⇦Chinese Physics Letters, 2019, Vol. 36, No. 2, Article code 026701 CH$_{3}$NH$_{3}$ Formed by Electron Injection at Heterojunction Inducing Peculiar Properties of CH$_{3}$NH$_{3}$PbI$_{3}$ Material * Ao Zhang (张翱)1,2**, Yun-Lin Chen (陈云琳)1**, Chun-Xiu Zhang (张春秀)2, Jun Yan (闫君)1 Affiliations 1Department of Physics, School of Science, Beijing Jiaotong University, Beijing 100044 2Beijing Institute of Graphic Communication, Beijing 102600 Received 3 September 2018, online 22 January 2019 *Supported by the National Natural Science Foundation of China under Grant No 61875235, the Ph.D. Programs Foundation of Ministry of Education of China under Grant No 20130009110008, and the Beijing Municipal Education Commission Project under Grant No KM201210015008.
**Corresponding author. Email: zhangaog@bigc.edu.cn; ylchen@bjtu.edu.cn Citation Text: Zhang A, Chen Y L, Zhang C X and Yan J 2019 Chin. Phys. Lett. 36 026701    Abstract The effect of formed CH$_{3}$NH$_{3}$ at the heterojunction on properties of CH$_{3}$NH$_{3}$PbI$_{3}$ material is investigated based on experiment and theoretical calculation. Our calculation results show that the giant dielectric constant, anomalous hysteresis and long-lasting polarization for CH$_{3}$NH$_{3}$PbI$_{3}$ originate from the formed CH$_{3}$NH$_{3}$ at the heterojunction. It is found that the induced weak EPS by the reorientation of CH$_{3}$NH$_{3}$ sub-group along the built-in electric field enables us to effectively increase the ordering of entire lead-halide framework. In addition, the heterojunction has an advantage of channel separation between carrier transport and electron diffusion. These properties of the heterojunction are the main origin of the high efficiency of CH$_{3}$NH$_{3}$PbI$_{3}$ solar cells. DOI:10.1088/0256-307X/36/2/026701 PACS:67.30.hp, 71.23.An, 72.40.+w, 88.40.H- © 2019 Chinese Physics Society Article Text Hybrid halide perovskite has been utilized as light-absorbing materials in solar cells because of their good properties for light harvesting and carrier transport.[1-3] The power conversion efficiency (PCE) of perovskite solar cells has rapidly increased from 3.8% to 23.3%.[4,5] Despite the rapid progress in cell performance, some puzzling experimental phenomena remain unanswered, such as giant dielectric constant (GDC), anomalous hysteresis and long-lasting polarization.[6-8] The theoretical development has become a barrier that restricts the further progress of these materials. The computed optical absorption spectra and lattice parameters with the DFT method based on periodic boundary conditions (PBCs) are in excellent agreement with the experiments,[9,10] which implies that this method is very effective when calculating the characteristics of the inorganic framework in CH$_{3}$NH$_{3}$PbI$_{3}$. Strictly speaking, room-temperature CH$_{3}$NH$_{3}$PbI$_{3}$ has no typical crystal structure because the geometrical arrangement of CH$_{3}$NH$_{3}^{+}$ is unknown in detail and the inorganic framework is distorted from the perfect crystal structure.[6] Thus the mandatory PBCs in density functional theory (DFT) calculations are not applicable to disordered CH$_{3}$NH$_{3}^{+}$ in CH$_{3}$NH$_{3}$PbI$_{3} $ at room temperature. The carrier transport properties play an extremely role in high efficiency of perovskite solar cells. The carrier mobility in tetragonal CH$_{3}$NH$_{3}$PbI$_{3}$ shows a temperature dependence ($\mu \propto T^{-3/2}$) from microwave conductivity and THz spectroscopy,[11-13] which indicates that charge transport is dominated by pure acoustic phonon (deformation potential) scattering.[14] The structural fluctuations of inorganic framework, which results primarily from the disordered and activated CH$_{3}$NH$_{3}^{+}$, limiting efficiency of carrier transport.[14] Actually, the mobilities of CH$_{3}$NH$_{3}$PbI$_{3}$ at room temperature are rather modest, at least 1–2 order of magnitude lower than those of Si, GaAs.[15] However, why do room-temperature CH$_{3}$NH$_{3}$PbI$_{3} $ solar cells exhibit such high efficiency? In this work, we study the origin of GDC, anomalous hysteresis, and long-lasting polarization, and investigate the effect of formed CH$_{3}$NH$_{3}$ at the heterojunction on properties of CH$_{3}$NH$_{3}$PbI$_{3}$ material. These calculations were carried out using Gaussian 09 and Multiwfn software.[16-18] Because it is closely related to polarization, the dielectric constant is highly dependent on applied electric field and phase structure.[19,20] In the orthorhombic phase, the CH$_{3}$NH$_{3}^{+}$ in CH$_{3}$NH$_{3}$PbI$_{3}$ is pinned and can only rotate along C–N axis,[21] which leads to freezing out of dipolar orientational polarization. In the cubic phase, the dielectric measurement between 50 GHz and 150 GHz reveals a dynamic disorder of CH$_{3}$NH$_{3}^{+}$ group.[22] In the tetragonal phase, the dielectric constants between 20 Hz and 90 GHz reported by Onoda–Yamamuro confirms that the room-temperature CH$_{3}$NH$_{3}^{+}$ is activated and disordered in CH$_{3}$NH$_{3}$PbI$_{3}$,[23] which is consistent with the high-rate rotation of room-temperature CH$_{3}$NH$_{3}^{+}$ from $^{2}$H and $^{14}$N spectra.[24,25] The dielectric constant of CH$_{3}$NH$_{3}$PbI$_{3}$ is closely related to whether electrons are injected into the material or not. For no electron injection case, the dielectric constant of room-temperature CH$_{3}$NH$_{3}$PbI$_{3}$ between 20 Hz and 1 MHz has no frequency dependence, and is about 60.[23] The calculated polarization magnitude maximum 8 µC/cm$^{2}$ is far less than 8 mC/cm$^{2}$ observed by Fan et al.[26] For the electron injection case, the dielectric constants in Au/CH$_{3}$NH$_{3}$PbI$_{3}$/PEDOT:PSS/ITO structure[26] increase with the voltage from 1 V to 3 V at 3 kHz, and decrease with the frequency from 5 Hz to 3 kHz at 1 V, which implies the voltage amplitude- and frequency-dependence of dielectric constant. The dielectric constants of CH$_{3}$NH$_{3}$PbI$_{3}$ even reach $1.8\times10^{4}$ at 3 V and 3 kHz, which are consistent with GDC of CH$_{3}$NH$_{3}$PbX$_{3}$ reported by Juárez–Pérez et al.[27] Some researchers ruled out the phenomenon due to CH$_{3}$NH$_{3}^{+}$ dipole alignment, and speculated that the ion migration driven by electric field is the possible origin.[28,29] Senocrate et al. reported that the ion conduction in CH$_{3}$NH$_{3}$PbI$_{3}$ is primarily due to $I^{-}$ migration.[30] Although this experiment had proved the existence of $I^{-}$ migration in cubic phase, this phenomenon has not been observed in tetragonal phase. Meanwhile, the timescale of $I^{-}$ migration is far greater than the timescale of long-lasting polarization.[28-30] What then causes the GDC of CH$_{3}$NH$_{3}$PbI$_{3}$? In the Au/CH$_{3}$NH$_{3}$PbI$_{3}$/PEDOT:PSS/ITO structure,[26] the electrons in Au electrode under electric field are accumulated at Au/CH$_{3}$NH$_{3}$PbI$_{3}$ interface. Figure 1 shows the molecular orbitals and energies of optimized CH$_{3}$NH$_{3}^{+}$ at B3LYP/6-311++G(d,p) level. The lowest unoccupied molecular orbital (LUMO) ($-$5.96 eV) of CH$_{3}$NH$_{3}^{+}$ has a lower energy than the LUMO ($-$3.93 eV) of CH$_{3}$NH$_{3}$PbI$_{3}$,[31] which allows interfacial electrons easily entering unoccupied molecular orbitals of CH$_{3}$NH$_{3}^{+}$ with the process CH$_{3}$NH$_{3}^{+}+e^{-}\to$CH$_{3}$NH$_{3}$.
cpl-36-2-026701-fig1.png
Fig. 1. The molecular orbital isosurfaces and energies of isolated CH$_{3}$NH$_{3}^{+}$ at B3LYP/6-311++g(d,p) level, here green and blue isosurfaces represent positive and negative regions (0.07 a.u. and $-$0.07 a.u.), respectively.
Figure 2 shows that CH$_{3}$NH$_{3}^{+}$ and CH$_{3}$NH$_{3}$ have a strong electrostatic attraction, which makes them approach each other. The molecular orbital of outermost unpaired electron for CH$_{3}$NH$_{3}$:CH$_{3}$NH$_{3}^{+}$ heterodimer is distributed around the line NH–HN in Fig. 3(a). The NH–HN electrostatic interaction is usually accompanied by charge transfer under electric field via hopping mechanism.[32] The local integral curve of electron density difference in Multiwfn Software[17,18] is known as charge displacement curve, and is useful in the process of charge transfer. As shown in Fig. 3(b), the electron transfer between two CH$_{3}$NH$_{3}^{+}$ increases with the strength of electric field. It is inferred that when the strength is stronger and the duration of the electric field is longer, the more interfacial electrons are injected into CH$_{3}$NH$_{3}$PbI$_{3}$ and the more layers of CH$_{3}$NH$_{3}$ are formed at the heterojunction. Thus, the formed CH$_{3}$NH$_{3}$ in CH$_{3}$NH$_{3}$PbI$_{3} $ increases with increasing voltage amplitude and decreasing frequency, which is kept with the voltage amplitude- and frequency-dependence of observed dielectric constant.[26]
cpl-36-2-026701-fig2.png
Fig. 2. Four initial and optimized CH$_{3}$NH$_{3}^{+}$:CH$_{3}$NH$_{3}$ heterodimers at MP2/Aug-cc-PVTZ level. Here $d$ and $E_{\rm int}$ are the distance between centroid of two organic ions and interaction energy of dimers, respectively.
cpl-36-2-026701-fig3.png
Fig. 3. (a) The molecular orbital of outermost unpaired electron for optimized CH$_{3}$NH$_{3}$:CH$_{3}$NH$_{3}^{+}$ heterodimer. (b) The local integral curve of electron density difference in the $YZ$ plane corresponding to different $x$ coordinates with different strengths of electric field.
The strong polarization of CH$_{3}$NH$_{3}$PbI$_{3}$ induced by interfacial electron injection in Fig. 4 is caused by the relative displacement between Au$^{+}$ and [PbI$_{3}$]$^{-}$, as given by Ref. [33], $$\begin{align} {\boldsymbol P}=\frac{\sum {\boldsymbol p}_{i}}{\Delta V},~~ \tag {1} \end{align} $$ where $i$, ${\boldsymbol p}_{i}$, and $\Delta V$ are the $i$th layer number of formed CH$_{3}$NH$_{3}$, dipole moment of $i$th layer [PbI$_{3}$]$^{-}$, and volume of CH$_{3}$NH$_{3}$PbI$_{3}$, respectively. The total polarization magnitude induced by $n$ layers of CH$_{3}$NH$_{3}$ is approximated as $$\begin{align} P=\frac{{\frac{1}{2}n}^{2}de}{nd^{3}}=n\times 2.0\times {10}^{-2}\,{\rm mC/cm}^{2},~~ \tag {2} \end{align} $$ where $e$ and $d$ are the electron charge and lattice constant of CH$_{3}$NH$_{3}$PbI$_{3}$, respectively. When the layer number $n$ of formed CH$_{3}$NH$_{3}$ is 500 (the thickness about 300 nm), the total polarization magnitude reaches 10 mC/cm$^{2}$, which is consistent with the observed maximum value of 8 mC/cm$^{2}$.[26] Thus the GDC, anomalous hysteresis, and long-lasting polarization in CH$_{3}$NH$_{3}$PbI$_{3}$ material are mainly originated from the formed CH$_{3}$NH$_{3} $ by electron injection at the heterojunction.
cpl-36-2-026701-fig4.png
Fig. 4. The strong polarization ${\boldsymbol P}$ induced by electrons injection into CH$_{3}$NH$_{3}$PbI$_{3}$ under applied electric field ${\boldsymbol E}$, $d$ is the lattice constant of CH$_{3}$NH$_{3}$PbI$_{3}$.
In an FTO/TiO$_{2}$/CH$_{3}$NH$_{3}$PbI$_{3}$/spiro-OMeTAD /Ag structure, the electron diffusion process from TiO$_{2}$ to CH$_{3}$NH$_{3}$PbI$_{3}$ at TiO$_{2}$/CH$_{3}$NH$_{3}$PbI$_{3}$ heterojunction is attributed to three reasons: (i) the room-temperature CH$_{3}$NH$_{3}^{+}$ in CH$_{3}$NH$_{3}$PbI$_{3}$ is activated and disordered; (ii) CH$_{3}$NH$_{3}^{+}$ has a strong electrostatic attraction to CH$_{3}$NH$_{3}$ in Fig. 2; (iii) these unoccupied molecular orbital energies for CH$_{3}$NH$_{3}^{+}$ in Fig. 1 are lower than the conduction band energy $-$4 eV for TiO$_{2}$. After joining TiO$_{2}$ and CH$_{3}$NH$_{3}$PbI$_{3}$, the conduction band electrons in TiO$_{2}$ tend to diffuse into CH$_{3}$NH$_{3}$PbI$_{3}$ leaving behind positively charged ions, and the CH$_{3}$NH$_{3}$PbI$_{3}$ carries negative charges in the form of [PbI$_{3}$]$^{-}$. There are two reverse processes: the electron diffusion process tends to generate more CH$_{3}$NH$_{3}$, and the built-in electric field induced by space charge tends to oppose electron diffusion. With the enhancement of built-in electric field, the electron diffusion decreases gradually and the inorganic framework is highly polarized. When equilibrium is reached, a stable built-in electric field is formed. Even without applied electric field, CH$_{3}$NH$_{3}$ may easily orient along the C–N axis due to the electrostatic attraction between CH$_{3}$NH$_{3}$, as shown in Fig. 5. Compared with disordered CH$_{3}$NH$_{3}^{+}$, the orientational order of CH$_{3}$NH$_{3}$ group along the built-in electric field may generate the weak electrostatic field at inorganic framework based on the ESP contour map in Fig. 5, and can effectively increase the structural order of lead-halide framework, which significantly reduces the deformation potential scattering by acoustic phonons.[34-36] Thus, the orientational order of CH$_{3}$NH$_{3}$ group at the heterojunction can remarkably improve the efficiency of carrier separation and transport. Meanwhile, the channel separation between carrier transport and electron diffusion can markedly improve carrier transport. These properties of the TiO$_{2}$/CH$_{3}$NH$_{3}$PbI$_{3}$ heterojunction are the main origin of the excellent performance of the CH$_{3}$NH$_{3}$PbI$_{3} $ solar cell.
cpl-36-2-026701-fig5.png
Fig. 5. Optimized geometric structure and ESP contour map for CH$_{3}$NH$_{3}$ trimer without applied electric field.
In conclusion, our calculation results have shown that the formed CH$_{3}$NH$_{3}$ by electron injection at the heterojunction is the main origin of GDC, anomalous hysteresis and long-lasting polarization of CH$_{3}$NH$_{3}$PbI$_{3}$ material, and the total polarization magnitude of CH$_{3}$NH$_{3}$PbI$_{3}$ is dependent on the applied voltage amplitude and frequency. The calculated maximum value of polarization magnitude is in good agreement with the experimental results. The induced weak EPS by the reorientation of CH$_{3}$NH$_{3}$ sub-group along the built-in electric field at TiO$_{2}$/CH$_{3}$NH$_{3}$PbI$_{3}$ heterojunction enables us to effectively increase the ordering of entire lead-halide framework in CH$_{3}$NH$_{3}$PbI$_{3}$. These properties of heterojunctions are the main origin of the high efficiency of CH$_{3}$NH$_{3}$PbI$_{3}$ solar cells. References Modulating the Electron–Hole Interaction in a Hybrid Lead Halide Perovskite with an Electric FieldPhase Engineering of Perovskite Materials for High-Efficiency Solar Cells: Rapid Conversion of CH 3 NH 3 PbI 3 to Phase-Pure CH 3 NH 3 PbCl 3 via Hydrochloric Acid Vapor Annealing Post-TreatmentUnderstanding the physical properties of hybrid perovskites for photovoltaic applicationsOrganometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic CellsNanoscale Charge Localization Induced by Random Orientations of Organic Molecules in Hybrid Perovskite CH 3 NH 3 PbI 3Anomalous Hysteresis in Perovskite Solar CellsOrganometal perovskite light absorbers toward a 20% efficiency low-cost solid-state mesoscopic solar cellComputed and Experimental Absorption Spectra of the Perovskite CH 3 NH 3 PbI 3Crystal Structures, Optical Properties, and Effective Mass Tensors of CH 3 NH 3 PbX 3 (X = I and Br) Phases Predicted from HSE06Improved Understanding of the Electronic and Energetic Landscapes of Perovskite Solar Cells: High Local Charge Carrier Mobility, Reduced Recombination, and Extremely Shallow TrapsTemperature-Dependent Charge-Carrier Dynamics in CH 3 NH 3 PbI 3 Perovskite Thin FilmsUltrafast Terahertz Probes of Charge Transfer and Recombination Pathway of CH 3 NH 3 PbI 3 PerovskitesPhonon–Electron Scattering Limits Free Charge Mobility in Methylammonium Lead Iodide PerovskitesAre Mobilities in Hybrid Organic–Inorganic Halide Perovskites Actually “High”?Multiwfn: A multifunctional wavefunction analyzerQuantitative analysis of molecular surface based on improved Marching Tetrahedra algorithmOrganolead Halide Perovskite: New Horizons in Solar Cell ResearchRevealing the role of organic cations in hybrid halide perovskite CH3NH3PbI3Dynamic disorder in methylammoniumtrihalogenoplumbates (II) observed by millimeter‐wave spectroscopyDielectric study of CH3NH3PbX3 (X = Cl, Br, I)Cation rotation in methylammonium lead halidesAtomistic Origins of High-Performance in Hybrid Halide Perovskite Solar CellsFerroelectricity of CH 3 NH 3 PbI 3 PerovskitePhotoinduced Giant Dielectric Constant in Lead Halide Perovskite Solar CellsIon Migration in Organometal Trihalide Perovskite and Its Impact on Photovoltaic Efficiency and StabilityIonic transport in hybrid lead iodide perovskite solar cellsDepleted hole conductor-free lead halide iodide heterojunction solar cellsResonance Raman and Excitation Energy Dependent Charge Transfer Mechanism in Halide-Substituted Hybrid Perovskite Solar CellsElectric polarization as a bulk quantity and its relation to surface chargeRoom-Temperature Coherent Optical Phonon in 2D Electronic Spectra of CH 3 NH 3 PbI 3 Perovskite as a Possible Cooling BottleneckCalculating polaron mobility in halide perovskitesFree Excitons and Exciton–Phonon Coupling in CH 3 NH 3 PbI 3 Single Crystals Revealed by Photocurrent and Photoluminescence Measurements at Low Temperatures
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