contain any adjustable parameter, is a generalization of self-consistent hybrid functionals introduced for homogeneous solids, where the screened Coulomb interaction is defined using a spatially varying, local dielectric function. The latter is determined self-consistently using density functional calculations in finite electric fields. We present results for the band gaps and dielectric constants of 3D and 2D bulk materials, and band offsets for interfaces, showing an accuracy comparable to that of GW calculations.

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“…Fundamentally, many of these deficiencies are relevant to the localization/delocalization error. In recent years, this problem has been overcome by using range‐separated (RS) hybrid functionals (e.g., ωB97XD and LC‐ωPBE) with the RS parameters ( ω ) optimized by a self‐consistent procedure (not an empirical fitting) . The partition of the Coulomb operator into short‐range (SR) and long‐range (LR) components can be achieved by using the identity

\frac{1}{r} = \frac{e r f (ω r)}{r} + \frac{1 - e r f (ω r)}{r}

where r is the inter‐electronic distance and

e r f (ω r)

denotes the standard error function.…”

Section: Theoretical Description Of Electronic Processes In Organic Smentioning

confidence: 99%

“…The LR part (first term) is treated by using the HF exchange, while the SR part (second term) is treated by using a local or semi‐local DFT functional. Following Koopmans’ theorem, the ω value can be optimized by minimizing the expression

J (ω)

J false(ω false) = {((), I P + E_{H O M O})}^{2} + {((), E A + E_{L U M O})}^{2}

Importantly, this gap‐tuning or the original

I P

‐tuning procedure can be performed in conjugation with the well‐developed polarizable continuum model (PCM) to reproduce the environmental effect in a simple way …”

Section: Theoretical Description Of Electronic Processes In Organic Smentioning

confidence: 99%

Origin of Photocurrent and Voltage Losses in Organic Solar Cells

Han

2019

Advcd Theory and Sims

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Organic solar cells (OSCs) have recently achieved power conversion efficiencies (PCEs) of over 16%. However, there still exist large losses in photocurrent and/or voltage in state-of-the-art OSCs, making the PCEs still far below those of inorganic counterparts. Here, the factors and electronic processes for photocurrent and voltage losses are identified and discussed in the framework of device physics and photophysics. To simultaneously obtain both high photocurrent density and low voltage loss toward 20% PCEs, it is crucial to suppress the non-radiative (NR) recombination of the lowest charge-transfer (CT) state at the donor-acceptor interface. In principle, theoretical simulations can provide molecular insight into the origin of these losses, which is essential to guide material design. In particular, the authors highlight the importance of the local interface morphologies and the vibronic couplings on suppressing the NR decay of the lowest CT state according to recent theoretical studies. (1 of 17)www.advancedsciencenews.com www.advtheorysimul.com as A, has achieved a high J SC of 25 mA cm −2 . [5] Nevertheless, the value of J SC /J SC,SQ for the E g of 1.33 eV is only 0.71, implying that even in the best OSCs, the photocurrent loss is still non-negligible. Now we turn to the loss in open-circuit voltage. The voltage loss ( V OC ) or energy loss (E los s , i.e., q V OC ) is defined asEven in the ideal SQ limit, the V OC is inevitable. [9] The V OC can be as low as 0.3 V in GaAs and slightly higher (0.4-0.55 V) in c-Si and perovskite solar cells, while the V OC in high-efficiency OSCs is usually around 0.6 V or larger. [10] For example, the best fullerene-based OSCs based on PffBT4T-C 9 C 13 :PC 71 BM have a large V OC of 0.87 V for an E g of 1.65 eV, despite of a high J SC /J SC,SQ value of 0.82. [11] In order to improve the PCE for a given E g , it is important to minimize V OC without sacrificing the generation of photocurrent. [12,13] Here, the PCE versus E g and V OC is calculated by Equations (1), (3), and (6), based on two reliable assumptions: i) the E QE P V is set to a fixed value of 85% when E ≥ E g , even though the highest value has reached 90%, [14] because it is very difficult to obtain the maximum value over the whole range in real systems, and ii) the FF is set to 80%, since the highest FF of 80.79% has been reported, [15] which is comparable to those of c-Si and GaAs solar cells (80-86%). [8] Hence, a low V OC of, for example, 0.45 V can produce PCEs over 20% at a wide E g range of 1.1-1.6 eV (Figure 1b). This suggests that a PCE of 20% should be a reasonable target for single-junction OSCs, providing a large area to explore in the future. To achieve this target, as a preliminary step, the origin of photocurrent and voltage losses in OSCs must be identified.In the following, we first describe the optical and electronic processes in OSCs and especially, point out the adverse factors or processes that can result in the photocurrent loss. Second, we

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Dielectric Screening Meets Optimally Tuned Density Functionals

Cited by 137 publications

References 138 publications

Charge‐Transfer States at Organic–Organic Interfaces: Impact of Static and Dynamic Disorders

Charge‐Transfer States at Organic–Organic Interfaces: Impact of Static and Dynamic Disorders

Dielectric-dependent hybrid functionals for heterogeneous materials

Origin of Photocurrent and Voltage Losses in Organic Solar Cells

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