Electronic structure and thermal conductance of the MASnI3/Bi2Te3 interface: a first-principles study

To develop high-performance thermoelectric devices that can be created using printing technology, the interface of a composite material composed of MASnI3 and Bi2Te3, which individually show excellent thermoelectric performance, was studied based on first-principles calculations. The structural stability, electronic state, and interfacial thermal conductance of the interface between Bi2Te3 and MASnI3 were evaluated. Among the interface structure models, we found stable interface structures and revealed their specific electronic states. Around the Fermi energy, the interface structures with TeII and Bi terminations exhibited interface levels attributed to the overlapping electron densities for Bi2Te3 and MASnI3 at the interface. Calculation of the interfacial thermal conductance using the diffuse mismatch model suggested that construction of the interface between Bi2Te3 and MASnI3 could reduce the thermal conductivity. The obtained value was similar to the experimental value for the inorganic/organic interface.

www.nature.com/scientificreports/ films on nylon, and the resulting material exhibited a relatively high power factor of ~ 389.7 µW/(m·K 2 ) at 418 K 27 . Kumar et al. fabricated a PEDOT:PSS/Te composite material, which reduced the thermal conductivity owing to the enhanced phonon-phonon scattering in the polymer matrix 28 . Many researchers have also studied the combination of Bi 2 Te 3 and PEDOT:PSS 8,[29][30][31][32] . Du et al. fabricated Bi 2 Te 3 based alloy nanosheet/PEDOT:PSS composite films, which exhibited high electrical conductivity (1295.21 S/cm) relative to BI 2 Te 3 -based alloy bulk materials (850-1250 S/cm), and a power factor of ~ 32.26 µW/(m·K 2 ) was obtained 30 . In a Te-Bi 2 Te 3 /PEDOT:PSS hybrid film synthesized through a solution-phase reaction at low temperature, a power factor of 60.05 µW/ (m·K 2 ) with a Seebeck coefficient of 93.63 µV/K and an electrical conductivity of 69.99 S/cm were reported by Bae et al 31 . Based on these results, it can be concluded that the electronic properties of the interface between the organic and inorganic materials play a critical role in improving the ZT of organic-inorganic hybrid materials.
Here, we focus on halide perovskites instead of PEDOT:PSS to fabricate a printable thermoelectric material. The thermoelectric properties of inorganic halide perovskite (CsSnI 3 ) have previously demonstrated relatively high values as a printable thermoelectric material (ZT > 0.1 at room temperature) 33,34 . Organic-inorganic hybrid perovskites, ABX 3 (A: methylammonium cation (CH 3 NH 3 + ), B: lead or tin, X: iodide) have been investigated as candidate thermoelectric materials and are well known in the field of thin-film solar cells 35,36 . Regarding the thermoelectric properties of organic-inorganic perovskites, Pisoni et al. reported that CH 3 NH 3 PbI 3 exhibited an ultra-low thermal conductivity of 0.3-0.5 W/(m·K) at room temperature due to the slowly rotating CH 3 NH 3 + cations within the crystal structure 37 . Theoretical studies also predicted that CH 3 NH 3 PbI 3 would have a low thermal conductivity of ~ 1 W/(m·K) compared with other perovskites such as CsPbI 3 , CH 3 NH 3 Br 3 , and CH 3 NH 3 PbCl 3 [38][39][40] . On the other hand, CH 3 NH 3 SnI 3 (MASnI 3 ) is expected to exhibit low thermal conductivity compared with CH 3 NH 3 PbI 3 , with improved thermal properties obtained through chemical doping 41 . The advantage of perovskite compounds such as MASnI 3 over the organic materials PEDOT: PSS is that they have a variety of constituent elements, which enable the system elemental substitution. It is possible to change the energy level near the Fermi level, and it is expected that the electric conductivity and Seebeck coefficient will be improved. Such electronic state control can be performed more easily with perovskite than with PEDOT:PSS.
In this study, we aimed to understand the interface structure of hybrid materials composed of Bi 2 Te 3 and organic-inorganic perovskite (MASnI 3 ) to improve the thermoelectric conversion properties. We previously reported the structural stability and electronic properties of different Bi 2 Te 3 (001) termination surfaces based on first-principles calculations 42 . Based on the results, we prepared three structures with different Bi 2 Te 3 termination structures and explored statically stable structures through structural optimization. Additionally, we calculated the electronic states and distribution of the charge density near the Fermi energy. The calculation of the diffuse mismatch model (DMM) 43,44 obtained from the results of phonon dispersion in Bi 2 Te 3 and MASnI 3 confirmed a decrease in the interfacial thermal conductance at the interface.

Computational methods
Density functional theory calculations for Bi 2 Te 3 /MASnI 3 interfaces. To create the interface structure, the crystal structure of Bi 2 Te 3 was transformed from a rhombohedral lattice to an orthorhombic lattice, and the lattice parameter of MASnI 3 was reduced to fit the lattice parameter of Bi 2 Te 3 . The interface models consisted of orthorhombic Bi 2 Te 3 (001) and tetragonal MASnI 3 (001), and a vacuum layer of ~ 15 Å was inserted. For simplicity, the termination structure of MASnI 3 was fixed as SnI 2 at the interface. For the structure of Bi 2 Te 3 in contact with MASnI 3 , three termination structures were considered: Te I , Te II , and Bi terminations, which are relatively stable surface structures that were described in our previous study 42 (Fig. 1c-e). The Vienna ab-initio simulation package (VASP) 45,46 with the projector-augmented wave method 47,48 was used for the first-principles calculations. For the exchange-correlation function, the generalized gradient approximation and Perdew-Burk-Ernzerhof function were used 49 . The cutoff energy was set at 520 eV, and structural optimization was performed using the Gaussian smearing method with a sigma value of 0.1 eV. The K-points were set at 5 × 6 × 1, and the convergence value for the structural optimization was set to 10 −3 eV. The Blöchl-corrected tetrahedron method was used for accurate calculation, and its convergence value was set at 10 −4 eV. To perform more accurate band structure, density of states (DOS), and charge distribution, we considered the spin-orbit coupling (SOC).
Calculation of thermal conductance using DMM. For the thermal conductance calculation, phonon calculation of the interface structure between Bi 2 Te 3 and MASnI 3 is the most direct calculation method. However, for an interface structure, the number of atomic displacement patterns are required to obtain the highly accurate atomic force, and it is impossible to calculate by the first-principles calculation. Therefore, in this paper, we used DMM 44 , which is often used as a simple method for evaluating interfacial thermal conductance.
The interfacial thermal conductance (thermal boundary conductance) obtained by the DMM is defined as the ratio of the heat current density to the temperature differential. To estimate the thermal boundary conductance for hybrid materials A/B, Reddy et al. defined the thermal boundary conductance, G, as follows: where α A→B (k, i) is the transmission probability of A to B, ω(k, i) is the phonon frequency corresponding to wave vector k and phonon mode I, and |V (k, i).n| is the group velocity along the unit vector n to the interface of A to B. Calculations of the transmission probability of A to B and the phonon frequency and group velocity of A and B obtained from phonon dispersion are required. Here, the transmission probability is calculated from the group velocities of A and B as follows: www.nature.com/scientificreports/ where K A and K B are the discretized cells of the Brillouin zones of A and B, respectively, and δ ω(k,i),ω ′ is the Kronecker delta function. Therefore, to evaluate the thermal boundary conductance with DMM, only the phonon dispersions of A and B are required. The calculated thermal conductance will be severely underestimated (by a factor of 1/2) when the transmission probability between similar materials is calculated using the DMM. Therefore, the maximum transmission model (MTM) was employed to evaluate the extreme upper limit of the thermal conductance if needed 50 . The phonon dispersions of Bi 2 Te 3 and MASnI 3 were evaluated using first-principles phonon calculations, and the group velocity was calculated from the results. To calculate the phonon dispersion, we used the finite displacement method with a displacement distance of 0.01 Å. The supercell sizes of Bi 2 Te 3 and MASnI 3 were 2 × 2 × 2 for the rhombohedral cells and 1 × 1 × 1 for the orthorhombic cells, respectively (Fig. 1a,b). We note that the longer lattice parameter of the orthorhombic cell of MASnI 3 is along the b-axis, and the a-and b-axes are rotated 45° relative to the cubic perovskite phase. To estimate the force due to the introduction of displacements, we used the VASP code with the following parameters: a plane wave energy cutoff of 400 eV, a convergence value for the electronic self-consistency loop of 10 −8 eV, Γ-point centered k-mesh limited to 0.1 Å −1 , and the Gaussian smearing method with a smearing width of 0.05 eV. In the phonon calculation, SOC does not significantly affect the phonon dispersion relation, therefore, SOC is not considered. We used the phonopy code 51 to create the displacement using the finite displacement method, and the ALAMODE 52 code for the phonon properties calculation. To obtain the phonon density of states (DOS) and group velocity for both structures, the reciprocal space was sampled using 10 × 10 × 10 meshes.

Results and discussion
Optimized interface structure. We constructed three interface structures with different Bi 2 Te 3 termination structures: Bi 2 Te 3 (Te I )/MASnI 3 , Bi 2 Te 3 (Te II )/MASnI 3 , and Bi 2 Te 3 (Bi)/MASnI 3 (Fig. 1). The crystal plane in contact with each structure in the interface was determined from the lowest lattice deformation ratio of various combinations of crystal planes; the selected structure of MASnI 3 was tetragonal, which was stable at room temperature. In the creation of the interface models, the lattice distance of MASnI 3 was reduced to fit that of Bi 2 Te 3 . Table 1 lists the lattice parameters of various interface models after structural optimization. The termination structure of Bi 2 Te 3 affected the lattice constant of the interface model; the Te II termination exhibited the lowest  (Table 1). This result also led to a decrease in the lattice deformation ratio in the Bi 2 Te 3 (Te II )/MASnI 3 structure, as indicated in Table 2. The lattice deformation ratio was calculated using the following equation: deformation (%) = (d 2 /d 1 -1) × 100, where d 2 and d 1 represent the lattice distance of the transformed or optimized structure and the lattice distance of the bulk structure, respectively. On the other hand, the Bi 2 Te 3 (Bi)/MASnI 3 structure exhibited a high lattice deformation ratio among the three interface models; the lattice of Bi 2 Te 3 in the interface structure was particularly expanded. A low lattice deformation ratio is expected in the case of easy formation and relatively high stability of the interface structure experimentally. After structural optimization, the atoms in the interface moved strongly with an incomplete structure for Bi 2 Te 3 with the Te II and Bi termination structures, and this phenomenon was prominent for the Bi termination. This result suggests that Bi and Sn atoms can move easily into each structure, and the Te II and Bi termination structures form an interaction between Bi 2 Te 3 and MASnI 3 compared with the Te I termination. The relationship between the reconstruction of atoms in the structural optimization, lattice parameters, and lattice deformation ratio was not observed.
To evaluate the interface stability between Bi 2 Te 3 and MASnI 3 , we calculated the binding energy using the following equation: where E total , E p , and E b denote the energies of Bi 2 Te 3 /MASnI 3 , the MASnI 3 (001) surface, and the Bi 2 Te 3 (001) surface, respectively (Fig. 2). E p , and E b means reference energies. For these (001) surface structures, we used the lattice constant of the ground state structure. A positive binding energy value indicates low stability of the interface structure, which makes formation of the interface difficult. Hence, Bi 2 Te 3 (Te I )/MASnI 3 is the most unstable interface structure; in contrast, Bi 2 Te 3 (Bi)/MASnI 3 is the most stable interface structure, with a binding energy of − 1.7 eV. Similar to the Bi termination model, Bi 2 Te 3 (Te II )/  Fig. 3 (corresponding band structures are also shown in Fig. S1). The valence band of each interface structure consists of Sn s-, I p-, Bi s-, Bi p-, and Te p-orbitals, and the conduction band consists of Sn p-, I p-, Bi p-, and Te p-orbitals. In the interface structures, the shapes of the partial DOS of Bi 2 Te 3 in each termination structure were similar to that of the bulk structure. However, the energy levels of the DOS changed with the termination structure in Bi 2 Te 3 , which is attributed to the difference in the ratio of Bi and Te atoms. The partial DOS of MASnI 3 in each interface structure exhibited different electronic states from the bulk structure over a range of − 0.5 eV to 0 eV; these states are attributed to the I p-orbital in MASnI 3 in contact with the vacuum layer. In the DOS around the Fermi energy in the Te II and Bi termination structures (Fig. 3b,c), the additional electronic state appeared at similar energy levels for both Bi 2 Te 3 and MASnI 3, indicating that the additional electronic state includes the contributions of both Bi 2 Te 3 and MASnI 3 .
To investigate the additional electronic state, the decomposed DOS for each layer near the interface is shown in Fig. 4. The atoms included in the decomposed layer are shown in Fig. 5. The DOS for Bi, Te, Sn, and I consist of the s-and p-orbitals. The DOS for the middle layer of MASnI 3 (MASnI 3 -3L) exhibited a similar shape despite the different interface structures. However, the shapes of the DOS for Sn and Bi changed significantly near the interface, and they exhibited a different electronic state with the variation in Bi 2 Te 3 termination. In particular, on the Bi 2 Te 3 (Bi)/MASnI 3 interface, the conduction band of MASnI 3 -1L moved to near the Fermi energy. This result is attributed to the large change in the atomic positions of Sn and I at the interface. On the other hand, the shape of the DOS for Bi 2 Te 3 depended on its termination structure; in particular, it changed significantly in the layer in contact with the interface. This phenomenon originates from the different ratios of Bi and Te atoms in the incomplete Bi 2 Te 3 structure. The Bi 2 Te 3 (Bi)/MASnI 3 interface also had the potential to be affected by the movement of Bi atoms.
Focusing on the first layers from the interface of Bi 2 Te 3 and MASnI 3 , the additional electronic state is observed at the same energy level in the layer near the interface between Bi 2 Te 3 and MASnI 3 . Figure 4(b) and (c) shows additional interface levels, denoted by arrows, with an overlapping electronic density appeared in both structures around the Fermi energy in the Bi 2 Te 3 (Te II )/MASnI 3 and Bi 2 Te 3 (Bi)/MASnI 3 structures. These results also suggest that the incomplete structure of Bi 2 Te 3 , such as the Te II and Bi terminations, plays an important role in the formation of interface states. The Te I termination did not produce an overlap in the DOS between Bi 2 Te 3 and MASnI 3 at the interface.
The charge densities of each interface structure around the Fermi energy are shown in Fig. 6. Figure 6(a) shows the charge distribution in the interface structure with the Te I termination, which is localized at the MASnI 3 www.nature.com/scientificreports/ side, and is not observed at the interface between Bi 2 Te 3 and MASnI 3 . This suggests a decreasing affinity of Bi 2 Te 3 and MASnI 3 . On the other hand, the interface structure with the Te II termination possesses a localized charge distribution at the near interface and an overlapping charge density between Sn and Te atoms in the energy range of 0.2 to 0.5 eV (Fig. 6c). Phonon properties of Bi 2 Te 3 and MASnI 3 . Next, we estimated the interfacial thermal conductance of the Bi 2 Te 3 /MASnI 3 interface. Figure 7 shows the phonon dispersions and atomic projected phonon DOS of (a) Bi 2 Te 3 and (b) MASnI 3 . Bi 2 Te 3 exhibited low energy phonon modes below 150 cm −1 , and MASnI 3 had low (f < 120 cm −1 ) and high (f > 120 cm −1 ) energy phonon modes. Because of the difference in atomic mass, the vibrations of Sn and I appeared at low energies, and the vibrations of C, N, and H appeared at high energies. Therefore, the phonon dispersion of MASnI 3 showed a low-energy mode in the same range as Bi 2 Te 3 until approximately 150 cm −1 . Based on the phonon dispersion results for Bi 2 Te 3 and MASnI 3 , these structures are dynamically stable at T = 0 owing to the lack of observation of the imaginary mode. Our calculated phonon dispersions for both structures are similar to those reported in previous studies for Bi 2 Te 3 54 and MAPbI 3 (not MASnI 3 ) 55,56 . The group velocities of phonons are necessary for the evaluation of the interfacial thermal conductance using DMM, as shown in Eqs. (1) and (2). Figure 8 shows the absolute values of the calculated group velocities in the direction of the c-axis in Bi 2 Te 3 and a-, b-, and c-axes in MASnI 3 . The group velocity (speed of sound) was estimated from the three low-energy phonon modes within the phonon dispersion; hence, it corresponds to a gradient of the phonon dispersion. In calculated results, Bi 2 Te 3 exhibited a high group velocity at under 10 cm −1 , whereas MASnI 3 had a high group velocity above 10 cm −1 . Moreover, we found that the distribution of the group velocity with respect to the frequency differed between Bi 2 Te 3 and MASnI 3 . For MASnI 3 , the group velocity was not dependent on the direction of the crystal axis. It has been experimentally reported that Bi 2 Te 3 exhibits a group velocity of 1750 m/s based on nuclear resonant inelastic scattering 57 , whereas MAPbI 3 has exhibited group velocities of acoustic modes of 2400 or 1200 m/s based on neutron scattering 58 . Although there is a difference in the structures between our calculations (MASnI 3 ) and the previous experiments (MAPbI 3 Figure 9 shows the interfacial thermal conductance of the Bi 2 Te 3 /MASnI 3 interface; the combination of all axes of MASnI 3 and the c-axis of Bi 2 Te 3 was evaluated. The obtained values for the interfacial thermal conductance with different Bi 2 Te 3 /MASnI 3 interfaces were 1.5-2.0 MW/m 2 K. This result indicates that the interfacial thermal conductance was not affected by the orientation of MASnI 3 because the differences between different directions were small, as shown in the phonon dispersion curve (Fig. 7b). The calculated interfacial thermal conductance of Bi 2 Te 3 /MASnI 3 was lower than the calculated value of the inorganic/inorganic interface 44 . The reason for this is explained as follows: calculated phonons in Bi 2 Te 3 and MASnI 3 are distributed in the low energy region. This is due to the fact that they have relatively heavy elements and complicated structures. When the phonon dispersion is distributed in the low energy region, the group velocity becomes small. The interfacial thermal conductance calculated by DMM depends on the group velocity and phonon frequency, as shown in Eq. (1), therefore Bi 2 Te 3 /MASnI 3 interface shows a relatively low interfacial thermal conductance. Moreover, it was as low as the experimental values for inorganic/organic interfaces such as a graphene-Bi 2 Te 3 heterostructure (~ 3.46 MW/(m 2 ·K)) 59 and PEDOT:PSS-Bi 2 Te 3 heterostructure (~ 10 MW/(m 2 ·K)) 60 Therefore, these results suggest that the Bi 2 Te 3 /MASnI 3 interface has a low interfacial thermal conductance, and we expect that the application of this interface to thermoelectric materials can reduce the thermal conductivity. An extremely low thermal conductance is expected even for a stable structure at the Bi 2 Te 3 /MASnI 3 interface, although the morphological effects are not included in the DMM model. Direct numerical simulations, such as molecular dynamics, may be necessary for further discussion.
Effective thermal conductivity of the Bi 2 Te 3 and MASnI 3 hybrid material. Although the actual thermal transport mechanism, such as superlattices with very short periodicity 61 , is too complex to explore here, we have aimed to discuss the effect of the interfacial thermal conductance of Bi 2 Te 3 /MASnI 3 on the effective thermal conductivity, κ using a simple composite model. Here, a one-dimensional model is used, in which Bi 2 Te 3 layers and MASnI 3 layers with a thickness of D µm are alternately arranged, as shown in the inset of Fig. 10; the parameters are the interfacial thermal conductance, ITC, and the thickness of each layer. The results indicate that the effective thermal conductivity of Bi 2 Te 3 /MASnI 3 asymptotically approaches 0.17 W/(m·K) at a film thickness sufficiently larger than 1 µm. This value is calculated from the experimental values of Bi 2 Te 3 and MASnI 3 : 2.11 W/(m·K) 62 and 0.09 W/(m·K) 41 , respectively. This upper limit does not depend on the interfacial thermal conductance because the influence of the interface is negligible in the limit of large D. In contrast, when the film thickness is sufficiently smaller than 1 µm, the interfacial thermal conductance significantly influences  www.nature.com/scientificreports/ the effective thermal conductivity. The blue line in the figure shows the effective thermal conductivity estimated from the calculated interfacial thermal conductance of 1.75 MW/(m 2 ·K). The smaller the film thickness, the more effectively the interfacial thermal conductance of Bi 2 Te 3 /MASnI 3 can be utilized. Thus, it is expected that the thermal conductivity of the Bi 2 Te 3 /MASnI 3 composite, which consists of small Bi 2 Te 3 grains in MASnI 3 , will be significantly reduced.

Conclusion
In this study, we evaluated the stability and electronic state of interface structures of Bi 2 Te 3 (001) and MASnI 3 (001), and the thermal conductance of the interface between Bi 2 Te 3 and MASnI 3 along the (001) direction was estimated. In the structural optimization, the termination of MASnI 3 was fixed with SnI 2 at the interface and surface, whereas for the structure of Bi 2 Te 3 in contact with MASnI 3 , three termination structures were considered: Te I , Te II , and Bi termination. After structural optimization, around the Fermi energy, the interface structures with Te II and Bi termination resulted in the formation of interface levels attributed to the overlapping electron densities for both Bi 2 Te 3 and MASnI 3 at the interface. It is believed that the formation of interface levels enhances the affinity for the interface structure of Bi 2 Te 3 and MASnI 3 , and the binding energies for these interface structures are negative. Based on the calculation of the interfacial thermal conductance using DMM, it is expected that the Bi 2 Te 3 /MASnI 3 interface can significantly reduce the thermal conductivity. These results indicate that the Bi 2 Te 3 / MASnI 3 composite material is a possible candidate for an excellent thermoelectric material because it has the potential to decrease the thermal conductivity.