Introduction

Printed electronics are attractive next-generation technologies that make full use of printing technology and are used to manufacture various electronic devices, such as organic EL TVs, electronic paper, and solar cells. In addition to making the devices thinner and lighter and increasing the area, printed electronics also save resources, allow for reduced process temperatures, and are more environmentally friendly. In the field of printed electronics, the thermoelectric conversion demand has increased with the development of energy-saving technology, which has a crucial role in the achievement of energy harvesting1,2,3. Madan et al.4 and Navone et al.5 reported early composite printing of thermoelectric devices. Navone et al.5 also noted that a previous study6 attempted to achieve this in 1990 using screen printing. For thermoelectric devices, it is necessary to improve the energy conversion efficiency in addition to reducing costs. The performance of thermoelectric conversion materials is described as the figure of merit, ZT = S2σT/(κel + κlat), which is proportional to the square of the Seebeck coefficient (S), electrical conductivity (σ), and absolute temperature (T), and is inversely proportional to the thermal conductivity (κ)7,8,9. Many studies have been conducted on the doping of heterogeneous elements to modify the electronic structure directly; this technique is effective for preventing an increase in the Seebeck coefficient and/or the electrical conductivity10,11,12.

On the other hand, a thousand-fold reduction in thermal conductivity was reported with the use of organic/inorganic interfaces13. This broadened the outlook of the field because the previous strategy improved semiconductor characteristics by controlling impurities, but new characteristics arose in the obtained composites. To decrease the lattice thermal conductivity, many researchers have introduced crystal grain boundaries and nanostructures, which led to phonon scattering between crystal grains14,15,16,17,18,19. These techniques also affect improving the electrical conductivity and Seebeck coefficient, and their mechanisms are complex. As mentioned above, the interfacial thermal conductance has attracted attention for enhancing ZT, and this enhancement is attributed to the difference in lattice vibrations between heterogeneous materials3,20,21. Considering the fabrication of thin and flexible thermoelectric materials, hybridization of organic and inorganic materials is a critical technique for improving ZT owing to the formation of many interfaces3,8,22,23,24. Generally, to maintain the electric conduction ability, the organic materials used are conductive polymers such as poly (3,4-ethylenedioxythiophene) doped with poly (4-styrenesulfonate) (PEDOT:PSS)25,26. Lu et al. developed flexible PEDOT:PSS/Cu2Se nanocomposite films on nylon, and the resulting material exhibited a relatively high power factor of ~ 389.7 µW/(m·K2) at 418 K27. 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 matrix28. Many researchers have also studied the combination of Bi2Te3 and PEDOT:PSS8,29,30,31,32. Du et al. fabricated Bi2Te3 based alloy nanosheet/PEDOT:PSS composite films, which exhibited high electrical conductivity (1295.21 S/cm) relative to BI2Te3-based alloy bulk materials (850–1250 S/cm), and a power factor of ~ 32.26 µW/(m·K2) was obtained30. In a Te-Bi2Te3/PEDOT:PSS hybrid film synthesized through a solution-phase reaction at low temperature, a power factor of 60.05 µW/(m·K2) with a Seebeck coefficient of 93.63 µV/K and an electrical conductivity of 69.99 S/cm were reported by Bae et al31. 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 (CsSnI3) have previously demonstrated relatively high values as a printable thermoelectric material (ZT > 0.1 at room temperature)33,34. Organic–inorganic hybrid perovskites, ABX3 (A: methylammonium cation (CH3NH3+), B: lead or tin, X: iodide) have been investigated as candidate thermoelectric materials and are well known in the field of thin-film solar cells35,36. Regarding the thermoelectric properties of organic–inorganic perovskites, Pisoni et al. reported that CH3NH3PbI3 exhibited an ultra-low thermal conductivity of 0.3–0.5 W/(m·K) at room temperature due to the slowly rotating CH3NH3+ cations within the crystal structure37. Theoretical studies also predicted that CH3NH3PbI3 would have a low thermal conductivity of ~ 1 W/(m·K) compared with other perovskites such as CsPbI3, CH3NH3Br3, and CH3NH3PbCl338,39,40. On the other hand, CH3NH3SnI3 (MASnI3) is expected to exhibit low thermal conductivity compared with CH3NH3PbI3, with improved thermal properties obtained through chemical doping41. The advantage of perovskite compounds such as MASnI3 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 Bi2Te3 and organic–inorganic perovskite (MASnI3) to improve the thermoelectric conversion properties. We previously reported the structural stability and electronic properties of different Bi2Te3 (001) termination surfaces based on first-principles calculations42. Based on the results, we prepared three structures with different Bi2Te3 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 Bi2Te3 and MASnI3 confirmed a decrease in the interfacial thermal conductance at the interface.

Computational methods

Density functional theory calculations for Bi2Te3/MASnI3 interfaces

To create the interface structure, the crystal structure of Bi2Te3 was transformed from a rhombohedral lattice to an orthorhombic lattice, and the lattice parameter of MASnI3 was reduced to fit the lattice parameter of Bi2Te3. The interface models consisted of orthorhombic Bi2Te3 (001) and tetragonal MASnI3 (001), and a vacuum layer of ~ 15 Å was inserted. For simplicity, the termination structure of MASnI3 was fixed as SnI2 at the interface. For the structure of Bi2Te3 in contact with MASnI3, three termination structures were considered: TeI, TeII, and Bi terminations, which are relatively stable surface structures that were described in our previous study42 (Fig. 1c–e). The Vienna ab-initio simulation package (VASP)45,46 with the projector-augmented wave method47,48 was used for the first-principles calculations. For the exchange–correlation function, the generalized gradient approximation and Perdew–Burk–Ernzerhof function were used49. 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).

Figure 1
figure 1

Structural models of (a) Bi2Te3 and (b) orthorhombic MASnI3 used for the DMM calculation; calculated interface structures of (c) Bi2Te3(TeI)/MASnI3, (d) Bi2Te3(TeII)/MASnI3, and (e) Bi2Te3(Bi)/MASnI3. The interface crystal plane is (001). The (001) crystal plane was used for both Bi2Te3 and MASnI3, with an ~ 15 Å vacuum layer inserted.

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Calculation of thermal conductance using DMM

For the thermal conductance calculation, phonon calculation of the interface structure between Bi2Te3 and MASnI3 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 DMM44, 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:

$$ G = \frac{1}{{2\left( {2\pi } \right)^{3} }}\mathop \sum \limits_{i} \mathop \int \limits_{{\varvec{k}}} \frac{1}{{k_{B} T^{2} }}\alpha_{A \to B} \left( {{\varvec{k}},i} \right) \times \left( {\hbar \omega \left( {{\varvec{k}},i} \right)} \right)^{2} \left| {{\varvec{V}}\left( {{\varvec{k}},i} \right).{\varvec{n}}} \right|\frac{{{\text{exp}}\left( {\frac{{\hbar \omega \left( {{\varvec{k}},i} \right)}}{{k_{B} T}}} \right)}}{{\left[ {{\text{exp}}\left( {\frac{{\hbar \omega \left( {{\varvec{k}},i} \right)}}{{k_{B} T}}} \right) - 1} \right]^{2} }}d\user2{k,} $$
(1)

where \(\alpha_{A \to B} \left( {{\varvec{k}},i} \right)\) is the transmission probability of A to B, \(\omega \left( {{\varvec{k}},i} \right)\) is the phonon frequency corresponding to wave vector k and phonon mode I, and \(\left| {{\varvec{V}}\left( {{\varvec{k}},i} \right).{\varvec{n}}} \right|\) 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:

$$ \alpha_{A \to B} \left( {\omega^{\prime } } \right) = \frac{{\Delta K_{B} \left[ {\mathop \sum \nolimits_{{j,{\varvec{k}}}} \left| {{\varvec{V}}\left( {{\varvec{k}},j} \right).{\varvec{n}}} \right|} \right]\delta_{{\omega \left( {{\varvec{k}},j} \right),\omega^{\prime } }} }}{{\Delta K_{A} \left[ {\mathop \sum \nolimits_{{i,{\varvec{k}}}} \left| {{\varvec{V}}\left( {{\varvec{k}},i} \right).{\varvec{n}}} \right|} \right]\delta_{{\omega \left( {{\varvec{k}},i} \right),\omega^{\prime } }} + \Delta K_{B} \left[ {\mathop \sum \nolimits_{{j,{\varvec{k}}}} \left| {{\varvec{V}}\left( {{\varvec{k}},j} \right).{\varvec{n}}} \right|} \right]\delta_{{\omega \left( {{\varvec{k}},j} \right),\omega^{\prime } }} }}, $$
(2)

where \(\Delta K_{A}\) and \(\Delta K_{B}\) are the discretized cells of the Brillouin zones of A and B, respectively, and \(\delta_{{\omega \left( {{\varvec{k}},i} \right),\omega^{{^{\prime } }} }}\) 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 needed50.

The phonon dispersions of Bi2Te3 and MASnI3 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 Bi2Te3 and MASnI3 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 MASnI3 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 code51 to create the displacement using the finite displacement method, and the ALAMODE52 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 Bi2Te3 termination structures: Bi2Te3(TeI)/MASnI3, Bi2Te3(TeII)/MASnI3, and Bi2Te3(Bi)/MASnI3 (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 MASnI3 was tetragonal, which was stable at room temperature. In the creation of the interface models, the lattice distance of MASnI3 was reduced to fit that of Bi2Te3.

Table 1 lists the lattice parameters of various interface models after structural optimization. The termination structure of Bi2Te3 affected the lattice constant of the interface model; the TeII termination exhibited the lowest values for the a- and b-axes compared with the TeI and Bi termination structures (Table 1). This result also led to a decrease in the lattice deformation ratio in the Bi2Te3(TeII)/MASnI3 structure, as indicated in Table 2. The lattice deformation ratio was calculated using the following equation: deformation (%) = (d2/d1 – 1) × 100, where d2 and d1 represent the lattice distance of the transformed or optimized structure and the lattice distance of the bulk structure, respectively. On the other hand, the Bi2Te3(Bi)/MASnI3 structure exhibited a high lattice deformation ratio among the three interface models; the lattice of Bi2Te3 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.

Table 1 Lattice parameters of various interfaces after structural optimization.
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Table 2 Lattice deformation ratios of various interfaces after structural optimization.
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After structural optimization, the atoms in the interface moved strongly with an incomplete structure for Bi2Te3 with the TeII 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 TeII and Bi termination structures form an interaction between Bi2Te3 and MASnI3 compared with the TeI 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 Bi2Te3 and MASnI3, we calculated the binding energy using the following equation: Ebind = Etotal – Ep – Eb, where Etotal, Ep, and Eb denote the energies of Bi2Te3/MASnI3, the MASnI3 (001) surface, and the Bi2Te3 (001) surface, respectively (Fig. 2). Ep, and Eb 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, Bi2Te3(TeI)/MASnI3 is the most unstable interface structure; in contrast, Bi2Te3(Bi)/MASnI3 is the most stable interface structure, with a binding energy of − 1.7 eV. Similar to the Bi termination model, Bi2Te3(TeII)/MASnI3 exhibited a negative binding energy of − 0.3 eV. Note that the corresponding interfacial energy, which is represented by energy/area, are 1.59 eV/nm2 for Bi2Te3(TeI)/MASnI, − 0.42 eV/nm2 for Bi2Te3(TeII)/MASnI3, and − 2.36 eV/nm2 for Bi2Te3(Bi)/MASnI3. The optimized structures suggest that the stability of the interface structure is attributable to the reconstruction of atoms in the interface.

Figure 2
figure 2

Binding energies of various Bi2Te3/MASnI3 interfaces with different Bi2Te3 termination structures.

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Electronic properties of Bi2Te3/MASnI3 interfaces

The total and partial DOS around the Fermi energy for various Bi2Te3/MASnI3 interfaces are shown in 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 Bi2Te3 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 Bi2Te3, which is attributed to the difference in the ratio of Bi and Te atoms. The partial DOS of MASnI3 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 MASnI3 in contact with the vacuum layer. In the DOS around the Fermi energy in the TeII and Bi termination structures (Fig. 3b,c), the additional electronic state appeared at similar energy levels for both Bi2Te3 and MASnI3, indicating that the additional electronic state includes the contributions of both Bi2Te3 and MASnI3.

Figure 3
figure 3

Total and partial DOS around the Fermi energy of (a) Bi2Te3(TeI)/MASnI3, (b) Bi2Te3(TeII)/MASnI3, and (c) Bi2Te3(Bi)/MASnI3.

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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 MASnI3 (MASnI3-3L) 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 Bi2Te3 termination. In particular, on the Bi2Te3(Bi)/MASnI3 interface, the conduction band of MASnI3-1L 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 Bi2Te3 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 Bi2Te3 structure. The Bi2Te3(Bi)/MASnI3 interface also had the potential to be affected by the movement of Bi atoms.

Figure 4
figure 4

Decomposed DOS of each layer near interface for (a) Bi2Te3(TeI)/MASnI3; (b) Bi2Te3(TeII)/MASnI3; and (c) Bi2Te3(Bi)/MASnI3. The DOS of Bi, Te, Sn, and I consist of the sum of the s- and p-orbitals. The atoms included in each layer are shown in Fig. 5. The arrows indicate interface levels formed from Bi2Te3 and MASnI3.

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Figure 5
figure 5

Decomposition method for each layer in the (a) Bi2Te3(TeI)/MASnI3, (b) Bi2Te3(TeII)/MASnI3, and (c) Bi2Te3(Bi)/MASnI3 interface structures and the atoms included in each layer.

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Focusing on the first layers from the interface of Bi2Te3 and MASnI3, the additional electronic state is observed at the same energy level in the layer near the interface between Bi2Te3 and MASnI3. 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 Bi2Te3(TeII)/MASnI3 and Bi2Te3(Bi)/MASnI3 structures. These results also suggest that the incomplete structure of Bi2Te3, such as the TeII and Bi terminations, plays an important role in the formation of interface states. The TeI termination did not produce an overlap in the DOS between Bi2Te3 and MASnI3 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 TeI termination, which is localized at the MASnI3 side, and is not observed at the interface between Bi2Te3 and MASnI3. This suggests a decreasing affinity of Bi2Te3 and MASnI3. On the other hand, the interface structure with the TeII 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). Figure 6(d) and (e) show that the charge distribution of Bi2Te3(Bi)/MASnI3 is localized at the interface, similar to Bi2Te3(TeII)/MASnI3. In this case, the overlap of the charge density appears in the valence band of − 0.5 to − 0.2 eV. These results suggest that the overlapping of the charge distribution increases the affinity of the interface and assists in charge transfer between Bi2Te3 and MASnI3. For all interface structures, the charge density is localized at the surface of MASnI3 at − 0.2 eV to 0.2 eV. From the perspective of a thermoelectric material, the material requires a high electrical conductivity and Seebeck coefficient and a low thermal conductivity. The Seebeck coefficient is related to the shape of the DOS around the Fermi energy53, and the formation of interface levels may lead to a change in its value. Further work is needed to clarify the thermoelectric properties of the Bi2Te3/MASnI3 interface structure.

Figure 6
figure 6

Visualization of charge distributions at selected energy levels for (a) Bi2Te3(TeI)/MASnI3; (b) and (c) Bi2Te3(TeII)/MASnI3; (d) and (e) Bi2Te3(Bi)/MASnI3. The indicated energy ranges are − 0.2 to 0.2 eV for (a), (b), and (d); 0.2–0.5 eV for (c); and − 0.5 to − 0.2 eV for (e).

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Phonon properties of Bi2Te3 and MASnI3

Next, we estimated the interfacial thermal conductance of the Bi2Te3/MASnI3 interface. Figure 7 shows the phonon dispersions and atomic projected phonon DOS of (a) Bi2Te3 and (b) MASnI3. Bi2Te3 exhibited low energy phonon modes below 150 cm−1, and MASnI3 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 MASnI3 showed a low-energy mode in the same range as Bi2Te3 until approximately 150 cm−1. Based on the phonon dispersion results for Bi2Te3 and MASnI3, 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 Bi2Te354 and MAPbI3 (not MASnI3)55,56.

Figure 7
figure 7

Phonon dispersions and atomic projected phonon DOS of (a) Bi2Te3 and (b) MASnI3.

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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 Bi2Te3 and a-, b-, and c-axes in MASnI3. 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, Bi2Te3 exhibited a high group velocity at under 10 cm−1, whereas MASnI3 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 Bi2Te3 and MASnI3. For MASnI3, the group velocity was not dependent on the direction of the crystal axis. It has been experimentally reported that Bi2Te3 exhibits a group velocity of 1750 m/s based on nuclear resonant inelastic scattering57, whereas MAPbI3 has exhibited group velocities of acoustic modes of 2400 or 1200 m/s based on neutron scattering58. Although there is a difference in the structures between our calculations (MASnI3) and the previous experiments (MAPbI3), our calculated values are approximately consistent with the experimental data.

Figure 8
figure 8

Group velocities of Bi2Te3 along the c-axis and MASnI3 along the a-axis, b-axis, and c-axis.

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Interfacial thermal conductance between Bi2Te3 and MASnI3 at the interface

The interfacial thermal conductance of the Bi2Te3/MASnI3 interfaces was estimated by DMM using the group velocities of both structures. Figure 9 shows the interfacial thermal conductance of the Bi2Te3/MASnI3 interface; the combination of all axes of MASnI3 and the c-axis of Bi2Te3 was evaluated. The obtained values for the interfacial thermal conductance with different Bi2Te3/MASnI3 interfaces were 1.5–2.0 MW/m2K. This result indicates that the interfacial thermal conductance was not affected by the orientation of MASnI3 because the differences between different directions were small, as shown in the phonon dispersion curve (Fig. 7b). The calculated interfacial thermal conductance of Bi2Te3/MASnI3 was lower than the calculated value of the inorganic/inorganic interface44. The reason for this is explained as follows: calculated phonons in Bi2Te3 and MASnI3 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 Bi2Te3/MASnI3 interface shows a relatively low interfacial thermal conductance.

Figure 9
figure 9

Interfacial thermal conductance of the Bi2Te3/MASnI3 interface along the a-axis, b-axis, and c-axis of MASnI3.

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Moreover, it was as low as the experimental values for inorganic/organic interfaces such as a graphene-Bi2Te3 heterostructure (~ 3.46 MW/(m2·K))59 and PEDOT:PSS-Bi2Te3 heterostructure (~ 10 MW/(m2·K))60 Therefore, these results suggest that the Bi2Te3/MASnI3 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 Bi2Te3/MASnI3 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 Bi2Te3 and MASnI3 hybrid material

Although the actual thermal transport mechanism, such as superlattices with very short periodicity61, is too complex to explore here, we have aimed to discuss the effect of the interfacial thermal conductance of Bi2Te3/MASnI3 on the effective thermal conductivity, κ using a simple composite model. Here, a one-dimensional model is used, in which Bi2Te3 layers and MASnI3 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 Bi2Te3/MASnI3 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 Bi2Te3 and MASnI3: 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 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/(m2·K). The smaller the film thickness, the more effectively the interfacial thermal conductance of Bi2Te3/MASnI3 can be utilized. Thus, it is expected that the thermal conductivity of the Bi2Te3/MASnI3 composite, which consists of small Bi2Te3 grains in MASnI3, will be significantly reduced.

Figure 10
figure 10

Thermal conductivity of the Bi2Te3 and MASnI3 hybrid material.

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Conclusion

In this study, we evaluated the stability and electronic state of interface structures of Bi2Te3 (001) and MASnI3 (001), and the thermal conductance of the interface between Bi2Te3 and MASnI3 along the (001) direction was estimated. In the structural optimization, the termination of MASnI3 was fixed with SnI2 at the interface and surface, whereas for the structure of Bi2Te3 in contact with MASnI3, three termination structures were considered: TeI, TeII, and Bi termination. After structural optimization, around the Fermi energy, the interface structures with TeII and Bi termination resulted in the formation of interface levels attributed to the overlapping electron densities for both Bi2Te3 and MASnI3 at the interface. It is believed that the formation of interface levels enhances the affinity for the interface structure of Bi2Te3 and MASnI3, 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 Bi2Te3/MASnI3 interface can significantly reduce the thermal conductivity. These results indicate that the Bi2Te3/MASnI3 composite material is a possible candidate for an excellent thermoelectric material because it has the potential to decrease the thermal conductivity.