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Xinyi He, Kenji Matsuo, [Takayoshi Katase](https://orcid.org/0000-0002-2593-7487), [Kota Hanzawa](https://orcid.org/0000-0002-0995-9360), Hideto Yoshida, [Shigenori Ueda](https://orcid.org/0000-0001-9425-0614), [Hidenori Hiramatsu](https://orcid.org/0000-0002-5664-5831), [Hideo Hosono](https://orcid.org/0000-0001-9260-6728), Toshio Kamiya

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in ACS Applied Nano Materials, copyright ©  2025 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acsanm.5c00686.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Nanoscale Origin of Strong Charge Carrier Scattering at Grain Boundaries in Orthorhombic SnSe Semiconductor Thin Films](https://mdr.nims.go.jp/datasets/bcfac7a0-012d-4e7c-af86-9a83433e3797)

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1  Nanoscale Origin of Strong Charge Carrier Scattering at Grain Boundaries in Orthorhombic SnSe Semiconductor Thin Films Xinyi He1,2, Kenji Matsuo1, Takayoshi Katase1,3,*, Kota Hanzawa3, Hideto Yoshida4, Shigenori Ueda5,6, Hidenori Hiramatsu1,3, Hideo Hosono1,and Toshio Kamiya1,3,* 1 MDX Research Center for Element Strategy, Institute of Integrated Research, Institute of Science Tokyo, 4259 Nagatsuta, Midori, Yokohama 226-8501, Japan 2 Kanagawa Institute of Industrial Science and Technology, 705-1 Shimoimaizumi, Ebina, Kanagawa 243-0435, Japan 3 Materials and Structures Laboratory, Institute of Integrated Research, Institute of Science Tokyo, 4259 Nagatsuta, Midori, Yokohama, 226-8501, Japan 4 SANKEN, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan 5 Research Center for Electronic and Optical Materials, National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki, 305-0044, Japan 6Synchrotron X-ray Station at SPring-8, NIMS, 1-1 Sayo, Hyogo 679-5148, Japan  * Correspondence to: katase.t.aa@m.titech.ac.jp, kamiya.t.aa@m.titech.ac.jp  Keywords: Tin selenide; Thermoelectric material; Epitaxial film; Carrier transport; Defect; Density functional theory  2  ABSTRACT: Tin mono-selenide (SnSe) is one of the high-performance thermoelectric materials, and recent progress has been made in its application to thin-film thermoelectric devices. However, the performance of SnSe polycrystalline and epitaxial films has been limited by their electronic conductivity lower than the single crystal due to strong carrier scattering. In this paper, we investigated the origin of carrier scattering through nanoscale characterization of a-axis oriented SnSe films with different grain boundary (GB) structures (i.e., a-axis misorientations and in-plane rotational GBs). The a-axis oriented SnSe polycrystalline films grown on glass substrates and epitaxial films on MgO (001) substrates show p-type conduction. In-grain carrier mobility increases with the increased grain size and improved out-of-plane a-axis orientation at higher growth temperatures, but the hole transport in the films is dominated by GB scattering. For SnSe films with the out-of-plane misorientation angles larger than 5°, GBs form potential barriers with a height (Eb) of up to 62 meV and significantly reduce carrier mobility (μ). Meanwhile, when the out-of-plane misorientation angles are less than 5°, the effect of a-axis orientation fluctuations on μ becomes small, but the room-temperature µ is limited to ~50 cm2/(Vs), regardless of the different in-plane misorientations. It is found that (100) SnSe epitaxial films on a MgO (001) substrate form 90° rotational domains composed of in-plane [011] and [01-1] oriented grains, and have GB potential barriers with Eb = 30 meV, which is lower than those in the a-axis misoriented SnSe polycrystalline films but still deteriorates µ. Density functional theory calculations show that the 90° rotational domain boundary causes a shift of SnSe molecular layers between the [011] and [01-1] oriented grains, and the distorted Sn-Se3 polyhedra form hole trap states above the fundamental valence band maximum, which can explain the formation of the GB potential barriers. Controlling crystallite orientation and size is a critical factor to realize high µ SnSe films for thermoelectric device applications.     3  1. INTRODUCTION Tin mono-selenide (SnSe) has received great attention as a high-performance thermoelectric material with a record conversion efficiency (ZT) of up to 2.6 for single crystals.1 SnSe is a p-type semiconductor with a band gap of 0.9-1.0 eV,2,3 and its single crystals exhibit a high hole mobility (µ) of ~200 cm2/(Vs) at room temperature (RT).4-7 On the other hand, we previously reported high-quality SnSe epitaxial films on MgO (001) substrates.8 The SnSe epitaxial film exhibits µ ~50 cm2/(Vs) with a low hole concentration ~8×1015 cm-3 at RT. Additionally, a high µ ~50 cm2/(Vs) in maximum was demonstrated also for SnSe polycrystalline films on glass substrates, and a relatively high µ ~10 cm2/(Vs) was achieved in SnSe films deposited even at RT (without heating the substrate). Therefore, SnSe is a promising semiconductor for thin film devices that can be formed at low temperatures on glass or flexible substrates. Recently, significant progress has been made in thin film growth,9,10 carrier doping,11-12 investigation of thermoelectric properties,13-17 and development of thin-film thermoelectric modules.12,18 However, the electrical conductivity of SnSe polycrystalline and epitaxial films has been an order of magnitude lower than that of single crystal, because the µ of polycrystalline/epitaxial films are limited by strong carrier scattering. SnSe has a GeS-type orthorhombic crystal structure (space group: Pnma) composed of alternately stacked one-molecule-thick SnSe layers along the a-axis (Fig. 1).19 Each SnSe layer has Sn-Se3 coordination structure (purple polyhedron), in which an Sn atom is coordinated by two Se atoms in the same b–c plane and one Se atom at the adjacent atomic plane in the stacking direction. The layered structure of SnSe causes highly anisotropic carrier transport; i.e., the effective masses of holes along the a-axis (perpendicular to the layer) are much larger than those along the b- and c-axes (parallel to the layer),20 indicating that much higher µ can be realized along the in-plane b- and c-axes rather than those along the out-of-plane a-axis. In addition, SnSe exhibits strong in-plane anisotropy in electrical conductivity,21  4  due to the different atomic structures and bonding characteristics along the b- and c-axes (Fig. 1). Rock-salt type atomic arrangement is seen along the b-axis (left panel of Fig. 1), while the adjacent SnSe layer is shifted by [0, 0, 0.38] in fractional coordinates along the c-axis, as indicated by the arrow in right panel of Fig. 1. The a-axis oriented SnSe films can be grown on MgO (001) and glass substrates, which is advantageous for achieving high µ films. However, the orthorhombic lattice of SnSe along the b- and c-axes forms in-plane 90° rotational domain structures in the a-axis oriented epitaxial films on MgO (001) substrates, which likely cause strong carrier scattering and reduces µ to ~50 cm2/(Vs), which is far lower than that of single crystal ~200 cm2/(Vs).8 On the other hand, the µ of a-axis oriented SnSe polycrystalline films on glass substrates was expected to further decrease compared to the epitaxial films. Interestingly, nearly the same µ ~ 50 cm2/(Vs) is maintained despite the completely unoriented domains along the in-plane direction. The electronic performance of polycrystalline thin films critically depends on the crystallite quality of each domain and the properties of grain boundaries (GBs). Typically, strain, defects, and dislocations formed at GBs act as strong scattering centers for carrier transport.22 Also, charge trapping states formed at the GBs create potential barriers for carrier transport, limiting the µ. The broken local symmetry and chemical bonding strongly affect the electronic states at GBs.23 Understanding the effects of crystallite misorientations and rotational GBs on carrier transport of layered SnSe thin films is crucial to design and improve semiconductor devices.  In this paper, we investigate the electron transport properties of a-axis oriented SnSe films with different GB structures such as a-axis misorientations and rotational GBs, and evaluate the electronic structure of 90o rotational GBs to explore the nanoscale origin of strong carrier scattering. SnSe polycrystalline and epitaxial films grown on glass and MgO (001) substrates exhibit p-type conduction, and the hole transport in the films is dominated by GB scattering at RT. We evaluate GB characteristics from temperature dependence of µ, and discuss the correlation between carrier transport and microstructures of the SnSe films.  5   2. EXPERIMENTAL SECTION 2.1. Thin film growth. 100-nm thick SnSe films were fabricated on alkali-free glass substrates (Corning® EAGLE XG®) at growth temperature (Tg) = RT-500 oC in a vacuum by pulsed laser deposition (PLD). A SnSe epitaxial film was grown on a MgO (001) substrate at Tg = 500 oC. Note that the maximum Tg was limited by severe re-evaporation of the films at ≥ 600 °C. The Se-rich SnSe1.2 bulk polycrystal was used as a PLD target, because the transferability of Se from the PLD target to thin films is lower than that of Sn even at low temperatures.8,24,25 A KrF excimer laser (wavelength of 248 nm) with a repetition rate of 10 Hz was used to ablate the SnSe1.2 polycrystalline target. The base pressure of deposition chamber was ~1×10−5 Pa. Note that we first optimized the growth rate for SnSe films on glass substrates at Tg = 500 oC by changing laser energy fluence from 0.6 to 3 J/cm2 (Fig. S1 of Supporting Information). Lower growth rate increased the µ, and the decrease of nucleation density led to increase of grain sizes and the improved crystallite orientation. Therefore, the film growth rate was optimized at the lowest value of 0.4 nm/s. 2.2. Thin film characterization. Lattice parameters and crystal orientation of SnSe films for out-of-plane (i.e., perpendicular to the sample surface) and in-plane (i.e., parallel to the surface) were analyzed by x-ray diffraction (XRD) using a Smart Lab. (Rigaku Corp.). The films on glass substrates were measured by XRD with a parallel-beam Cu Kα radiation source at RT. The films on the MgO (001) substrate were measured by high-resolution XRD with a parallel-beam Cu Kα1 radiation source monochromated with a two-bounce Ge (220) crystal. The out-of-plane measurements were performed by w-coupled 2q scans, while the in-plane measurements were performed by f-coupled 2qc scans. For in-plane measurements, the x-ray incident angle was set to the total reflection critical angle, w ~0.5o. For the SnSe films on MgO substrate, 2qc was initially set at 200 diffraction angle of MgO and f was adjusted to the  6  strongest peak position, after which f-coupled 2qc scans were performed. In-plane crystallite sizes (D) were estimated from Scherrer’s equation of D = Kλ/(bcosθ), where K is the Scherrer constant (K = 0.94), λ the wavelength of x-ray, b the full width at half-maximum (FWHM) value of diffraction peak, and θ the Bragg angle. The b values were obtained from 020 diffraction peaks for the SnSe films on glass substrates and 002 diffraction peak for the SnSe film on the MgO substrate by in-plane XRD. The intrinsic b values of the samples were estimated by correcting the apparatus function using the Gaussian profile approximation, 𝛽!"#$!"%!& = $(𝛽'"'()) − (𝛽*+,))  (𝛽*+,  is a FWHM from a reference ‘ideal’ sample. We employed the 200 diffraction peak of the MgO single crystal). Since the obtained b values are dependent on q, it is preferable to use the diffraction peaks (200 or 020) of SnSe, whose diffraction angles are close to those of the 200 diffraction peak of MgO. The tilting angle of the crystallites was analyzed by 2q-fixed w scans (out-of-plane x-ray rocking curve). The in-plane orientation of the crystallites was investigated by 2qc-fixed f scans (in-plane x-ray rocking curve). The film thickness (d) was determined by x-ray reflectivity measurement. The chemical composition (i.e., atomic ratio of Sn and Se) was evaluated with an electron probe micro analyzer (EPMA). Film surface morphology was observed by atomic force microscopy (AFM). Microstructure observation of the films was conducted by a scanning transmission electron microscope (STEM, JEM-ARM200F, JEOL Ltd.) with an acceleration voltage of 200 kV, where the samples were thinned by focused ion beam (FIB) and Ar+ ion milling. Electronic properties from RT to lower temperatures were measured by the Hall effect using the van der Pauw configuration under AC-modulated magnetic fields of 0.35 T (ResiTest 8300, Toyo Corp.), which provided electrical conductivity (σ), Hall coefficient (RH), carrier concentration (n), and μ. Constant current of 1 µA was applied for the Hall effect measurements. Pt electrode, deposited by electron-beam evaporation, was used for Ohmic contact.  2.3. Density functional theory calculation. Electronic structure calculations of SnSe model  7  with rotational GBs (explained later in detail) were conducted using the projector-augmented wave (PAW) method, as implemented in the Vienna Ab initio Simulation Package (VASP).26,27 The valence states included Sn [4d5s5p] and Se [4s4p] states. The structure optimization calculations employed the generalized gradient approximation (GGA) Perdew–Burke–Ernzerhof (PBE) functional28 with a plane wave cutoff energy of 350 eV and a Γ-centered k-spacing of 0.2 Å–1.   3. RESULTS & DISCUSSION 3.1. Crystal structures. Table 1 summarizes the crystal structure characteristics and chemical compositions of the SnSe films grown on glass and MgO (001) substrates. Detailed information of crystal structure and chemical composition analyses are summarized in Figs. S2-S9 of Supporting Information. The a-axis oriented SnSe polycrystalline films were grown on glass substrates at Tg = RT-500 oC (Fig. S2 of Supporting Information). The Se/Sn ratio was almost constant at 1.00-1.01, regardless of Tg. With increase of Tg, the a-axis lattice parameter (a) decreased and the c-axis one (c) increased, while the b-axis one (b) was almost constant. As seen in Fig. 1, Se-Sn-Se chemical bonding is formed along the b-axis while non-bonding Sn-Se connects along the a- and c-axes; that is, the non-bonding states are more fragile and easily deformed by temperature variation. As a result, the lattice volume (V) increased and became close to that (212.29 Å3) of SnSe bulk29 at higher Tg. FWHM values of out-of-plane 400 diffraction peaks (Dw400) decreased from 10.5o to 4.8o with increase of Tg up to 500 oC; i.e., the degree of a-axis orientation was significantly improved by increasing Tg. The in-plane Scherrer crystallite sizes (D) increased from ~8 to ~20 nm with increase of Tg. The a-axis oriented SnSe film was epitaxially grown on the MgO (001) substrate with 90° rotational in-plane domain structure, i.e., the epitaxial relationship was [100] SnSe || [001] MgO for out-of-plane direction and [010][001]SnSe || MgO [100] for in-plane direction. The c was slightly  8  smaller and the a was larger than those of the film grown on glass substrate at same Tg = 500 oC. It is considered that the in-plane compressive strain -3.7% along the c-axis from the MgO substrate (a = 4.210 Å) decreased the c of the film, while the expansion of a was caused by the epitaxial strain.8 The Dw400 was 0.2o, indicating the strong a-axis orientation along out-of-plane direction. The SnSe epitaxial film exhibited the spiral domain growth (Fig. S6 of Supporting Information), and the in-plane Scherrer D was estimated to be ~17 nm.  Figure 2 compares the plan-view STEM images for the a-axis oriented SnSe polycrystalline film grown on glass substrate and the epitaxial film grown on MgO (001) substrate at the same Tg = 500 oC. For the SnSe film on glass substrate (Fig. 2(a)), 100-200 nm sized granular structures were observed. The electron diffraction showed the ring pattern (inset of Fig. 2(a)), indicating that the SnSe films formed randomly oriented domain structures along the in-plane direction. On the other hand, a unique GB structure was found for the SnSe epitaxial film on MgO substrate (Fig. 2(b)). The lattice images of SnSe in A and B domains, rotated by 90o, were clearly observed, but the boundary between A and B domains was formed along the [011] and [01-1] directions, as indicated by the yellow line. In the crystal structure of layered SnSe, the adjacent layer is shifted by [0, 0, 0.38] along the c-axis, as indicated by the arrow in the right panel of Fig. 1. It was thought that two simple 90° rotational coincident GB structures could exist. One is built directly by the connection of a [010] oriented domain to a [001] oriented domain (Fig. 1). However, in this structure, the top SnSe molecular layer can form Sn-Se bonds but the second SnSe molecular layer would form Sn-Sn and Se-Se bonds; therefore, we can speculate this GB structure would be energetically / chemically unstable. On the other hand, as will be discussed later with Fig. 7(a), a GB structure where a [011] oriented domain connected to a [01-1] oriented domain forms Sn-Se bonds in all the layers and is expected to be stabler. This structure is actually observed by STEM in Fig. 2(b).   3.2. Electron transport properties. Figure 3 compares the temperature (T) dependences of  9  electronic properties for the a-axis oriented SnSe polycrystalline films on glass substrates and the epitaxial film on MgO (001) substrate. Here, Hall effect measurements and analyses were conducted by selecting samples with the significantly different conditions of low Tg (RT, 100°C) and high Tg (400°C, 500°C). All the films showed the decreasing s with decreasing T, being semiconducting behaviors (Fig. 3(a)). The SnSe polycrystalline films on glass substrates exhibited s = 0.1 S/cm at 300 K, regardless of different Tg. The s was almost the same with the epitaxial film on MgO substrate. All films showed positive RH, substantiating p-type conduction. The n of holes decreased with decrease of T (Fig. 3(b)). The n at 300 K for SnSe polycrystalline films on glass substrates gradually decreased from 1017 cm-3 to 1016 cm-3 with increasing Tg from RT to 500 oC. It is well known that the Sn vacancy (VSn) acts as a shallow acceptor in SnSe.30,31 We could not detect any difference in the Sn/Se chemical compositions (Table 1); however, the increase of n is speculated to originate from the increase in the amount of VSn as Tg decreases. Detailed discussion is described in Supporting Information (Figs. S10-S12). The µ of all the films decreased with decreasing T due to the strong carrier scattering at lower T. On the other hand, µ at 300 K varied significantly with the change of Tg. The µ was 5 cm2/(Vs) at 300 K for SnSe films grown at RT, and it increased to 46 cm2/(Vs) as Tg increased to 500 oC. On the other hand, the SnSe epitaxial film showed comparable µ = 49 cm2/(Vs) at 300 K and a similar T dependence to those for the SnSe films grown on glass substrate at 500 oC, despite the large difference in the in-plane domain orientations.   3.3. Carrier mobility analysis. The T dependence of μ in the Arrhenius plots (Fig. 4(a)) showed thermally activated behaviors. For all the films, the ln(μT1/2) vs T–1 plots exhibited negative-sloping straight lines in the whole T range, suggesting that the hole transport in these films was dominated by GB scattering, as proposed by Seto,32 with the form of ln*𝜇𝑇-/)- =− /!0"1+ ln / 234)56∗0"0, where Eb is the GB potential barrier height, L domain size, m* the carrier  10  effective mass, kB Boltzmann constant, q elementary charge. In this case, hole transport is disturbed by potential barriers formed due to the holes trapped by donor-type defects at the GBs. The Eb and L were estimated by fitting the Seto model to the experimental results, as shown by solid lines in Fig. 4(a). The Eb decreased from 62 meV to 30 meV with increasing Tg from RT to 500 oC (top panel of Fig. 4(b)). By the Seto model, Eb in many semiconductors tend to decrease with increasing n, because higher-density carriers screen the GB background charges and reduce the GB barrier height. However, the Eb of SnSe polycrystalline films on glass substrates showed an opposite trend; i.e., Eb decreased with decreasing n. This result suggests that the improved a-axis orientation of SnSe polycrystalline films leads to low hole trap density and the reduction of Eb at the GBs with increasing Tg, as will be discussed later. Then, L was estimated using reported m* values of 0.16 m0 along the c-axis and 0.38 m0 along the b-axis.33 The L values averaged along the b- and c-axes are plotted in the middle panel of Fig. 4(b). L increased from 3 to 8 nm, which is almost consistent with the Scherrer D from XRD measurements (Table 1). We calculated the mean free path of hole using the thermal velocity (𝑣 =  23𝑘7𝑇/𝑚∗) (note the films are non-degenerated) and carrier life time (t) estimated from the Hall mobility and the band effective mass (𝜏 = 𝜇𝑚∗/𝑒). The mean free path of hole is estimated to be 1.69 nm for SnSe epitaxial film with µ = 49 cm2/(Vs) at T = 300 K. This value is smaller than the Scherrer radius, indicating the intra-grain scattering such as phonon scattering dominates and reduces the mean free path. Then, we estimated in-grain carrier mobility (μg) by extrapolating Eb to 0, leading to the formula 𝜇+ = / 234)56∗0"0𝑇9-/). The μg at T = 300 K increased from 58 to 157 cm2/(Vs) with increase of Tg (bottom panel of Fig. 4(b)), which related to the increase of grain size, the improvement of the crystal quality, and the decrease of VSn defects at higher Tg. The SnSe epitaxial film exhibited almost the same GB properties (Eb = 30 meV, L = 9 nm) as the polycrystalline film grown on glass substrate at the same Tg = 500 oC. The μg = 186 cm2/(Vs) is comparable to µ = 240 cm2/(Vs) along the b-axis  11  and 130 cm2/(Vs) along the c-axis of the SnSe single crystal.1 Therefore, each crystallite in the SnSe films grown both on MgO (001) and glass substrates at Tg = 500 oC exhibited single-crystal-like electron transport properties, but the GB potential barrier is the limiting factor of carrier transport. Based on the Seto model, the hole trap state density (Qt) at the GBs was characterized by the equation of  𝑄: = −$;/!<=$3, where the e is the dielectric permittivity and the nA is acceptor state density. The nA was estimated from the Arrhenius plots of n (Fig. S10(c) of Supporting Information), and the Qt was calculated by using the reported ε values ~62 along the b-axis and ~42 along the c-axis.34 The Qt values averaged along the b- and c-axes are plotted in Fig. 5(a). The Qt of all the films were smaller than the total number of the acceptors in a grain (LnA), suggesting that only the region near the GBs was depleted while free holes remain in the other regions. The Qt of SnSe films on glass substrates decreased from 4.9×1013 cm–2 to 2.0×1013 cm–2 as Tg increased from RT to 500 oC. On the other hand, the SnSe epitaxial film on MgO (001) substrate showed much smaller Qt = 1.3×1013 cm–2. The variation of Eb and Qt in the SnSe films at low and high Tg is illustrated in Fig. 5(b). The grain size of the SnSe films increases at higher Tg condition, resulting in the decrease of GB density. The LnA value was almost unchanged with the change of Tg, while the Qt decreased, resulting in the lower Eb and higher µ for SnSe films grown at higher Tg.    3.4. Origin of carrier scattering in SnSe films. Here, we summarize the relationship between μ, crystallite orientations, and GB characteristics for SnSe films. The μ for a-axis oriented SnSe polycrystalline films increases as the out-of-plane Dw400 decreases with increasing Tg, indicating that the a-axis orientation of the SnSe layers affects the carrier transport significantly (Fig. 6(a)). At the same time, the decrease of Dw400 results in a decrease of Eb, which also leads to an increase in μ (Figs. 6(b)). On the other hand, the μ and Eb hardly change when Dw400  12  becomes below 5°. Based on these findings, it can be concluded that the GBs of SnSe films with poor a-axis orientation form higher Eb, significantly reducing the μ. On the other hand, if the SnSe layers are strongly oriented along the a-axis with Dw400 ≤ 5o, the impact of a-axis orientation fluctuations on μ becomes small. The SnSe epitaxial film with much smaller Dw400 = 0.2o exhibits almost the same μ ~ 50 cm2/(Vs) for the SnSe polycrystalline films grown at Tg = 500 oC, regardless of the large difference in the in-plane domain orientations. This result suggests that the GBs formed by 90° rotational domain structure are the limiting factor of μ in the SnSe films with Dw400 ≤ 5o. Note that the FWHM of rocking curves represents not only misorientations of the crystallites but also other factors such as dislocations and lattice strain. Further analysis by atomic-scale characterization is necessary to separately address the effect of dislocations, misorientations, and lattice strain on the carrier mobility of SnSe films. We have previously reported the electronic properties of SnSe films on MgO (001) substrates with different Tg = 300-500 oC.8 Epitaxial growth of SnSe film was confirmed at Tg = 400-500 oC, but the out-of-plane a-axis oriented films with no in-plane orientation was obtained at Tg = 300 oC. The µ of SnSe epitaxial films at RT slightly decreased from 49 cm2/(Vs) for Tg = 500 oC to 41 cm2/(Vs) for Tg = 400 oC. The low Tg growth decreases the grain size and reduces in-grain mobility. The Dw400 increased from 0.2o for Tg = 500 oC to 0.5-0.7o for Tg = 400 oC. The SnSe epitaxial film for Tg = 400 oC shows higher a-axis orientation and higher µ than 20 cm2/(Vs) for the a-axis oriented film on glass substrate at the same Tg. The grain size and a-axis orientation should be dominant factor for in-grain carrier mobility, but the µ also limited by GB scattering. We then evaluated the electronic structures of SnSe with 90o rotational domains by density functional theory calculations. As discussed in section 3.1, the SnSe epitaxial film on MgO (001) substrate formed a boundary with a [011] oriented and a [01-1] oriented domains. We built a SnSe GB model based on the experimental observations as follows. First the primitive SnSe cell was fully relaxed including the lattice parameters and the atomic positions. Then a  13  1×2×2 supercell was generated based on the relaxed structure. The SnSe domain was created by cutting the supercell with the (011) surface, followed by a 90° rotation to create another SnSe domain. These two domains were connected by the (011) surface to form the final SnSe GB model.  Figures 7(a,b) show the plan view and cross-sectional view of the SnSe GB model with the boundary between the [011]-oriented A domains and the [01-1]-oriented B domains (indicated by blue dashed lines). The A and B domains are connected through the Sn-Se3 polyhedra at the boundary in 1st and 2nd SnSe layers. Figure 7(c) shows the electronic band structure of SnSe GB model with the domain boundary. The in-gap state (red colored band) is found above the fundamental VBM of ideal SnSe (black bands). Figures 7(a,b) map the charge density at the VBM (indicated by arrow in Fig. 7(c)), which primarily concentrates in the vicinity of the domain boundary. A shift of SnSe molecular layers is observed between the A and B domains (arrows in Fig. 7(a)), and the domain boundary structure shows a distortion of chemical bonds; i.e., the in-plane Sn-Se bond lengths (2.76-2.95 Å) differ from those in the bulk SnSe model (2.82 Å), and the in-plane Sn-Sn distance (4.06-4.62 Å along b-axis and 4.07-4.89 Å along c-axis) are more diverse compared to the bulk SnSe model (4.20 Å along b-axis and 4.56 Å along c-axis). This distortion originates from the strain induced by the connection of the [011] and the [01-1] oriented SnSe domains that have different in-boundary b-axis length (4.20 Å) and c-axis length (4.56 Å). From the partial density of states (DOSs) of the SnSe GB model (Fig. 7(d)), Sn 5s, 5p and Se 5p form the VBM. Therefore, the distortion increases the Sn(5s,5p)-Se(5p) hybridization, causing the holes to become localized within the Sn-Se3 polyhedra, which contributes to the hole trapping state with large Eb and restricts the µ of SnSe films.   4. CONCLUSIONS  14  We investigated the origin of carrier scattering through nanoscale characterization of a-axis oriented SnSe films with different a-axis misorientations and rotational GBs. The a-axis oriented SnSe polycrystalline films grown on glass substrates and epitaxial films on MgO (001) substrates showed p-type conduction, and the hole transport in the films was dominated by GB scattering. GBs of SnSe films with low a-axis orientation (Dw400 ≥ 5o) formed high GB potential barriers with Eb up to 60 meV and significantly reduced the μ. The µ at 300 K for SnSe polycrystalline films on glass substrates was 5 cm2/(Vs) at RT, but increased to 46 cm2/(Vs) due to the increased grain size and improved Dw400 as the Tg increased to 500 oC. Meanwhile, when Dw400 of the SnSe layers was decreased to < 5o, the impact of a-axis orientation fluctuations on μ became small. It was found that SnSe epitaxial films with 90° rotational domain structure formed the domain boundary between the [011] oriented and the [01-1] oriented domains. The 90° rotational domain boundary caused a shift of SnSe molecular layers between the [011] and [01-1] oriented grains and the distorted Sn-Se3 polyhedra formed hole trap states with Eb = 30 meV, limiting the maximum µ ~50 cm2/(Vs) of SnSe films. We also believe that similar GB structures widely present in polycrystalline films, which should be further investigated in future work. It should be noted that the orthorhombic SnSe can be considered distorted from the cubic structure.24 While the orthorhombic one employs covalent bonding, the cubic one utilizes metavalent bonding.35 The degree of structural distortions affects the bonding mechanism and thus the transport properties through the GBs by changing the Tg, but further structure analyses are necessary for the discussion. These findings would be beneficial for understanding the carrier transport properties of SnSe films and the control of crystallite orientation and size is important to further enhance the carrier mobility and thermoelectric properties for device applications. The crystallite orientation can be improved and the crystallite size can be enlarged by increasing the Tg. However, the maximum Tg is limited by severe re-evaporation of the films at ≥ 600 °C in a vacuum. Therefore, it is considered difficult to improve the mobility by changing the Tg during the deposition. On the other hand, post-heat treatment at higher  15  temperature, while suppressing the volatilization, should be effective in further improving the crystal quality and enlarging the grain size. For example, preparing a surface capping layer to suppress the volatilization, followed by post-annealing in Ar atmosphere, or performing rapid laser annealing, could be more effective. It also should be noted that the poor performance of polycrystalline SnSe bulk is attributed to the formation of tin oxides covering the surface of SnSe powders, which increases thermal conductivity, reduces electronic conductivity and thereby reduces ZT.36 It should be important to investigate nanoscale chemical composition analysis near the GBs and the effect of heat treatment under reducing conditions on the electronic properties through rotational GBs in the SnSe films. Finally, it should be noted that the deterioration of µ by GBs is also observed in tin mono-sulfide (SnS),37,38 a potential semiconductor for solar cells, and tin monoxide (SnO),39,40 a potential wide-gap p-type semiconductor. They have similar layered crystal structures, and there may be a similar mechanism limiting the µ at the GBs. Further investigation is expected in the epitaxial films to improve their semiconductor device properties.   ASSOCIATE CONTENT Supporting Information  Supporting Information is available free of charge. Supporting information for growth and carrier transport analyses of SnSe films on glass and MgO (001) substrates.  AUTHOR INFORMATION Corresponding Authors Takayoshi Katase; katase.t.aa@m.titech.ac.jp Toshio Kamiya; kamiya.t.aa@m.titech.ac.jp   16  Author contributions X.H., K.M., K.H., H.Y. contributed to the thin film fabrication and characterization. All authors discussed the results and commented on the study. X.H., Ta.K., and To.K. co-wrote the manuscript. Ta.K. and To.K. proposed the idea and supervised the entire project. Note The authors declare no conflict of interest.  ACKNOWLEDGMENT This work was supported by a project of Kanagawa Institute of Industrial Science and Technology (KISTEC). Part of this research was also supported by MEXT Program: Data Creation and Utilization Type Material Research and Development Project (Grant No. JPMXP1122683430), as well as by Design and Engineering by Joint Inverse Innovation for Materials Architecture, MEXT. Ta.K. was supported by Japan Society for the Promotion of Science (JSPS) through Grants-in-Aid for Scientific Research (B) (Grant No. JP23K23034), Scientific Research (S) (Grant No. JP22H04964), and Challenging Research (Exploratory) (Grant No. JP24K21671). H.Hi. was supported by JSPS through Grants-in-Aid for Scientific Research (A) (Grant Nos. JP20H00302, JP21H04612, and JP24H00376). The numerical calculations were carried out on the TSUBAME3.0 supercomputer at Tokyo Institute of Technology supported by the MEXT Project of the Tokyo Tech Academy for Convergence of Materials and Informatics (TAC-MI). A part of the present experiments was carried out by using a facility in the Comprehensive Analysis Center, SANKEN, Osaka University. The HAXPES experiments at SPring-8 were performed with the approval of NIMS Synchrotron X-ray Station (Proposal Nos. 2018A4701). The crystal structures in Figs. 1, 2(b), 7(a,b), S4(b), S7, and S12(a) were drawn using the VESTA code.41    17  References (1) Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 2014, 508, 373-377. (2) Parenteau, M.; Carlone, C. Influence of temperature and pressure on the electronic transitions in SnS and SnSe semiconductors. Phys. Rev. B 1990, 41, 5227.  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Tg: growth temperature, a: a-axis lattice parameter, b: b-axis lattice parameter, c: c-axis lattice parameter, V: unit cell volume, Dw400: full width at half maximum values of 400 diffraction peak, D: in-plane crystallite size estimated from Scherrer’s equation using in-plane 020 and 002 diffractions. Film form Sub. Tg (oC) Sn/Se ratio a  (Å) b  (Å) c  (Å) V  (Å3) Dw400 (o) D (nm) a-axis oriented film with in-plane randomly oriented domains Glass RT 1.01 11.649 4.179 4.261 207.43 10.5 7.99 100 1.00 11.610 4.180 4.310 209.13 7.7 7.03 400 1.00 11.513 4.179 4.404 211.88 5.8 18.41 500 1.01 11.513 4.186 4.392 211.67 4.8 19.99 Epitaxial film with in-plane 90o rotational domains MgO (001) 500 1.01 11.540 4.191 4.369 211.30 0.2 16.53       24        Figure 1. Crystal structure of a-axis oriented SnSe viewed from c-axis (left) and b-axis (right). SnSe has a layered crystal structure composed of alternately stacked SnSe layers along the a-axis. The 3-fold coordinated Sn–Se3 unit of the SnSe layer is shown by the purple polyhedrons. SnSe has the largely different bonding network structures in plane along b-axis and c-axis.     25      Figure 2. Plan-view STEM images of (a) a-axis oriented SnSe polycrystalline film grown on glass substrate at Tg = 500 oC and (b) SnSe epitaxial film grown on MgO (001) substrate at Tg = 500 oC. Electron diffraction pattern of SnSe polycrystalline film is shown in the inset of (a). The lattice illustrations of SnSe are superimposed in the inset of (b). Green and pink spheres indicate Sn and Se atoms, respectively.     26     Figure 3. Temperature (T) dependences of electron transport properties for the a-axis oriented SnSe polycrystalline films on glass substrates and the epitaxial film on MgO (001) substrate. (a) Electrical conductivity (s), (b) hole concentration (n), and (c) Hall mobility (µ).     27      Figure 4. (a) Arrhenius plots of µ for SnSe films on glass and MgO (001) substrates. (b) Grain boundary potential barrier height (Eb), domain size (L), and in-grain carrier mobility (μg) at T = 300 K and Eb = 0 eV, estimated by fitting the Seto model to experimental results, as shown by solid lines in (a).    28      Figure 5. (a) Tg dependences of hole trap state density (Qt) at GBs and the total number of acceptors in a grain (LnA) for SnSe polycrystalline films on glass substrates and the epitaxial film on MgO (001) substrate. (b) Energy diagram of the valence band maximum (VBM, blue lines) near the GBs for SnSe films with low Tg (upper image) and high Tg (bottom image). Green dotted lines indicate the EF position. The trapped holes (h+) are shown by red circles.    29      Figure 6. Relationship between μ, crystallite orientations, and GB characteristics for SnSe films at RT. (a) µ vs. FHWM values of out-of-plane 400 rocking curves (Dw400). (b) GB potential barrier height (Eb) vs. Dw400.     30     Figure 7. (a) Plan view of SnSe GB model with 90o-rotational A and B domains, where the boundary is formed along [110] and [01-1] direction, indicated by blue dotted lines. Charge density map at VBM is shown in the top image. The middle and bottom images show the Sn-Se3 polyhedra in 1st and 2nd SnSe layers, respectively. (b) Cross-sectional view of the SnSe GB model and charge density map at VBM. (c) Electronic band structures along the k-path of X (0.5, 0, 0), G (0, 0, 0), D (0, -0.5, -0.5), Y (0, 0.5, 0), B (0, 0.5, -0.5), (d) partial DOSs of the SnSe model.