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二维铅卤钙钛矿太阳能电池以其高稳定性等优良性质展现出重要的应用价值, 越来越多的二维铅卤钙钛矿材料被用作太阳能电池的光吸收层, 但是关于二维铅卤钙钛矿材料构效关系的理论研究十分匮乏. 本文以苯甲胺铅碘、邻氟苯甲胺铅碘和对氟苯甲胺铅碘二维钙钛矿为出发点, 通过第一性原理计算比较了它们的晶体结构、形成能、激子结合能、载流子迁移率以及对应器件的光电性能, 以考察不同间隔基阳离子对钙钛矿结构、性质以及光电器件性能的影响. 结果表明, 二维钙钛矿的形成能绝对值越大, 光电器件的稳定性越高; 钙钛矿的激子结合能越小, 光电器件的短路电流密度越大, 归纳总结出预测器件短路电流密度的关系式. 在间隔基末端使用吸电子基团修饰有望同时提高光电器件的寿命和短路电流密度. 本研究对于二维钙钛矿材料有机间隔阳离子的设计和筛选具有指导意义.Two-dimensional lead halide perovskite solar cell has shown great potential applications because of its relatively high stability in comparison with normal three-dimensional perovskite. More and more two-dimensional lead halide perovskites are used as absorbers in solar cells, but theoretical study on the structure-performance relationship of two-dimensional lead halide perovskites is still lacking. Therefore, starting form 3 kinds of fluorobenzylamine perovskites, first-principle calculations are carried out. By comparing their crystal structures, non-covalent interactions, formation energy, band structures, exciton binding energy, carrier mobilities of theses perovskites, and short-circuit current densities of their corresponding solar cells, the influences caused by organic spacers on the structural and electronic properties are studied. This research shows that the more negative the formation energy, the higher the stability of the optoelectronic device is, and the smaller the exciton binding energy, the larger the short-circuit current of the optoelectronic device is. A relationship for quantitative prediction of short-circuit current is proposed, and substitution with electron-withdrawing groups at the end of the spacer is expected to improve both the stability and short-circuit current density of optoelectronic device. The research results of this work can contribute to the design of new perovskite solar cells with high conversion efficiency.
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Keywords:
- perovskite solar cells /
- first principles /
- fluorbenzidine /
- exciton binding energy
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图 1 优化后的晶体结构图 (a) PMA2PbI4; (b) oFPMA2PbI4; (c), (d) pFPMA2PbI4
Fig. 1. The optimized crystal structures: (a) PMA2PbI4; (b) oFPMA2PbI4; (c), (d) pFPMA2PbI4.
图 2 NCI等值面图. 蓝色和绿色的等值面分别代表强的和中等强度的弱相互作用, 红色等值面代表斥力 (a) PMA2PbI4; (b) oFPMA2PbI4; (c) pFPMA2PbI4
Fig. 2. Isosurface NCI plots of (a) PMA2PbI4, (b) oFPMA2PbI4 and (c) pFPMA2PbI4. The isosurfaces are coloured in blue, green and red. Blue and green isosurfaces represent strong and medium-to-weak interactions, while red represents repulsive interactions.
图 3 能带结构图 (a) PMA2PbI4; (b) oFPMA2PbI4; (c) pFPMA2PbI4
Fig. 3. Band structures of (a) PMA2PbI4; (b) PEA2PbI4; (c) oFPEA2PbI4.
表 1 氟苯甲胺钙钛矿晶格常数、Pb-I键键长和形成能
Table 1. Lattice constants, Pb-I bond lengths and formation energies of fluoroaniline perovskites.
体系 a/Å b/Å 平均Pb—I键键长/Å 形成能/(kJ·mol–1) PMA2PbI4 8.42[8.63] 9.05[9.13] 3.19[3.20] –332 oFPMA2PbI4 8.38[8.70] 8.94[9.16] 3.17[3.21] –315 pFPMA2PbI4 8.35[8.70] 8.67[9.24] 3.17[3.21] –338 注: 方括号中为实验数据. 由图1可以看出, 三种钙钛矿具有相同的晶体结构, 其间隔基呈人字形排列, 氟化位置的改变并不影响间隔基的排列方式. 这一现象与氟苯乙胺钙钛矿有所不同, 在氟苯乙胺钙钛矿的实验中, 氟化位置的不同使间隔基呈现多种排列方式[19]. 造成这种区别的原因在于, 氟苯乙铵的苯环侧链长, 苯环可以旋转, 使间隔基具有多种排列方式. 而氟苯甲铵的侧链短, 苯环的旋转受到了甲铵基的限制, 由于甲铵基朝向[PbI6]4-无机八面体赤道面的I原子, 因此氟苯甲铵的位置和取向不能够轻易发生变动, 使得氟化位置无法改变间隔基的排列方式. 此外, 由于苯环侧链长度的差异, 氟苯乙铵中的苯环趴伏在无机八面体上, 而氟苯甲铵中的苯环几乎直立在无机八面体的空隙中, 缺乏苯环与I原子的相互作用, 使得氟苯甲胺钙钛矿的稳定性逊色于氟苯乙胺钙钛矿, 但间隔基排列方式的固定避免了氟苯甲胺钙钛矿产生间隔基取向紊乱的现象[19], 从而确保其光电性能. 
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表 2 氟苯甲胺钙钛矿激子结合能、载流子折合质量、介电常数以及对应器件的短路电流密度
Table 2. The calculated exciton binding energies, carrier-reduced masses, dielectric constants of fluoroaniline perovskites and short circuit current densities of the corresponding devices.
体系 激子结合能/meV 载流子折合质量/m0 介电常数 短路电流密度/(mA·cm–2) PMA2PbI4 254 0.110 2.42 15.64 oFPMA2PbI4 260 0.114 2.43 12.79 pFPMA2PbI4 228 0.114 2.60 17.84
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表 3 氟苯甲胺钙钛矿的载流子迁移率
Table 3. The calculated carrier mobilities of fluoroaniline perovskites.
体系 电子/空穴迁移率
/(cm2·V–1·s–1)平均电子迁移率/(cm2·V–1·s–1) [1 0 0] [0 1 0] PMA2PbI4 1798/112 138/117 256 oFPMA2PbI4 2152/107 121/123 229 pFPMA2PbI4 6054/147 60/107 119 注: 使用调和平均数计算平均电子迁移率.
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表 4 回归结果
Table 4. Regression results.
参数 回归系数 标准差 t检验 p 值 F检验 p 值 a 67 7.1 0.003 0.0096 b –0.23 0.033 0.006 c 0.19 0.051 0.032
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表 A1 氟苯甲胺钙钛矿的晶格常数和空间群
Table A1. The lattice constants and space groups of fluoroaniline perovskites.
体系 a/Å b/Å c/Å α/(°) β/(°) γ/(°) V/Å3 空间群 PMA2PbI4 8.4216 9.0458 35.4988 90.0000 90.2879 90.0000 2704.3 P1 oFPMA2PbI4 8.3798 8.9357 35.7913 90.0001 91.1255 90.0000 2679.5 P1 pFPMA2PbI4 8.3543 8.6668 32.1230 90.0165 94.2669 89.9990 2319.4 P1
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表 A2 PMA2PbI4的原子坐标
Table A2. Coordinates of atoms within PMA2PbI4.
原子 x y z 原子 x y z C1 0.51717 0.55489 0.58411 H14 0.9406 0.1811 0.42597 C2 0.55366 0.518 0.62436 H15 0.90045 0.05108 0.46057 C3 0.6666 0.40972 0.63252 H16 0.80301 0.04595 0.4208 C4 0.70092 0.37303 0.66976 H17 0.28947 0.21097 0.3243 C5 0.50874 0.5523 0.69118 H18 0.94737 0.89128 0.28593 C6 0.62202 0.44457 0.6991 H19 0.1494 0.08341 0.27174 C7 0.47453 0.58909 0.65387 H20 0.88719 0.82566 0.35248 C8 0.01717 0.94511 0.41589 H21 0.38406 0.45023 0.4338 C9 0.05366 0.982 0.37564 H22 0.53383 0.32753 0.41889 C10 0.1666 0.09028 0.36748 H23 0.2711 0.64492 0.39045 C11 0.20092 0.12697 0.33024 H24 0.5594 0.6811 0.42597 C12 0.00874 0.9477 0.30882 H25 0.59955 0.55108 0.46057 C13 0.12202 0.05543 0.3009 H26 0.69699 0.54595 0.4208 C14 0.97453 0.91091 0.34613 H27 0.21053 0.71097 0.3243 C15 0.48283 0.44511 0.41589 H28 0.55263 0.39128 0.28593 C16 0.44634 0.482 0.37564 H29 0.3506 0.58341 0.27174 C17 0.3334 0.59028 0.36748 H30 0.61281 0.32566 0.35248 C18 0.29908 0.62697 0.33024 H31 0.88406 0.04977 0.5662 C19 0.49126 0.4477 0.30882 H32 0.03383 0.17247 0.58111 C20 0.37798 0.55543 0.3009 H33 0.7711 0.85508 0.60955 C21 0.52547 0.41091 0.34613 H34 0.0594 0.8189 0.57403 C22 0.98283 0.05489 0.58411 H35 0.09955 0.94892 0.53943 C23 0.94634 0.018 0.62436 H36 0.19699 0.95405 0.5792 C24 0.8334 0.90972 0.63252 H37 0.71053 0.78903 0.6757 C25 0.79908 0.87303 0.66976 H38 0.05263 0.10872 0.71407 C26 0.99126 0.0523 0.69118 H39 0.8506 0.91659 0.72826 C27 0.87798 0.94457 0.6991 H40 0.11281 0.17434 0.64752 C28 0.02547 0.08909 0.65387 I1 0.04189 0.52535 0.59029 H1 0.61594 0.54977 0.5662 I2 0.2009 0.19417 0.49275 H2 0.46617 0.67247 0.58111 I3 0.54189 0.97465 0.40971 H3 0.7289 0.35508 0.60955 I4 0.7009 0.30583 0.50725 H4 0.4406 0.3189 0.57403 I5 0.95811 0.47465 0.40971 H5 0.40045 0.44892 0.53943 I6 0.7991 0.80583 0.50725 H6 0.30301 0.45405 0.5792 I7 0.45811 0.02535 0.59029 H7 0.78947 0.28903 0.6757 I8 0.2991 0.69417 0.49275 H8 0.44737 0.60872 0.71407 N1 0.40969 0.436 0.5683 H9 0.6494 0.41659 0.72826 N2 0.90969 0.064 0.4317 H10 0.38719 0.67434 0.64752 N3 0.59031 0.564 0.4317 H11 0.11594 0.95023 0.4338 N4 0.09031 0.936 0.5683 H12 0.96617 0.82753 0.41889 Pb1 0 0.5 0.5 H13 0.2289 0.14492 0.39045 Pb2 0.5 0 0.5
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表 A3 oFPMA2PbI4的原子坐标
Table A3. Coordinates of atoms within oFPMA2PbI4.
原子 x y z 原子 x y z C1 0.97272 0.42186 0.34429 H14 0.47991 0.16751 0.58306 C2 0.00262 0.45129 0.30696 H15 0.62368 0.03074 0.56934 C3 0.11933 0.55545 0.29847 H16 0.40004 0.94859 0.54165 C4 0.20308 0.62829 0.327 H17 0.29985 0.95755 0.58088 C5 0.1708 0.59565 0.36416 H18 0.43315 0.81415 0.57534 C6 0.05535 0.4906 0.37357 H19 0.06506 0.60701 0.71463 C7 0.02251 0.45422 0.41357 H20 0.85522 0.4204 0.73068 C8 0.47272 0.07814 0.65571 H21 0.7064 0.28985 0.67958 C9 0.50263 0.04871 0.69304 H22 0.76321 0.34938 0.61344 C10 0.61933 0.94455 0.70153 H23 0.0201 0.66751 0.58306 C11 0.70308 0.87171 0.673 H24 0.87632 0.53075 0.56934 C12 0.6708 0.90435 0.63584 H25 0.09996 0.44859 0.54165 C13 0.55535 0.0094 0.62643 H26 0.20015 0.45755 0.58088 C14 0.52252 0.04578 0.58643 H27 0.06685 0.31415 0.57534 C15 0.02728 0.57814 0.65571 H28 0.56506 0.89299 0.28537 C16 0.99738 0.54871 0.69304 H29 0.35522 0.0796 0.26932 C17 0.88067 0.44455 0.70153 H30 0.2064 0.21015 0.32042 C18 0.79692 0.37171 0.673 H31 0.26321 0.15062 0.38656 C19 0.8292 0.40435 0.63584 H32 0.5201 0.83249 0.41694 C20 0.94465 0.5094 0.62643 H33 0.37632 0.96925 0.43066 C21 0.97749 0.54578 0.58643 H34 0.59997 0.05141 0.45835 C22 0.52728 0.92186 0.34429 H35 0.70015 0.04245 0.41912 C23 0.49738 0.95129 0.30696 H36 0.56685 0.18585 0.42466 C24 0.38067 0.05545 0.29847 F1 0.85786 0.32118 0.35266 C25 0.29692 0.12829 0.327 F2 0.35786 0.17882 0.64734 C26 0.3292 0.09565 0.36416 F3 0.14214 0.67882 0.64734 C27 0.44465 0.9906 0.37357 F4 0.64214 0.82118 0.35266 C28 0.47749 0.95422 0.41357 I1 0.53033 0.47436 0.41067 H1 0.93494 0.39299 0.28537 I2 0.30729 0.18552 0.49512 H2 0.14478 0.5796 0.26932 I3 0.03033 0.02564 0.58933 H3 0.2936 0.71015 0.32042 I4 0.80729 0.31448 0.50488 H4 0.23679 0.65062 0.38656 I5 0.46967 0.52564 0.58933 H5 0.9799 0.33249 0.41694 I6 0.69271 0.81448 0.50488 H6 0.12368 0.46925 0.43066 I7 0.96967 0.97436 0.41067 H7 0.90004 0.55141 0.45835 I8 0.19271 0.68552 0.49512 H8 0.79985 0.54245 0.41912 N1 0.90727 0.56611 0.42973 H9 0.93315 0.68585 0.42466 N2 0.40727 0.9339 0.57027 H10 0.43494 0.10701 0.71463 N3 0.09273 0.43389 0.57027 H11 0.64478 0.9204 0.73068 N4 0.59273 0.06611 0.42973 H12 0.7936 0.78985 0.67958 Pb1 0.5 0.5 0.5 H13 0.73679 0.84938 0.61344 Pb2 0 0 0.5
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表 A4 pFPMA2PbI4的原子坐标
Table A4. Coordinates of atoms within pFPMA2PbI4.
原子 x y z 原子 x y z I1 0.43998 0.49329 0.60085 H24 0.222 0.91848 0.25715 I2 0.07098 0.33645 0.49607 H25 0.17257 0.90258 0.33308 I3 0.35163 0.54478 0.3987 H26 0.20598 0.02654 0.40327 I4 0.71978 0.69941 0.50336 H27 0.35886 0.16774 0.41412 I5 0.85083 0.99328 0.39911 H28 0.93079 0.60433 0.44934 I6 0.22003 0.83635 0.50392 H29 0.91473 0.71294 0.40637 I7 0.93937 0.04487 0.60125 H30 0.06 0.57621 0.41199 I8 0.57128 0.19934 0.49664 H31 0.6696 0.63041 0.33122 Pb1 0.39566 0.51785 0.49982 H32 0.72093 0.60266 0.25562 Pb2 0.89544 0.01789 0.50014 H33 0.08874 0.26613 0.28799 F1 0.8574 0.59929 0.77335 H34 0.03749 0.2931 0.36323 F2 0.35379 0.91958 0.77233 H35 0.84862 0.37588 0.41492 F3 0.43329 0.09867 0.22666 H36 0.70462 0.52402 0.40267 F4 0.93524 0.4196 0.22759 C1 0.93788 0.57312 0.6482 N1 0.85283 0.43786 0.58256 C2 0.82255 0.675 0.66192 N2 0.35046 0.10108 0.58261 C3 0.79449 0.68504 0.70405 N3 0.43798 0.93789 0.41745 C4 0.88414 0.59105 0.73208 N4 0.94071 0.60122 0.41737 C5 1.00048 0.4892 0.71972 H1 0.86487 0.4342 0.55066 C6 0.02674 0.48097 0.67738 H2 0.73234 0.45931 0.58741 C7 0.96141 0.55953 0.60253 H3 0.88169 0.32725 0.59393 C8 0.4389 0.96453 0.64786 H4 0.75407 0.74796 0.63941 C9 0.52799 0.05126 0.67825 H5 0.70514 0.76388 0.71502 C10 0.50017 0.03661 0.72038 H6 0.06846 0.41876 0.74288 C11 0.3819 0.93418 0.73127 H7 0.11791 0.40251 0.66695 C12 0.29166 0.8457 0.70198 H8 0.08482 0.52648 0.59676 C13 0.32154 0.86187 0.66012 H9 0.93199 0.6677 0.5859 C14 0.46457 0.98378 0.60245 H10 0.36072 0.10414 0.55065 C15 0.35286 0.073 0.35181 H11 0.37635 0.21281 0.59363 C16 0.46834 0.17466 0.33809 H12 0.2311 0.07612 0.58791 C17 0.49638 0.18451 0.29595 H13 0.6206 0.13035 0.66896 C18 0.40657 0.09057 0.26793 H14 0.56837 0.10266 0.7445 C19 0.29009 0.98893 0.2803 H15 0.20074 0.76623 0.71181 C20 0.26385 0.98087 0.32265 H16 0.25291 0.7931 0.63663 C21 0.32939 0.05954 0.39749 H17 0.44251 0.87572 0.58511 C22 0.85149 0.4646 0.35216 H18 0.58643 0.02384 0.59748 C23 0.76207 0.55131 0.32184 H19 0.42596 0.93425 0.44934 C24 0.78939 0.53661 0.27967 H20 0.55846 0.95934 0.41259 C25 0.9075 0.43417 0.26868 H21 0.40913 0.82727 0.40607 C26 0.99801 0.34566 0.2979 H22 0.53694 0.24759 0.36059 C27 0.96863 0.36187 0.3398 H23 0.58585 0.26318 0.28498 C28 0.82637 0.48392 0.3976
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