Jan 27, 2017 - Table 1. Here, VX (where X is an atom or a group of atoms) .... observation can be supported by the fact that PbI2 species remains in grain ...
Jan 27, 2017 - ... the PerdewâBurkeâErnzerhof formalism of the generalized gradient approximation (GGA-PBE)(30) was adopted without the inclusion of spinâorbit coupling (SOC) as it is widely used for DFT studies of OIHPs including MAPbI3 and ha
Jan 24, 2014 - Electronic Structure of CH3NH3PbX3 Perovskites: Dependence on the Halide Moiety. Rebecka Lindblad , Naresh K. Jena , Bertrand Philippe , Johan Oscarsson , Dongqin Bi , Andreas Lindblad , Suman Mandal , Banabir Pal , D. D. Sarma , Olof
Jan 24, 2014 - The systems studied in the present investigation show promising conversion efficiencies. For example, in TiO2/CH3NH3PbI3/spiro-OMeTAD solar cell configurations, a short-circuit current of 18.3 mA/cm2 was obtained for the two-step metho
Nov 30, 2017 - Organicâinorganic lead halide perovskites have attracted significant attention during the last decade because of their applications in various fields, such as next-generation photovoltaics, light-emitting devices, photodetectors, las
Nov 30, 2017 - Center of Materials Technology and Photonics, Electrical Engineering Department, Technological Educational Institute (TEI) of Crete, 71004 Heraklion, Crete, Greece. Â§Physics Department and â¥Department of Materials Science and Techno
Nov 30, 2017 - CH3NH3PbI3 perovskite thin films have been deposited on glass/indium tin oxide (ITO)/Hole Transport Layer (HTL) substrates, utilizing two ...
Nov 30, 2017 - Department of Materials Science and Technology, University of Crete, 71003 Heraklion, Crete, Greece. â¢S Supporting Information. ABSTRACT: CH3NH3PbI3 perovskite thin films have been deposited on glass/indium tin oxide/hole transport l
Jun 26, 2016 - ... by In Situ Formation of 2D Perovskite at (FAPbI 3 ) 0.88 (CsPbBr 3 ) 0.12 /CuSCN Interface. Jiangzhao Chen , Ja-Young Seo , Nam-Gyu Park.
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Role of Ionic Charge Accumulation in Perovskite Solar Cell: Carrier Transfer in Bulk and Extraction at Interface Tianyuan Zhu, and Da-Jun Shu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01059 • Publication Date (Web): 13 Feb 2019 Downloaded from http://pubs.acs.org on February 13, 2019
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Role of Ionic Charge Accumulation in Perovskite Solar Cell: Carrier Transfer in Bulk and Extraction at Interface Tian-Yuan Zhu† and Da-Jun Shu∗,†,‡ National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China E-mail: [email protected]
To whom correspondence should be addressed National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China ‡ Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China †
Abstract By combining a simplified drift-diffusion modelling with the density functional theory, we quantitatively explore the contributing effects of the mobile defects in perovskites on the hysteresis of perovskite solar cells from aspects of both carrier transfer in the perovskite and extraction at the interface. Based on the solution of the onedimensional Poisson Equation, we demonstrate that at a positive biasing voltage applied to the hole contact layer that is larger than the presetting voltage, the carriers in perovskite need to overcome an energy barrier to transfer towards their selective contacts. The dependence of the energy barrier on the scanning voltage is determined by properties of both the perovskite and the contacts. By using the first-principles calculations, we further find that the perovskite/TiO2 band offsets are larger at a higher positive presetting voltage. The results reveal that the contributions of the defect migration to the hysteresis depend not only on the structural properties of perovskite but also on the choice of the contact materials, via both carrier transfer in the bulk perovskite and carrier extraction at the interface between perovskite and the contact materials.
INTRODUCTION Organic-inorganic halide perovskites are emerging as one of the most promising photovoltaic materials since the power conversion efficiencies of the perovskite solar cells (PSCs) have been improved from 3.8% to 22.7% in the past few years. 1–6 The tremendous growth is attributed to their desirable properties, such as high optical absorption coefficients, long carrier diffusion lengths and high carrier mobility. 7–10 Despite the significant performance of PSCs, the presence of current-voltage (J-V ) hysteresis not only makes the determination of the power conversion efficiency ambiguous, 11–14 but also reveals the problem of long-term stability. 15 Among the proposed hypotheses for the origins of the hysteresis, charge trapping and ferroelectric polarization are unlikely to be the dominant mechanism considering their
faster timescales than those observed in experiments. 16,17 Instead, migration of ionic defect was assessed to be dominantly responsible for the hysteresis. 18–22 Experiments have revealed that the diffusion of ionic defects in the halide perovskites have important influences on the performance of the PSCs. 23–26 By combining the experimental measurements with the first-principles calculations, the mobile defects are commonly attributed to the halogen vacancies or organic vacancy, 27–31 although other kinds of point defects can form under different growth conditions. 32 When keeping at a presetting or poling voltage for a sufficiently long time, the mobile positively charged defects (D+ ) and negatively charged defects (D− ) in the perovskite layer (PVT) can be driven by the build-in electric field in opposite directions. 28 Very recently, the ionic charge accumulation at the interface has indeed been visualized in experiments, although the formation mechanism is unclear. 22 The redistribution of the mobile defects is expected to alter the band diagram of the perovskite and thus the efficiency of the charge transfer. 24–28 Based on the drift diffusion equations, several work have modeled the influence of the ionic accumulation at interfaces of perovskite on the distribution of the photo-generated carriers via screening or compensating the electric field. 18,19,21 As accumulation of the mobile ions is dependent on the biasing history, the carrier injection, extraction and recombination that are determined by the carrier density at the interfaces are also biasing-history dependent. In this way the ionic migration leads to the hysteresis of the perovskite cell, the extent of which depends on the the trap density, recombination rate and extraction barriers at the interfaces between perovskite and the contact materials. In spite of the depiction of the models, there still lacks a quantitative way to address the effect of the defect migration on the hysteresis. For instance, people still do not know how the structural properties of the perovskite and the contact materials quantitatively influence the ion-accumulation induced electric field at different bias voltage. Moreover, the influences of the carrier transfer materials were only taken account for via the interface effects. Experimentally it is commonly known that the hysteresis is affected by choice of the
selective contacts, i.e., hole transfer layer (HTL) and the electron transfer layer (ETL). 11,33 While this has been usually taken as a support for the interface-related origination of the hysteresis, 34–36 it is worthy to evaluate whether it is also a concurring consequence of the defect migration in PVT. Furthermore, the interaction between the defects in the selective contacts and PVT may make the situation ever more complicated. 22,37,38 In this work, by combining a simplified drift-diffusion modelling with the density functional theory calculations, we quantitatively explore the contributing effects of the mobile defects in perovskites on the hysteresis of PSCs from aspects of both carrier transfer in the perovskite and extraction at the interface. Based on the solution of the one-dimensional Poisson Equation, we deduce the variation of the electrostatic potential in the perovskite during the fast scanning, supposing the migration of ionic defects is frozen by the presetting condition. There is an energy barrier for the carriers to transfer in PVT towards their selective contact layers if the positive scanning voltage is larger than the presetting voltage. The energy barrier increases with the scanning voltage approximately linearly, with a slope depending not only on the properties of PVT, but also on those of the HTL and ETL material. Furthermore, by using first-principles calculations carried out for the MAPbI3 /TiO2 interface, we demonstrate that the band offsets at the PVT/ETL interface vary with the presetting voltage. The efficiency of the electron extraction at the interface becomes higher when the presetting voltage increases from short-circuit (SC) to forward bias (FB), since the number of D− in perovskite accumulated at the interface decreases. The involvement of oxygen vacancies in TiO2 can slightly enhance this effect. As a result, the mobile defects contribute to the anomalous hysteresis in PSCs via the energy barrier of the carrier transfer in the bulk of PVT and the band offsets at the PVT/ETL interface. Both the bulk and the interface effects are dependent on the structural properties of not only PVT but also the selective contacts.
METHODS Model of Perovskite Solar Cell In order to make the derivation in concise format, we made two main approximations. Firstly, the density of electronic carrier in perovskite is assumed to be small relative to the density of the mobile ions, so that the influence of carriers on the potential is neglected. 19 It is indeed well known that despite the high defect concentration, the measured carrier concentrations in equilibrium are remarkably low, the origin of which has been attributed to a self-regulation mechanism for charged point defects. 39 Even under illumination, if the bias voltage is within the range smaller than the built-in voltage the influence of carriers on the electric field in perovskite can be neglected when compared with that of the ionic defects. 19 We stress that as demonstrated in Ref., 19 even if one neglects the influence of the electrons and holes on the electric field, the electric field induced by the ionic accumulation is expected to play roles on the distribution and transfer of the photo-generated carriers. Therefore our work does not just address the dark response of the solar cells. Secondly, we assume that the charges are distributed homogeneously in the ionic space charge layers with the same density at the two perovskite-contact interfaces. The homogeneous accumulation model can be regarded as a simplified drift-diffusion model, which has been compared and found consistent with the drift-diffusion model by Jacobs. 20 Consider the PSC in a sandwich structure of HTL/PVT/ETL as a p-i-n device, where the two contacts HTL and ETL are respectively p-type and n-type semiconductors, and the PVT is regarded as an electronic insulator. With regards to their properties, we hereafter use the subscript p, n and i to refer to HTL, ETL and PVT, respectively. Besides, the subscript c is used when common properties of HTL and ETL are discussed. The positive bias voltage V is applied to the HTL contact with the ETL is grounded. Due to the difference between the Fermi levels (EF ) in HTL and ETL, there is an built-in electric field within PVT even under the SC condition, pointing from ETL to HTL. It corresponds to an electric potential
drop of Vbi = (EFn −EFp )/q from ETL to HTL, where q is the value of an elementary charge. A positive bias voltage produces an electric field opposite the built-in field. Therefore when V < Vbi , the electric field in perovskite remains its direction with a smaller magnitude. While the electric field pointing from ETL to HTL favors the separation and transfer of the photo-generated holes and electrons towards their selective contacts, the mobile ionic defects in PVT may also be driven to accumulate at the HTL/PVT or PVT/ETL interfaces. As schematically shown in the inset of Fig. 1(a), two space charge layers with a thickness of li present in PVT around the interfaces at a certain bias voltage, with positive charges at the HTL side and negative at the ETL side. Meanwhile there is a negative charge layer with thickness of lp in HTL and positive charge layer with thickness ln in ETL around the interfaces. Suppose the magnitudes of the charge concentration of the space charge layers are ρp , ρn and ρi in HTL, ETL and PVT, respectively. The magnitudes of the corresponding areal charge density are σi ≡ qρi li in both space charge layers in PVT and σc ≡ qρp lp ≡ qρn ln in the two contacts.
Computational Details of Perovskite/TiO2 Interface A symmetric slab consisting of four MAI layers and three PbI2 layers are used to model the MAI terminated MAPbI3 (110) surface. The perovskite/ETL interface is constructed by putting the (1×1) MAPbI3 (110) surface coherently on a four-trilayer (2×4) rutile TiO2 (110) slab, leaving a vacuum with a thickness of 16 Å along the nonperiodic direction. The in-plane size of the supercell is set according to the bulk TiO2 lattice parameters. The MAPbI3 is thus under 2.11% tensile strain and 4.10% compressive strain along its  direction and [1¯10] direction, respectively. While other interfaces between MAPbI3 and rutile TiO2 have been studied, such as α-MAPbI3 (001)/r-TiO2 (110) 40 and β-MAPbI3 (001)/r-TiO2 (001), 41 the current interface not only consists of the most stable surfaces of both materials, but also possesses a relative small average in-plane lattice misfit. Moreover, we stress that a sufficient thickness of TiO2 slab is necessary to describe the properties of oxygen vacancy (VO ) at the 6
interface and the surface. 38 Using the current settings, the formation energy of a single VO as a function of its depth relative to the in TiO2 surface is consistent with the previous work. 42,43 The density functional theory (DFT) calculations 44 are carried out by using Vienna ab initio simulation package (VASP) code 45 with projector augmented wave method. 46,47 The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 48 with the optB86b-vdW correction 49 is employed. Real space projection with an energy cutoff of 500 eV is used in the calculations, which has been tested to be sufficiently large for convergence. All the atoms are relaxed without constraints until the atomic forces are converged to 0.01 eV/Å. The DFT plus U scheme 50 is employed with Uef f = U −J = 6.0 eV for Ti 3d electrons, which correctly reproduces the two distinct band-gap states of oxygen vacancy in rutile (110) TiO2 surface. 51 The lattice constants of the rutile TiO2 are a = 4.65 Å and c = 2.97 Å. 52 For the MAPbI3 in tetragonal phase, the lattices are a = 8.76 Å, c = 12.88 Å. These values are in good agreement with the corresponding experimental 53,54 and theoretical results. 55,56
RESULTS AND DISCUSSION Barrier of Carrier Transfer in the Bulk Perovskite If the steady-state distribution of the mobile ionic defects is reached after a sufficiently long time at a presetting voltage Vpre , we have the steady magnitude of the areal charge density in the space charge layers as σst = σi = σc . The potential energy U (x) of an electron varies within the space charge layers, beyond which it remains constant. Following the onedimensional Poisson Equation, σst is determined by the overall drop of electronic potential energy ∆U0 from HTL to ELT of the model cell,
where λ is an intrinsic structural parameter determined by the properties of PVT, ETL and HTL of the solar cell, λ=
εi ρ i εi ρi + . 2εp ρp 2εn ρn
Here ε0 is the vacuum dielectric constant, while εp , εn and εi are the relative dielectric constants in HTL, ETL and PVT, respectively. Accordingly the stabilized thickness of the ionic space charge layer in PVT can be written as lst =
√ ld , 1+λ
where ld is defined as the
following, s ld =
ε0 εi (Vbi − Vpre ) , qρi
ld is similar to the Debye length except that it is determined by the net voltage drop instead of the thermal energy. It decreases with increasing ionic density and at higher presetting voltage. By using the value εi = 6.5, Vbi = 1.0V and ρi = 1017 cm−3 , we can estimate the Debye-like length ld defined in Eq. (3) as 60 nm when presetting in short-circuit. In practice, li = min(lst , L/2) because the space charge layer in PVT cannot exceed L/2. Therefore the steady state li = lst can only be reached when lst < L/2. The ratio η =
is thus a key structure parameter in the preset perovskite. According to Eq. (1-3), we have η=
√2α , 1+λ
where α is the ratio between the Debye-like length to the PVT thickness, α = ld /L.
It is worthy to note that the influences of properties of PVT and presetting condition on stabilized thickness of the ionic space charge layer in PVT are included in ld and thus in α, while the influences of the contact materials are described by λ. Now we check the potential energy of an electron U (x) in PVT at a bias voltage V during a scan, with position x measured relative to the HTL/PVT interface. For the time being we assume the scan is fast so that ion distribution σi is frozen by the presetting condition. Instead, the areal charge density σc varies with the scanning voltage. By setting σi = qρi li , U (x) can be obtained numerically by solving the one-dimensional Poisson Equation under the electrostatic boundary conditions. We find that at a certain normalized voltage ∆V˜ ≡
Figure 1: Numerical solutions of the one-dimensional Poisson Equation. (a) The distribution of the potential energy of an electron in the HTL/PVT/ETL structure. A nonzero energy barrier ∆G appears when V > Vpre for the light-induced carriers transferring to the corresponding contacts. (b) The dependence of the energy barrier on the scanning voltage.
parameters λ and α. As shown in Fig. 1(a) for typical λ and α, U˜ (x) goes downhill from HTL to ETL when ∆V˜ is negative. By contrast, it goes uphill when ∆V˜ is positive. In this case the photogenerated carriers have to overcome an energy barrier ∆G when transferring towards their selective contacts. The energy barrier varies with ∆V depending on the value of α and λ as demonstrated in Fig. 1(b). If η < 1, i.e., lst < L/2, the energy barrier is always present ˜≡ whenever ∆V˜ > 0, and the normalized barrier ∆G
increases approximately linearly
with ∆V˜ . If η > 1, however, the barrier occurs only when ∆V˜ is larger than a critical value ∆V˜cr . The quantitative dependence of the barrier ∆G on the scanning voltage can be alternatively obtained in the analytical way. According to the the one-dimensional Poisson Equation, σc at a certain bias voltage V is determined by the overall drop of electronic potential energy from HTL to ETL,
e(Vbi − V ) =
1 [λσc2 + σi2 + qρi L(σc − σi )]. ε0 εi ρ i
While the first term in the brackets gives the voltage drop within the space charge layers of contacts, the rest terms cover the voltage drop in PVT. As σi = qρi li is determined by the presetting condition, σc decreases with increasing V . Whenever σc < σi , there is a residual electric field pointing from HTL side to ETL side between the two interfacial space charge layers in PVT, which results into an uphill variation of U (x) from HTL to ELT. Therefore, the carriers in PVT have to overcome an energy barrier ∆G before reaching their correct selective contacts when σc < σi . After a simple deduction, it follows that
1 [σ 2 − σi2 − qρi L(σc − σi )]. ε0 εi ρ i c
The condition σc = σi can be used to obtain the critical bias voltage Vcr above which the barrier is present. It is easy to find that Vcr = Vpre and ∆V˜cr = 0 for lst < L/2 since 10
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σi = σst . It means that the barrier is present for any voltage larger than Vpre . For lst > L/2, σi = qρi L/2, which according to Eqs. (1) and (4) gives that Vcr = Vpre η12 + Vbi (1 − thus ∆V˜cr = 1 −
1 . η2
1 ) η2
It means that the range of bias voltage with which the energy barrier
occurs shrinks with increasing lst when lst > L/2. Although the energy barrier at a certain biasing voltage does not change with the presetting condition for lst > L/2, it increases obviously with decreasing Vpre when lst < L/2. Since the energy barrier ∆G within PVT prehibits the transfer of the photo-generated carriers to their selective contacts, a higher recombination loss must occur both in the bulk of PVT and the interface between PVT and the contacts for smaller presetting voltage Vpre . Therefore the transfer of the carriers and thus the photo-induced current is dependent on the presetting condition as discussed by Reenen. 18 The actual hysteresis comes from the lagging ionic migration compared to the fast scanning. For certain ionic diffusion properties and at a certain scanning rate, more severe hysteresis would be expected in situation of more rapid increasing of ∆G with qV . Therefore the derivative of ∆G with respective qV can be used to quantitatively measure the dependence of the ionic migration induced hysteresis on the device parameters. (a)
λ ˜ with ∆V˜ as a function of λ and α. The Figure 2: Contour map of the derivation of ∆G black region in the top left corner in (a) and (b) corresponds to ∆G = 0 since ∆V˜ < ∆V˜cr . By combining equations (4) with (5), one can find out the derivative of ∆G when V > Vpre with respective to qV for a fixed Vpre , k = k'
1−η , 1+λη
∂∆G ∂(qV )
1−η(σc /σst ) . 1+λη(σc /σst )
When α and ∆V˜ are small,
which means that ∆G increases with V approximately linearly. The results are 11
consistent with those obtained from the above numerical solutions of the Poisson Equation shown in Fig. 1(b). The accurate value of k as a function of α and λ is numerically solved and plotted in Fig. 2. One can see that the main features are similar for different ∆V˜ , except that the isolines globally lift towards larger α for larger ∆V˜ . Obviously k is more sensitive to the change of α than to that of λ. As α increases from 0 to 1, the value of k decreases from 1.0 monotonously to 0, more rapidly for larger λ. The variation of k with λ depends on the value of η. For η < 0.5, k decreases monotonically with increasing λ. For larger η, k increases with increasing λ until it reaches a maximum, and then it gradually decreases. In the region of q 2α > (1 + λ)/(1 − ∆V˜ ), as shown in the dark area in the top left corner in Fig. 2(a-b), ∆G and k equals to zero since ∆V˜ < ∆V˜cr . Based on the dependence of k on α and λ, we can now discuss the factors that influence the hysteresis during the J-V scan of the solar cell quantitatively. First of all, since smaller L and ρi leads to a larger α and thus a smaller slope k, the hysteresis can be reduced by decreasing the thickness or/and the density of mobile defects of PVT. The results are consistent with the previous experimental studies. For instance, it has been shown that hysteresis-less J-V curves can be obtained by decreasing the concentration of defects in perovskite. 5,57–60 Moreover, the magnitude of hysteresis was found to increase with thickness of the perovskite film in planar perovskite solar cells. 61 Especially, the dark areas in the top left corner in Fig. 2(a-b) suggest that even with a certain density of the mobile defects in PVT, the hysteresis may be eliminated in a small range of ∆V˜ when PVT is extremely thin. The influence of the properties of the selective contacts on the hysteresis is more complicated. Since k decreases in the limit of large λ, small ρn or ρp relative to ρi may reduce the hysteresis. It can be understood as the electric potential drops largely within the selective contacts, and thus the space charge areal density σst is small. However the photo-generated current is also low due to low density of the carriers in the contacts. On the other hand, λ = 0 corresponds to a local minimum of k for η larger than 0.5 and small ∆V˜ according
to Fig. 2. Therefore, in the region of large α and small λ, the hysteresis may be reduced by increasing ρn and ρp relative to ρi for small ∆V˜ . This situation is more favorable for the performance of the solar cell. It is thus quite clear that the hysteresis is affected not just by the properties of the perovskite, but also by those of HTL and ETL. The conclusion is consistent with the reported experimental observations. For example, it has been widely reported that the hysteresis can be reduced by improving the carriers concentration of the ETL materials via dopants. 62–66 The choice of a specific HTL material also leads to hysteresis-less characteristics. 67,68 The previous work have attributed the contacts dependence of the hysteresis to the interface effect. We stress that according to our theoretical analysis, the influences of the HTL and ETL materials on the hysteresis can also be a consequence of the migration of the ionic defects in PVT, not just the interface effects.
Band Offsets at the MAPbI3 /TiO2 Interface In addition to build up the electric field in PVT, the redistribution of defects attained at the presetting voltage may change the band offsets at the interfaces. 36,37 It is vital for the performance of the PSCs because the valance band offset (VBO) and conduction band offset (CBO) can influence the extraction efficiency of holes and electrons at the interfaces, respectively. Since the PVT/ELT(TiO2 ) interface has been found critical for high performance, 38,65,69,70 we take the PVT/TiO2 interface as an example and explore the band offsets after the defect redistribution at the presetting voltage, leaving the HTL/perovskite interface open in the future. We consider tetragonal MAPbI3 and rutile TiO2 as the typical perovskite and ETL respectively. 40,41,71 These phases are chosen because the tetragonal phase of MAPbI3 at room temperature is more stable than other phases, 72 and the nanocrystalline rutile TiO2 is more effective in extracting photo-generated electrons from MAPbI3 than the anatase TiO2 film. 73–75 The defect-free MAPbI3 /TiO2 interface after relaxation is shown in Fig. 3(a). The 13
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MAPbI3 /TiO2 interface forms through Ti-I ionic bonds and H-O hydrogen bonds. The binding energy of the interface is 3.56 eV per surface unit cell, much larger than the strain energy 0.02 eV per surface unit cell. The local density of states (LDOS) of the interface are shown in Fig. 3(b). The CBO at the interface is defined as the difference between the conduction band minimum of the contacting layers in MAPbI3 and that in TiO2 , as marked by the arrowed lines in Fig. 3(b). The VBO is defined similarly as the difference between the valence band maximum. While the CBO provides the driving force for electron extraction from MAPbI3 to TiO2 , the VBO can block the hole transfer to TiO2 . For the defect-free MAPbI3 /TiO2 interface, the CBO and VBO are 0.72 eV and 1.14 eV, respectively. (a)
Figure 3: Atomic structure and Local density of states (LDOS) of defect-free MAPbI3 /TiO2 interface. (a) Atomic structure of the interface. The C, N, H, Pb, I, Ti, and O atoms are depicted as brown, light blue, white, black, purple, cyan, and red spheres, respectively. (b) LDOS of the interface. The gray shadowed regions and the black solid lines denote the contribution of the whole TiO2 substrate and the interfacial TiO2 trilayer, respectively. The dark cyan shadowed regions and the cyan solid lines show the density of states of the MAPbI3 slab and the interfacial MAPbI3 layer, respectively. We then introduce mobile defects in the supercell. Three types of vacancies are considered, namely MA vacancy (VMA ), I vacancy (VI ) and VO . There are seven complexes consisting of the three types of defects in total, including three one-type defects (VMA , VI and VO ), three two-types defects (VMA +VI , VMA +VO and VI +VO ), and one three-types defect (VMA +VI +VO ). Only zero or one defect for each type is included in each supercell, 14
corresponding a maximal in-plane defect concentration of 25% for VI , 25% for VMA , and 12.5% for VO , respectively. It is reasonable to assume that the interactions between defects in neighboring supercells remain the same for different distribution of the defects. Therefore, the errors due to the finite defect densities are expected to be cancelled out when we only concern about the difference between distributions of the defect complexes. The defects are placed at the surface or interface according to the presetting condition. The formation energies and the corresponding LDOS are calculated after full relaxation of the structures. As the built-in electric field decreases gradually when the presetting voltage increases from SC to FB, the numbers of D− in PVT and D+ in ETL accumulated around the PVT/ETL interface at the lower presetting voltage become larger than those at the higher one. In order to compare the effects of different presetting voltage, we consider the following two extreme distributions of the defects. The first one corresponds to a lower presetting L voltage (Vpre ), in which only D− in PVT and D+ in ETL are at the PVT/ETL interface,
while D+ in PVT and D− in ETL are at their surfaces. The second one corresponds to H a higher presetting voltage (Vpre ), in which only D+ in PVT and D− in TiO2 are at the
PVT/ETL interface, while D− in PVT and D+ in ETL are at their surfaces. The structures and the corresponding LDOS of four typical defect complexes are shown H L , respectively. In Fig. 4, the negatively charged VMA in and in Fig. 5 for Vpre in Fig. 4 for Vpre
perovskite and the positively charged VO in TiO2 are at the perovskite/ETL interface, while the positively charged VI is at the MAPbI3 surface site. In Fig. 5, only VI is placed at the interface, while VO is at the TiO2 surface and VMA at the MAPbI3 surface. By comparing the different Fermi levels of the structures, we can see that VI and VO result in n-type doping, while VMA results in p-type doping. It indicates that the local charging characters of the defects are described correctly although no extra charge is included in the simulations, as VI and VO are predicted to be positively charged and VMA is negatively charged. 32 The formation energies of the defects and the band offsets of all the considered defect complexes are summarized in Table 1. Nearly all of the defect complexes are more stable
Figure 4: Atomic structures (Left) and LDOS (Right) of defective MAPbI3 /TiO2 interfaces L preset at lower voltage (Vpre ). (a) VMA at the MAPbI3 /TiO2 interface. (b) VI at the surface of MAPbI3 . (c) VO at the MAPbI3 /TiO2 interface. (d) The defect complex consisting of the three kinds of vacancies.
Figure 5: Atomic structures (Left) and LDOS (Right) of defective MAPbI3 /TiO2 interH faces preset at higher voltage (Vpre ). (a) VMA at the surface of MAPbI3 . (b) VI at the MAPbI3 /TiO2 interface. (c) VO at the surface of TiO2 . (d) The defect complex consisting of the three kinds of vacancies.
H L at Vpre than at Vpre . The exception of VMA +VO complex is attributed to the electrostatic L . This is interaction between VMA and VO since VMA and VO are close to each other at Vpre
confirmed by checking VMA and VO located at other different sites, which turns out to be that smaller distance between VMA and VO always leads to lower total energy. Table 1: Relative total energy (∆E) and band offsets of defective MAPbI3 /TiO2 interfaces. Defect (complex) VMA VI VO VMA +VI VMA +VO VI +VO VMA +VI +VO
∆E (eV) L H (Vpre − Vpre ) 0.39 0.27 0.41 0.45 -0.10 0.62 0.49
CBO H Vpre 0.72 0.65 0.73 1.11 1.34 0.64 1.11
(eV) L Vpre 0.69 0.42 0.71 0.64 1.05 0.40 0.60
VBO H Vpre 1.11 0.88 1.16 1.27 1.45 0.88 1.26
(eV) L Vpre 1.00 0.74 1.09 1.01 1.36 0.63 0.99
A more important feature shown in Table 1 is that both CBO and VBO of the MAPbI3 /TiO2 L H . The higher CBO indicates that than preset at Vpre interface are larger when preset at Vpre
the electron extraction is relatively more efficient if the solar cell is preset under higher H voltage. Besides, the larger VBO at Vpre means that the blockage of the hole transport
from MAPbI3 towards TiO2 is more efficient at higher presetting voltage. Therefore, the MAPbI3 /TiO2 based solar cell is expected to possess higher efficiency of both electron and hole extraction when preset at higher forward voltage compared to the situation of presetting at lower voltage. It is also worthy to mention that among the considered defect complexes, L H the one consisting of VMA +VO possesses the largest CBO and VBO, both at Vpre and Vpre . L Furthermore, the inclusion of VO leads to a slightly larger difference between the CBO in Vpre H and Vpre , suggesting that the interaction between the defect in TiO2 and that in perovskite
enhances the difference of the presetting voltage. The presetting dependent band offsets naturally leads to the hysteresis of the J-V curves of the perovskite solar cell. 11 At a certain voltage, a higher photocurrent is expected when the scanning starts from a larger voltage than reversely, supposing that the ionic distribution 18
is frozen at the presetting voltage before the scanning. As the band offsets depend on the materials of PVT and ETL, the hysteresis can be reduced by designing the structures of PVT and ETL such that the band offsets are almost unchanged by the redistribution of the defects at the interface under different presetting voltage. It is worthy to mention that when a perovskite solar cell device is operated at the maximum power point, a new steady-state ion distribution would be reached after a sufficiently long time. The stable interface band offsets and thus the charge carrier extraction efficiencies are determined by the working condition and would not decay.
CONCLUSIONS In summary, we have studied the influence of the mobile defects on the performance of perovskite solar cell. During a fast scanning process, the distribution of the mobile ionic defects in the PVT and ETL remains as built at the presetting voltage. It results into an energy barrier for the photo-generated carriers transferring to HTL or ETL when the scanning voltage V positively applied to the HTL is larger than the presetting voltage Vpre . The energy barrier increases with the scanning voltage approximately linearly, with a slope depending not only on the properties of PVT, but also on those of the HTL and ETL material. Meanwhile, different distribution of the defects reached at the presetting voltage also changes the band offsets at the interface. As less D− /D+ accumulate around the PVT/ETL interface, the band offsets and thus the extraction of the photo-generated carriers at the interface are more favorable when preset at a higher voltage than at a lower voltage. Both factors contribute to the scan-dependent hysteresis depending not only on the properties of PVT, but also the properties of the contacts. Accordingly, the magnitude of the hysteresis can be reduced by tuning the density of the carriers of ETL and HTL materials, in addition to decreasing the thickness and the density of mobile defects of PVT. Our finding would provide a quantitative understanding in the mechanism of current-voltage hysteresis.
ACKNOWLEDGMENTS The calculations were carried out at the High Performance Computing Center of Nanjing University. This work was supported by the Basic Research Program of Jiangsu Province (Grant No. BK20161390) and the Fundamental Research Funds for the Central Universities (Grant No. 020414380100).
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