Efficient Passivation of Surface Defects by Lewis Base in Lead-free Tin-based Perovskite Solar Cells

Lead-free tin-based perovskites are highly appealing for the next generation of solar cells due to their intriguing optoelectronic properties. However, the tendency of Sn2+ oxidation to Sn4+ in the tin-based perovskites induces serious film degradation and performance deterioration. Herein, we demonstrate, through the density functional theory based first-principle calculations in a surface slab model, that the surface defects of the Sn-based perovskite FASnI3 (FA = NH2CHNH2+) could be effectively passivated by the Lewis base molecules. The passivation performance of Lewis base molecules in tin-based perovskite is tightly correlated with their molecular hardness. We reveal that the degree of hardness of Lewis adsorbate governs the stabilization via dual effects: first, changing the stubborn spatial distribution of tin vacancy (VSn) by triggering charge redistribution; second, saturating the dangling states while simultaneously reducing the amounts of deep band gap states. Specifically, the hard Lewis base molecules like edamine (N-donor group) and Isatin-Cl (Cl-donor group) would show a better healing effect than other candidates on the defects-contained tin-based perovskite surface with a somehow hard Lewis acid nature. Our research provides a general strategy for additive engineering and fabricating stable and high-efficiency lead-free Sn-based perovskite solar cells.


Introduction
Perovskite solar cells (PSCs) have been under the spotlight due to their superior optoelectronic properties and solution processability for the next 3 generation of photovoltaic technology. 1,2 In the past decade, the power conversion efficiency (PCE) of lead-based PSCs boost rapidly from 3.8% to 25.7%, comparable with the commercial silicon solar cell. 3 However, the toxicity of lead and potential environmental hazard hinder their practical application. 4 As an alternative, a series of lead-free perovskite materials, including Sn, Bi, and Ge-based perovskites have been widely explored. [5][6][7][8] In particular, tin-based alternatives resemble their leadcontained counterpart, as the neighboring Sn and Pb elements in the periodic table share a similar valence structure. 9 The alike electronic configurations and atomic radius between Pb and Sn stabilize the octahedral inorganic ABX 3 (A = organic or inorganic cation, B = metal ion, X = halogen) frameworks, leading to comparable electronic structure and carriers dynamics. 10 However, so far the highest PCE of 14.81% achieved in FASnI 3 PSCs is generally inferior to that of lead-based PSCs. 11 The main reason for this inferiority is the easy oxidation of Sn 2+ to Sn 4+ in the tinbased perovskite, leading to a degradation of performance. 12,13 From a chemical perspective, lone pair electrons in Sn 2+ have a stronger chemical activity compared with that of Pb 2+ due to the absence of the lanthanide shrinkage effect. 14 The Sn 2+ is prone to lose two 5s electrons transferred to Sn 4+ , accounting for the oxidation of tin-based perovskite. This oxidation process further accelerates the decomposition of perovskite film 15,16 akin to the process: 4 2FASnI 3 + O 2 → SnI 4 + SnO 2 + 2FAI (1) A recent work also proved the strong coupling between film oxidation and tin vacancy (V Sn ) defect formation, which is the dominant type of defect for both the Sn-rich and I-rich situations in FASnI 3 . 17 Moreover, the energy level of Sn-5s orbital is higher than that of Pb-6s orbital, impelling both the defect formation and tin oxidation. 18 The lowered redox potential of Sn 2+ /Sn 4+ at +0.15 eV makes Sn 2+ easily oxidized to Sn 4+ . 19,20 This is associated with a higher energetically lying antibonding orbital and thus weaker Sn-I bonds than the Pb-contained compounds. The breaking of Sn-I bond also facilitates the formation of V Sn defects 17 via: 2Sn 2+ = Sn 2+ + 2h + + V Sn + Sn 0 bulk = Sn 4+ + V Sn + Sn 0 bulk (2) here, the first equation from the left means the formation of each V Sn is accompanied with the release of two holes and a neutral interstitial Sn atom. The second equation suggests that those two holes can be further trapped by a Sn 2+ which is oxidized into Sn 4+ . Therefore, as dictated by equation (1) and (2)

Computational details
The calculations using density functional theory (DFT) were performed based on the projector augmented wave (PAW) potential method implemented in the Vienna ab initio simulation package (VASP). 33,34 The generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerh function (PBE) was employed to describe the exchange-correlation potential. 35 By setting a 500 eV cutoff energy on the wave function, a 2×2×1 and another denser 3×3×1 Monkhorst-Pack k-point mesh were applied for the surface model optimization and the electronic properties calculation, respectively. The van der Waals interactions were described by the DFT-D3 method. 36 The convergence criteria were set to 10 −3 and 10 −5 eV for both the atomic force and energy. The spin-orbital coupling was 8 not considered due to the non-significant relativity effect in the tin element and charge transfer process. The Bader charges were calculated by using the method of Hen Kelman et al. 37 The optimized cell structure parameters of the tetragonal phase FASnI 3 unit cell are a = b = 8.859 Å, and c = 12.651 Å, which show good agreement with the experiment results. 38,39 The surface models are constructed based on this bulk FASnI 3 structure with the bottom atomic layer be fixed. A vacuum layer with a thickness of 15 Å was added along the z-direction to avoid the impact of image atoms. defective states of V Sn is plotted in Fig. 1b. Surprisingly, the defective states do not locate at the dangling I atoms as normal vacancy states do.

Localized state of pristine surface of FASnI3:
Instead, such a localized state is found at the neighboring Sn atom toward the bulk interior and penetrates several atom layers, indicating a strong redox ability of V Sn for producing Sn 2+ /Sn 4+ oxidation. Thus, the presence of V Sn defect tends to cause the oxidation of adjacent Sn atoms and the surface structure unstable. This self-doping mechanism is responsible for the degraded performance and structural instability of the nonstoichiometric tin-based perovskite. 19,40 To this end, we aim to passivate such surface states by introducing the Lewis base molecules. respectively. The iso-surface value of charge density is 0.001e/Bohr 3 .

Energetics of adsorption of Lewis base molecules:
10 Herein we choose several typical Lewis base molecules including edamine, p-TA, EDT, and Isatin-Cl molecules. We consider the Sn deficient FASnI 3 (001) surface where a V Sn is created at the top surface plane (Fig. 1b). As expected, such molecules are less likely to be adsorbed at the V Sn core where weak van der Waals interactions occur between the molecule and dangling iodine groups. The Lewis base molecules passivate the V Sn through an indirect way, the molecules bonding with the exposed Sn atoms surrounding the V Sn core rather than the V Sn core itself. The edamine molecule interacts with the exposed Sn atoms by forming a where the E total is the total energy of the surface model, E molecule and E perovskite are the energy of the isolated molecule and perovskite surface, 11 respectively. 48 The values of E ads , listed in Table.

Charge transfer and passivation of localized defective states:
Similarly, the charge transfer between the molecules and perovskite surface can be obtained according to the formula: where the ρ transfer is the charge density of the surface model, ρ molecule and ρ perovskite are the charge density of the isolated molecule and perovskite surface, respectively. 42 In Fig. 2, the charge gain and loss regions are marked by red and green, respectively. The quantitative estimation of the amount of charge transfer is listed in Table. 1 through spatial integration of the ρ transfer . We find that the edamine, and Isatin-Cl molecules transfer their electrons to passivate the surface defect, where a charge accumulation region is formed in the perovskite side. The largest amount of charge transfer in the p-TA/perovskite system (Fig. 2c) is consistent with its largest E ads , while the Isatin-Cl (Fig. 2b) has the smallest charge transfer, as the Cl atom has a relatively weak interaction with the perovskite surface. We next performed the electron localization function (ELF) analysis to illustrate the electronic coupling between the organic and perovskite surface. The ELF value ranges from 0 to 1, which represents the electronic states from a strong localization state to a low-density state. 49 As shown in   Table. S2.
Therefore, the charged defects on the perovskite surface have been stabilized through interacting with the functional ligands.

Mechanism and effectiveness of Lewis base molecules:
We next discuss the effectiveness of the Lewis base molecules on passivation of the defective states of V Sn . As discussed above, each V Sn is likely to induce excess holes which cause the oxidation of the nearby Sn 2+ to Sn 4+ , thus the healing effect to these vacancies induced background charge is so-called charge compensation. Upon the introduction of the external dopant such as the Lewis base molecules shown here, the additional charged center of these adsorbates would disturb the spatial distribution of the defective states and achieve passivation. As shown in Fig. 6, however, the effect of the passivation seems to vary with molecules.
Upon the adsorption of EDT, the V Sn associated defective state is still located at the Sn atom beneath the V Sn site, which suggests a remarkable barrier for the polaron hopping around these two Lewis adsorbates. In Herein the benzene sulfonic acid (BSA) as a soft Lewis base was considered. As shown in Fig. S2, the passivation effect of the BSA is close to that of the sulfur-contained EDT and carboxyl-contained p-TA. Thus, the Lewis base mainly influences the perovskite surface through two aspects: Firstly, the functional ligand coordinates with the undersaturated tin atoms, the following charge compensation reduce the SnI 5 distortion and avoid further tin oxidation (Fig. 7a); Secondly, surface passivation can 21 eliminate the amounts of shallow defects (unsaturated tin atoms) and shift the deep defects (V Sn ) to shallow defects (Fig. 7b).

Conclusion
In summary, we have performed DFT calculations to investigate the passivation ability of soft and hard Lewis base molecules decorating on the  24 The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.