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第一性原理对CsSnBr3施加静水压力后光电性质的探究

高立科 赵先豪 刁心峰 唐天宇 唐延林

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第一性原理对CsSnBr3施加静水压力后光电性质的探究

高立科, 赵先豪, 刁心峰, 唐天宇, 唐延林

First-principles study of photoelectric properties of CsSnBr3 under hydrostatic pressure

Gao Li-Ke, Zhao Xian-Hao, Diao Xin-Feng, Tang Tian-Yu, Tang Yan-Lin
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  • CsSnBr3作为一种重要的钙钛矿太阳能电池材料已经被广泛研究. 基于密度泛函理论, 利用第一性原理来研究在不同静水压力下CsSnBr3的光电性质. 结果发现, 当压力为2.6 GPa时, CsSnBr3具有最佳光学带隙值1.34 eV, 因此, 本文只对比研究CsSnBr3在0和2.6 GPa静水压力下的光电性质. 当压力为2.6 GPa时, CsSnBr3具有更大的介电值、电导率、吸收系数及折射率, 吸收光谱有红移现象, 且其电子和空穴的有效质量、激子的结合能都比较小, 这表明CsSnBr3是一种高效的光吸收材料. 通过Born-Huang 稳定标准判据, 容差因子T和声子谱有无虚频的三重计算, 发现在压力0和2.6 GPa下, CsSnBr3都是稳定的. 由加压前后CsSnBr3的弹性模量值可知他们都是偏软性的, 具有良好的延展性和各向异性. 加压后CsSnBr3的德拜温度和热容量很快趋于稳定, 与温度无关; 而焓和熵则随着温度升高而增加, 增加的幅度大于未加压的情况; 吉布斯自由能都呈现出降低的趋势, 未加压时降低得稍快. 本研究表明, 施加静水压力后的CsSnBr3是一种良好的光电材料, 适合用于钙钛矿太阳能电池.
    As an important perovskite solar cell (PSC) material, CsSnBr3 has been widely studied. Based on the density functional theory (DFT), the photoelectric properties of CsSnBr3 are studied by using the first-principles at different hydrostatic pressures. It is found that CsSnBr3 has an optimal optical band gap value of 1.34 eV under a pressure of 2.6 GPa, so only the photoelectric properties of CsSnBr3 under the hydrostatic pressure of 0 GPa and 2.6 GPa are studied, respectively. When the pressure is 2.6 GPa, CsSnBr3 has larger values of dielectric, conductivity, absorption coefficient and refractive index, the red-shifted absorption spectrum, and relatively small effective mass of electron and hole and exciton binding energy, indicating that CsSnBr3 is an efficient light absorbing material. According to the triple calculations of Born-Huang stability standard criterion, the tolerance factor T and phonon spectrum with or without virtual frequency, it is found that CsSnBr3 is stable under the pressure of 0 GPa and 2.6 GPa. According to the elastic modulus value of CsSnBr3 before and after pressure, it can be seen that the CsSnBr3 is soft, with good ductility and anisotropy. The Debye temperature and heat capacity of CsSnBr3, soon after it has been pressured, tend to be stable and are independent of temperature. The enthalpy and entropy increase with temperature increasing, and the increased amplitude is larger than those of the unpressured CsSnBr3. Gibbs free energy shows a decreasing trend, and the decrease is slightly faster when unpressured. This study shows that CsSnBr3 is a good photoelectric material after having been pressured hydrostatically, which is suitable for perovskite solar cells.
      通信作者: 唐延林, tylgzu@163.com
    • 基金项目: 国家自然科学基金(批准号: 11164004, 61835003)、贵州省光子科技创新团队(黔科联合人才团队)(批准号: [2015]4017)和贵州省产业研究项目(批准号: GY[2012]3060)资助的课题
      Corresponding author: Tang Yan-Lin, tylgzu@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11164004, 61835003), the Photonic Science and Technology Innovation Team of Guizhou Province (Qianke Joint Talents Team), China (Grant No. [2015]4017), and the Industrial Research Project of Guizhou Province, China (Grant No. GY[2012]3060)
    [1]

    Kojima A, Teshima K, Shirai Y, Miyasaka T 2009 J. Am. Chem. Soc. 131 6050Google Scholar

    [2]

    Kim H S, Lee C R, Im J H, Lee K B, Moehl T, Marchioro A, Moon S J, Humphry-Baker R, Yum J H, Moser J E, Gratzel M, Park N G 2012 Sci. Rep. 2 591Google Scholar

    [3]

    Lee M M, Teuscher J, Miyasaka T, Murakami T N, Snaith H J 2012 Science 338 643Google Scholar

    [4]

    Snaith H J 2013 J. Phys. Chem. Lett. 4 3623Google Scholar

    [5]

    Katan C, Mercier N, Even J 2019 Chem. Rev. 119 3140Google Scholar

    [6]

    Tan Z K, Moghaddam R S, Lai M L, Docampo P, Higler R, Deschler F, Price M, Sadhanala A, Pazos L M, Credgington D, Hanusch F, Bein T, Snaith H J, Friend R H 2014 Nat. Nanotechnol. 9 687Google Scholar

    [7]

    Jeon N J, Na H, Jung E H, Yang T Y, Lee Y G, Kim G, Shin H W, Seok S I, Lee J, Seo J 2018 Nat. Energy 3 682Google Scholar

    [8]

    Ehli C, Oelsner C, Guldi D M, Mateo-Alonso A, Prato M, Schmidt C, Backes C, Hauke F, Hirsch A 2009 Nat. Chem. 1 243Google Scholar

    [9]

    Piao Y M, Meany B, Powell L R, Valley N, Kwon H, Schatz G C, Wang Y H 2013 Nat. Chem. 5 840Google Scholar

    [10]

    Williams S T, Rajagopal A, Chueh C C, Jen A K Y 2016 J. Phys. Chem. Lett. 7 811Google Scholar

    [11]

    Boix P P, Agarwala S, Koh T M, Mathews N, Mhaisalkar S G 2015 J. Phys. Chem. Lett. 6 898Google Scholar

    [12]

    Saliba M, Matsui T, Domanski K, Seo J Y, Ummadisingu A, Zakeeruddin S M, Correa-Baena J P, Tress W R, Abate A, Hagfeldt A, Gratzel M 2016 Science 354 206Google Scholar

    [13]

    Kieslich G, Sun S J, Cheetham A K 2014 Chem. Sci. 5 4712Google Scholar

    [14]

    Sutton R J, Filip M R, Haghighirad A A, Sakai N, Wenger B, Giustino F, Snaith H J 2018 ACS Energy Lett. 3 1787Google Scholar

    [15]

    Wang K, Jin Z W, Liang L, Bian H, Bai D L, Wang H R, Zhang J R, Wang Q, Liu S Z 2018 Nat. Commun. 9 1Google Scholar

    [16]

    Sanehira E M, Marshall A R, Christians J A, Harvey S P, Ciesielski P N, Wheeler L M, Schulz P, Lin L Y, Beard M C, Luther J M 2017 Sci. Adv. 3 eaao4204Google Scholar

    [17]

    Perdew J P, Ruzsinszky A 2018 Eur. Phys. J. B 91 6Google Scholar

    [18]

    Cheng X R, Kuang X Y, Cheng H, Tian H, Yang S M, Yu M, Dou X L, Mao A J 2020 RSC Adv. 10 12432Google Scholar

    [19]

    Peedikakkandy L, Bhargava P 2016 RSC Adv. 6 19857Google Scholar

    [20]

    Ou T J, Yan J J, Xiao C H, Shen W S, Liu C L, L iu, X Z, Han Y H, Ma Y Z, Gao C X 2016 Nanoscale 8 11426Google Scholar

    [21]

    Jaffe A, Lin Y, Umeyama D, Beavers C, Voss J, Mao W, Karunadasa H 2017 ACS Energy Lett. 253 1549Google Scholar

    [22]

    Schwarz U, Wagner F, Syassen K, Hillebrecht H 1996 Phys. Rev. B 53 19Google Scholar

    [23]

    Gupta N, Thiele G, Seo D K, Whangbo M H, Hillebrecht H 1998 Inorg. Chem. 37 407Google Scholar

    [24]

    Jing H J, Sa RJ, Xu G 2019 Chem. Phys. Lett. 732 136642Google Scholar

    [25]

    Coduri M, Strobel T A, Szafranski M, Katrusiak A, Mahata A, Cova F, Bonomi S, Mosconi E, De Angelis F, Malavasi L 2019 J. Phys. Chem. Lett. 10 7398Google Scholar

    [26]

    Yalameha S, Saeidi P, Nourbakhsh Z, Vaez A, Ramazani A 2020 J. Appl. Phys. 127 085102

    [27]

    Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B 49 16223Google Scholar

    [28]

    Kohn W, Sham L J 1965 Phys. Rev. A 140 A1133Google Scholar

    [29]

    Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys. Condens. Matter 14 2717Google Scholar

    [30]

    Shockley W, Queisser H J 1961 J. Appl. Phys. 32 510

    [31]

    Lang L, Yang J H, Liu H R, Xiang H J, Gong X G 2014 Phys. Lett. A 378 290Google Scholar

    [32]

    Qian J Y, Xu B, Tian W J 2016 Org. Electron. 37 61Google Scholar

    [33]

    Jung M C, Raga S R, Qi Y B 2016 RSC Adv. 6 2819Google Scholar

    [34]

    Gajdoš M, Hummer K, Kresse G, Furthmüller J, Bechstedt F 2006 Phys. Rev. B 73 045112Google Scholar

    [35]

    Sahin S, Ciftci Y O, Colakoglu K, Korozlu N 2012 J. Alloys Compd. 529 1Google Scholar

    [36]

    Saha S, Sinha T P, Mookerjee A 2000 Phys. Rev. B 62 13Google Scholar

    [37]

    Rodina A V, Dietrich M, Göldner A, Eckey L, Meyer B K 2001 Phys. Rev. B 64 115204Google Scholar

    [38]

    Manser J S, Christians J A, Kamat P V 2016 Chem. Rev. 116 12956Google Scholar

    [39]

    Galkowski K, Mitioglu A, Miyata A, Plochocka P, Portugall O, Eperon G E, Wang J T W, Stergiopoulos T, Stranks S D, Snaith H J, Nicholas R J 2016 Energy Environ. Sci. 9 962Google Scholar

    [40]

    De Wolf S, Holovsky J, Moon S J, Loper P, Niesen B, Ledinsky M, Haug F J, Yum J H, Ballif C 2014 J. Phys. Chem. Lett. 5 1035Google Scholar

    [41]

    Li B, Long R, Xia Y, Mi Q 2018 Angew. Chem. 57 13154Google Scholar

    [42]

    Born M 1955 Am. J. Phys. 23 474Google Scholar

    [43]

    Goldschmidt V M 1926 Naturwissenschaften 14 477Google Scholar

    [44]

    Li C H, Lu X G, Ding W Z, Feng L M, Gao Y H, Guo Z G 2008 Acta. Crystallogr., Sect. B 64 702Google Scholar

    [45]

    Pugh S F 1954 Philos. Mag. 45 823Google Scholar

    [46]

    Ranganathan S I, Ostoja-Starzewski M 2008 J. Mech. Phys. Solids 56 2773

  • 图 1  CsSnBr3的晶体结构

    Fig. 1.  Crystal of CsSnBr3.

    图 2  CsSnBr3在不同压力下的结构参数 (a)能量曲线; (b)晶格常数曲线; (c)体积曲线; (d)晶胞角曲线; (e) Sn—Br键长曲线; (f)应变曲线

    Fig. 2.  Structure parameters of CsSnBr3 under different pressure conditions: (a) Curve of energy; (b) curve of the lattice constant (c) curve of volume; (d) curve of cell angle; (e) curve of bond length of Sn—Br; (f) curve of the strain.

    图 3  CsSnBr3在不同压力下的能带值

    Fig. 3.  Band gap of CsSnBr3 under different pressure conditions.

    图 4  CsSnBr3的能带结构 (a)采用PBE和PBE + SOC计算得到的能带; (b) 0和2.6 GPa压力下采用HSE06计算得到的能带

    Fig. 4.  Band structures of CsSnBr3: (a) Band structure calculated by PBE and PBE + SOC; (b) band structure calculated by HSE06 at the pressure of 0 and 2.6 GPa.

    图 5  CsSnBr3在 (a) 0 GPa和(b) 2.6 GPa压力下的态密度

    Fig. 5.  Density of states (DOS) of CsSnBr3 under the pressure of (a) 0 GPa and (b) 2.6 GPa.

    图 6  Cs, Sn和Br原子之间电荷的转移

    Fig. 6.  Charge transfer of the Cs, Sn and Br atoms.

    图 7  在0和2.6 GPa压力下CsSnBr3介电函数的(a)实部和(b)虚部

    Fig. 7.  Dielectric function of CsSnBr3 of (a) real and (b) imaginary under the pressure of 0 and 2.6 GPa.

    图 8  在0和2.6 GPa压力下CsSnBr3电导率的(a)实部和(b)虚部

    Fig. 8.  Conductivity of CsSnBr3 of (a) real and (b) imaginary under the pressure of 0 and 2.6 GPa.

    图 9  (a) CsSnBr3在0和2.6 GPa压力下的吸收系数; (b) CsSnBr3在0和2.6 GPa压下的折射率n和消光系数k

    Fig. 9.  (a) Absorption of CsSnBr3 under the pressure of 0 and 2.6 GPa; (b) refractive index n and extinction coefficient k of CsSnBr3 under the pressure of 0 and 2.6 GPa.

    图 10  CsSnBr3在(a) 0 GPa和(b) 2.6 GPa压力下的声子谱

    Fig. 10.  Phonon spectrum of CsSnBr3 under the pressure of (a) 0 GPa and (b) 2.6 GPa.

    图 11  在0和2.6 GPa压力下CsSnBr3的热力学性质 (a)德拜温度; (b)热容量; (c)焓、温度-熵和吉布斯自由能

    Fig. 11.  Thermodynamic properties of CsSnBr3 of (a) Debye temperature, (b) heat capacity and (c) enthalpy, temperature-entropy and free energy under the pressure of 0 and 2.6 GPa.

    表 1  Findit找到的CsSnBr3的晶格参数与几何优化后的对比

    Table 1.  Lattice parameters of CsSnBr3 with Findit compared with geometry optimization (GO).

    a = b = cα = β = γ/(°)V3Space group
    Findit5.8090.00195.11$Pm\bar3m$
    GO5.9490.00209.58$ Pm\bar 3m $
    下载: 导出CSV

    表 2  在0和2.6 GPa压力下CsSnBr3的有效质量和激子结合能(质量的单位是自由电子的质量m0)

    Table 2.  Effective masses and exciton binding energy calculated for CsSnBr3 under the pressure of 0 and 2.6 GPa. Masses are given in units of the free electron mass m0.

    Pressure/GPame (RX)me (RM)me(RG)${\bar m_{\rm{e}}}$mh (RX)mh (RM)mh (RG)${\bar m_{\rm{h}}}$εsEb /meV
    00.5230.5240.1840.4100.0720.0750.0720.0733.858
    2.60.4180.4180.1430.3260.0520.0630.0510.0553.942
    下载: 导出CSV

    表 3  在0和2.6 GPa压力下CsSnBr3的弹性常数、体积模量(B)、剪切模量(G)和弹性各向异性(A)

    Table 3.  Calculated elastic constant, bulk modulus (B), shear modulus (G) and elastic anisotropy (A) of CsSnBr3 under the pressure of 0 and 2.6 GPa.

    Pressure/GPaC11C12C44BGB/GA
    037.406.325.2116.688.222.030.34
    2.667.3611.565.2030.1710.992.730.19
    下载: 导出CSV

    表 4  CsSnBr3的各元素的离子半径

    Table 4.  Ionic radium of CsSnBr3.

    Cs+Sn2+Br–T
    R/nm0.1670.1120.1960.83
    下载: 导出CSV
  • [1]

    Kojima A, Teshima K, Shirai Y, Miyasaka T 2009 J. Am. Chem. Soc. 131 6050Google Scholar

    [2]

    Kim H S, Lee C R, Im J H, Lee K B, Moehl T, Marchioro A, Moon S J, Humphry-Baker R, Yum J H, Moser J E, Gratzel M, Park N G 2012 Sci. Rep. 2 591Google Scholar

    [3]

    Lee M M, Teuscher J, Miyasaka T, Murakami T N, Snaith H J 2012 Science 338 643Google Scholar

    [4]

    Snaith H J 2013 J. Phys. Chem. Lett. 4 3623Google Scholar

    [5]

    Katan C, Mercier N, Even J 2019 Chem. Rev. 119 3140Google Scholar

    [6]

    Tan Z K, Moghaddam R S, Lai M L, Docampo P, Higler R, Deschler F, Price M, Sadhanala A, Pazos L M, Credgington D, Hanusch F, Bein T, Snaith H J, Friend R H 2014 Nat. Nanotechnol. 9 687Google Scholar

    [7]

    Jeon N J, Na H, Jung E H, Yang T Y, Lee Y G, Kim G, Shin H W, Seok S I, Lee J, Seo J 2018 Nat. Energy 3 682Google Scholar

    [8]

    Ehli C, Oelsner C, Guldi D M, Mateo-Alonso A, Prato M, Schmidt C, Backes C, Hauke F, Hirsch A 2009 Nat. Chem. 1 243Google Scholar

    [9]

    Piao Y M, Meany B, Powell L R, Valley N, Kwon H, Schatz G C, Wang Y H 2013 Nat. Chem. 5 840Google Scholar

    [10]

    Williams S T, Rajagopal A, Chueh C C, Jen A K Y 2016 J. Phys. Chem. Lett. 7 811Google Scholar

    [11]

    Boix P P, Agarwala S, Koh T M, Mathews N, Mhaisalkar S G 2015 J. Phys. Chem. Lett. 6 898Google Scholar

    [12]

    Saliba M, Matsui T, Domanski K, Seo J Y, Ummadisingu A, Zakeeruddin S M, Correa-Baena J P, Tress W R, Abate A, Hagfeldt A, Gratzel M 2016 Science 354 206Google Scholar

    [13]

    Kieslich G, Sun S J, Cheetham A K 2014 Chem. Sci. 5 4712Google Scholar

    [14]

    Sutton R J, Filip M R, Haghighirad A A, Sakai N, Wenger B, Giustino F, Snaith H J 2018 ACS Energy Lett. 3 1787Google Scholar

    [15]

    Wang K, Jin Z W, Liang L, Bian H, Bai D L, Wang H R, Zhang J R, Wang Q, Liu S Z 2018 Nat. Commun. 9 1Google Scholar

    [16]

    Sanehira E M, Marshall A R, Christians J A, Harvey S P, Ciesielski P N, Wheeler L M, Schulz P, Lin L Y, Beard M C, Luther J M 2017 Sci. Adv. 3 eaao4204Google Scholar

    [17]

    Perdew J P, Ruzsinszky A 2018 Eur. Phys. J. B 91 6Google Scholar

    [18]

    Cheng X R, Kuang X Y, Cheng H, Tian H, Yang S M, Yu M, Dou X L, Mao A J 2020 RSC Adv. 10 12432Google Scholar

    [19]

    Peedikakkandy L, Bhargava P 2016 RSC Adv. 6 19857Google Scholar

    [20]

    Ou T J, Yan J J, Xiao C H, Shen W S, Liu C L, L iu, X Z, Han Y H, Ma Y Z, Gao C X 2016 Nanoscale 8 11426Google Scholar

    [21]

    Jaffe A, Lin Y, Umeyama D, Beavers C, Voss J, Mao W, Karunadasa H 2017 ACS Energy Lett. 253 1549Google Scholar

    [22]

    Schwarz U, Wagner F, Syassen K, Hillebrecht H 1996 Phys. Rev. B 53 19Google Scholar

    [23]

    Gupta N, Thiele G, Seo D K, Whangbo M H, Hillebrecht H 1998 Inorg. Chem. 37 407Google Scholar

    [24]

    Jing H J, Sa RJ, Xu G 2019 Chem. Phys. Lett. 732 136642Google Scholar

    [25]

    Coduri M, Strobel T A, Szafranski M, Katrusiak A, Mahata A, Cova F, Bonomi S, Mosconi E, De Angelis F, Malavasi L 2019 J. Phys. Chem. Lett. 10 7398Google Scholar

    [26]

    Yalameha S, Saeidi P, Nourbakhsh Z, Vaez A, Ramazani A 2020 J. Appl. Phys. 127 085102

    [27]

    Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B 49 16223Google Scholar

    [28]

    Kohn W, Sham L J 1965 Phys. Rev. A 140 A1133Google Scholar

    [29]

    Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys. Condens. Matter 14 2717Google Scholar

    [30]

    Shockley W, Queisser H J 1961 J. Appl. Phys. 32 510

    [31]

    Lang L, Yang J H, Liu H R, Xiang H J, Gong X G 2014 Phys. Lett. A 378 290Google Scholar

    [32]

    Qian J Y, Xu B, Tian W J 2016 Org. Electron. 37 61Google Scholar

    [33]

    Jung M C, Raga S R, Qi Y B 2016 RSC Adv. 6 2819Google Scholar

    [34]

    Gajdoš M, Hummer K, Kresse G, Furthmüller J, Bechstedt F 2006 Phys. Rev. B 73 045112Google Scholar

    [35]

    Sahin S, Ciftci Y O, Colakoglu K, Korozlu N 2012 J. Alloys Compd. 529 1Google Scholar

    [36]

    Saha S, Sinha T P, Mookerjee A 2000 Phys. Rev. B 62 13Google Scholar

    [37]

    Rodina A V, Dietrich M, Göldner A, Eckey L, Meyer B K 2001 Phys. Rev. B 64 115204Google Scholar

    [38]

    Manser J S, Christians J A, Kamat P V 2016 Chem. Rev. 116 12956Google Scholar

    [39]

    Galkowski K, Mitioglu A, Miyata A, Plochocka P, Portugall O, Eperon G E, Wang J T W, Stergiopoulos T, Stranks S D, Snaith H J, Nicholas R J 2016 Energy Environ. Sci. 9 962Google Scholar

    [40]

    De Wolf S, Holovsky J, Moon S J, Loper P, Niesen B, Ledinsky M, Haug F J, Yum J H, Ballif C 2014 J. Phys. Chem. Lett. 5 1035Google Scholar

    [41]

    Li B, Long R, Xia Y, Mi Q 2018 Angew. Chem. 57 13154Google Scholar

    [42]

    Born M 1955 Am. J. Phys. 23 474Google Scholar

    [43]

    Goldschmidt V M 1926 Naturwissenschaften 14 477Google Scholar

    [44]

    Li C H, Lu X G, Ding W Z, Feng L M, Gao Y H, Guo Z G 2008 Acta. Crystallogr., Sect. B 64 702Google Scholar

    [45]

    Pugh S F 1954 Philos. Mag. 45 823Google Scholar

    [46]

    Ranganathan S I, Ostoja-Starzewski M 2008 J. Mech. Phys. Solids 56 2773

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出版历程
  • 收稿日期:  2021-03-01
  • 修回日期:  2021-03-16
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-08-05

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