Stability of Low-index Surfaces of Cs2SnI6 Studied by First-principles Calculations

LIN Aming, SUN Yiyang

Stability of Low-index Surfaces of Cs2SnI6Studied by First-principles Calculations

LIN Aming1,2, SUN Yiyang1,2

(1. Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China; 2. University of Chinese Academy of Sciences, Beijing 100049, China)

Cs2SnI6is a stable and environmentally friendly halide perovskite material with great potential for photovoltaic and optoelectronic applications. While the surface properties are of paramount importance for device fabrications, there have been no such theoretical studies on this material. Using density functional theory calculations with the SCAN+rVV10 functional, the (001), (011) and (111) surfaces of Cs2SnI6were studied to reveal their thermodynamic stability. We constructed seven models for these surfaces, including two along the (001) orientation (CsI2- and SnI4-terminated surfaces), two along the (011) orientation (I4- and Cs2SnI2-terminated surfaces) and three along the (111) orientation (non-stoichiometric CsI3-, Sn- and stoichiometric CsI3-terminated surfaces). Because most of the surfaces are non-stoichiometric, their relative stability depends on the experimental preparation condition, which is reflected by the chemical potentials of the constituent elements in the calculation. By determining the allowed chemical potential region, the thermodynamic stability of these Cs2SnI6surfaces is analyzed. The results show that the surface energies of the (001) and (011) surfaces are affected by the chemical potentials, while the stoichiometric CsI3-terminated (111) surface is unaffected by the chemical potentials and is energetically the most stable surface of Cs2SnI6. Thus, the observed exposure of (111) surface of Cs2SnI6crystals in several recent experiments is determined to be driven by thermodynamics.

perovskite; surface energy; Cs2SnI6; photovoltaic material; luminescent material

Organic-inorganic hybrid lead halide perovskites, such as CH3NH3PbI3[1–3]have attracted enormous research interests for applications in efficient photovoltaic[4], light- emitting[5]and photodetection devices[6].As their lead-free counterparts, Sn-based halide perovskites, such as CH3NH3SnI3[7–9]and CsSnI3[10–12], have been proposed for such applications because of their nontoxicity. However, because 2+ state is not the most stable valence state of Sn, the Sn-based perovskites are prone to further oxidation, rendering them even less stable than the Pb-based perovskites,which are already well known to have the stability issue[13].It is highly desirable to develop air-stable alternatives. For this purpose, Cs2SnI6is a promising material, in which Sn is already in 4+ valence state and resistant to further oxidation[14–16]. Meanwhile, it has a suitable band gap and strong optical absorption for photovoltaic applications[17–19].

The halide perovskite materials are usually reported to exhibit defect tolerance in the bulk[20-21]. Therefore, the surfaces, interfaces and grain-boundaries are usually the main concerns for optimizing the device performance. The surface properties of Cs2SnI6, which are expected to play an important role in the devices, remain poorly understood. Recently, several groups have devoted to the study on the surfaces of Cs2SnI6. Kapil[22]suggested the existence of the surface state in Cs2SnI6. Shin[23]investigated the role of the surface states in the presence of a redox mediator. Xu[24]reported a general approach to synthesize layered nanoplateletsof Cs2SnI6. Zhu[25]revealed that Cs2SnI6crystals have a preferential growth of (111) surface.Several experiments also proved that Cs2SnI6tends to grow along the <111> direction[26–28]. However, it is not clear that this preference is thermodynamically driven or just a result of growth condition specific to individual experiments.

In this work, as motivated by the experimental works, we study the surface properties of Cs2SnI6using first- principles calculations. As an initiative work, we attempt to understand the preference to the (111) surface in different crystal growth experiments. Different surface models with different surface orientations and terminations were set up to compare their thermodynamic stability. As some terminations are non-stoichiometric, to evaluate their relative stability it is necessary to calculate the chemical potentials to consider the crystal growth conditions. By analyzing the surface stability, it is expected to provide useful information for future experimental synthesis and device fabrication.

1 Computational method

Our first-principles calculations were based on density functional theory and performed using the ViennaSimulation Package (VASP)[29]. Projector augmented wave (PAW) potentials were used to describe the interaction between ion cores and valence electrons[30]. The strongly constrained and appropriately normed (SCAN) functional in combination with the rVV10 van der Waals (vdW) functional was used for the exchange-correlation functional[31].The cutoff energy of planewave basis set was taken to be 340 eV and the Γ-centered 3×3×3-point mesh was used for optimizing the 9-atom primitive cell of Cs2SnI6. A cutoff energy of 272 eV and a Γ-centered 3×3×1-point mesh were used for the surface calculations.

2 Results and discussion

Experimentally, it is reported that bulk Cs2SnI6exhibits a cubic structure with Fm-3mspace group symmetry, as shown in Fig. 1(a), and the lattice parameter0is 1.165 nm[20]. The calculated0using the SCAN+rVV10 functional is 1.156 nm, 0.8% smaller than the experimental value. The SCAN functional without considering the vdW effect yields0=1.178 nm, 1.1% larger than the experimental value, suggesting that the vdW effect is significant for Cs2SnI6. For comparison, the commonly used PBE and HSE functional is also considered, which yield0=1.203 and 1.197 nm, respectively. The reason for this large vdW effect is that the material is rather soft. The calculated bulk modulus using the SCAN+rVV10 method is only 13.1 GPa. Using the other functionals mentioned above would yield even smaller bulk modulus.

The band structure and projected density of states (pDOS) of Cs2SnI6were calculated, as shown in Fig. 1(b). The direct gap at the Γ point is 0.19 eV, significantly smaller than the experimental band gap of ～1.3 eV, suggesting that the meta-generalized gradient approximationis not sufficient for studying band-gap-sensitive properties of this material, for which the HSE functional including spin-orbit coupling will be necessary[20]. According to the pDOS plot, the top valence bands are mainly contributed by I5p orbitals, while the bottom conduction bands are contributed by both I5p orbitals and Sn5s orbitals. The Sn5s orbitals form a separate band, above which is another band gap and the Sn5p bands.

The surface properties are studied in the next step. We adopt the symmetric slab models for the surfaces, which possess a mirror symmetry through the middle of the slabs. Such models also avoid spurious interaction between periodic slabs due to dipole-dipole interactions. For all calculations, sufficient vacuum region (more than 1-nm-thick) was used to ensure negligible interaction between the slabs. Seven different terminations of Cs2SnI6surface models were considered, as shown in Fig. 2. The non-stoichiom-etric (001) surfaces were modeled with CsI2-terminated (or A-termination) and SnI4-terminated (or B-termination) slabs, whose unit-cell formulae were Cs12Sn5I32and Cs8Sn5I28, respectively. Similarly, the non-stoichiometric (011) surfaces were modeled with I4-terminated (A-term-ination) and Cs2SnI2-terminated (B-termination) slabs, whose unit-cell formulae were Cs10Sn5I34and Cs10Sn5I26, respectively. Along the [111] direction, the atomic stacking sequence is –Sn–CsI3– CsI3–Sn–. Correspondingly, the non-stoichiometric Sn-terminated (A-termination), non- stoichiometric CsI3-terminated (B-termination) and stoic-hiometric CsI3-terminated surfaces were modeled, whose unit-cell formulae were Cs8Sn5I24, Cs12Sn5I26and Cs10Sn5I30, respectively.

Fig. 1 (a) Atomic structure and (b) band structure and projected density of states (pDOS) of Cs2SnI6

Colorful figures are available on website

Fig. 2 Seven supercell models of Cs2SnI6 surfaces

(a) For (001) surface: CsI2-terminated and SnI4-terminated slabs; (b) For (011) surface: I4-terminated and Cs2SnI2-terminated slabs; (c) For (111) surface: non-stoichiometric Sn-terminated, CsI3-terminated and stoichiometric CsI3-terminated slabs

The cleavage energy are firstly evaluated, which is the energy required to split a crystal into two complementary non-stoichiometric terminations. It is noted that CsI2- and SnI4-terminations for Cs2SnI6(001) surfaces are mutually complementary, and so are I4- and Cs2SnI2-terminated slabs for (011) surfaces, as well as Sn- and CsI3-terminatedslabs for (111) surfaces. As two complementary surfaces (also referred to as A- and B-termination above) are created simultaneously when a crystal is cleaved, the total cleavage energy of two complementary surfaces can be obtained by

wThe calculated results of total cleavage energy, total relaxation energy and total surface energy of the two complementary non-stoichiometric terminations with different surface orientations are shown in Fig. 3. For comparison, the cleavage, relaxation and surface energies of the stoichiometric CsI3-terminated (111) surface are also shown. It can be seen that the total surface energies of the two complementary non-stoichiometric terminations are relatively high compared with that of stoichiometric CsI3-terminated (111) surface whose surface energy is only 0.11 J/m2, regardless of the surface orientations. However, the contributions to the cleavage energy from the A- and B-terminations are not equal. Further study is needed to determine whether A- or B-termination could individually have surface energy lower than 0.11 J/m2. In order to evaluate the relative stability of each surface termination under various experimentally preparation conditions, the consideration of chemical potential μCs, μSn and μI is necessary[21,32].

Using the determined chemical potential region, the surface energy for each individual termination can be obtained using[35-36]

where Eslab is the total energy of relaxed A-termination, NCs, NSn and NI are the numbers of Cs, Sn and I atoms in the slab, respectively. Considering the variation of chemical potential with reference phase as mentioned above, the surface energy can be finally rewritten as

Constraints imposed by the formation of competing secondary phases resulting in the allowed region shaded in green

The stability diagram of the Cs2SnI6(001) surface is shown in Fig. 5(a). The blue and orange regions represent the regions where CsI2- and SnI4-terminations are stable, respectively. The upper part of the green region is located in the blue region, indicating that the CsI2-termination is favored under the I-poor condition. There is still a small part of the green region located in the orange region,., at chemical potential points C and D, indicating that the SnI4-termination is more stable than the CsI2-termination under I-rich condition.

Similarly, the stability diagram of the Cs2SnI6(011) surface is shown in Fig. 5(b). The blue region represents that the Cs2SnI2-termination is thermodynamically more stable, while the orange part refers to the region where the I4-termination is more stable. It can be seen that the green region is also located in both blue and orange regions, indicating that different terminations are favored when varying the experimental environments. Under I-rich condition (., at chemical potential point A) the Cs2SnI2-termination is favored, while under I-poor condition (., the chemical point D) the I4-termination is favored.

In Fig. 5(c),the stability diagram of Cs2SnI6(111) surface is shown. Different from the stability diagrams of the (001) and (011) surfaces discussed above, the whole green region is located in the orange region for the (111) surface, indicating that the stoichiometric CsI3-terminated (111) surface is the most energetically favored among the three terminations regardless of the chemical potentials.

Finally, the surface energies of the seven terminations of Cs2SnI6low-index surfaces are compared in Fig. 5(d) as a function of the chemical potentials. It can be seen that the stoichiometric CsI3-terminated (111) surface consistently has the lowest surface energy, indicating that it is the most thermodynamically favored surface among the seven terminations, in agreement with the recent experimental reports[25-26].

Fig. 5 Stability of low-index surfaces of Cs2SnI6 as a function of chemical potentials

(a) Analysis of stability of the two terminations of Cs2SnI6(001) surface with respect to the allowed region for maintaining equilibrium with the primary phase Cs2SnI6. The orange and blue regions indicate the stable region for CsI2- and SnI4-terminations, respectively; (b) Similar to (a) for the Cs2SnI6(011) surface. The orange and blue regions are for the I4- and Cs2SnI2-terminations, respectively; (c) Similar to (a) for the Cs2SnI6(111) surface. The orange and blue regions are for the Sn- and stoichiometric CsI3-terminations, respectively; (d) Surface energies of the seven surface models of Cs2SnI6as a function of the chemical potentials.

Colorful figures are available on website

3 Conclusion

Based on density-functional theory calculations with the SCAN+rVV10 functional, seven models for the low- index Cs2SnI6surfaces were studied with different surface orientations and terminations to compare their thermodynamic stability. Overall, based on the calculated surface energies, we identified that the stoichiometric CsI3-termination for (111) surface is consistently the most stable, regardless of the chemical potentials, which is in agreement with the experimental observation that the (111) surface is often the most exposed surface. For the (100) and (110) surfaces, two different terminations were considered for each of them. Their relative stability depends on the chemical potentials. From an experimental point of view, when preparing these two surfaces, different terminations can be obtained by varying the growth condition,., by controlling the I-poor or I-rich conditions.

Acknowledgement

The authors thank Professor Lian Jie, Dr. Zhu Wei-guang and Shen Junhua from Rensselaer Polytechnic Institute for enlightening discussions.

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Cs2SnI6低指數(shù)晶面穩(wěn)定性的第一性原理計(jì)算研究

林啊鳴1,2, 孫宜陽(yáng)1,2

(1. 中國(guó)科學(xué)院 上海硅酸鹽研究所, 上海 201899; 2. 中國(guó)科學(xué)院大學(xué), 北京 100049)

Cs2SnI6是一種穩(wěn)定且環(huán)保的鹵化物鈣鈦礦材料, 在光伏和光電應(yīng)用方面具有巨大潛力。雖然表面性質(zhì)對(duì)于光電器件的制備至關(guān)重要, 但目前尚沒(méi)有對(duì)該材料開展相關(guān)的理論研究。利用密度泛函理論計(jì)算結(jié)合SCAN+rVV10泛函, 本工作研究了Cs2SnI6的(001)、(011)和(111)表面以揭示其熱力學(xué)穩(wěn)定性。針對(duì)每個(gè)表面, 研究考慮了具有不同截?cái)嗟哪Ｐ? 包括兩個(gè)沿(001)方向(分別為CsI2和SnI4終止的表面), 兩個(gè)沿(011)方向(分別為I4和Cs2SnI2終止的表面)和三個(gè)沿(111)方向(分別為非化學(xué)計(jì)量比的CsI3、Sn和滿足化學(xué)計(jì)量比的CsI3終止的表面)。由于大多數(shù)表面模型是非化學(xué)計(jì)量比的, 它們的相對(duì)穩(wěn)定性取決于實(shí)驗(yàn)制備條件, 因此需要考慮組成元素的化學(xué)勢(shì)。通過(guò)確定允許的化學(xué)勢(shì)區(qū)域, 研究分析了這些表面的熱力學(xué)穩(wěn)定性。結(jié)果表明, (001)和 (011)面的表面能會(huì)受到化學(xué)勢(shì)的影響, 而滿足化學(xué)計(jì)量比的CsI3終止的(111)表面不受化學(xué)勢(shì)影響, 是Cs2SnI6最穩(wěn)定的表面。該結(jié)果說(shuō)明, 近期實(shí)驗(yàn)普遍觀察到的暴露(111)面的晶體是受熱力學(xué)穩(wěn)定性驅(qū)動(dòng)形成的。

鈣鈦礦; 表面能; Cs2SnI6; 光伏材料; 發(fā)光材料

TQ174

A

2021-08-05;

2021-08-20;

2021-11-01

Shanghai International Cooperation Project (20520760900)

LIN Aming (1996–), female, Master candidate. E-mail: linaming@student.sic.ac.cn

林啊鳴(1996–), 女, 碩士研究生. E-mail: linaming@student.sic.ac.cn

SUN Yiyang, professor. E-mail: yysun@mail.sic.ac.cn

孫宜陽(yáng), 研究員. E-mail: yysun@mail.sic.ac.cn

1000-324X(2022)06-0691-06

10.15541/jim20210491