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

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C: Energy Conversion and Storage; Energy and Charge Transport

Interface Electrostatics of Solid-State Dye-Sensitized Solar Cells: A Joint Drift-Diffusion and Density Functional Theory Study Ajay Singh, Eros Radicchi, Simona Fantacci, Filippo De Angelis, and Alessio Gagliardi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03658 • Publication Date (Web): 28 May 2019 Downloaded from http://pubs.acs.org on May 28, 2019

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The Journal of Physical Chemistry

Interface Electrostatics of Solid-State Dye-Sensitized Solar Cells: A Joint Drift-Diffusion and Density Functional Theory Study Ajay Singh,† Eros Radicchi,‡,¶ Simona Fantacci,¶ 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 E-mail: [email protected]

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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 charge transport materials, the interface electrostatics becomes a key factor determining the overall performance of the cell. Liquid electrolyte based DSCs suffer 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 (DD) 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 to the adsorbed dye energy levels, its absorption spectrum and the related charge injection. In our 3D drift-diffusion model, we solve a set of drift-diffusion equations coupled to Poisson equation for electrons, holes, doping impurities and the 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 the energetics at the dye/TiO2 interface leading to poor charge injection from excited dye into the TiO2 . The simulations were carried out for different electronic trap density in TiO2 and different doping levels in the Spiro OMeTAD hole transport layer. This study helps to a better understanding of interface electrostatics and its role in the charge injection mechanism of solid-state DSCs.

Introduction 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 ) 2


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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− /I− 3 ) liquid as redox electrolyte for the 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 the dye regeneration. Electrolyte based DSCs have shown upto 13% power conversion efficiency. 5 In solid-state dye solar cells, the liquid electrolyte is replaced with a solid hole transporting material as shown in Figure 1b. Current state of art solid state dye solar cells employ copper complexes hole transport materials because of the more positive and tuneable oxidation potential of such species coupled to rapid hole transport in solid Cu(II/I) . 6

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

Liquid electrolyte based DSCs show good power conversion efficiencies even during poor sunlight, but they suffer 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 solid-state, 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 with perovskite semiconducting materials. 8,9,21–26 Solid-state DSCs are mechani-

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cally 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)2 TFSI2/1 , Cu(II/I) (4,4’,6,6’-tetramethyl-2,2’-bipyridine)2 TFSI2/1 , 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, CZTS (copper zinc tin sulfide) 29 and CuCrO2 30 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% of conversion efficiency. 6 Spiro-OMeTAD (2,2’,7,7’-tetrakis-(N,N-dipmethoxyphenylamine)9,9’-spirobifluorene) has been 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 Spiro-OMeTAD as 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 create 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 Liquid electrolyte based conventional DSCs, photoexcited dye leads to charge injection into TiO2 which is then collected by an external circuit, and the electrolyte leads to regeneration of the dye. Replacing 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 HTL into nanoporous TiO2 becomes a crucial 36 issue. Thus, it is necessary to investigate in details 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 positive charge into the hole conductor, retaining the negative charge adsorbed into the dye molecules itself. Tanaka 40 by simulation studies found that detachment of the HTL from TiO2 decrease shunt resistance, significantly limiting the efficiency of a solid-state DSC. Haque et al. 41 reported that in the case of organic

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p-type semiconductors, the yield of hole transfer from the dye is controlled by thermodynamics rather by the kinetics of the TiO2 /dye/HTL interface. They concluded that the free energy associated to regeneration of the oxidized dye, ∆G(dye-HTM) , where ∆G(dye-HTM) = Em (HTM*/HTM)-Em (Dye*/Dye), is determined by the electrostatic of the interface. They further concluded that higher value of ∆G(dye-HTM) is needed to achieve higher hole-transfer yield. A better understanding of the impact of the interface electrostatics on the injection of holes from the dye can lead to further developments in this direction. Interfacial traps are another factor limiting the performance of the solid-state DSCs. O Regan et al. 42 found the recombination in solid-state TiO2 /Dye/CuSCN solar cell, in short-circuit condition to be 100 times faster and in open circuit condition to be 10 times faster than 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 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 a change in mobility) so it can result in an increase or a decrease in the 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 photo-conversion 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 shape DSC, 47 solid-state DSCs, 48 and integrated tandem DSCs. 49 In this work, we present a multiscale (multiphysics) threedimensional (3D) drift-diffusion model to study 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

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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.

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 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 µm. In our simulations, we chose a smaller box of mesoporous TiO2 and HTL, because our main concern is studying the surface phenomenon, rather than the output power. To simulate the device, a block of 50 nm x 50 nm x 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 three-dimensional 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.

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(a)

(b)

Figure 2: (a) The 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. 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:    +  ∇ · (∇Φ) = −q n − p + Na− − Nd+ + n−  t − nt    ∇ · {µn n (∇Φn )} = −R + G       ∇ · {µp p (∇Φn )} = R − G

(1)

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

electron trap concentrations respectively. Φn and Φp are the electrochemical potentials of electrons and the holes. The last two equations are the continuity equations for the electrons

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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 edge: 58

nt = Nt e−α(qΦn −ECB )/kT

(2)

where nt is the trapped electron density, Nt is the effective density of localized states, ECB the TiO2 conduction band and α is parameter defining the depth of the exponential trap tail. k and T are the Boltzmann constant and the absolute temperature respectively. We considered interface electron traps given by equation (2) with an exponent α=0.31 58 (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. Table 1: List of parameters used in the drift-diffusion simulation Parameter Value Units Ref. Electron mobility in Spiro-OMeTAD 0.001 cm2 /Vs 59 Hole mobility in Spiro-OMeTAD 0.001 cm2 /Vs 59 Electron and hole mobility in TiO2 0.5 cm2 /Vs 60 * 61 Top metal contact fermi level -4.3 eV 62 Bottom metal contact fermi level -5.1 eV 63 Conduction band minimum of TiO2 -4 eV 63 TiO2 bandgap 3.3 eV 64* TiO2 dielectric constant 85 — 65 Spiro-OMeTAD bandgap 3 eV 65 Spiro-OMeTAD HOMO level -5.2 eV 66* Spiro-OMeTAD dielectric constant 3 — 17 −2 −1 Bimoleular recombination rate 1 × 10 cm s fit. 15 −2 −1 Optical generation rate 7 × 10 cm s fit. * Approximated valued based on the provided references. As a result, the simulation gives the electron and hole densities, 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.

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Results and discussion We calculated the orthogonal electric field component (E⊥ ) and hole density at the TiO2 /HTL interface, in short-circuit condition. The histogram in Figure 3 represents the (E⊥ ) distribution at the interface towards the Spiro-OMeTAD (HTL) side. For the histogram, we chose 255 bins to represent the (E⊥ ) at each value of the electron trap density. 3

% of of the HTL surface

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ntrap = 1012 cm−2 ntrap = 1014 cm−2 ntrap = 1015 cm−2

2.5 2 1.5 1 0.5 0 3 10

104

105 E⊥ (V/cm)

106

107

Figure 3: Orthogonal Electric field (E⊥ ) distribution at the Spiro-OMeTAD/TiO2 interface for undoped Spiro-OMeTAD. 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 the 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 density does not increase linearly with the electron trap density. The hole accumulation can be explained by the mechanism depicted Figure 5. The dye after absorbing sunlight creates electron-hole pairs which dissociate in 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 9



1015 Interface hole density(cm−2 )

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1014 1013 1012 1011 1010 109 108 11 10

1012

1013

1014

1015 −2

Interface trap density (cm

1016

)

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

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. 2. Step 3 shows the Coulombic attraction between electrons and the 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 towards 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 doping density in the organic HTL. We found that the 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 the E⊥ at the interface, for each value of HTL doping density. 10


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% of the HTL surface

10 Doping 1017 cm−3 Doping 1018 cm−3 Doping 1019 cm−3

8 6 4 2 0 2.5

3

3.5

4

4.5 5 E⊥ (V/cm)

5.5

6

6.5

·105

Figure 6: Orthogonal Electric field (E⊥ ) distribution at the interface for fixed interface trap density 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, the 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 accumulated hole density at the interface while varying the HTL doping. As shown in Figure 7, the interface hole density remains almost unchanged for doping density up to 1 × 1018 cm−3 . For a given electron trap density, the 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 photo-generated holes. For hole doping higher than the photo-generated charge carrier density ( i.e. beyond 1 × 1018 cm−3 in our case), the doping starts controlling the hole accumulation, and hence we observe an increase in the E⊥ . 1013 Interface hole density (cm−2 )

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1012

1011

1010

1016

1017

1018

1019

Doping density (cm−3 )

Figure 7: Surface hole density at the interface at fixed trap density 1 × 1013 cm−2 .

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For the increased HTL doping also, the E⊥ increases while increasing 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 below in Figure 8.

Figure 8: Orthogonal electric field E⊥ at the TiO2 /HTM interface (on the HTM side) at a fixed doping density 1 × 1016 cm−3 . 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 the E⊥ on the HTM side. This can be explained by the charge screening in TiO2 . A high dielectric constant of TiO2 helps maintaining electric → − → − displacement field ( D = E ) even with the low electron densities, at the same time offering easy electrons transport.

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. 67 We have considered a single JK2 on TiO2 68 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 elec12


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trolyte 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 may provide similar results. 71–73 All calculations have been carried out with the Gaussian 09 program package. 74

Figure 9: Molecular orbital diagram of the JK2/TiO2 system with varying electric field in vacuo (vac) and acetonitrile (solv), see text for definitions. 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 (a.u.) and Emax =2 × 107 V/cm = 4 × 10−3 (a.u.) respectively, we used Efield values of 0(no field) and, ± 1 × 10−3 a.u. and ± 1 × 10−2 a.u., (± 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 13



surface, a negative one shows an opposite direction.

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. The JK2@TiO2 electronic structure is that typical of a dye-sensitized interface, with the system’s HOMO being localized on the dye; and the manifold of TiO2 unoccupied states representing a set of LUMOs, see "no field" case in Figure 10. The HOMO density density partly shifts from the dye donor to the dye acceptor group by increasing the Ef ield 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 dyeTiO2 gap opening; while the negative field exerts an opposite effect. As an example, for a positive electric field of 1 × 10−3 a.u. the HOMO is stabilized by 0.2 eV and the LUMO is destabilized by 0.04 eV. The overall behavior is consistent with what previously reported, 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 14


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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 5 lowest electronic transitions have been computed only in vacuo, due to the similar behavior shown by the JK2@TiO2 electronic structure upon Ef ield application in vacuo and solution. Table 2: TDDFT calculated lowest 5 excitation energies and oscillator strengths for the JK2/TiO2 system in vacuo -10 E f 1.587 0.0001 1.806 0.0000 1.914 0.0002 1.948 0.0004 1.994 0.0006

E 2.398 2.582 2.631 2.670 2.747

-1 f 0.0011 1.9934 0.0029 0.0143 0.0601

No Field E f 2.485 0.0027 2.602 2.1064 2.718 0.0010 2.750 0.0055 2.822 0.0393

+1 E f 2.570 0.0143 2.620 2.1110 2.804 0.0008 2.830 0.0028 2.895 0.0263

+10 E f 2.745 2.2911 3.287 0.0001 3.458 0.0016 3.480 0.0032 3.522 0.0004

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 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 a.u. at 2.57 eV) which gains oscillator strength. At stronger positive fields of 1 × 10−2 a.u., 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 decreasing by increasing 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 15



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 charge dye is shown to alter the interface energetics, potentially leading to reduced injection yield from the dye excited state to the unoccupied TiO2 states.

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 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 towards the 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, the (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, the E⊥ increases only by a factor of ' 2. Furthermore, our first principle (DFT) study suggests that the built-up electric field (pointing towards TiO2 ) destabilizes TiO2 orbitals, leading to a dye/TiO2 gap opening. This dye/TiO2 gap increases with 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 the TiO2 , and hence, leading to a poor performing cell. Ultimately, reducing electron traps in TiO2 and using high mobility hole transport materials can help in stabilizing the

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interface energetics, by improving the charge injection and hence leading to an efficient solid-state dye sensitized solar cell.

Conflicts of interest The authors declare no conflict of interest.

Acknowledgements 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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Graphical TOC Entry

Hole accumulation (top panel) and the dye molecular orbitals (bottom)

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Hole accumulation (top panel) and the dye molecular orbitals (bottom)


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

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