First-principles prediction into robust high-performance photovoltaic double perovskites A 2 SiI 6 (A = K, Rb, Cs)
Qiaoqiao Li, Liujiang Zhou, Yanfeng Ge, Yulu Ren, Jiangshan Zhao, Wenhui Wan, Kaicheng Zhang, Yong Liu
FFirst-principles prediction into robust high-performance photovoltaicdouble perovskites A SiI (A = K, Rb, Cs) Qiaoqiao Li, Liujiang Zhou, Yanfeng Ge, Yulu Ren, JiangshanZhao, Wenhui Wan, Kai-Cheng Zhang, and Yong Liu ∗ State Key Laboratory of Metastable Materials Science and Technology andKey Laboratory for Microstructural Material Physics of Hebei Province,School of Science, Yanshan University, Qinhuangdao 066004, China Institute of Fundamental and Frontier science,University of Electronic Science and Technology, Chengdu 610054,China Key Laboratory of Soft Chemistry and Functional Materials of MOE,School of Chemical Engineering, Nanjing Universityof Science and Technology, Nanjing, 210094, China College of Mathematics and Physics,Bohai University, Jinzhou 121013, China
Abstract
Despite the exceeding 23% photovoltaic efficiency achieved in organic-inorganic hybrid perovskite solarcells obtaining, the stable materials with desirable band gap are rare and are highly desired. With the aidof first-principles calculations, we predict a new promising family of nontoxic inorganic double perovskites(DPs), namely, silicon (Si)-based halides A SiI (A = K, Rb, Cs; X = Cl, Br, I). This family containing theearth-abundant Si could be applied for perovskite solar cells (PSCs). Particularly A SiI exhibits superbphysical traits, including suitable band gaps of 0.84-1.15 eV, dispersive lower conduction bands, smallcarrier effective masses, wide photon absorption in the visible range. Importantly, the good stability at hightemperature renders them as promising optical absorbers for solar cells. PACS numbers: 71.20.-b,78.20.Bh,78.20.Ci,71.15.Mb ∗ Corresponding author: [email protected] or [email protected] a r X i v : . [ phy s i c s . a pp - ph ] F e b . INTRODUCTION Since the organic-inorganic hybrid perovskite was first proposed in 2009, the photovoltaic ef-ficiency has been significantly jumped to over 23% that is close to the maximum efficiency ofcrystalline silicon solar cell[1–3]. The hybrid perovskite has a chemical formula ABX , where A + is organic cation (e.g., CH NH +3 , CH(NH ) +2 ), B is the post-transition metal with ns electronicconfigurations (Pb , Sn , Ge , Sb , Bi ), and X − is the halide anion (Cl − , Br − , I − ). Theunique traits, including the ideal direct band gaps, high dielectric constants, shallow defect levels,low electron-hole recombination rates, and long carrier lifetime contribute to the prominent opto-electronic performances of organic-inorganic hybrid perovskites [4–10]. Despite the remarkableefficiencies of the hybrid lead-based perovskites, as seen in CH NH PbI (MAPbI ) [2, 11–16],the poor long-term stability against temperature, oxygen, moisture and exposure to light causeschemical and optical degradation that hinder their wide use [17–20]. This poor stability is as-sociated with the volatilization and disordered vibrations of small organic cations [18, 19, 21].Moreover, the toxicity of water-soluble lead compounds drives the exploitation of alternative in-organic lead-free halide perovskite materials with improved stability [22].Recently, the inorganic DPs (A B(I)B(III)X , A B(IV)X ) have been proposed as environmen-tally friendly and promising alternatives for lead-free hybrid perovskites [23]. However, the light-absorbing materials with suitable and direct band gaps are extremely scarce. For A B(I)B(III)X type, Volonakis et al. have performed a theoretical screening on Cs B(I)B(III)X , B(I) = Cu, Ag,Au, B(III) = Bi, Sb, some of which a portion of materials with appropriate but indirect band gapare predicted [24]. Zhao et al. also screened 64 compounds and only 5 potential direct-band-gaplight absorbing materials were obtained[25]. The same type of Cs AgBiBr has been synthesizedexperimentally and achieved 2.43% PCE [26], the low efficiency may be associated with the largeindirect band gap of about 2 eV [27]. For A B(IV)X type, there are several materials with suitableband gaps known in theory and experiment, such as Cs TeI , Cs SnI and Cs TiI [28–30], butonly Cs SnI possesses direct band gap. Therefore, the exploration of inorganic DPs with directand appropriate band gaps are highly desired. In addition, the fact that crystalline Si solar cells arewidely commercialized but more costly in production has inspired us to explore the properties ofSi-based DPs compounds in theory.In this paper, we initially calculated the structure and band gap for a series of earth-abundantSi-based DPs A SiX (A = K, Rb, Cs, X = Cl, Br, I ) based on the first-principles calculations.2hree iodides A SiI (A = K, Rb, Cs) are found to have suitable direct band gaps of 0.84-1.15 eV.The electronic, optical properties of the three candidates are systemically investigated. The resultsindicate that the three A SiI are more suitable for n-type semiconductors and can be utilized ashigh efficiency optical absorbers. Importantly, K SiI and Rb SiI exhibit high thermal stabilityand thus hold great promise for future optoelectronic devices. II. COMPUTATIONAL DETAILS
Density hybridized functional theory calculations were performed by the Vienna ab initio sim-ulation package with the projected augmented-wave pseudopotential[31, 32]. The generalized gra-dient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) and that revised for solids(PBEsol) exchange-correlation functional was employed for the structural relaxation[33–35]. Theconvergence criteria of the total energy and Hellmann-Feynman force on atom were set to 1 × − eV and 0.001 eV/ ˚A and the cut-off energy for the plane-wave basis was set to be 400 eV. In or-der to avoid the underestimates of the band gaps of semiconductors, the Heyd-Scuseria-Ernzerhof(HSE06) functional, which incorporates 25% Hartree-Fock exchange with a screening parameterof ω = 0.11 bohr − in addition to 75% exchange-correlation from the PBE hybrid functional, wasadopted to correct the electronic and optical properties [36]. Three-dimensional k-meshes weregenerated using the Gamma 5 × × s and 3 p orbitals for silicon, and the 5 s and 5 p orbitals for iodine and carbon, and the 3 s , 3 p , 4 s , 4 p , 5 s , 5 p , 6 s orbitals for the metals were taken[39]. III. MAIN RESULTS AND DISCUSSIONS
DP is a defect variant for typical perovskite ABX structure such as MAPbI [40]. In contrast,for the DP with the general formula A BX , half of the octahedral B-sites atoms are missing,generating nearly isolated octahedral [BX − ] units and presenting as the cubic Fm m phases[28].Represented by Cs SiI , the DP structure is shown in Fig. 1(a). We can see that the vacancy-3rdered DPs formed by face-centered [SiI − ] units and A-site Cs cations uniformly occupy thevoids outer the octahedrons. In our calculations, structural parameters of a series of optimizedA SiX DPs (A=K, Rb, Cs; X=Cl, Br, I) are provided in Table S1 (see Ref. [56]). It is found thatthe lattice constants and Si-X bond lengths gradually increase along with the atomic number ofA-site cation and X-site anion severally. Cs Si I (a) (b)(c) (d) FIG. 1. The crystal structure of Cs SiI with space group Fm m. (b) The band gaps of A SiX (A=K, Rb,Cs; X=Cl ,Br ,I) based on HSE06 functional. (c) The total electronic charge density of Cs SiI that areviewed from (1 0 0) planar. The isosurface level is 0.5 eV ˚A − . (d) ELF map sliced of (1 0 0) planar ofCs SiI . Because there are no related studies on Si-based DPs, and HSE06 hybridized functional pre-dicting band gaps of A B(IV)X type compounds are in good agreement with their experimentalvalues, such as Cs SnI , Cs TiI [30, 41]. Therefore, HSE06 functional is adopted for subsequentelectronics and optics investigations.The band gaps of A SiX (A=K, Rb ,Cs; X=Cl ,Br ,I) DPs are all direct types. Figure 1(b)displays their band gap values, range from 4.71 to 0.84 eV, including three small gaps with I-4ontaining compounds, namely, K SiI , Rb SiI and Cs SiI , which are 0.84 eV, 0.96 eV and 1.15eV, respectively. For compounds that have the same A-site cation, the gaps follow a tendency ofA SiCl > A SiBr > A SiI that is consistent with the trend of MAPbI (X = Cl, Br ,I) [42].This trend can be analyzed by the electronegativity and density of electronic states (DOS). Wepresent the charge density of Cs SiI in Fig. 1(c). As shown, the charge density mainly distributeover I atoms, while Si atoms has few, indicating charges transfer from the less electronegativeSi to the more electronegative I. The overlap of the orbitals along the bonding axis reveals its σ bonding type. And taking the DOS of Cs SiX as an example (see Ref. [56]), valence band edgesmainly origin from X atoms, while both X and Si atoms contribute to conduction band edges inthree cases. According to Pauling electronegativity[43], halogen atoms have the strength order ofI (2.66) < Br (2.96) < Cl (3.16). The higher electronegativity of X element, the stronger bondinteraction between X and Si atoms, thus raising the conduction band and generating larger bandgap. Whereas in the same X-site anion situation, the gaps form a tendency of Cs SiX > Rb SiX > K SiX and the reason will be explored later in detail.To achieve deeper insight into the bonding nature, we analysed the electron localization func-tion (ELF). The ELF renormalizes the values range from 0.00 to 1.00. And the values of 1.00and 0.50 characterize fully localized and delocalized electrons, respectively, while 0.00 denotes avery low charge density[44]. As displayed in Fig. 1(d), the large red region around I, correspond-ing to values about 0.90, implies the dominated localized features of valence electrons. Althoughlimbic region of the Si-I bond is in green, it demonstrates weakly delocalized behavior of theirhigh-energy orbital valence electrons.According to the Shockley-Queisser limit[45], which is utilized to evaluate the theoretical pho-tovoltaic conversion efficiency (PCE) in a single junction solar cell, a superior light absorbershould possess a band gap ranging from 1.0 to 1.5 eV so as to idealize the efficiency[35]. Intandem devices, the maximum PCE requires a rear cell with a gap of 0.9 to1.2 eV[46]. Therefore,we unify the ideal band gap to be in the range of 0.9-1.5 eV. Considering the slight deviation of theband gap of K SiI (0.84eV), we here have screened three candidates, K SiI , Rb SiI and Cs SiI (A SiI ) DPs that can be applied in single or tandem solar cells. Moreover, the spin-orbit coupling(SOC) effect is further considered to correct the band. The corrected values are 0.71 eV, 0.82 eV,and 0.99 eV for K SiI , Rb SiI , and Cs SiI , respectively. These effects on band gaps are muchsmaller than that of Cs SnI or Cs TeI due to the quite lighter B-site element[41].Figure 2(a)-2(c) show the projected band structures of the three promising I-based DPs. We can5 IG. 2. (a)-(c) The projected energy band structures of A SiI (A=K, Rb, Cs) DPs calculated by HSE06functional. Fermi-level is set as zero. (d)-(f) PDOS for Si and I atoms of A SiI DPs. see that in all three cases, the main components of the band edges are analogous to the situationwhen the anion are Cl − and Br − . With the A-site elements barely involve in the formation of bandedges, the lower conduction bands are dominated by the Si and I elements, and the upper valencebands mostly come from the I elements. Both conduction band minimum (CBM) and valenceband maximum (VBM) locate in the Γ points, proving direct band gaps in these A SiI DPs. Tovisualize the occupied states, Fig. S2(a)-S2(b)[56] provide the wave function distribution plots ofCs SiI at VBM and CBM in real space, which can further support our results.To acquire more band information, we analyze the projected density of electronic states (PDOS)of Si and I atoms near Fermi-level. As shown in Fig. 2(d)-2(f), I-5 p and hybridized Si-3 s and I-5 p orbitals separately constitute the majority of valence and conduction band edges in all three cases.The DOS peaks near the Fermi-level of the three I-based DPs have a significant trend of K SiI < Rb SiI < Cs SiI , indicating the increasing tendency of I-5 p bonding states and anti-bondingstates between Si-3 s and I-5 p orbitals, resulting in the band gap trend of K SiI < Rb SiI < Cs SiI . 6 a) (b) (c) -6.0e-76.0e-73.6e-71.2e-7-1.2e-7-3.6e-7 FIG. 3. (a) Wave fuction distributions of VBM related to Cs SiI . (b) and (c) are the wave function mapssliced from [1 0 0] direction of VBM and CBM for Cs SiI , respectively. Both slices renormalize the valuerange from -6.0e − to 6.0e − , and the common value bar are displayed in the right side. It is noticed that above the Fermi level, there exists a well dispersive and isolated band with abandwidth of 1.32 eV, 1.20 eV and 1.03 eV for K SiI , Rb SiI , and Cs SiI , respectively [Fig.2(a)-2(c)]. The wide band dispersion indicates the potential favorable electron mobility. Whereasthe dispersion of valence bands is weaker than that above conduction bands, which can be typicallyillustrated by the wave function distributions at VBM and CBM. Taking Cs SiI as an example,as shown in Fig. 3(a)-3(c), the states of VBM are distributed over partial I atoms, since there areno wave fuction distributions over one third I atoms [Fig. 3(a)]. But the wave fuction of CBMsignificantly spreads over all Si and I atoms in our observations. Owing to the smaller absolutevalue of wave function about CBM [Fig. 3(b)-3(c)], the large delocalized traits related to hybridSi-3 s and I-5 p states are also observed, producing the more dispersive conduction bands than theupper valence bands near the Fermi level.The well dispersive band directly reflects the small carrier effective mass. By using Equation1,the carrier effective masses for the K SiI , Rb SiI and Cs SiI were calculated around Γ points. m ∗ = 1 h · ∂ E ( k ) ∂k (1)As their dispersive conduction bands states revealed, all three DPs possess small effectiveelectron masses [Table I], indicating benign conductivity. The heavier hole masses are alsoin consistence with the prior wave function analysis, reflecting that A SiI DPs are more suit-able for n-type semiconductors. The effective masses of all the three A SiI DPs are slightly7
ABLE I. The calculated carrier effective masses for the K SiI , Rb SiI and Cs SiI based onHSE06+SOC method. m ∗ e = electron effective mass; m ∗ h = effective mass of a hole.Compounds m ∗ e /m m ∗ h /m Γ − X Γ − Y K SiI SiI SiI larger than MAPbI [47], but smaller than other A B(IV)X type compounds, such as Rb PtI and Cs SnI [41]. The electron effective masses of these three DPs have an increasing tendency:K SiI < Rb SiI < Cs SiI , which accords with the dispersion degree of their first conductionbands [Fig. 2(a)-2(c)].The band structure can directly determine the performance of photon absorption. Then the op-tical properties of the three A SiI DPs were investigated by calculating the frequency dependentdielectric tensor ε ( ω ) , ε ( ω ) = ε ( ω ) + iε ( ω ) , where ε ( ω ) and ε ( ω ) are the real and imag-inary parts in several, and ω is the photon frequency[48]. Utilizing dielectric tensor, the opticalabsorption coefficient α ( ω ) can be obtained by the following Equation2. α ( ω ) = √ ωc · (cid:20)(cid:113) ε ( ω ) + ε ( ω ) − ε ( ω ) (cid:21) / (2) FIG. 4. The optical absorption spectra of the three A SiI DPs calculated by HSE06 functional.
8s shown in Fig. 4, the three A SiI DPs happen to exhibit an absorption peak in the visibleregion. With the increase of band gap, the edges of absorption spectra show a blue shift trend.The absorption ability of these three DPs in visible region follows the trend of K SiI > Rb SiI > Cs SiI based on absorption peak and band width. The wide absorptions in visible regionare associated to their dispersive lower conduction band and band gap. To evaluate the opticalabsorption capacity of the three DPs, we have calculated as well the photon absorption coefficientsof monocrystalline silicon for the sake of comparison. As shown in Fig. S3[56], the indirect bandgap value of 1.19 eV is consistent with the experimental value of 1.12 eV[3]. The absorption peakof A SiI in the visible region is lower than that of Si, but the absorption width is significantlywider. Considering crystalline silicon solar cells have achieved efficiency exceeding 25%[3], thethree A SiI DPs seem to be promising lead-free perovskite optical absorption layers.
FIG. 5. (a) Band structure and parity at Γ of Cs SiI , the cyan lines represent the valence bands correspond-ing to VBM-4. (b) The cyan line represents the sum of transition matrix elements from the valence bandwhere VBM-4 is located to the conduction band located by CBM, and the black line represents the sum oftransition dipole moment from the valence band where VBM is located to the conduction band located byCBM. To probe the origin of the strong light-harvesting capability of the above three A SiI DPs, wehave analyzed the parity-forbidden transitions via calculating the parity and transition dipole mo-ment between valence bands and the conduction bands of interest. Taking Cs SiI as an example,9 ABLE II. Computed elastic constants C , C and C of three A SiI DPsCompounds C (GPa) C (GPa) C (GPa) stabilityK SiI SiI SiI the VBM at the Γ point exhibits the even parity, possessing a triple degeneracy and the CBM hasalso even parity [Fig. 5(a)]. Therefore, the transition from VBM to CBM would not occur andfinally produces the zero transition matrix elements. The lower three valence bands below the de-generately top three valence bands are also threefold degenerate and thus are denoted as VBM-4.VBM-4 owns the odd parity, indicating the transition from VBM-4 to CBM is allowed. As a result,there is transition dipole moment from VBM-4 to CBM. Our result reveals that the direct transi-tion from VBM to CBM is forbidden and the transition matrix elements are mainly originatedfrom transition between VBM-4 and CBM. The dipole-moment-allowed direct optical transitionsof Cs SiI , K SiI and Rb SiI are 1.73 eV, 1.57 eV and 1.63 eV, respectively. In general, accord-ing to the distributions of transition matrix elements in Fig. 5(b), the three A SiI DPs maintaintheir absorption characteristics in a wide visible region, suggesting the potential optical absorbersfor solar cells. It is worthy to note that K SiI would achieve the best optical performance amongthe three DPs due to the best optical transition gap of 1.57 eV according to the Shockley-Queisserstandard [45] and the optimum optical absorption in the visible region.Stability is one of the most important part of judging the application potential of materials.Therefore, we calculated the elastic constants to evaluate mechanical stability of the three I-basedDPs. For cubic crystal system, the elastic constants satisfy the Born stability criterion C − C > , C > and C + 2 C > , manifesting mechanical stability[49]. These elastic constants aredefined as C ij = 1 V · (cid:18) ∂ E∂ε i ∂ε j (cid:19) (3)Here E is the energy of the crystal, V denotes equilibrium volume, and ε gives a strain. TableII lists the elastic constants of the three A SiI DPs. Our results reveal the mechanical stability ofthe three A SiI DPs, since the Born stability criterion are well matched.10e also calculated the decomposition enthalpy ( ∆ H ) to evaluate the thermodynamical stability.The ∆ H is defined as ∆ H = E ( ASiI ) + E ( AI ) − E ( A SiI ) (4) TABLE III. The calculated decomposition enthalpy ( ∆ H in meV/atom) for three A SiI DPs based onPBEsol functional and Bader and Mulliken (in e) Charges in three A SiI DPs using HSE06 functional..Compounds ∆ H Bader Charge Mulliken Chargemental Si I mental Si IK SiI SiI SiI The detailed ∆ H are listed in Table III. The positive values of the three compounds indicatetheir thermodynamics stability, of which Rb SiI owns the maximum decomposition energy. Thecompositional stability can be also demonstrated by the charge transfer between atoms upon itsformation. We analyzed the Bader charge and the Mulliken charge[50, 51] and Table III lists thecharge transfer of each atom in A SiI . It shows that the metal and Si atoms are positively chargedand thus can be regarded as electron donors, while iodine is the only electron acceptor upon theformation of system. Focusing on the amount of charge obtained by iodine in all three cases,Rb SiI gains the most electrons in the two cases, indicating the optimum combination stability inthe three DPs, which is consistent with the result of decomposition energy. In addition, consideringthe facts that the Pauling electronegativity of Sn (1.96) is stronger than that of Si (1.90)[43] andCs SnI has been extensively synthesized in experiments[28, 29, 52, 53], so it is believed that thethree Si-based DPs have the great feasibility of experimental fabrications.According to international standard (IEC 61646 climatic chamber test), the long-term stabilityof the 85 ◦ C is required for PSCs. Hence, the molecular dynamics (MD) of the three I-based DPsat the temperature of 400K were simulated. Figure 6 shows the potential energy per formula (f.u.)and the final structures of K SiI and Rb SiI , which can be seen that the both potential energyfinally converges to a range less than 50 meV/atom, indicating outstanding dynamic stability. Thewell maintained structures of K SiI and Rb SiI also prove their stabilities. However, Cs SiI IG. 6. (a) and (b) are the simulated MD potential energy and final structure of K SiI and Rb SiI DPs atthe temperature of 400 K. was found to be dynamically unstable at 400 K [Fig. S4[56]] or at room temperature 300 K, whichis similar to Cs AgBiI [54]. So we calculated the integrated crystal orbital Hamilton population(ICOHP) to quantitative description the Si-I bond strength[55]. As demonstrated by Table S2[56],K SiI has the maximum value of 1.24, meaning the maximum bonding interactions in Si-X bondswithin three DPs. While, Cs SiI has the minimum value of 1.21. Therefore, the stability problemof Cs SiI stems from the longer Si-I bonding and the weaker Si-I covalency. IV. CONCLUSION
Using first-principles calculation, we explored and predicted a new kind of Si-based DPs forphotovoltaic applications. The results show K SiI , Rb SiI and Cs SiI DPs exhibit excellentelectronic, optical and stable properties, such as reasonable band gaps, small carrier effectivemasses, wide photon absorption in visible range, providing more options for the development oflead-free perovskite optical absorbers. These three DPs are more suitable for n-type semicon-ductors due to their well dispersive lower conduction bands and smaller electron effective masses.K SiI could achieve the best optical performance in the three DPS due to its best optical transitiongap of 1.57 eV and optimum optical absorption in the visible region. According to the compre-hensive stability results, Rb SiI has the best stability, followed by K SiI . Although Cs SiI hasdynamic stability problems, the prospects of the new family of DPs for PCSs are promising.12 CKNOWLEDGMENTS
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