⇦Chinese Physics Letters, 2020, Vol. 37, No. 10, Article code 107301 Perovskite Termination-Dependent Charge Transport Behaviors of the CsPbI$_{3}$/Black Phosphorus van der Waals Heterostructure Yong-Hua Cao (曹永华)1,2,3, Jin-Tao Bai (白晋涛)1,2, and Hong-Jian Feng (冯宏剑)1* Affiliations 1School of Physics, Northwest University, Xi'an 710127, China 2Institute of Photonics & Photon-Technology, Northwest University, Xi'an 710127, China 3School of Mechanical and Electrical Engineering, Henan Institute of Science and Technology, Xinxiang 453003, China Received 25 June 2020; accepted 6 August 2020; published online 29 September 2020 Supported by the National Natural Science Foundation of China (Grant Nos. 51972266, 51672214, 11304248, and 11247230), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2014JM1014), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant No. 2013JK0624), the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shaanxi Province of China, and the Youth Bai-Ren Project in Shaanxi Province of China.
*Corresponding author. Email: hjfeng@nwu.edu.cn; fenghongjian@126.com Citation Text: Cao Y H, Bai J T and Feng H J 2020 Chin. Phys. Lett. 37 107301    Abstract Fundamental understanding of interfacial charge behaviors is of great significance for the optoelectronic and photovoltaic applications. However, the crucial roles of perovskite terminations in charge transport processes have not been completely clear. We investigate the charge transfer behaviors of the CsPbI$_{3}$/black phosphorus (BP) van der Waals heterostructure by using the density functional theory calculations with a self-energy correction. The calculations at the atomic level demonstrate the type-II band alignments of the CsPbI$_{3}$/BP heterostructure, which make electrons transfer from the perovskite side to monolayer BP. Moreover, the stronger interaction and narrower physical separation of the interfaces can lead to higher charge tunneling probabilities in the CsPbI$_{3}$/BP heterostructure. Due to different electron affinities, the PbI$_{2}$-terminated perovskite slab tends to collect electrons from the adjacent materials, whereas the CsI-termination prefers to inject electrons into transport materials. In addition, the interface coupling effect enhances the visible-light-region absorption of the CsPbI$_{3}$/BP heterostructure. This study highlights the importance of the perovskite termination in the charge transport processes and provides theoretical guidelines to develop high-performance photovoltaic and optoelectronic devices. DOI:10.1088/0256-307X/37/10/107301 PACS:73.20.At, 73.40.-c, 88.40.H- © 2020 Chinese Physics Society Article Text Metal halide perovskites with the formula $ABX_{3}$ ($A$ = CH$_{3}$NH$_{3}$, Cs; $B$ = Pb, Ge, Sn; $X$ = I, Br, Cl) have attracted increasing attention in photovoltaic and optoelectronic industries including solar cells, light-emitting diodes, and photodetectors.[1–5] Theoretical and experimental results demonstrate the excellent properties of metal halide perovskites, for instance, the low exciton binding energy, and long diffusion length, with high defect tolerance, and low-cost processability.[6–8] In the last dozen years, owing to the optimizing device architecture and material processing, the certified power conversation efficiencies (PCEs) of perovskite solar cells (PSCs) have boomed from the initial 3.8% to the latest 25.2%.[9] It has become evident that the efficient extraction of electrons (holes) from the perovskite films is crucial for the high solar energy conversion.[10–13] However, the dangling bonds, rough surfaces, impurities of charge transport materials give rise to poor interface contacts, which are disadvantageous for further improving the device performance.[14,15] Research of 2D materials is also at the forefront of science and technology, due to their remarkably electronic and optical properties involving the high carrier mobility, superior flexibility, and fine transparency.[16–18] Importantly, compared with the 3D counterparts, the electronic properties of 2D materials are readily controlled by changing layers, doping, and forming van der Waals (vdW) heterostructures.[19,20] In particular, owing to the atomically sharp surfaces of 2D materials, the junction regions of vdW heterostructures can be as thin as monolayer.[21] In addition, although the interlayer interaction is the weak vdW force, the vdW heterostructures also display ultrafast interlayer charge transfer in experiments.[22–25] Recently, the vdW heterostructures with a stack of 2D materials and perovskite films have been proposed to improve device performances, which can be expected to possess a close-contact interface and efficient charge transfer.[26–28] In particular, integrated the outstanding mechanical flexibility and optical transparency of 2D materials, the perovskite-based vdW heterostructures have been considered as the competitive candidate for flexible electronics and wearable devices.[29–31] Wang et al. reported that by interface engineering with graphene, the PCE of the planar PSC achieved 20.2% with an improved fill factor of 82%.[32] Li et al. reported that both the PCEs and stabilities of PSCs were significantly improved when MoS$_{2}$ and WS$_{2}$ replaced the PEDOT:PSS as the hole transport layers.[33] In addition, it is reported that the different terminations of CH$_{3}$NH$_{3}$PbI$_{3}$ surface can impact the semiconductor properties of perovskite slabs.[34,35] Chen et al. reported that CH$_{3}$NH$_{3}$I-termination induces p-doping effect near the surface of CH$_{3}$NH$_{3}$PbI$_{3}$ film, which facilitates the carrier transport and photosynthesis.[36] However, it remains highly desirable to study how the perovskite termination affects the charge transport of photovoltaic and optoelectronic devices. In this work, we employ the CsPbI$_{3}$/BP heterostructure as the model to explore the charge transport and tunneling characteristics with density functional theory (DFT) calculations. By reasonably designing the PbI$_{2}$/BP and CsI/BP interfaces, we investigate the surface termination of CsPbI$_{3}$ slab and its effect on the charge transport process. A half occupation method with hole self-energy correction is adopted in DFT calculations to accurately reproduce the semiconductor properties of CsPbI$_{3}$ and BP. Additionally, the coupling effect on the heterostructure absorption is also studied. The DFT calculations were carried out using a plane-wave approach with the Perdew–Burke–Ernzerhof (PBE) functional.[37] The projector augmented wave (PAW) method was used to describe the core-electron interactions.[38] The generalized gradient approximation (GGA) was employed to describe the electron exchange and correlation potential.[39] The DFT-D3[40] and dipole correction[41] were used to compensate the vdW interaction and asymmetric layer arrangement, respectively. Here the self-energy correction was carried out with the GGA-1/2 method,[42] which removed half electron from the valence band of PBE pseudopotentials. Based on the GGA-optimized structures, the GGA/1-2 method with the spin-orbital coupling (SOC) was adopted for the following calculations of the CsPbI$_{3}$/BP heterostructure. The cutoff energy of the electron wave function was set to 500 eV. The convergence criteria of the total energy and Hellmann–Feynman forces were 10$^{-4}$ eV and 0.01 eV/Å, respectively. The $\varGamma$-centered $9\times 9\times 1$, $10\times 8\times 1$ and $9\times 3\times 1$ Monkhorst–Pack $k$-points grids[43] were employed for the Brillion zones of the CsPbI$_{3}$ slab, BP layers and CsPbI$_{3}$/BP heterostructure, respectively. The hybrid functional of Heyd, Scuseria, and Ernzerhof[44] (HSE06) was used to calculate the band gap of the CsPbI$_{3}$ slab and monolayer BP in comparison with the GGA-1/2 method. The details of the GGA-1/2 method and CsPbI$_{3}$/BP heterostructure were included in the Supplementary Material. Based on the optimized structure with the GGA functional, we calculated the electronic properties of BP layers with the GGA-1/2 method to check its reliability. Table 1 lists the calculated band gaps of the few-layer and bulk BP with different methods. The experimental gaps are also included as the reference. It can be seen that the GGA-1/2 band gaps of few-layer BP show agreement well with the experimental data, even exceeding the HSE06 functional. However, due to the incorrect self-energy correction, the GGA functional significantly underestimates the band gaps of BP, either few-layer or bulk phase.
Table 1. Band gaps (in eV) of the few-layer and bulk BP calculated with different methods.
Layers Experiment[45,46] GGA GGA-1/2 HSE06[47] GW[48]
1 L 1.45 0.91 1.48 1.51 1.60
2 L 1.3 0.59 1.23 0.98 1.32
3 L 0.98 0.44 1.13 0.80 1.06
4 L 0.88 0.34 1.07 0.66
5 L 0.79 0.23 0.97 0.59
Bulk 0.30–0.35 0.02 0.44 0.36 0.1
cpl-37-10-107301-fig1.png
Fig. 1. Calculated band structures of few-layer and bulk BP with the GGA-1/2 method. (a) The layer-dependent band gap and (b)–(d) band structures of monolayer, bilayer and bulk BP. For comparative purposes, the experimental band gaps and HSE06 band structures are also plotted.
It is well known that the layer-dependent band structure is the typical property of most 2D materials. As evidenced in Fig. 1(a), the band gaps of the few-layer BP with the GGA-1/2 method decrease rapidly as the layer number increases, which are in good agreement with the experimental data.[45,46] These results clearly confirm the feasibility of the GGA-1/2 method. The band structures of monolayer, bilayer and bulk BP are also calculated with the GGA-1/2 method and HSE06 functional, respectively, as shown in Figs. 1(b)–1(d). It can be noticed that the GGA-1/2 bands not only reproduce the direct band gap nature of BP layers but also display the similar dispersion characteristics with HSE06 bands. What's more, the Bader charge[49] and electron localization function (ELF)[50] analyses of the few-layer BP are performed with the GGA-1/2 method, as shown in Table S1 and Fig. S1 of the Supplementary Material. The calculated results identify the intralayer covalent bond characteristic of BP layers, which is similar to the GGA functional calculation. Therefore, the GGA-1/2 method can be used to study the chemical bonds at atomic levels. The accurate reproduction of electronic structures may allow direct comparison of the electronic transport levels of adjacent materials for designing photovoltaic and optoelectronic devices. The GGA functional without SOC was widely used to calculate the band structures of Pb-based perovskites, such as CsPbI$_{3}$ and CH$_{3}$NH$_{3}$PbI$_{3}$, and coincidentally achieved fine correspondence with experimental data. However, the SOC effect, which is very critical for $6s$ and $6p$ systems, splits the unoccupied $p$-orbitals and leads to a reducing band gap of Pb-based perovskites. Therefore, looking for a reliable and low-cost calculation method is necessary for developing efficient photovoltaic and optoelectronic devices.
cpl-37-10-107301-fig2.png
Fig. 2. Calculated band structures of the PbI$_{2}$- and CsI-terminations with [(a), (b)] GGA, [(c), (d)] HSE06 $+$ SOC, and [(e), (f)] GGA-1/2 $+$ SOC methods, respectively. The insets are the side views of the CsPbI$_{3}$ slab used in the corresponding calculations.
The band structures of CsPbI$_{3}$ slabs with the PbI$_{2}$- and CsI-terminations are calculated with the GGA, HSE06 $+$ SOC and GGA-1/2 $+$ SOC methods, respectively, as displayed in Fig. 2. It can be seen that the GGA functional without SOC can accurately predict the band gaps of CsPbI$_{3}$ slabs, in accordance with the experimental value (1.73 eV for bulk),[51] see Figs. 2(a) and 2(b). However, the GGA $+$ SOC calculations will significantly reduce the band gap of cubic CsPbI$_{3}$ to 0.32 eV.[52] As a result, the calculations without SOC likely make mistakes in predicting the absolute band position. It is believed that the hybrid functional with high-computational cost can partially correct the self-correction error in standard DFT calculations. As evidenced in Figs. 2(c) and 2(d), the band gaps of the CsPbI$_{3}$ slab are still smaller than the experimental data, suggesting that the HSE06 functional is insufficient to “open” the band gap of Pb halide perovskites. Surprisingly, the GGA-1/2 $+$ SOC method gives reasonable band gaps of CsPbI$_{3}$ slabs, which are in good agreement with the theoretical and experimental reports,[28,53] as shown in Figs. 2(e) and 2(f). What's more, the low cost of the GGA-1/2 $+$ SOC method makes it a powerful tool to investigate the electronic properties of large systems, which are generally used in the interface, defect and doping calculations. Before describing the charge transport, it is informative to study the interface interaction and band alignment of the CsPbI$_{3}$/BP heterostructure. After fully relaxation with the GGA functional, the optimized geometries of the CsPbI$_{3}$/BP heterostructures are presented in Figs. 3(a) and 3(b). No significant changes are observed in the geometries of monolayer BP and CsPbI$_{3}$ slab, indicating that the lattice mismatches can be neglected in the heterostructure models. The binding energy provides a sign for the energetic favorability of the heterostructure formation, which can also be employed to characterize the interfacial bond strength. In this study, the binding energy is defined as $$ E_{{\rm bin}} =E_{{\rm CsPbI}_{3} {\rm /BP}} -E_{{\rm BP}} -E_{{\rm CsPbI}_{3} },~~ \tag {1} $$ where the $E_{{\rm CsPbI}_{3} {\rm /BP}}$, $E_{{\rm BP}}$ and $E_{{\rm CsPbI}_{3}}$ denote the total energy of the vdW heterostructure, corresponding monolayer BP and CsPbI$_{3}$ slab, respectively. According to this definition, the smaller value of $E_{{\rm bin}}$ means the more energetically favorable of the interface. As shown in Table 2, the negative binding energies of CsPbI$_{3}$/BP heterostructures indicate that both interfaces are energetically favorable. Furthermore, compared to the CsI/BP interface, the more negative $E_{{\rm bin}}$ of the PbI$_{2}$/BP interface suggests the stronger bonding, which can be attributed to the more atop atoms at the PbI$_{2}$-termination. The equilibrium interfacial distance $d$ is defined as the shortest distance between the adjacent P atoms and Pb/I atoms closest the interface. The calculated $d$ values of the PbI$_{2}$/BP and CsI/BP interfaces are almost equal, which are similar to the other vdW crystals,[54] confirming the vdW interactions of CsPbI$_{3}$/BP heterostructures.
Table 2. Calculated binding energy $E_{{\rm bin}}$, and equilibrium interfacial distance of the PbI$_{2}$/BP and CsI/BP interfaces.
PbI$_{2}$/BP CsI/BP
$E_{{\rm bin}}$ (eV) $-2.26$ $-1.70$
$d$ (Å) 3.32 3.42
For examining the thermodynamic stability of the CsPbI$_{3}$/BP heterostructure, the ab initio molecular dynamics (AIMD) simulation has been carried out with the Vienna ab initio Simulation Package (VASP) package. The temperature of 300 K and time step of 2 fs are adopted in the AIMD stimulation. The varying free energy and ultimate geometry of the CsPbI$_{3}$/BP heterostructure are shown in Figs. 3(c) and 3(d). It can be seen that the PbI$_{2}$/BP and CsI/BP interfaces nearly remain the initial structures after a 5 ps stimulation, which further demonstrates the reliability of CsPbI$_{3}$/BP heterostructure.
cpl-37-10-107301-fig3.png
Fig. 3. Optimized heterostructures with (a) PbI$_{2}$/BP and (b) CsI/BP interfaces. Variation of the free energies of (c) PbI$_{2}$/BP and (d) CsI/BP interfaces during the AIMD simulation. The insets show the corresponding structures at the end of AIMD simulation from top and side views, respectively.
cpl-37-10-107301-fig4.png
Fig. 4. Projected band structures of (a) PbI$_{2}$/BP and (b) CsI/BP interfaces. Projected density of state (DOS) of (c) PbI$_{2}$/BP and (d) CsI/BP interfaces. The red and blue colors indicate the bands dominated by monolayer BP and CsPbI$_{3}$ slab, respectively. The Fermi levels are denoted by the dashed lines.
An appropriate energy level diagram between perovskite films and transport materials is necessary for designing high-performance optoelectronics and photovoltaics. Hence, the projected band structures of PbI$_{2}$/BP and CsI/BP interfaces are calculated and plotted in Figs. 4(a) and 4(b), respectively. The bands plotted in red and blue colors separately represent the contribution of monolayer BP and CsPbI$_{3}$ slab. In this case, the color maps varying from red to blue indicate the projected weights. As the reference, the projected band structures of CsPbI$_{3}$/BP heterostructure calculated with the GGA functional are plotted in Fig. S2 of the Supplementary Material. It can be seen that the electronic structures of CsPbI$_{3}$ slab and monolayer BP are well preserved after stacked together. Moreover, the conduction band minimum (CBM) and valence band maximum (VBM) of the CsPbI$_{3}$/BP heterostructures locate on the monolayer BP and CsPbI$_{3}$ slab, respectively. Specially, because the conduction band (CB) of the CsPbI$_{3}$ slab lies above that of the monolayer BP, it is energetically favorable that the photogenerated electrons transfer from CsPbI$_{3}$ to monolayer BP. On the other hand, the difference of valence band (VB) leads to photogenerated holes migrating from monolayer BP to perovskite, as shown in Fig. S3 of the Supplementary Material. Note that the type-II band alignments of the PbI$_{2}$/BP and CsI/BP interfaces are different from the previous report,[28] in which the GGA functional significantly underestimated the band gap of the monolayer BP. Next, the projected density of state (DOS) of the CsPbI$_{3}$/BP heterostructure is calculated to gain more insights into the interface electronic structures. As shown in Figs. 4(c) and 4(d), the conduction band offsets (CBO) and valence band offsets (VBO) of the PbI$_{2}$/BP interface are 0.63 eV and 0.51 eV, respectively, which are less than those of the CsI/BP interface (1.10 eV and 0.75 eV). The overlarge mismatches between energy levels can introduce detrimental barriers for the charge extraction. In addition, although the shape and size are fixed during the relaxation, the coupling effect slightly reduces the band gap of CsPbI$_{3}$ slabs, as listed in Table 3.
Table 3. Band gaps (in eV) of PbI$_{2}$- and CsI-terminations with and without monolayer BP.
With monolayer BP Without monolayer BP
PbI$_{2}$-surface 1.437 1.604
CsI-surface 1.730 1.762
Generally, the photogenerated carrier transport at the interface is the result of the energy level alignment of the heterostructure. Here the charge density difference is plotted to visualize the charge redistribution and transfer of the CsPbI$_{3}$/BP heterostructure, which is defined as $$ \Delta \rho =\rho_{{\rm CsPbI}_{3} {\rm /BP}} -\rho_{{\rm BP}} -\rho_{{\rm CsPbI}_{3} },~~ \tag {2} $$ where $\rho_{{\rm CsPbI}_{3} {\rm /BP}}$, $\rho_{{\rm BP}}$ and $\rho_{{\rm CsPbI}_{3}}$ are the charge densities of the fully relaxed CsPbI$_{3}$/BP heterostructure, and the corresponding isolated monolayer BP and CsPbI$_{3}$ slab, respectively. As shown in Figs. 5(a) and 5(b), the majorities of charge accumulation and depletion occur in the interface region, involving the monolayer BP side and atop perovskite atoms. Then, the weak interfacial interaction and large interfacial distance should be responsible for this case. Moreover, no visible bonding-like features emerge between CsPbI$_{3}$ slab and monolayer BP, confirming that the vdW force dominates the interface interactions.
cpl-37-10-107301-fig5.png
Fig. 5. Charge density difference of (a) PbI$_{2}$/BP and (b) CsI/BP interfaces. The yellow and cyan areas represent the charge accumulation and depletion, respectively. Charge displacement curve (CDC) of (c) PbI$_{2}$/BP and (d) CsI/BP interfaces along the $z$ direction. The green arrow labels the electron transfer direction in the heterostructure.
To assess the charge transport of the CsPbI$_{3}$/BP heterostructure, the charge displacement analysis is conducted by integrating the charge density difference along the $z$ direction as $$ \Delta {Q}=\int_{-\infty }^\infty {dx} \int_{-\infty }^\infty {dy} \int_{-\infty }^z {\Delta \rho dz}.~~ \tag {3} $$ According this definition, a positive $\Delta {Q}$ denotes electrons transferring from right to left across the normal plane.[55] What's more, the positive (negative) slope of the charge displacement curve (CDC) implies the charge accumulation (depletion) in the corresponding region. Figures 5(c) and 5(d) display the CDCs of PbI$_{2}$/BP and CsI/BP interfaces, respectively. For the PbI$_{2}$/BP interface, the different signs of CDCs indicate opposite charge transfer directions in the CsPbI$_{3}$ slab and interface region. In this case, the PbI$_{2}$/BP interface exhibits a low efficiency of charge collection. On the other hand, the overall CDC in the CsI/BP interface is identically negative, suggesting that the unambiguous electrons transfer from CsPbI$_{3}$ slab to monolayer BP. The different electronic structures of the PbI$_{2}$- and CsI-terminations should be responsible for the unlike CDCs of two interfaces. To check the electronic connectivity of the CsPbI$_{3}$/BP heterostructure, we conduct the ELF analysis for PbI$_{2}$/BP and CsI/BP interfaces. The position-dependent ELF ranges from 0 to 1, in which 0.5 and 1 correspond to the probabilities of the electron gas-like pairs and covalent bonds, respectively.[50] The 2D ELF slices of PbI$_{2}$/BP and CsI/BP interfaces along the $z$ direction are plotted in Figs. 6(a) and 6(b). The variational colors between the Pb and I atoms denote electron local distributions, which offer a continuous pathway for the transport of carriers. It is noteworthy that the ELF at the interface regions is very small, confirming the absence of strong covalent bonds between CsPbI$_{3}$ slab and monolayer BP.
cpl-37-10-107301-fig6.png
Fig. 6. 2D ELF slices along the $z$ direction across (a) PbI$_{2}$/BP and (b) CsI/BP interfaces. Average effective potential profiles of (c) PbI$_{2}$/BP and (d) CsI/BP interfaces along the $z$ direction.
Due to the weak interaction and large physical separation of the vdW heterostructure, the electron tunneling dominates the charge transfer process at the interface. The tunneling barrier (TB) is employed to evaluate the carrier injection efficiency across the interface. As shown in Figs. 6(c) and 6(d), the TB height ($\varPhi_{\rm TB}$) is the minimum potential barrier that electrons have to overcome when crossing the interface, which is defined as the potential difference between vdW gap (${\rm V}_{\rm gap}$) and CsPbI$_{3}$-terminated surface (${\rm V}_{P}$). The TB width (${\rm W}_{\rm TB}$) is the physical separation at the interface, which is replaced by the full width at half maximum of the TB in following calculations. To quantify the carrier injection efficiency of the CsPbI$_{3}$/BP heterostructure, the electron tunneling probability $T_{\rm TB}$ from CsPbI$_{3}$ to BP is calculated as[56,57] $$ T_{\rm TB} =\exp \Big(-2\frac{\sqrt {2m\varPhi_{\rm TB} } }{\hslash }\times {\rm W}_{\rm TB} \Big),~~ \tag {4} $$ where $m$ and $\hslash$ are the free electron mass and reduced Planck's constant, respectively. Note that the $T_{\rm TB}$ is inversely proportional to the TB height $\varPhi_{\rm TB}$ and width ${\rm W}_{\rm TB}$. It can be seen that reducing TB height and narrowing TB width can promote the tunneling probability and then enhance the device performance. The calculation results are listed in Table 4. As discussed above, owing to the relatively strong interaction and narrow separation, the tunneling probability of the PbI$_{2}$/BP interface is nearly twice that of the CsI/BP interface. Even so, the electron tunneling probabilities of the CsPbI$_{3}$/BP heterostructure are still larger than that of metal/BP interface.[58]
Table 4. Calculated TB height $\varPhi_{\rm TB}$, width ${W}_{\rm TB}$ and tunneling probability $T_{\rm TB}$ of CsPbI$_{3}$/BP heterostructures.
PbI$_{2}$/BP CsI/BP
${\rm \varPhi }_{\rm TB}$ (eV) 2.47 3.25
${W}_{\rm TB}$ (Å) 0.632 0.905
$T_{\rm TB}$ 36.22% 18.88%
The average effective potential can also be used to study the electronic interactions in the CsPbI$_{3}$/BP heterostructure. Because of the electron-affinities differences between Pb and Cs atoms, the local electron densities of the layer-like CsPbI$_{3}$ slab display a “push-pull” tendency along the (001) direction. That is, the PbI$_{2}$ layer with the higher electron affinities acts a quasi-electron acceptor (or puller) and the CsI layer with the lower electron affinities serves as a quasi-electron donor (or pusher), as shown in Figs. 6(c) and 6(d). As a result, the CsPbI$_{3}$ slab with the PbI$_{2}$-terminated surface tends to collect electrons from adjacent materials, which can account for the aforementioned CDC of the PbI$_{2}$/BP interface. These cases are also found in the CH$_{3}$NH$_{3}$PbI$_{3}$/graphene and CsPbI$_{3}$/SnS vdW heterostructures.[59,60] Therefore, the PbI$_{2}$ termination stacked with low work-function materials can be expected to exhibit a strong hole-extraction ability, whereas the CsI-terminated perovskite slabs will act as a quasi-electron donor in many cases. The optical absorption of the CsPbI$_{3}$/BP heterostructure is calculated to evaluate the coupling effect on the optical properties, which is of great importance for photovoltaic and optoelectronic devices. Herein, the real part $\varepsilon_{1}$ and imaginary part $\varepsilon_{2}$ are computed with the GGA-1/2 $+$ SOC method. The optical absorption coefficient is calculated as follows: $$ \alpha (\omega)=\frac{2\omega }{c\hslash }\Big(\frac{\sqrt {\varepsilon_{1}^{2} +\varepsilon_{2}^{2} } -\varepsilon_{1} }{2}\Big)^{1/2},~~ \tag {5} $$ where $\omega$ and $c$ represent the angular frequency and velocity of light in vacuum, respectively. The obtained absorption spectra of CsPbI$_{3}$/BP heterostructures are shown in Fig. 7. The isolated CsPbI$_{3}$ slab and monolayer BP are also plotted as references. For monolayer BP, the optical absorption in the out-of-plane direction is very small in the visible-light region that can be neglected. Compared with the isolated CsPbI$_{3}$ slab, the absorption spectra of PbI$_{2}$/BP and CsI/BP interfaces present an apparent red shift in the visible-light region, which can be attributed to the aforementioned reduction of the band gap. The enhanced absorption indicates that the CsPbI$_{3}$/BP heterostructure becomes more suitable for photovoltaic and optoelectronic applications.
cpl-37-10-107301-fig7.png
Fig. 7. Optical absorption spectra of (a) PbI$_{2}$/BP and (b) CsI/BP interfaces. For comparison, the absorption spectra of the isolated CsPbI$_{3}$ slab and monolayer BP are also plotted.
In summary, we have carried out a comprehensive study of perovskite termination-dependent charge transport behaviors of CsPbI$_{3}$/BP heterostructures with the GGA-1/2 $+$ SOC method. Our calculations show that: (1) Due to the high accuracy and low computation cost, the GGA-1/2 method can be regarded as a powerful tool to accurately investigate the optoelectronic properties of large systems. (2) The PbI$_{2}$/BP and CsI/BP interfaces both present the type-II band alignments, where the CBM and VBM reside in the monolayer BP and CsPbI$_{3}$ slab, respectively. Compared with the CsI/BP interface, the PbI$_{2}$/BP interface possesses a relatively strong interfacial interaction and high electron tunneling probability. (3) Because of different electron affinities, the PbI$_{2}$ and CsI layers respectively act as quasi-electron acceptors and donors. Therefore, the PbI$_{2}$-terminated CsPbI$_{3}$ slab tends to collect electrons from adjacent materials. (4) The coupling effect enhances the optical absorption of the CsPbI$_{3}$/BP heterostructure and leads to the absorption spectra a red-shift in the visible-light region. This work not only highlights the crucial role of the perovskite termination in the charge transport of vdW heterostructures, but also provides theoretical references for designing high-performance optoelectronic and photovoltaic devices. The authors thank Dr. S. X. Tao and Dr. M. Wu for helpful discussions, and Dr. B. Zhou for technical support. The work was carried out partly on the High Performance Computing Center in Henan Institute of Science and Technology. 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PhosphoreneHigh-mobility transport anisotropy and linear dichroism in few-layer black phosphorusQuasiparticle band structure and tight-binding model for single- and bilayer black phosphorusA quantum theory of molecular structure and its applicationsA simple measure of electron localization in atomic and molecular systemsFormamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cellsCation Role in Structural and Electronic Properties of 3D Organic–Inorganic Halide Perovskites: A DFT AnalysisQuantum dot-induced phase stabilization of -CsPbI3 perovskite for high-efficiency photovoltaicsImproved description of soft layered materials with van der Waals density functional theoryCharge-Transfer Energy in the Water−Hydrogen Molecular Aggregate Revealed by Molecular-Beam Scattering Experiments, Charge Displacement Analysis, and ab Initio CalculationsA theoretical model for metal–graphene contact resistance using a DFT–NEGF methodDoes p-type ohmic contact exist in WSe 2 –metal interfaces?The study of interaction and charge transfer at black phosphorus–metal interfacesInterface Engineering of Graphene/CH 3 NH 3 PbI 3 Heterostructure for Novel p–i–n Structural Perovskites Solar CellsAsymmetric Strain‐Introduced Interface Effect on the Electronic and Optical Properties of the CsPbI 3 /SnS van der Waals Heterostructure
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