Why Cannot All Divalent Cations Completely Substitute the Pb Cations

Physics Letters A 383 (2019) 2130–2138

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Physics Letters A

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Why cannot all divalent cations completely substitute the Pb cations of CH3NH3PbI3 perovskite? ∗ Denghui Ji a, , Shuling Wang b, Hong Zhang b, Huaying Wang b, Buqin Zhang c, Congmin Zhang a, Xiuling Li d a College of Physics, Mechanical and Electronical College, Shijiazhuang University, Shijiazhuang City, 050035, People’s Republic of China b School of Mathematics and Physics, Hebei University of Engineering, Handan city, 056038, People’s Republic of China c Fengfeng Group Co. Ltd., JZEG, Handan city, 056107, People’s Republic of China d College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang City, 050024, People’s Republic of China a r t i c l e i n f o a b s t r a c t

Article history: Organic-inorganic hybrid CH3NH3PbI3 perovskite has a great potential for applications in low-cost Received 3 August 2018 photovoltaic devices. However, the doped and substitution of Pb sites in CH3NH3PbI3 has not been widely Received in revised form 21 December 2018 reported. In this article, a quantum mechanical model was applied to determine why all divalent cations Accepted 8 April 2019 cannot substitute the Pb cations of CH NH PbI perovskite. The evaluation was performed by comparison Available online 12 April 2019 3 3 3 the model with experimental results. On this basis, we carefully examined 42 types of cations and Communicated by R. Wu + + + + + + + + + identified only nine kinds of cations including Ca2 , Sr2 , Sc2 , Ti2 , V2 , Y2 , Zr2 , Nb2 and Sn2 Keywords: for doped into Pb sites. In these cases, it is expected that the corresponding compound would be single Organic-inorganic hybrid phase. Finally, an analysis was performed based on first principle, and the results indicate that divalent Pb site substitution cations substituting the Pb sites modify the band structure and influence the performance of perovskite- Quantum mechanical model based photostatics. The first principle © 2019 Elsevier B.V. All rights reserved.

1. Introduction erties [6]. Michael Saliba et al. achieved a stabilized efficiency of + up to 21.6% for Rb cations doped into the A sites [7]. Burschka, J. = Organic-inorganic hybrid perovskite is widely investigated ow- et al. reported that CH3NH3PbX3 (X Cl, Br, I) perovskite absorbers ing to its excellent structural and optical properties, and its poten- demonstrated power conversion deficiencies over 15% [8]. The ef- tial electronic applications. In particular, CH3NH3PbI3 perovskite fect of Cl substitution on the shift current, and the Cl substitution has been investigated due in part to its high efficiency which ap- at the equatorial site induces a larger response than substitution proaches 22.1% for photovoltaic applications [1]. Perovskites have at the apical site were explored by Fan Zheng et al. [9]. the general formula ABX3, which consists of a network of BX6 oc- Javier Navas et al. [10]first presented results on the synthe- + tahedra where the B atom is a metal cation (typically Sn2 or sis of the organic-inorganic hybrid perovskite, CH3NH3Pb1−xBxI3, + − − − 2+ 2+ 2+ 2+ Pb2 ), and the X is a monovalent anion (such as F , Cl , Br , B = Sn , Sr , Cd and Ca , x = 0.05, 0.10, 0.15. The XRD re- − 2+ 2+ 2+ or I ); the A cation is selected to balance the total charge, and it sults showed that the cations Sn , Sr , and Ca can be doped 2+ can be a small molecular species. into the Pb sites and form a single phase, but the cations Cd Doped is widely performed in various areas such as spinel [2], seems to hinder the formation reaction of perovskite, and instead diluted magnetic semiconductors [3], spin systems [4], and inor- formed PbI2 or CdI2 as the second phase. Moreover, DR-UV-Vis ganic perovskites [5], and continues to attract significant attention. spectroscopy revealed a decrease in the band gap with the ad- 2+ 2+ 2+ B. Slimi et al. synthesized formamidinium methylammonium lead dition of the dopants following the trend Sr < Cd < Ca ≈ 2+ 2+ triiodide (NH2CHNH2)1−x(CH3NH2)xPbI3(FA1−xMAxPbI3) thin films < CH3NH3PbI3 Sn . These results indicated that all the Sn , 2+ 2+ 2+ and investigated their morphological, structural and optical prop- Sr , Ca cations and a part of the Cd cations can be doped into the B sites. With the further doped level, the physical mechanism changed into substituted mechanism. Unfortunately, no ex- * Corresponding author. planation of this behavior is given in the article. In general, there E-mail address: [email protected] (D. Ji). are many reports on CH3NH3PbI3 perovskites doped into the A or https://doi.org/10.1016/j.physleta.2019.04.014 0375-9601/© 2019 Elsevier B.V. All rights reserved. D. Ji et al. / Physics Letters A 383 (2019) 2130–2138 2131

+ Fig. 1. The curves of the second ionization energy and the content ratio R versus 42 kinds of cations. The red line represents the second ionization energy of the Pb2 cations. (For interpretation of the colors in the ﬁgure(s), the reader is referred to the web version of this article.)

X sites [11,12], but there are few reports on B site doped or substi- shapes of the two potential barriers deviate from a square barrier. tution. Naturally, the inability of divalent cations to be doped into The content ratio R between the B-site cations can be obtained the Pb sites of CH3NH3PbI3 perovskite has become a very impor- as: tant physical problem. TB1 V B2 1/2 1/2 In our early investigations [13,14], we proposed a quantum- R = = exp 10.24 rB2 V − c • rB1 V , (2) T V B2 B1 mechanical method for estimating the cation distribution in ABO3 B2 B1 type inorganic perovskites and cubic spinel ferrites. This approach where T B1, T B2 represents the probability of the last ionized elec- 4+ 4+ successfully explained why there are Mn ions, but no La or tron of the B1, B2 cations at the B sites, jumping to the anions 3+ Ca ions in the La1−xCaxMnO3 system. In addition, the difference through the potential barriers with the height V B1, V B2 and width between the observed and the traditional theoretical magnetic mo- rB1, rB2, respectively; V B1 and V B2 are the ionization energies of ments of the spinel structure ferrites MFe2O4 (M = Mn, Fe, Co, Ni, the last ionized electron of the cations B1 and B2, respectively; Cu) was explained, and fitted the dependence of the magnetic mo- and rB1 and rB2 are the distances from the cations B1 and B2 to ments of the ferrites M1−xZnxFe2O4 (M = Mn, Fe, Co, Ni, Cu) on the anions, respectively. the doped level x perfectly. Since both the B1 and B2 cations are at the B sites, rB1 = rB2. 2+ In this paper, we used the quantum-mechanical method to elu- Based on ref. [10], the distance (rB2) between the Pb (B2) cations cidate why not all divalent cations substitute the Pb cations of − 2+ and the I anions is 0.31515 nm. The content ratio R0 of the Pb CH3NH3PbI3 perovskite completely. In addition, the proposed con- cations are shown in Table 1. Because the distance (rB2) becomes cepts were compared with experimental results. Based on our find- smaller or larger when the B1 cations are doped into the B sites, ings, we predict that only 9 kinds of cations can be doped into the we allow the distance to change in the range −5% and +5%, and 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ Pb sites, including Ca , Sr , Sc , Ti , V , Y , Zr , Nb the content ratio labeled as R− and R+ are also shown in Ta- + 0.5 0.5 and Sn2 . In addition, related physical properties were obtained ble 1. It can be seen that this ratio R increases with a decrease by using the first principle. of the second ionization energy, and decreases with an increase of the distance between the cations B1 and B2 to the anions. This 2. The quantum-mechanical method response results from the increase of the height of the potential barrier and the width of the potential barrier are reported by Tang + We supposed that there is a square potential barrier between et al. [13,14]. In the case of B2 as the Pb2 cations, R is equal to 2+ a cation-anion pair [13,14]. The height of the potential barrier is 1 because the cations of both B1 and B2 are Pb . This indicates 2+ proportional to the ionization energy of the last ionized electron, that all the Pb cations can be doped into the B sites. Therefore, and the width of the potential barrier is related to the distance be- the value of R greater than or less than 1 is essentially the crite- tween neighboring cations and anions. The content ratio R of the rion which determines whether all the cations can replace the Pb cations. A-site cations to the B-site cations which is related to the probabil- In order to show this idea in a more intuitive manner, Fig. 1 ity of their last ionized electrons penetrating the potential barrier represents the curves of the second ionization energy and the can be derived, and takes the following form: content ratio R for 42 kinds of cations. The content ratio R 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ TA V B 1/2 1/2 of only Ca , Sr , Sc , Ti , V , Y , Zr , Nb , Sn , and = = − • 2+ R exp 10.24 rB V B c rA V A , (1) Pb is greater than or equal to 1, indicating that these 10 kinds TB V A of cations can completely replace the Pb cations. Meanwhile, the where rA (nm) or rB (nm) are the distances between the A-site 32 other kinds of cations have R values less than 1, indicating cations or B-site cations and the O anions; and c is a barrier shape that they cannot completely replace the Pb cations, and a part of correcting constant related to the different extent to which the the cations will separate out and form BI2 as the second phase. 2132 D. Ji et al. / Physics Letters A 383 (2019) 2130–2138

Table 1 2+ The content ratio R of the 42 different cations to Pb cation at the Pb sites. Here, V B is the second ionization = = = = × = energy, R0, R−0.5, and R+0.5 denote the R with rB1 rB2 0.31515, rB1 rB2 0.31515 0.95 0.2994, and rB1 = rB2 = 0.31515 × 1.05 = 0.3309. Occupation site Cations The second ionization R0 R−0.5 R+0.5 energy, V B, (eV) + *B2 sites Sn2 14.63 1.2148 1.20467 1.22502 + B2 sites Tl2 20.43 0.09234 0.10243 0.08324 + B2 sites Bi2 16.69 0.45952 0.47523 0.44433 + *B2 sites Sc2 12.80 3.08326 2.93803 3.23566 + *B2 sites Ti2 13.58 2.05495 1.99237 2.11949 + *B2 sites V2 14.65 1.20295 1.19342 1.21256 + B2 sites Cr2 15.50 0.79859 0.80638 0.79088 + B2 sites Mn2 15.64 0.74741 0.75686 0.73808 + B2 sites Fe2 16.18 0.58069 0.59448 0.56721 + B2 sites Co2 17.06 0.38874 0.40497 0.37317 + B2 sites Ni2 18.17 0.23819 0.25348 0.22383 + B2 sites Cu2 20.29 0.09775 0.10816 0.08834 + B2 sites Zn2 17.96 0.26098 0.27663 0.24621 + B2 sites Ga2 20.51 0.08939 0.0993 0.08047 + B2 sites Ge2 15.93 0.65227 0.66442 0.64035 + B2 sites As2 18.63 0.1954 0.20975 0.18203 + *B2 sites Y2 12.24 4.16248 3.91612 4.42433 + *B2 sites Zr2 13.13 2.59256 2.48878 2.70068 + *B2 sites Nb2 14.32 1.41548 1.39448 1.4368 + B2 sites Mo2 16.15 0.58881 0.60244 0.57549 + B2 sites Tc2 15.26 0.89534 0.89962 0.89108 + B2 sites Ru2 16.76 0.44514 0.46099 0.42982 + B2 sites Rh2 18.08 0.24769 0.26314 0.23314 + B2 sites Pd2 19.43 0.13936 0.15183 0.12792 + B2 sites Ag2 21.49 0.06041 0.06828 0.05345 + B2 sites Cd2 16.91 0.41591 0.432 0.40043 + B2 sites In2 18.87 0.17641 0.19021 0.16361 + *B2 sites Sn2 14.63 1.2148 1.20467 1.22502 + B2 sites Sb2 16.43 0.51748 0.53243 0.50296 + B2 sites Ta2 16.2 0.57534 0.58924 0.56176 + B2 sites W2 17.7 0.29247 0.30847 0.2773 + B2 sites Re2 16.6 0.47875 0.49424 0.46375 + B2 sites Os2 16.9 0.4178 0.43387 0.40232 + B2 sites Pt2 18.56 0.20134 0.21584 0.18781 + B2 sites Au2 20.5 0.08975 0.09968 0.08081 + B2 sites Hg2 18.76 0.18486 0.19891 0.17179 + B2 sites Tl2 20.43 0.09234 0.10243 0.08324 + B1 sites Pb2 15.03 1.00000 1.00000 1.00000 + B2 sites Bi2 16.69 0.45952 0.47523 0.44433 + B2 sites Al2 18.83 0.17943 0.19333 0.16654 + B2 sites Si2 16.35 0.53686 0.55149 0.52263 + B2 sites P2 19.73 0.12302 0.13476 0.11231 + B2 sites B2 25.15 0.01518 0.01824 0.01264 + B2 sites C2 24.38 0.0201 0.02385 0.01694 + B2 sites N2 29.60 0.00327 0.0042 0.00254 + *B2 sites Ca2 11.87 5.09756 4.75482 5.46501 + *B2 sites Sr2 11.03 8.18891 7.48691 8.95674 * indicates the cations can replace the Pb cations completely.

These results are in accord with the experimental results related ter, we change the value from 0.95 to 1.02. Fig. 2 shows the content 2+ 2+ 2+ 2+ to CH3NH3Pb1−xBxI3 perovskites (B = Sn , Sr , Cd and Ca ratio R versus different values of c. It can be seen that: i). the value + ions and x = 0.05, 0.10, 0.15), which are synthesized by Javier R decreases with an increase of c; ii). the value of Sn2 is just Navas et al. [10]. Based on the results of XRD analysis, it is de- equal to 1.00 when c = 1.016 based on experimental results of 2+ 2+ termined that the samples CH3NH3Pb0.90B0.10I3 (B = Ca , Sr , 2+ + ref. [15]. This indicates that Sn can replace the Pb sites, and Sn2 cations) have a single phase without PbI as the second 2 therefore parameter c should be less than 1.016; iii). If the param- phase, and the Cd-doped perovskite sample CH3NH3Pb0.90Cd0.10I3 eter c is less than 1.016, then the content ratio R of all 9 kinds of exhibits peaks assigned to PbI plane reﬂections as the second 2 2+ 2+ 2+ 2+ 2+ 2+ 2+ phase, as does the undoped perovskite. Thus we predict only 9 divalent cations including Ca , Sr , Sc , Ti , V , Y , Zr , + + + + + 2+ 2+ kinds of divalent cations which include Ca2 , Sr2 , Sc2 , Ti2 , V2 , Nb , and Sn are all greater than 1.00. Therefore, we identify + + + + 2+ 2+ 2+ 2+ Y2 , Zr2 , Nb2 , and Sn2 can perfectly replace the Pb cations. only 9 kinds of divalent cations including Ca , Sr , Sc , Ti , + + + + + It should be noted that these results were obtained using the V2 , Y2 , Zr2 , Nb2 , and Sn2 that can replace the Pb cations parameter, c = 1.00. In order to determine the role of this parame- completely. D. Ji et al. / Physics Letters A 383 (2019) 2130–2138 2133

Table 2 = 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ Cohesive energy (ECoh) and optimized√ structure √of CH3NH3BI3 (B Ca , Sr , Sc , Ti , V , Y , Zr , Nb ) including lattice parameters (a, b, c), cell volumes (V ). 3 = a/ 2−a = b/ 2−c Unites are Å, Å . Here, n1 a , and n2 c . 3 Cations ECoh (eV) a (Å) b (Å) c (Å) V (Å ) n1 n2 + Sc2 −54.60357 8.511592 11.568610 8.171342 804.609950 −0.03878 0.00124 + Ti2 −55.68894 8.376362 11.231729 8.028360 755.316381 −0.05171 −0.0106 + V2 −54.81828 8.249273 11.190131 8.039050 742.088319 −0.04067 −0.01558 + Y2 −52.86721 9.677705 12.305236 7.704217 917.467833 −0.10078 0.12957 + Zr2 −55.81634 8.554407 11.736797 8.220070 825.305982 −0.02969 0.00978 + Nb2 −56.00060 8.188497 11.272286 8.182977 755.313995 −0.02645 −0.02579 + Sn2 −50.27006 8.798453 12.858145 8.168971 924.170280 0.03353 0.11317 + Ca2 −53.84645 8.815288 12.442120 8.312723 911.746710 −0.00182 0.05853 + Sr2 −49.79440 11.91046 13.092936 6.715717 1047.268703 −0.22257 0.37878

2+ 2+ Fig. 3. Diagram of the formation energies of CH3NH3BxPb1−xI3 (B = Ca , Sr , + + + + + + Fig. 2. The content ratio R versus different c values in the range from 0.95 to 1.02. Sc2 , Ti2 , V2 , Y2 , Zr2 , Nb2 ; x = 0.25, 0.50, 0.75, 1.00).

In addition, the preparation temperature determines the elec- developed by Perdew, Burke, and Ernzerhof (PBEsol) [19]was em- tronic kinetic energy. This temperature is about 373.15 K for the ployed. This approach is the same as the investigation of charged organic-inorganic hybrid perovskites, and the electronic kinetic en- point defects in hybrid perovskites reported by Aron Walsh et al. ergy is given by Eqn. (3), [20]. Umari P. et al. reported that the spin-orbit coupling (SOC) effect had little influence on the geometric structures [21] and = • = • • = EK 1.5 kB T 1.5 373.15 K 0.0258 eV/K 14.44 eV, (3) physical properties, so the SOC effect was ignored in order to so only the cations with a second ionization energy less than 14.44 improve computational efficiency. Based on test results, ultra-soft (eV) can be ionized and form divalent cations, and the electrons pseudopotentials with a cutoff energy of 310 eV were used to de- are free electrons. Eqn. (3)can be applied, and the limit is rep- scribe the interactions between the valence electrons and the ionic resented by the magenta line in Fig. 1. This indicates that the core. Relativistic effects for Pb and I atoms were also included. × × cations associated with the magenta line can be completely ion- A4 4 4 Monkhorst-Pack k-point scheme was used to calculate ized, and completely enter the Pb sites. Although the preparation the absorption spectra. The convergence tolerances for geometry optimization calculations were set to a maximum displacement of temperature considered did not affect the results, we believe that − 5.0 × 10 4 Å, a maximum force of 0.01 eV/Å, a maximum energy the preparation temperature is an important factor. − change of 5.0 × 10 6 eV/atom, and a maximum stress of 0.02 GPa. 3. Analysis of structure and physical properties based on the first = 2+ 2+ 2+ 2+ principle 3.2. Optimized structures of CH3NH3BI3 (B Ca , Sr , Sc , Ti , + + + + + V2 , Y2 , Zr2 , Nb2 , Sn2 ) 3.1. Computation methods The cohesive energy is defined as the difference value be- CH3NH3PbI3 perovskite has two phase transitions; one at a tween the energy per atom of the bulk material at equilibrium temperature of 160 K (orthorhombic to tetragonal) and another and the sum of energy of a free atom in its ground state. For the 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ at a temperature of 330 K (tetragonal to cubic). The orthorhom- CH3NH3BI3 (B = Ca , Sr , Sc , Ti , V , Y , Zr , Nb , bic CH NH PbI structure could be similar in structure to that at 2+ 3 3 3 Sn ) perovskites, the cohesive energy per unit cell (ECoh) can be 0K and could be closer to the ground state in terms of energy. expressed as Eqn. (4), As such, we chose the orthorhombic CH3NH3PbI3 structure as the research object. Fig. 3 represents the CH3NH3PbI3 orthorhombic ECoh = ETotal − EC − EN − 6EH − EB − 3EI, (4) crystal structure with space group Pnma (no. 62) which was con- structed according to the refs. [16,17]. The physical properties were where ETotal is the energy per unit cell obtained by the calculated obtained using the Cambridge Serial Total Energy Package (CASTEP) results, EC, EN, EH, EB, EI are the energy of a free C, N, H, B, I [18] program. The generalized gradient approximation functional atom in its ground state, respectively, as shown in Table 2. All the 2134 D. Ji et al. / Physics Letters A 383 (2019) 2130–2138 cohesive energies are negative values, indicating potential possibly stable structure. Table 2 also shows the lattice parameters, band distance, band angle, and cell volume for the orthorhombic CH3NH3BI3 + + + + + + + + + (B = Ca2 , Sr2 , Sc2 , Ti2 , V2 , Y2 , Zr2 , Nb2 , Sn2 ) perovskites with different cations at the B sites. It can be seen that: (i). The CH3NH3SrI3 perovskite has the largest unit cell volume of 3 1047.268703 Å , and the CH3NH3VI3 perovskite has the smallest unit cell volume of 742.088319 Å3, which results from the different + effective radii since the Sr2 cation with 6 coordination is 0.118 Å, + and V2 cation with 6 coordination is 0.079 Å. (ii). The lattice parameter a is greater than c, which indicates that all the optimized structures are not standard orthorhombic structures. The orthogonal structure will be transformed into a cubic structure with a lattice constant a√0 if the√ lattice parameters a, b and c satisfy the relationship b √= 2a = 2c = 2a√0 [17]. We applied two param- = b/ 2−a = b/ 2−c eters (n1 a , and n2 c ) to describe the degree of distortion for deviation from the cubic structure. It can be seen that only the n1 and n2 parameters for CH3NH3SnI3 perovskite are positive, indicating that the orthogonal structure belongs to the O type, and the others belong to the O types. All the cohesive energies are negative values, indicating potential possibly stable structure. However, whether these new compounds can be stable depends on whether they will phase-separate into competing compounds. These can be predicted through com- paring their calculated formation energies of the compounds. Based on the Ref. [23], the formation energy of a doped atom X (X = N, P, As, F, Cl, Br and I) on a sulfur site can be calculated as the total energy difference reported by Xia C. X. et al. [24], as the following formula (5), f q q E SnS2 : X = E SnS2 : X − E[SnS2]−ni(Ei + μi)

+ q(EF + EV + V ), (5)

q where E[SnS2: X ] and E[SnS2] express the total energies of the X-doped and the SnS2 monolayer nanosheets, respectively. The parameter ni (i = S, Sn and X) is the number of atoms that has been added to or removed from the supercell, μi is the corresponding chemical potential of the constituent referenced to elemental solid/gas with energy Ei . EF is the Fermi level, EV is the energy position of the VBM of a perfect SnS2 monolayer nanosheet. The correction term V aligns the reference potential in the doped cell with that in the bulk with the same size cells. + Similarly, the formation energy of a doped atom B (B = Ca2 , 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ Sr , Sc , Ti , V , Y , Zr , Nb , Sn ) on a lead site (BPb) can be calculated as the total energy difference, f tot tot E q = E (CH3NH3)BxPb1−xI3 − E (CH3NH3)PbI3 B Pb + nPbμPb − nBμB + q(Ef + EV + V ), (6) where x is the doped concentration, nPb and nB are the number of Pb and doped cations, μPb and μB denote the chemical potential of Pb and doped cations, respectively. q is the charge state of the defect, which is caused by the coulomb repulsive force of the 2+ 2+ 2+ 2+ 2+ 2+ Fig. 4. Band structures of CH3NH3B0.5Pb0.5I3 (B = Ca , Sr , Sc , Ti , V , Y , 2+ 2+ transfer of local carriers to the non-local. q(EF + EV + V ) reﬂects Zr , Nb ) calculated using GGA+PBEsol. the free energy changes in the process of forming a non-neutral charge state due to the release or capture of electrons. Owing to The calculated neutral formation energies are shown in Fig. 3. the valance of doped cations being equal to that of Pb, the charge, The formation energies increase with the substitution level in- q, was set as zero. And the formula (6)was rewritten as the for- creasing, and can be ﬁtted linearly as E = 275.50x − 138.1. The mula (7), numerical results are negative when x ≤ 0.50, which indicates that the formation of substitution with x ≤ 0.50 is thermody- f tot 2+ E q = E (CH3NH3)BxPb1−xI3 namically favorable. It can be understood that the Pb cations B Pb of CH3NH3PbI3 perovskite can be completely substituted by the tot 2+ 2+ 2+ 2+ 2+ 2+ 2+ − E (CH3NH3)PbI3 + nPbμPb − nBμB. (7) divalent cations (B = Ca , Sr , Sc , Ti , V , Y , Zr , D. Ji et al. / Physics Letters A 383 (2019) 2130–2138 2135

Fig. 4. (continued) Fig. 4. (continued)

the formula (7), and the values will be negative. Based on the re- + + Nb2 , Sn2 ) with x ≤ 0.50, and all the compounds have a single quest of lowest energy principle, the competing compound could perovskite phase. Moreover, with the substitution level increas- consist of two components including CH3NH3BxPb1−xI3 substituted ≥ ing further, x 0.50, the formation energies become positive val- by the B divalent cations and CH3NH3Pbx B1−x I3 substituted by ues, which suggests that the compounds will phase-separate into the Pb divalent cations. Here, x and x are the content of sub- competing compounds. If the substituted mechanism changed into stitution by B and Pb cations. In addition, when the content of the CH3NH3Pbx B1−x I3 perovskites substituted by the Pb divalent substitution is determined, the formation energy caused by differ- cations, the formation energies will be equal to the reciprocal of ent substitute elements does not change much. It indicates that the 2136 D. Ji et al. / Physics Letters A 383 (2019) 2130–2138

3d2, 3d3, 4d1, 4d2, 4d3, 5s24d10, respectively. In order to ensure the existence of s electrons to couple with p orbitals of I anions, the substituted level of CH3NH3BxPb1−xI3 should be very small ex- + + cept Sn2 , owing to Sn2 cations have the s electron of electronic number of not ﬁlled subshell. The range of permissible bands from −7.710 eV to 0.470 eV and suitable substituted level could produce different CBM and VBM, and imply a high probability of imple- menting bandgap engineering design.

2+ 2+ 2+ 3.4. Density of states of CH3NH3B0.5Pb0.5I3 (B = Ca , Sr , Sc , + + + + + + Ti2 , V2 , Y2 , Zr2 , Nb2 , Sn2 )

Fig. 6 shows the total density of states (TDOS) of 2+ 2+ 2+ 2+ 2+ 2+ 2+ CH3NH3B0.5Pb0.5I3 (B = Ca , Sr , Sc , Ti , V , Y , Zr , + + Nb2 , Sn2 ). It can be seen that: (i). There are forbidden bands for 2+ 2+ CH3NH3B0.5Pb0.5I3 (B = Ca , Sn ) perovskites near the Fermi level. The overlap between the valence band and the conduction 2+ 2+ 2+ 2+ 2+ 2+ band for CH3NH3BI3 (B = Sr , Sc , Ti , Y , Zr , Nb ) perovskites according to the results based on the band structures are also indicated. (ii). The total density of states with the lowest en- 2+ 2+ 2+ 2+ Fig. 5. Diagram of Fermi level of CH3NH3BxPb1−xI3 (B = Ca , Sr , Sc , Ti , + + + + ergy is attributed to the s electrons. The s electrons attributed to V2 , Y2 , Zr2 , Nb2 ). Pb cations, and d electrons attributed to B cations, and p electrons attributed to I anions near the Fermi level clearly forms hybrids 2+ 2+ 2+ 2+ 2+ 2+ 2+ formation energy is sensitive to the content of substitution, but not for CH3NH3B0.5Pb0.5I3 (B = Ca , Sr , Sc , Ti , V , Y , Zr , + + the substituted element. Nb2 , Sn2 ). It should be noted that the overlap bands between the valence band and conduction band for CH3NH3B0.5Pb0.5I3 (B = 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 3.3. Band structures of CH3NH3 B0.5Pb0.5 I3 (B = Ca , Sr , Sc , Sr , Sc , Ti , V , Y , Zr , Nb ) perovskite are attributed 2+ 2+ 2+ 2+ 2+ 2+ + Ti , V , Y , Zr , Nb , Sn ) to the d electrons of the B2 cations.

2+ 2+ The band structures of CH3NH3B0.5Pb0.5I3 (B = Ca , Sr , 4. Conclusions + + + + + + + Sc2 , Ti2 , V2 , Y2 , Zr2 , Nb2 , Sn2 ) are shown in Fig. 4 2+ (a–i). It can be seen that: (i). CH3NH3B0.5Pb0.5I3 (B = Ca , In summary, the quantum-mechanical method has been applied 2+ Sn ) perovskites are semiconductors, and CH3NH3B0.5Pb0.5I3 (B to explain why some divalent cations cannot replace the Pb cations = 2+ 2+ 2+ 2+ 2+ 2+ 2+ Sr , Sc , Ti , V , Y , Zr , Nb ) perovskites are con- of CH3NH3PbI3 perovskite completely. Whether or not the sec- ductors. (ii). For the CH3NH3CaI3 and CH3NH3SnI3 perovskites, the ond ionization energy of the divalent elements is greater than that energy band of spin up completely coincides with that of spin of the Pb element determines whether the divalent elements can down, which indicates that there are no intrinsic magnetic mo- completely enter into the Pb sites. The preparation temperature ments for these configurations. (iii). The energy bands of spin influences the electronic kinetic energy which determines whether 2+ 2+ 2+ up near the Fermi level for CH3NH3BI3 (B = Sr , Sc , Ti , the electrons can be ionized. Only nine kinds of cations including + + + + + + + + + + + + + V2 , Y2 , Zr2 , Nb2 ) are different from that of spin down, in- Ca2 , Sr2 , Sc2 , Ti2 , V2 , Y2 , Zr2 , Nb2 and Sn2 can replace dicating that there are intrinsic magnetic moments and could be the Pb cations. We believe that the quantum-mechanical method controlled by an external magnetic field. (iv). As a first-order ap- can provide a new approach for identifying potential materials 2+ proximation, CH3NH3PbI3 substituted in the Pb position by B for substituting Pb sites in perovskite, such as APbX3 (A = NH4, − + cations can be understood as (1 x)CH3NH3PbI3 (x)CH3NH3BI3, H3NOH, CH3NH3, H3NNH2, (CH2)3NH2, NH2(CH2)NH2, C3N2H5, where x is the substituted level. This is similar to the results (CH3)2NH2, (C2H5)NH3, C(NH2)3, and (CH3)4N, where X = F, Cl, based on ref. [22]. When the (x)CH3NH3BI3 was substituted Br, and I)). The results based on first principle indicates that the − in (1 x)CH3NH3PbI3, the Fermi level of both CH3NH3BI3 and bandgaps of stable CH3NH3B0.5Pb0.5I3 structure are 2.822, 0.00, CH3NH3PbI3 perovskites will achieve a uniform value, which is 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.203 eV, corresponding to B = 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ the Fermi level of CH3NH3Pb1−xBxI3 perovskite. The bandgap of Ca , Sr , Sc , Ti , V , Y , Zr , Nb , Sn , respectively. orthorhombic CH3NH3BI3 has a high probability to control the The different CBM and VBM characteristic with the suitable sub- bandgaps of CH3NH3Pb1−xBxI3 because the bandgap difference be- stituted level has potential application in band gap engineering tween CH3NH3PbI3 with 1.656 eV [17] and CH3NH3B0.5Pb0.5I3 design. from 0.00 eV to 2.822 eV. A diagram of the Fermi level of CH3NH3BxPb1−xI3 is shown in Fig. 5, which indicates both the sub- Acknowledgements stituted elements and the substituted level influence the energy of the Fermi level, and control the range from −7.710 eV to 0.470 We thank the National Science Foundation of China under Con- eV. The difference between the Fermi level of CH3NH3PbI3 with tract 11504078, the Key Project of the Education Department of −2.379 eV shown in red dashed line and the others indicates the Guizhou Province, China, (No. KY2015379), the Joint Funds of the effective substitution. The difference between the conduction band Department of Science and Technology of Guizhou Province, Liu- minimum (CBM) and the value valence band maximum (VBM) is Panshui Administration of Science and Technology and LiuPanshui defined as the band gap (Eg), and the Fermi level often be used Normal University, China, under Contract No. LH[2014]7449, the as the VBM. For the CH3NH3PbI3, the CBM are mainly derived Research Foundation for Advanced Talents of LiuPanshui Normal from p orbitals of Pb cations, and the VBM is occupied s orbitals University, China, (Grant No. LPSSYKYJJ201404), Hebei Province of Pb cation possess coupling with p orbitals of I anions [25]. As High Education School Science and Technology Research Project, + + + we know, the electron configuration of cations Ca2 , Sr2 , Sc2 , China, (No. BJ201613), and Science and Technology Fund of Hebei + + + + + + Ti2 , V2 , Y2 , Zr2 , Nb2 , Sn2 are 3s23p6, 4s23d104p6, 3d1, Agricultural University, China, under Contract No. LG201812. D. Ji et al. / Physics Letters A 383 (2019) 2130–2138 2137

2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ Fig. 6. The total density of states (TDOS) of CH3NH3B0.5Pb0.5I3 (B = Ca ,Sr ,Sc ,Ti ,V ,Y ,Zr ,Nb ) calculated using GGA+PBEsol.

References [9] F. Zheng, H. Takenaka, F. Wang, N.Z. Koocher, A.M. Rappe, First-principles cal- culation of the bulk photovoltaic effect in CH3NH3PbI3, and CH3NH3PbI3-xClx, [1] Woon Seok Yang, Byung-Wook Park, Eui Hyuk Jung, Nam Joong Jeon, Young J. Phys. Chem. Lett. 6 (2014) 31–37. Chan Kim, Dong Uk Lee, Seong Sik Shin, Jangwon Seo, Eun Kyu Kim, Jun Hong [10] J. Navas, A. Sánchez-Coronilla, J.J. Gallardo, N.C. Hernández, J.C. Piñero, R. Al- Noh, Sang Il Seok, Iodide management in formamidinium-lead-halide-based cántara, C. Fernández-Lorenzo, D.M.D. los Santos, T. Aguilar, J. Martín-Calleja, perovskite layers for efficient solar cells, Science 356 (2017) 1376–1379. New insights into organic-inorganic hybrid perovskite CH3 NH3PbI3 nanoparti- 2+ 2+ [2] S. Repp, E. Harputlu, S. Gurgen, Mike Castellano, Nora Kremer, Nils Pompe, cles. An experimental and theoretical study of doped in Pb sites with Sn , 2+ 2+ 2+ Jakob Wörner, Anke Hoffmann, Ralf Thomann, Fatih M. Emen, Stefan We- Sr , Cd and Ca , Nanoscale 7 (2015) 6216. + ber, Kasim Ocakoglu, Emre Erdem, Synergetic effects of Fe3 doped spinel [11] D.H. Ji, S.L. Wang, X.Z. Ge, Q.Q. Zhang, C.M. Zhang, Z.W. Zeng, Y. Bai, The maxi- Li4Ti5O12 nanoparticles on reduced graphene oxide for high surface electrode mum predicted content of cation vacancies in inorganic and organic-inorganic hybrid supercapacitors, Nanoscale 7(1) (2018) 11222. perovskites: the role of the tolerance factor, Phys. Chem. Chem. Phys. 19 (2017) [3]. J.T Yang, S.J. Luo, Y.C. Xiong, Magnetic mechanism investigations on K and Mn 17121–17127. co-doped diluted magnetic semiconductor (Sr, K)(Zn, Mn)2As2, J. Magn. Magn. [12] E. Edri, S. Kirmayer, S. Mukhopadhyay, K. Gartsman, G. Hodes, D. Ca- Mater. 407 (2016) 334. hen, Elucidating the charge carrier separation and working mechanism of [4] M. Ishikawa, T. Oka, Y. Fujita, H. Sugiyama, Y. Saito, K. Hamaya, Spin relax- CH3NH3PbI3-xClx perovskite solar cells, Nat. Commun. 5 (2014) 3461. ation through lateral spin transport in heavily doped n-type silicon, Phys. Rev. [13] G.D. Tang, D.H. Ji, Y.X. Yao, S.P. Liu, Z.Z. Li, W.H. Qi, Q.J. Han, X. Hou, D.L. Hou, B 95 (11) (2017) 115302. Quantum-mechanical method for estimating ion distributions in spinel ferrites, [5] Jia Liang, Zonghao Liu, Longbin Qiu, Zafer Hawash, Lingqiang Meng, Zhifang Appl. Phys. Lett. 98 (2011) 072511. Wu, Yan Jiang, Luis K. Ono, Yabing Qi, Enhancing optical, electronic, crystalline, [14] G.D. Tang, D.L. Hou, W. Chen, X. Zhao, W.H. Qi, Quantum-mechanical model for and morphological properties of cesium lead halide by Mn substitution for estimating the number ratio between different valence cations in multiatom high-stability all-inorganic perovskite solar cells with carbon electrodes, Adv. compounds, Appl. Phys. Lett. 90 (14) (2007) 144101. Energy Mater. (2018) 1800504. [15] P. Kanhere, S. Chakraborty, C.J. Rupp, R. Ahuja, Z. Chen, Substitution induced [6] B. Slimi, M. Mollar, I. Ben Assaker, I. Kriaa, R. Chtourou, B. Marí, Perovskite band structure shape tuning in hybrid perovskites (CH3NH3Pb1−xSnxI3) for ef- FA1−xMAxPbI3 for solar cells: films formation and properties, Energy Proc. 102 ficient solar cell applications, RSC Adv. 5 (130) (2015) 107497–107502. (2016) 87–95. [16] E. Menéndez-Proupin, P. Palacios, P. Wahnón, J.C. Conesa, Self-consistent rela- [7] M. Saliba, T. Matsui, K. Domanski, Ji-Youn Seo, A. Ummadisingu, S.M. Zakeerud- tivistic band structure of the CH3NH3PbI3 perovskite, Phys. Rev. B 90 (2014) din, J.P. Correa-Baena, W.R. Tress, A. Abate, A. Hagfeldt, M. Grätzel, Incorpo- 045207. ration of rubidium cations into perovskite solar cells improves photovoltaic [17] D.H. Ji, X.J. Xiao, C.M. Zhang, X.L. Li, M.Z. Hu, Y. Yin, Regulatory band gap of va- performance, Science 354 (2016) 206–209. cancy at the B sites in CH3NH3Pb1−xI3 perovskite, Mod. Phys. Lett. B 30 (2016) [8] J. Burschka, N. Pellet, S.J. Moon, R. Humphry-Baker, P. Gao, M.K. Nazeeruddin, 1650294. M. Grätzel, Sequential deposition as a route to high-performance perovskite- [18] V. Milman, B. Winkler, J.A. White, C.J. Pickard, M.C. Payne, E.V. Akhmatskaya, sensitized solar cells, Nature 499 (2013) 316–319. R.H. Nobes, Electronic structure, properties, and phase stability of inorganic 2138 D. Ji et al. / Physics Letters A 383 (2019) 2130–2138

crystals: a pseudopotential plane-wave study, Int. J. Quant. Chem. 77 (2000) [22]F. W. Wang, J. Su, L. Zhang, Y. Lei, Y. Wang, D. Lu, Y. Bai, Growth of mixed-halide 895. perovskite single crystals, CrystEngComm 20 (2018) 1635. [19] John P. Perdew, Adrienn Ruzsinszky, Gábor I. Csonka, Oleg A. Vydrov, Gustavo [23] C.G. Van de Walle, J. Neugebauer, First-principles calculations for defects and E. Scuseria, Lucian A. Constantin, Xiaolan Zhou, Kieron Burke, Restoring the impurities: applications to III-nitrides, J. Appl. Phys. 95 (2004) 3851. density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. [24] C.X. Xia, Y.T. Peng, H. Zhang, T.X. Wang, S.Y. Wei, Y Jia, The characteristics of n- 100 (2008) 136406. and p-type dopants in SnS2 monolayer nanosheets, Phys. Chem. Chem. Phys. [20] Aron Walsh, O. Scanlon, Shiyou Chen, X.G. Gong, Su-Huai Wei, Self-regulation 16 (2014) 19674. mechanism for charged point defects in hybrid halide perovskites, Angew. [25] T. Umebayashi, K. Asai, T. Kondo, A. Nakao, Electronic structures of lead iodide Chem. Int. Ed. 54 (2015) 1791. based low-dimensional crystals, Phys. Rev. B 67 (2003) 155405. [21] P. Umari, E. Mosconi, F. De Angelis, Relativistic GW calculations on CH3NH3PbI3 and CH3NH3SnI3 perovskites for solar cell applications, Sci. Rep. 4 (2014) 4467.