Interface Electrostatics of Solid-State Dye-Sensitized Solar Cells: A

Article Cite This: J. Phys. Chem. C 2019, 123, 14955−14963

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Interface Electrostatics of Solid-State Dye-Sensitized Solar Cells: A Joint Drift-Diffusion and Density Functional Theory Study Ajay Singh,† Eros Radicchi,‡,§ Simona Fantacci,§ Francesca Nunzi,‡,§ Filippo De Angelis,‡,§,∥ and Alessio Gagliardi*,† †

Department of Electrical and Computer Engineering, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany Department of Chemistry, Biology and Biotechnology, University of Perugia, Via Elcedi Sotto, 8, 06123 Perugia, Italy § Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, Via Elce di Sotto 8, 06123 Perugia, Italy ∥ D3-CompuNet, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy

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‡

ABSTRACT: Dye-sensitized solar cells (DSCs) have gained great attention in recent years due to their low-cost fabrication, flexibility, and high power conversion efficiency. In a DSC, due to interfaces between the dye and the chargetransport materials, the interface electrostatics becomes a key factor determining the overall performance of the cell. Liquidelectrolyte-based DSCs suffer from low stability, electrolyte leakage, and, in some cases, electrode corrosion. Replacing liquid electrolyte with a solid semiconducting material leads to poor interfacial contacts, hence the interface electrostatics becomes one of the limiting factors. In this work, we present a drift-diffusion and density functional theory (DFT) study of solid-state DSCs to investigate the electrostatics at the TiO2/ organic dye/Spiro-OMeTAD interface and its impact on the adsorbed dye energy levels, its absorption spectrum, and the related charge injection. In our three-dimensional drift-diffusion model, we solve a set of drift-diffusion equations coupled to Poisson equation for electrons, holes, doping impurities, and interface traps simultaneously. After that, we use first-principles DFT modeling of dye-sensitized interfaces in the presence of the calculated electric fields. We find that interface traps located below the conduction band edge of mesoporous TiO2 influence the accumulation of photogenerated holes and built-in electric field near the interface. The built-in electric field leads to change in the energetics at the dye/TiO2 interface, leading to poor charge injection from excited dye into TiO2. The simulations were carried out for different electronic trap densities in TiO2 and different doping levels in the Spiro-OMeTAD hole-transport layer. This study helps to a better understanding of the interface electrostatics and its role in the charge injection mechanism of solid-state DSCs.

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INTRODUCTION

potential of such species coupled to rapid hole transport in solid Cu(II/I).6 Liquid-electrolyte-based DSCs show good power conversion efficiencies even during poor sunlight, but they suffer from low stability, electrolyte leakage, and in, some cases, electrode corrosion.7−9 There have been various efforts to solve this problem by replacing the liquid electrolyte with quasi-solidstate,10−12 solid-state hole conductor,2,4,8,9,13,14 ionic liquid electrolyte,2,4,8,9,14−17 polymer electrolyte,8,9,12,18−20 wide-gap p-type semiconductors, and, more recently, perovskite semiconducting materials.8,9,21−26 Solid-state DSCs are mechanically and chemically stable and offer easy film formation and a high degree of freedom in terms of molecular design.2,8,9 Copper complexes such as Cu(II/I)(6,6′-dimethyl-2,2′-bipyridine)2TFSI2/1, Cu(II/I)(4,4′,6,6′-tetramethyl-2,2′-bipyridi-

Dye-sensitized solar cells (DSCs) are organic/inorganic hybrid solar cells belonging to the group of thin-film solar cells.1 DSCs offer low-cost fabrication, flexibility, and high conversion efficiency.2−4 Fundamentally, DSCs employ a mesoporous semiconducting layer (usually TiO2) covered by a monolayer of dye molecules. The dye-covered semiconductor is in contact with a redox electrolyte. Conventional DSCs use an iodide/ triiodide (I−/I3−) liquid as a redox electrolyte for dye regeneration. Figure 1a shows a schematic representation of a DSC. In the cell, the dye monolayer after absorbing light injects electrons into the mesoporous TiO2 followed by dye regeneration. Electrolyte-based DSCs have shown upto 13% power conversion efficiency.5 In solid-state dye solar cells, the liquid electrolyte is replaced by a solid hole-transporting material as shown in Figure 1b. Current state-of-the-art solidstate dye solar cells employ copper complexes hole-transport materials because of the more positive and tuneable oxidation © 2019 American Chemical Society

Received: April 18, 2019 Revised: May 27, 2019 Published: May 28, 2019 14955

DOI: 10.1021/acs.jpcc.9b03658 J. Phys. Chem. C 2019, 123, 14955−14963

Article

The Journal of Physical Chemistry C

Figure 1. (a) Schematic representation of a dye-sensitized solar cell (DSC) and (b) schematic representation of a solid-state DSC.

ne)2TFSI2/1,27 [Cu(4,4′,6,6′-tetramethyl-2,2′-bipyridine)2](TFSI)2, [Cu(4,4′,6,6′-tetramethyl-2,2′-bipyridine)2](TFSI),6 CuI,28 CuSCN, copper zinc tin sulfide (CZTS),29 and CuCrO230 are some of the copper-based complexes used in solid-state DSCs. Recently reported Cu(II) complex-based solid-state DSCs have shown up to 11% conversion efficiency.6 Spiro-OMeTAD (2,2′,7,7′-tetrakis-(N,N-dipmethoxyphenylamine)9,9′-spirobifluorene) has become one of the most attractive solid-state hole-transport layer (HTL) material over the years because of its nice pore-filling capability in TiO2.31−35 In our present study, we will employ SpiroOMeTAD as a HTL. In a DSC, the functional element (the dye), which is responsible for the charge carrier generation by light absorption, is not the same as the charge-transport layers. Use of additional charge-transport material (TiO2 and electrolyte/HTL) leads to the creation of additional interfaces within the system. Hence, the charge-transfer reaction at the TiO2/dye/HTL (or electrolyte) interface becomes a key factor determining the overall performance of the DSC. In liquidelectrolyte-based conventional DSCs, photoexcited dye leads to charge injection into TiO2, which is then collected by an external circuit, and the electrolyte leads to the regeneration of the dye. Replacing the electrolyte with a solid-state material leads to a different charge-transport mechanism in the system. Due to the solid-state nature, wetting and pore filling of the HTL into nanoporous TiO2 becomes a crucial36 issue. Thus, it is necessary to investigate in detail the electrostatics and charge dynamics at the TiO2/HTL interface. Bach et al.37−39 reported that the dye regeneration by HTL takes place on the picosecond time scale, and it is at least one order of magnitude faster than the electrolyte-based dye regeneration system. Mahrov et al.38 investigated that dye molecules inject a positive charge into the hole conductor, retaining the negative charge adsorbed into the dye molecules itself. By simulation studies, Tanaka40 found that the detachment of the HTL from TiO2 decreases the shunt resistance, significantly limiting the efficiency of a solid-state DSC. Haque et al.41 reported that in the case of organic p-type semiconductors, the yield of hole transfer from the dye is controlled by thermodynamics rather than by the kinetics of the TiO2/dye/HTL interface. They concluded that the free energy associated with the regeneration of the oxidized dye, ΔG(dye‑HTM), where ΔG(dye‑HTM) = Em(HTM*/HTM) − Em(Dye*/Dye), is determined by the electrostatics of the interface. They further concluded that the higher value of ΔG(dye‑HTM) is needed to achieve a higher holetransfer yield. A better understanding of the impact of the

interface electrostatics on the injection of holes from the dye can lead to further development in this direction. Interfacial traps are another factor limiting the performance of the solidstate DSCs. O’Regan et al.42 found the recombination in solidstate TiO2/Dye/CuSCN solar cell in short-circuit condition to be 100 times faster and in the open-circuit condition to be 10 times faster than that of the (I−/I3) electrolyte-based solar cells. This faster recombination leads in a poor collection and hence a low fill-factor solar cell. From here, it can be concluded that the electrostatics of the interface TiO2/dye/HTL determines the interfacial recombination, hole injection, charge separation, and hence the overall performance of the system. Doping of organic hole-transport layer in solid-state DSCs has been reported to play a role in the solar cell performance.31,43−45 In the case of organic materials, the doping can have several effects (such as change in mobility), so it can result in an increase or a decrease in conductivity.46 The doping can also influence the interface electrostatics, as it affects the available charge carrier density and the energetics near the interface. Many processes involved in photoconversion and charge transport especially at the interface remain poorly understood. Drift-diffusion models are widely accepted to describe the charge transport in photovoltaic devices. Drift-diffusion has already been used to study charge transport in DSCs including three-dimensional ring-shaped DSC,47 solid-state DSCs,48 and integrated tandem DSCs.49 In this work, we present a multiscale (multiphysics) three-dimensional (3D) drift-diffusion model to study the interface electrostatics of DSC, accounting for the effect of doping, trap states, electric field, charge carrier transport, and generation/recombination process simultaneously. By using our 3D model for mesoporous TiO2 and HTL, we calculate the electric field at the interface for different trap densities in TiO2 and different HTL doping densities. Then, we use density functional theory (DFT) calculations to study the effect of the interface electrostatics on the dye monolayer. We study how the photochemical and photophysical properties of the dye are changed under different environments of the interface electrostatics. This helps in understanding how the charge injection (from the dye to the charge-transport layers) mechanism is affected by the interface electrostatics. Ultimately, our study leads to provide a deep insight into the role of different device parameters in the interface electrostatics and the charge injection mechanism. 14956


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Figure 2. (a) Drift-diffusion simulation block (left) and the extracted interface (right). (b) Energy band diagram at the HTL (Spiro-OMeTAD)/ TiO2 interface. TiO2 conduction band has exponential tail for the electron traps. The dye is treated like a electron−hole pair source.

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hole and electron trap concentrations, respectively. Φn and Φp are the electrochemical potentials of electrons and holes. The last two equations are the continuity equations for the electrons and holes. R and G describe the net recombination and generation rates, respectively. For the photogeneration, we considered constant generation G at the interface. It is experimentally known that trap states located at the interface, affect the electronic transport, and they are defined by the exponential density of electron traps below the conduction band edge58

DRIFT-DIFFUSION MODEL For the simulations, we adopt a finite-element drift-diffusion (DD) implemented within TiberCAD.50,51 The model has been already used to simulate perovskite solar cells,52 organic solar cells,53−55 organic devices,56 and dye-sensitized solar cells.49,57 The model accounts for the absorption of sunlight into the dye and the charge transport simultaneously. We define a simulation box with a mesoporous TiO2-interfacing Spiro-OMeTAD hole-transport layer as shown in Figure 2a, and the corresponding band diagram is shown in Figure 2b. Typical dye solar cells thicknesses are in the order of micrometer. In our simulations, we chose a smaller box of mesoporous TiO2 and HTL because our main concern is to study the surface phenomenon, rather than the output power. To simulate the device, a block of 50 nm × 50 nm × 100 nm is considered taking computational cost into consideration. The block is large enough to properly include photogeneration, charge transport, and surface phenomenon. Our model is based on solving drift-diffusion and Poisson equations simultaneously for electrons, holes, and traps in the threedimensional domain. At the DD level, we consider that the electrostatics is dominated by the electron and hole-transport materials, and the charge densities at the interface including traps. For the initial calculations, we assume that the dye monolayer is thin to affect the interface electrostatics. The thin dye layer is treated just as a source of electron−hole pairs after absorbing the sunlight. We solve the DD model considering TiO2/HTL interface only. Later in DFT calculations, we consider the effect of the electrostatics on the dye. Charges generated in the dye are transferred to the HTL (holes) and the TiO2 (electron). The charge transport is governed by diffusion and electrically induced drift. The complete system of equations in the present DD model reads as follows l o ∇·(ϵ∇Φ) = −q(n − p + Na− − Nd+ + nt− − nt+) o o o o o o ∇·{μn n(∇Φn)} = −R + G m o o o o o o∇·{μp p(∇Φn)} = R − G o n

nt = Nt e−α(qΦn − ECB)/ kT

(2)

where nt is the trapped electron density, Nt is the effective density of localized states, ECB is the TiO2 conduction band, and α is the parameter defining the depth of the exponential trap tail. k and T are the Boltzmann constant and the absolute temperature, respectively. We considered the interface electron traps given by eq 2, with an exponent α = 0.3158 (see Figure 2b). We also consider direct recombination at the TiO2/HTL interface. The parameters used for the drift-diffusion simulations are shown in Table 1. As a result, the simulation gives the electron and hole densities, the hole and electron current, and the electric field components at the interface. The effect of the trap states and the HTL doping is explained in the next section. Table 1. List of Parameters Used in the Drift-Diffusion Simulation parameter electron mobility in Spiro-OMeTAD hole mobility inSpiro-OMeTAD electron and hole mobility in TiO2 top metal contact Fermi level bottom metal contact Fermi level conduction band minimum of TiO2 TiO2 band gap TiO2 dielectric constant Spiro-OMeTAD band gap Spiro-OMeTAD highest occupied molecular orbital (HOMO) level Spiro-OMeTAD dielectric constant bimolecular recombination rate optical generation rate

(1)

where ϵ is the material the dielectric constant, Φ is the electrostatic potential, q is the elementary charge, n is the electron density, p is the hole density, N+d is ionized donor density, N−a is the ionized acceptor density, μn is the electrons mobility, and μp is the hole mobility. n+t and n−t represent the

a

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value 0.001 0.001 0.5 −4.3 −5.1 −4 3.3 85 3 −5.2 3 1 × 1017 7 × 1015

unit

refs

2

59 59 60a 61 62 63 63 64a 65 65

cm /(V s) cm2/(V s) cm2/(V s) eV eV eV eV eV eV −2

−1

cm s cm−2 s−1

66a fit. fit.

Approximated valued based on the provided references. DOI: 10.1021/acs.jpcc.9b03658 J. Phys. Chem. C 2019, 123, 14955−14963

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RESULTS AND DISCUSSION We calculated the orthogonal electric field component (E⊥) and the hole density at the TiO2/HTL interface in short-circuit condition. The histogram in Figure 3 represents the (E⊥)

Figure 5. Interface hole accumulation mechanism. (1) Electron−hole separation and transfer to TiO2 and HTL. (2) Trapping of electrons in the TiO2 at the interface. (3) Coulombic attraction of electrons and holes. (4) Accumulation of holes at the interface on the HTL side.

attraction between the electrons and holes, leading to the hole accumulation near the HTL/TiO2 interface on the HTL side. The trapping of electrons and the accumulation of holes at the interface lead to develop an electric field (E⊥) pointing toward the TiO2 from the Spiro-OMeTAD HTL as previously shown in Figure 3 (see the inset). To investigate the effect of doping, we calculated E⊥ at the TiO2/HTL interface while changing the doping density in the organic HTL. We found that E⊥ has a weak dependence on the doping in the HTL. The amplitude of E⊥ at the interface calculated for a fixed interface trap density 1 × 1013 cm−2 is shown in the histogram in Figure 6. We used 250 bins to represent E⊥ at the interface for each value of HTL doping density.

Figure 3. Orthogonal electric field (E⊥) distribution at the SpiroOMeTAD/TiO2 interface for undoped Spiro-OMeTAD.

distribution at the interface toward the Spiro-OMeTAD (HTL) side. For the histogram, we chose 255 bins to represent the (E⊥) at each value of the electron trap density. From the histogram, we can see that almost 50% of the points on the surface have E⊥ ≃ 1 × 105, 2.5 × 106, and 1.25 × 107 V/cm for the trap density ntrap = 1 × 1012, 1 × 1014, and 1 × 1015 cm−2, respectively. We see that E⊥ increases with the interface trap density. Trapping of the electrons in TiO2 at the interface leads to the increased surface electron density. The trapped electrons attract holes at the interface (on the HTL surface) due to electrostatic attraction, leading to the hole accumulation near the interface. Surface hole density at the interface (on HTL side) against the electron trap density (on the TiO2) is shown in Figure 4. It is evident from the figure that the surface hole

Figure 6. Orthogonal electric field (E⊥) distribution at the interface for fixed interface trap density of 1 × 1013 cm−2.

For low HTL doping density, the orthogonal electric field remains almost unchanged because of the screening of electrons at the interface. At higher doping levels, E⊥ jumps up almost by a factor of 2. A possible explanation for this effect can be the hole density profile at the interface. We calculated the accumulated hole density at the interface while varying the HTL doping. As shown in Figure 7, the interface hole density remains almost unchanged for the doping density up to 1 × 1018 cm−3. For a given electron trap density, E⊥ is determined by the number of available holes (to be trapped) at the interface. For low doping, the hole accumulation is controlled by the photogenerated holes. For hole doping higher than the photogenerated charge carrier density (i.e., beyond 1 × 1018 cm−3 in our case), the doping starts controlling the hole accumulation; hence, we observe an increase in E⊥.

Figure 4. Hole density at the Spiro-OMeTAD/TiO2 interface at fixed HTL doping density of 1 × 1013 cm−3.

density does not increase linearly with the electron trap density. The hole accumulation can be explained by the mechanism depicted in Figure 5. The dye after absorbing sunlight creates electron−hole pairs that dissociate into electrons and holes. Step 1 in Figure 5 shows the transfer of the electrons to the TiO2 and the holes to the organic HTL. Then, the electrons in TiO2 are trapped in the trap tail, as shown in step 2. Step 3 shows the Coulombic 14958


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may provide similar results.71−73 All calculations have been carried out with the Gaussian 09 program package.74 We calculated the effect of an electric field pointing in a direction orthogonal to the TiO2 surface both on the dye/TiO2 ground state and excited states. Considering the minimum and maximum electric field values taken from the drift diffusion simulations, Emin = 2 × 104 V/cm = 4 × 10−6 (au) and Emax = 2 × 107 V/cm = 4 × 10−3 (au), respectively, we used Efield values of 0 (no field) and ±1 × 10−3 au and ±1 × 10−2 au (±5.1 × 106, ±5.1 × 107 V/cm). The ground-state electronic structure as a function of the electric field strength is summarized in Figure 9. A positive electric field points from the dye to the TiO2 surface, a negative one shows an opposite direction. Figure 7. Surface hole density at the interface at fixed trap density of 1 × 1013 cm−2.

For the increased HTL doping also, E⊥ increases with increase in the electron traps at the interface. The orthogonal electric field (E⊥) distribution for doped HTM at the TiO2/ HTM interface (on the HTM side) is shown in Figure 8. We also calculated E⊥ at the interface on the TiO2 side, and we found it to be at least two orders of magnitude smaller compared to E⊥ on the HTM side. This can be explained by the charge screening in TiO2. A high dielectric constant of TiO2 helps maintain the electric displacement field (D⃗ = ϵE⃗ ) even with the low electron densities while time offering easy electron transport.

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ATOMISTIC CALCULATIONS We carried out first-principles simulations on a typical organic dyes (JK2) sensitized TiO2 interface. The interface model structure has been discussed in ref 67. We have considered a single JK2 on TiO268 and calculated the ground-state electronic structure and lowest electronic excitations by means of DFT/TDDFT calculations using the CAM-B3LYP exchange−correlation functional both in vacuo and in acetonitrile solution (a solvent typically used in DSCs electrolyte solutions), the latter described through a polarizable continuum model.69 Such computational approach ensures a fairly accurate description of charge-transfer excitations within the dye and at the dye/TiO2 interface.70 CM-B3LYP has been used in this case, since it has proven successful in describing the optical properties of the JK2 dye, though different functionals including a reduced amount of exact exchange

Figure 9. Molecular orbital diagram of the JK2/TiO2 system with varying electric field in vacuo (vac) and acetonitrile (solv), see text for definitions.

The JK2@TiO2 electronic structure is typical of a dyesensitized interface, with the system’s HOMO being localized on the dye; and the manifold of TiO2 unoccupied states

Figure 8. Orthogonal electric field E⊥ at the TiO2/HTM interface (on the HTM side) at a fixed doping density of 1 × 1016 cm−3. 14959


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second lowest transition (2.602 eV) has a dye → dye character and is characterized by a strong oscillator strength. Moving to positive electric fields, the aforementioned downshift of dye LUMOs introduces a significant dye character into the lowest transition (calculated for field = 1 × 10−3 au at 2.57 eV), which gains oscillator strength. At stronger positive fields of 1 × 10−2 au, the lowest transition shows mainly of dye HOMO → dye LUMO character, with the TiO2 excited states lying at higher energy. An opposite trend is found for negative electric field values, with the energy and the oscillator strength of the lowest excited states decreases with increase in the electric field strength. For Efield = −1 × 10−2, the lowest excitations are increasingly dominated by TiO2 unoccupied states, which are stabilized compared to dye LUMOs. The variation of alignment of energy levels at the dye/TiO2 interface has important consequences for the operational functioning of a related DSC, since the positive field exerted by the TiO2-injected electrons on the positively charged dye is shown to alter the interface energetics, potentially leading to reduced injection yield from the dye excited state to the unoccupied TiO2 states.

representing a set of lowest unoccupied molecular orbitals (LUMOs), see “no field” case in Figure 10. The HOMO

Figure 10. Isodensity plot of the HOMOs (lower panel) and LUMOs (upper panel) for the JK2/TiO2 interface in solution as a function of the applied field.

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density partly shifts from the dye donor to the dye acceptor group by increasing the Efield from negative to positive values. In the absence of the field, the dye LUMO lies within the manifold of TiO2 unoccupied states. It can be noticed that similar electronic structure variations are computed upon application of an electric field both in vacuo and in solution. A positive electric field stabilizes the dye orbitals and destabilizes the TiO2 orbitals in an asymmetric way, leading to a dye-TiO2 gap opening, while the negative field exerts an opposite effect. As an example, for a positive electric field of 1 × 10−3 au, the HOMO is stabilized by 0.2 eV and the LUMO is destabilized by 0.04 eV. The overall behavior is consistent with that reported previously, whereby positive dipolar fields (i.e., pointing from the dye to the TiO2 surface) raised the TiO2 conduction band and led to the observation of higher Voc in DSC devices.75 Due to the asymmetric stabilization/destabilization field effect, at high field strengths the LUMO of the combined dye/TiO2 system becomes the dye LUMO, since TiO2 states are pushed at higher energies, see right panel of Figure 10. The ground-state electronic structure variation upon application of an electric field translates into a consistent change in the excited state properties for the JK2@TiO2 system, see Table 2. The five lowest electronic transitions have been computed only in vacuo due to the similar behavior shown by the JK2@TiO2 electronic structure upon Efield application in vacuo and solution. In the absence of electric field, the lowest excitation energy (2.485 eV) corresponds to the direct dye → TiO2 excitation. This transition has negligible oscillator strength due to the small overlap of the dye HOMO and TiO2 LUMOs. The

CONCLUSIONS Solid-state DSCs are promising dye solar cells, as they overcome low stability, electrolyte corrosion, and electrolyte leakage issues, which the conventional dye solar cells possess. However, due to the solid-state nature of the hole-conducting material, the interface electrostatics at the TiO2/dye/HTL interface becomes more crucial. In this work, we study in detail the interface electrostatics of a solid-state DSCs. Using our drift-diffusion model, we found that there is a built-in electric field (E⊥) developed at the TiO2/HTL interface, pointing toward TiO2. This electric field is developed by the electrons trapped in the electronic trap states located below the conduction band edge of TiO2 and the accumulated holes (in HTL) at the interface. Simulations show that the accumulation of holes and hence the built-in electric field increases rapidly with the interface electron-trap density. On the other hand, E⊥ shows a poor dependence on the HTL doping density. For HTL doping exceeding the photogenerated charge carrier density, when the HTL doping increases by a factor of 10, E⊥ increases only by a factor of ≃2. Furthermore, our first-principle (DFT) study suggests that the built-up electric field (pointing toward TiO2) destabilizes TiO2 orbitals, leading to a dye/TiO2 gap opening. This dye/ TiO2 gap increases with increase in the electric field. At a high electric field strength, the TiO2 states are pushed at high energy level and hence the dye LUMO determines the system LUMO. This change in the alignment of energy levels leads to lower injection from the excited dye into TiO2, leading to a poor performing cell. Ultimately, reducing electron traps in TiO2 and using high mobility hole-transport materials can help

Table 2. TDDFT Calculated Lowest Five Excitation Energies and Oscillator Strengths for the JK2/TiO2 System in Vacuo −10

−1

no field

+1

+10

E

f

E

f

E

f

E

f

E

f

1.587 1.806 1.914 1.948 1.994

0.0001 0.0000 0.0002 0.0004 0.0006

2.398 2.582 2.631 2.670 2.747

0.0011 1.9934 0.0029 0.0143 0.0601

2.485 2.602 2.718 2.750 2.822

0.0027 2.1064 0.0010 0.0055 0.0393

2.570 2.620 2.804 2.830 2.895

0.0143 2.1110 0.0008 0.0028 0.0263

2.745 3.287 3.458 3.480 3.522

2.2911 0.0001 0.0016 0.0032 0.0004

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stabilize the interface energetics by improving the charge injection, hence leading to an efficient solid-state dyesensitized solar cell.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ajay Singh: 0000-0003-2249-4497 Filippo De Angelis: 0000-0003-3833-1975 Alessio Gagliardi: 0000-0002-3322-2190 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the TUM International Graduate School of Science and Engineering (IGSSE) and the German Academic Exchange Service (DAAD). Also, the Ministero Istruzione dell’Università e della Ricerca (MIUR) and the University of Perugia are acknowledged for the financial support through the program “Dipartimenti di Eccellenza 2018-2022” (grant AMIS) to FDA.

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REFERENCES

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Interface Electrostatics of Solid-State Dye-Sensitized Solar Cells: A

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