Tin oxides are the most promising electron transport layers in perovskite solar cells. An ambipolar carrier transport property has been recently demonstrated which enables a simple interconnection structure for all-perovskite tandem solar cells. However, the underlying mechanism for its ambipolar behavior is unclear, which cannot be explained by the intrinsic defects in SnO2−x. Here, by using density functional theory calculations, we unveil the origin of the ambipolar carrier transport of non-stoichiometry SnO2−x with a structure of SnO embedded in the SnO2 matrix. The hybridization of O 2p and Sn 5s orbitals of SnO introduces mid-gap states in the bandgap of SnO2, enabling hole transport property for SnO2−x when x is > 0.2. Increasing the percentage of SnO in SnO2−x significantly enhances the hole transport capability of SnO2−x due to the enlarged Sn–O–Sn angles that increase orbital overlapping between O and Sn atoms, thus providing strategies for the further tuning of the carrier transport properties of SnO2−x by compositional and structural designs.
Tin dioxide (SnO2) has attracted great research interest for its application as excellent electron transport layers in record-high-efficiency perovskite solar cells due to its high bulk electron mobility, large bandgap, good stability with perovskites, and versatile fabrication processes.1–3 It has a deeper conduction band level compared to other electron transport materials like titanium dioxide and, thus, can easily form good band alignment with perovskites to facilitate electron extraction from perovskites.4 SnO2 can be fabricated by a variety of methods including solution deposition using pre-synthesized nanoparticles,3,5 atomic layer deposition (ALD),6–8 chemical bath deposition,1,9 electrochemical deposition,10 sputtering,11–13 and other physical vapor depositions.14,15 Like all types of oxides, tin oxides are not stoichiometric due to the presence of large density of O vacancies (VO). The incomplete oxidation of Sn2+ to Sn4+ is nearly inevitable due to low formation energy of VO and Sn interstitials (Sni) during the synthesis of SnO2, thus commonly leading to a dominant product of SnO2−x (0 < x < 1).16
A recent breakthrough discovery made by Yu et al.17 showed that using a simplified fullerene (C60)/SnO2−x structure as an interconnection layer in all-perovskite tandem solar cells enabled high efficiency tandem cells, which was mainly fulfilled by the ambipolar carrier transport capability of the nonstoichiometric ALD-grown SnO2−x layer. The ambipolar carrier transport of SnO2−x was realized when a certain amount of Sn2+ existed, as schematically shown in Fig. 1. However, it has not been fully understood how the presence of Sn2+ in SnO2−x affects the electronic structure of SnO2−x and leads to the ambipolar carrier transport. To date, Sni and VO in SnO2 have been widely considered as the origin of n-type conductivity for SnO2−x as revealed by early density functional theory (DFT) studies.18 Later, the DFT work focusing on the nonstoichiometric defects in SnO2 showed that the only defect which could induce p-type doping in SnO2 was Sn4+ vacancies which, however, had even higher formation energy than VO under oxygen-rich conditions,16 thus contradicting experiment results. The discrepancies likely arose from the inappropriate models used that only took point defects in SnO2 into consideration for the non-stoichiometry of SnO2−x, whereas in experiment the non-stoichiometry could also come from the alloying of SnO2 and SnO in a composition [i.e., (SnO2)1−x(SnO)x] when O is significantly deficient.13,17 Therefore, there was no theoretical investigation on the alloy structure of SnO2 and SnO to uncover the composition-tunable electronic properties and the ambipolar carrier transport characteristics of SnO2−x.
In this work, we calculate the influences of incorporating Sn2+ into SnO2 on the electronic properties of SnO2−x by constructing a SnO2–SnO alloy structure to mimic the ALD-grown SnO2−x within the framework of DFT calculation. Different from previous simulation approaches in which the SnO2−x was constructed by creating local VO or Sni, we embedded a complete layer-structured SnO into the matrix of SnO2 to uncover the ambipolar carrier transport mechanism of SnO2−x. The hole transport property of SnO2−x is further investigated upon the changing of SnO concentrations, providing future experimental design guidelines to improve the carrier transport properties of Sn-based oxides.
The unit cell of SnO2−x with the alloy structure of SnO2 and SnO was constructed by first building a 2 × 3 × 4 (x × y × z) SnO2 matrix with the primitive cell of SnO2 as shown in Fig. 2(a). Then parts of Sn and O atoms in the matrix were removed and replaced with a layer-structured SnO primitive unit [Fig. 2(b)] with the (001) facet of SnO aligned to the (100) facet of the matrix, as schematically shown in Fig. 2(c). The mixing of SnO2 and SnO generates defects in the interconnected areas, which was caused by removing of one O atom and replacement of two Sn4+ with Sn2+ in the interconnected areas on average. These defects could be equivalently regarded as negatively charged traps of the alloy. By changing the numbers of Sn and O atoms of SnO in the matrix, we obtained SnO1.95, SnO1.83, SnO1.75, SnO1.7, SnO1.65, SnO1.5, and SnO1.4, which correspond to nominal perfect alloy compositions of (SnO2)0.96(SnO)0.04, (SnO2)0.84(SnO)0.16, (SnO2)0.81(SnO)0.19, (SnO2)0.79(SnO)0.21, (SnO2)0.75(SnO)0.25, (SnO2)0.625(SnO)0.375, and (SnO2)0.5(SnO)0.5, respectively. We have also considered the variation of VO in different locations including in SnO or at the SnO2/SnO boundary, which as a result did not significantly affect the calculation results within the framework of the alloy structure of SnO2 and SnO. In addition, we considered the co-presence of VO and Sni in the SnO2 matrix of SnO1.95 and SnO1.83 [Fig. 2(c)] to further verify whether these point defects could make SnO2−x n-type doped.18
DFT calculations were performed by using the CASTEP package. Perdew–Burke–Ernzerhof (PBE) correlation exchange functional at the generalized gradient approximation (GGA) level and ultrasoft pseudopotentials with a plane wave basis set energy cutoff of 340 eV were adopted. The geometric optimization of each periodic cell was carried out until the change in energy and force in each atom were less than 1 × 10−5 eV/atom and 0.03 eV/Å, respectively. For the density of states (DOS) calculation, pseudo atomic calculations were performed for O 2s2 2p4 and Sn 5s2 5p2 with a Γ-centered (5 × 3 × 3) Monkhorst–Pack k-point grid sampling for the three-dimensional Brillouin zone. To obtain a more accurate bandgap values that are comparable to experimental results, a hybrid functional B3LYP with norm-conserving pseudopotentials and an energy cutoff of 750 eV were set to calculate the density of states (DOS) with high accuracies for selected models.
We first calculated the formation enthalpies (HF) of SnO2−x by using19,20
where E(SnO2−x) was the total energy of SnO2−x at the ground state after geometric optimization, n and m were the total numbers of Sn and O atoms in the unit cell of SnO2−x, respectively, and μSn and μO were the chemical potentials of Sn and O, respectively. Here, μSn was fixed at the atomic energy of metal Sn which was −95.451 eV, and the atomic energy of O in an O2 molecule which was −434.348 eV was chosen as the zero reference for μO. μO = 0, thus, refers to the most oxygen-rich situation. To estimate the range of μO in H2O during the ALD process, we calculated the total energies of H2O and H2 molecules, which were −468.716 and −31.562 eV, respectively. μO in H2O was then estimated by using μO = μH2O − 2μH = −2.806 ± ΔE eV (ΔE indicates the variation of μO in different chemical environments) with the reference zero μO set to the atomic energy of O in O2. Figure 2(d) plots the dependence of HF on the change of μO in the vicinity of −2.8 eV for SnO2−x, simulating the synthetic environment of SnO2−x by ALD, where H2O was used as the precursor for O. In general, O-deficient atmospheres (μO < −2.8 eV) favor the growth of SnO2−x with low O/Sn ratios like SnO1.4 as they own lower HF in this range. In contrast, O-rich atmospheres (μO > −2.8 eV) lead to the growth of more completely oxidized SnO2−x like SnO1.95. It is interesting that the HF of SnO2−x with medial O/Sn ratios, such as SnO1.83 and SnO1.7, are always larger than the intersectional minimum HF of SnO1.4 and SnO1.95 [indicated by the black dashed line in Fig. 2(d)], indicating that the formations of SnO1.83 and SnO1.7 are not thermodynamically favored during the ALD growing process. This result implies that the growth of SnO2−x with medium O/Sn ratios of ∼1.7 by ALD is likely determined by the dynamic process of the chemical reaction, rather than controlled by thermodynamics. Experiment results have shown that once the as-synthesized SnO1.76 was oxidized in dry O2, it turned from the ambipolar to n-type unipolar charge transport layer accompanied by the increase in the O/Sn ratio, verifying the thermodynamically metastable property of ALD grown SnO2−x with medium O/Sn ratios.17
Then we move to investigating the electronic properties of SnO2−x. Figure 3 shows the DOS spectra of SnO2−x with 2−x varying from 2 to 1.5. The DOS spectra of SnO2, SnO1.83, and SnO1.50 were first calculated by using both the GGA-PBE and B3LYP functionals to check the accuracy of the norm-conserving pseudopotentials in calculating the electronic states of SnO2−x. It is seen that though the GGA-PBE method underestimated the bandgap of SnO2 by ∼2.26 eV, whereas B3LYP yields a bandgap of ∼4.15 eV, which is closer to the experimentally measured value of ∼3.6 eV,21–23 the relatively energetic distributions of the DOS with respect to the band edges that obtained from both two methods were basically identical.
For SnO1.95, when there is no VO–Sni pair in the SnO2 matrix, trap states are introduced near the valence band edge. After incorporating the VO–Sni pair to SnO2, additional donor states occur at the conduction band edge of the system, validating that the n-type doping of SnO2−x is realized by the co-formation of VO and Sni in SnO2. Similar scenario of VO–Sni induced n-type doping appears in SnO1.83. With the decrease in the O/Sn ratio from 1.95 to 1.50, the trap states near the valence band edge gradually increase and broaden toward both the valence band and the middle of the bandgap, forming band tail states next to the valence band edge of SnO2−x. This agrees with experiment results that substantial band tail states were detected in ALD-grown SnO1.76 from near-infrared absorption measurement.17 These high densities of band tail states would serve as charge traps for charge carriers, leading to the low conductivity of ∼10−4 S cm−1 for ALD-grown SnO2−x.17 In the meantime, an additional mid-gap state appears in the bandgap of SnO2−x, when the O/Sn ratio is lower than 1.83, which gradually merges with the band tail states and the conduction band edge with the further decrease in the O/Sn ratio. This result also agrees with the experimentally observed presence of mid-gap states in ALD-grown SnO1.76.17 The DOS spectrum of SnO1.83 calculated with B3LYP shows that the mid-gap states locate within the energy range of 0.68–1.56 eV below the conduction band edge, consistent with the measured energy range of 0.8–1.4 eV for the ALD-grown SnO1.76 by Yu et al.17 These results demonstrate that current calculations based on the alloy structure of SnO2 and SnO could accurately simulate the experimentally ALD-grown SnO2−x, which has an ambipolar carrier transport property. When the ALD-grown SnO2−x was adopted as an interconnection layer for perovskite tandem cells, the mid-gap states in SnO2−x are the key to realize hole transport through them. Therefore, it is important to understand the origin of the mid-gap states in SnO2−x and their correlation with the carrier transport properties upon changing of the composition.
To figure out the origins of the band tail states and mid-gap states in SnO2−x, we calculated the distributions of the isosurface for the electron wavefunctions of these states in SnO1.95, SnO1.83, and SnO1.50, as shown in Fig. 4. For SnO1.95, there are no mid-gap states. The isosurface for the electron wavefunctions of the tail states is localized at the back-bond of Sn2+, where the equivalently existing negatively charged defects accumulate at the SnO2/SnO boundary. These interfacial defects contribute to the band tail states above the valence band edge of SnO1.95 as well as in SnO1.83 and SnO1.50 [Figs. 4(b) and 4(c)]. Figure 4(a) also shows the isosurface of the electron wavefunctions of the donor states in SnO1.95 when a VO–Sni pair exists in the SnO2 matrix. As a result, the electron wavefunctions of these donor states mainly localize around the VO–Sni pair in SnO2. For the mid-gap states of SnO1.83 and SnO1.50, it is found that the isosurface of the electron wavefunctions is mainly distributed around the Sn and O atoms of SnO in the alloy structure. This indicates that the mid-gap states are introduced by the SnO component of SnO2−x, specifically caused by the hybridization of O 2p and spherical Sn 5s orbitals. This is similar to the orbital configuration for the valence bands of SnO, as both are caused by the O 2p and Sn 5s orbitals, which give rise to a much higher valence band maximum (VBM) and smaller bandgap of ∼1.2 eV for SnO compared to SnO2.24,25 This hybridization leads to a more dispersed VBM with smaller hole effective mass for SnO, thus enabling efficient hole transport in SnO. In contrast to SnO2, which is commonly an n-type oxide, SnO has been extensively reported as a p-type oxide owing to its efficient hole transport and unintentional doping by Sn vacancies.26–29 Therefore, the SnO-induced mid-gap states in the bandgap of SnO2 could facilitate hole transport through these states and make SnO2−x as an ambipolar oxide. Experiments of Yu et al. further revealed that once the O/Sn ratio of the ALD-grown SnO2−x increased from 1.76 to 1.91, the SnO2−x changed from ambipolar to n-type doping only (Fig. 1).17 This again consists with our simulation results that in highly oxide SnO2−x (e.g., SnO1.95), there is no more mid-gap states for the realization of hole transportations.
Eventually, we calculated the band structures of SnO2−x and derived the effective masses of holes (mh) with the E–k relationship at the vertex of the defect-induced or SnO-induced mid-gap bands to evaluate the hole transport capabilities of SnO2−x with different compositions. Figs. 5(a)–5(c) representatively show the band structures of SnO1.95, SnO1.83, and SnO1.50. The energy level of 0 eV corresponds to the Fermi level, which is set to the highest occupied electronic state of the system. With the decrease in the O/Sn ratio, i.e., the increase in the SnO concentration, the mid-gap bands become more dispersed. The mh of SnO1.95, SnO1.83, and SnO1.50 are 5.27, 1.39, and 0.58 m0, respectively, implying a tendency of enhancement of hole mobilities with the decrease in the O/Sn ratio in SnO2−x. To further understand the underlying correlation between mh and the O/Sn ratio of SnO2−x, we calculated the average Sn–O–Sn angles of SnO in geometrically optimized SnO2−x as the Sn–O–Sn angle determined the orbital overlapping between the dumb-belled O 2p and spherical Sn 5s orbitals of SnO, which eventually affected the mh of SnO.30 The relationship between mh and the average Sn–O–Sn angles of SnO in SnO2−x with different O/Sn ratios is shown in Fig. 5(d). A clear trend of decrease in mh with the decrease in O/Sn ratio is observed for SnO2−x, which is attributed to the increase in the Sn–O–Sn angles in SnO that enhances the orbital coupling between O and Sn atoms. The fitted trend of the dependence of mh on the average Sn–O–Sn angle of SnO is similar to the observation of Ha et al. on different p-type Sn-based oxides.26 It is noteworthy that the average Sn–O–Sn angles of SnO in SnO1.75 to SnO1.4 are even larger than that of pristine SnO, which is 116°, thus they own smaller mh and potentially higher hole mobilities than pristine SnO. We speculate that the enlargement of Sn–O–Sn angles is mainly caused by the strain imposed on SnO due to the lattice mismatches between SnO and the SnO2 matrix. To evaluate the strain at the SnO2/SnO boundaries, we calculated the lattice mismatches between SnO and SnO2 in the Y–Z plane of the alloy structure using (ySnO2 − ySnO)/ySnO2 × 100% and (zSnO2 − zSnO)/zSnO2 × 100%, as schematically illustrated in Fig. 2(c). Figure 2(e) shows the lattice mismatches between SnO and SnO2 in the Y and Z directions of the alloy structure, which are all positive and vary between 1% and 10%. This indicates that compressive and tensile strains are imposed to SnO2 and SnO, respectively. It is the tensile strain that enlarges the Sn–O–Sn angles in SnO after alloying with SnO2. This result also provides a strategy for acquiring desired carrier transport properties for Sn-based oxides by compositional and structural designs of SnO2−x with the alloy structure of SnO2 and SnO, to fulfill their functions as multiple-purpose interlayers in high performance perovskite solar cells.
In summary, we investigated the structural and electronic properties of SnO2−x based on the alloy structure of SnO2 and SnO that mimics the ALD-grown SnO2−x in experiment for its application as interconnected layers in all-perovskite tandem cells. The co-formation of VO and Sni in SnO2 makes SnO2−x n-type doped, while the incorporation of SnO into the SnO2 matrix introduces mid-gap states in the bandgap of SnO2 and enables the ambipolar carrier transport capability of SnO2−x. The decrease in the O/Sn ratio of SnO2−x (an increase in the SnO concentration) facilitates the hole transport through the SnO-induced mid-gap states as the effective mass of holes reduces. This highlights an important pathway for the further tuning of the carrier transport properties of SnO2−x by changing the SnO concentration in the alloy structure.
We thank the financial support from the Solar Energy Technologies Office (SETO) within the U.S. Department of Energy under Award No. DE-EE0008749 and the National Science Foundation under Award No. ECCS-2050764.
The authors declare no competing financial interest.
The data that support the findings of this study are available from the corresponding author upon reasonable request.