Solid Phase Epitaxy of Single Phase Two-Dimensional Layered InSe Grown by MBE

Single-phase two-dimensional (2D) indium monoselenide (γ-InSe) film is successfully grown via solid phase epitaxy in the molecular beam epitaxy (MBE) system. Having high electron mobility and high photoresponsivity, ultrathin 2D γ-InSe semiconductors are attractive for future field-effect transistor and optoelectronic devices. However, growing single-phase γ-InSe film is a challenge due to the polymorphic nature of indium selenide (γ-InSe, α-In2Se3, β-In2Se3, γ-In2Se3, etc.). In this work, the 2D α-In2Se3 film was first grown on a sapphire substrate by MBE. Then, the high In/Se ratio sources were deposited on the α-In2Se3 surface, and an γ-InSe crystal emerged via solid-phase epitaxy. After 50 min of deposition, the initially 2D α-In2Se3 phase was also transformed into a 2D γ-InSe crystal. The phase transition from 2D α-In2Se3 to γ-InSe was confirmed by Raman, XRD, and TEM analysis. The structural ordering of 2D γ-InSe film was characterized by synchrotron-based grazing-incidence wide-angle X-ray scattering (GIWAXS).


Introduction
Recently, two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted strong interest from the scientific community because of their unique electrical and optical properties, making them promising candidates for future electronic and optoelectronic applications [1,2]. In addition to 2D TMDs, 2D III-VI metal chalcogenides such as In 2 Se 3 and InSe were also shown potential applications in electronic devices [3][4][5] and optoelectronic devices [6][7][8]. Particularly, InSe with a six monolayer device exhibiting ultra-high mobility of 1000 cm 2 V −1 s −1 at room temperature reported by Denis A. Bandurin et al. [9] shows a promising candidate to surpass silicon technology in the future. Although the exfoliation methods have been widely used to investigate 2D III-VI semiconductors' exceptional electrical properties, synthesizing large-area high-quality layered materials still requires bottom-up strategies, which are more suitable to be realized for industrial applications. To date, epitaxial growth by chemical vapor deposition (CVD), pulsed laser deposition (PLD), or molecular beam epitaxy (MBE) has been used for the synthesis of 2D III-VI metal chalcogenides [10][11][12][13][14][15]. However, the synthesis of single-phase indium selenide is still a challenge by chemical vapor deposition (CVD). Because indium selenide has multiple structures (γ-InSe, α-In 2 Se 3 , β-In 2 Se 3 , γ-In 2 Se 3 , etc.) that co-exist at room temperature [16][17][18]. To be implemented for industrial applications, the growth of indium selenide film with a single-phase conducted by precise control of In and Se sources is required. Among the techniques used to fabricate 2D semiconductors, MBE is widely considered one of the most competitive, precisely controlling the ultra-low growth rate and making the grown film clean for device fabrication [19][20][21].
In this study, the MBE system successfully demonstrated the epitaxial 2D γ-InSe thin film via solid-phase epitaxy. The Raman, X-ray diffraction (XRD), and high-resolution transmission electron microscopy (HR-TEM) image show that the 2D α-In 2 Se 3 fully converted to 2D γ-InSe. We believe that the 2D γ-InSe growth mechanism is solid-phase epitaxy due to similar in-plane lattice and space groups between 2D α-In 2 Se 3 and 2D γ-InSe.

Materials and Methods
Indium selenide films were deposited on c-plane sapphire substrates using a homemade MBE system in an ultra-high vacuum chamber with a base pressure of 2 × 10 −8 Torr. In and Se sources were evaporated using Knudsen cells (K-cells), and the growth processes were monitored using in-situ RHEED(R-DEC Co., Ltd., Ibaraki, Japan). Before the deposition, the sapphire substrates were degreased in acetone by ultrasonic cleaning for 2 min, and then a mixture of phosphoric acid and sulfuric acid of 1:3 for 15 min. Finally, the substrates were immersed in deionized water for 2 min. After the chemical cleaning process, the substrates were introduced to the growth chamber, and the sapphire substrate was thermal cleaned at 650 • C for 30 min. To identify the growth conditions for α-In 2 Se 3 growth, the K-cells temperature of In (T In ) was varied at 720 • C, 730 • C, 740 • C, and 750 • C, and Se (T Se ) was fixed at 198 • C, denoted In/Se ratio 0.05, 0.06, 0.07, and 0.11, respectively. Detailed calculation of In/Se ratio has been shown in Appendix A. The growth time of all samples was 2 h and the growth process schematic was shown in Figure 1a. The optimal α-In 2 Se 3 film was achieved with In (T In ) at 740 • C and substrate temperature (T sub ) of 560 • C, resulting in growth rates of 0.58 nm/min. After having single-phase α-In 2 Se 3 film, the In and Se sources were deposited on the α-In 2 Se 3 surface by closing the Se shutter as a high In/Se ratio at T In of 740 • C, T Se of 198 • C, T sub of 560 • C The crystallographic properties of the α-In 2 Se 3 and γ-InSe were examined using XRD (D8, Bruker corp. Billerica, MA, USA) system and synchrotron-based grazing-incidence wide-angle X-ray scattering (GIWAXS) at Taiwan Photon Source (TPS) TPS25A (National Synchrotron Radiation Research Center, Hsinchu, Taiwan). The GIWAXS data were collected with an area detector. High-resolution transmission electron microscopy (HR-TEM) (ARM200F, JEOL Ltd., Tokyo, Japan) was used to probe the α-In 2 Se 3 and γ-InSe microstructure and obtain atomic-scale images. The Raman spectra were obtained using a 532 nm wavelength of solid-state laser (70 mW) as the excitation source and a triple grating spectrometer (iHR-550, HORIBA, Ltd., Kyoto, Japan) system as a signal detector. co-existence of both α-In2Se3 and γ-In2Se3 structures, which confirmed our Raman analysis that the film grown by TIn set at 750 °C had both α-In2Se3 and γ-In2Se3 vibration modes.
To gain more insight into the α-In2Se3 crystal configurations and microstructure, one may examine the streaky line spacing in the RHEED pattern. Figure 2a,b shows the RHEED pattern and intensity profile of optimal α-In2Se3 films, and ⃑ and ⃑ are (101 0) and (112 0). The calculated ⃑/ ⃑ is close to √3, where the ⃑ ⃑ spacing is 678 pixels and ⃑− ⃑ spacing is 1200 pixels, revealing that the α-In2Se3 crystalline layer is six-fold symmetry on the sapphire substrate. Figure 2c,d shows the SEM image and cross-sectional HR-TEM image of the α-In2Se3 microstructure. The shape of the α-In2Se3 grains exhibited a hexagonal pattern, and the microstructure of α-In2Se3 exhibited a layered structure on the sapphire, where the α-In2Se3 monolayer thickness is 1.2 nm. The growth mechanism of the α-In2Se3 on the sapphire substrate may be similar to quasi-van der Waals (vdW) epitaxy [28][29][30].

Results and Discussion
Figure 1b presents the in-situ RHEED patterns of In 2 Se 3 with T In varied from 720 • C to 750 • C, and T Se fixed at 198 • C. As seen in the RHEED pattern, the stripe patterns were obtained along with [1010] and [1120] azimuth, indicating that In 2 Se 3 was in layer-by-layer growth mode. When the T In was lower than 740 • C, both the ring and streaky lines were exhibited in the RHEED pattern, indicating the layered and polycrystalline structures of In 2 Se 3 were formed. Raman spectroscopy and XRD were used to identify the various indium selenide structures [22][23][24][25][26][27]. Figure 1c shows the Raman spectra of In 2 Se 3 thin film on the sapphire substrate grown by T In varied from 720 • C to 750 • C. The vibration modes of In 2 Se 3 at T In at 740 • C exhibit three peak features at 112, 176, and 207 cm −1 , which were characteristic of α-In 2 Se 3 [11,12,[22][23][24][25]. When the T In was up to 750 • C, the vibrational mode appeared with two additional peaks at 146 cm −1 and 244 cm −1 , which were characteristic of γ-In 2 Se 3 [11,12,22,23]. Figure 1d shows the XRD θ-2θ scans of In 2 Se 3 grown by T In varied from 720 • C to 750 • C. The (002) and (004) α-In 2 Se 3 diffraction peaks are at 9.43 • and 18.89 • , and the peak of (006) γ-In 2 Se 3 is at 27.03 • . As T In at 740 • C, the optimal α-In 2 Se 3 films were achieved because of the relatively high diffraction intensity and narrower full width at half maximum (FWHM)of 0.16 • of the α-In 2 Se 3 peaks. The crystal grain size is estimated as 52.6 nm from the Scherrer equation. However, the T In at 750 • C leads to the co-existence of both α-In 2 Se 3 and γ-In 2 Se 3 structures, which confirmed our Raman analysis that the film grown by T In set at 750 • C had both α-In 2 Se 3 and γ-In 2 Se 3 vibration modes.
To gain more insight into the α-In 2 Se 3 crystal configurations and microstructure, one may examine the streaky line spacing in the RHEED pattern. Figure 2a,b shows the RHEED pattern and intensity profile of optimal α-In 2 Se 3 films, and a and m are (1010) and (1120). The calculated a / m is close to √ 3, where the a − a spacing is 678 pixels and m − m spacing is 1200 pixels, revealing that the α-In 2 Se 3 crystalline layer is six-fold symmetry on the sapphire substrate. Figure 2c,d shows the SEM image and cross-sectional HR-TEM image of the α-In 2 Se 3 microstructure. The shape of the α-In 2 Se 3 grains exhibited a hexagonal pattern, and the microstructure of α-In 2 Se 3 exhibited a layered structure on the sapphire, where the α-In 2 Se 3 monolayer thickness is 1.2 nm. The growth mechanism of the α-In 2 Se 3 on the sapphire substrate may be similar to quasi-van der Waals (vdW) epitaxy [28][29][30]. From the above observations, we found that the single-phase α-In2Se3 could rely on simply controlling In/Se ratio, and we noted that the in-plane lattice of γ-InSe (4.01 Å) is close to that of α-In2Se3 (4.03 Å) and has the same space groups. Therefore, we proposed the solid-phase epitaxy method to grow single-phase γ-InSe films, which uses a single crystalline α-In2Se3 film as a template, followed by depositing In and Se sources for γ-InSe crystal growth on the α-In2Se3 and then heating the film to crystallize it. Figure 3a shows the process flow of InSe growth via solid-phase epitaxy. The optimal α-In2Se3 films were achieved with TIn set at 740 °C and a growth temperature of 560 °C. Then, the TIn and TSe were kept, and the K-cell of the Se shutter was closed to become a high In/Se ratio with deposition times of 10 min to 50 min. Figure 3b presents the Raman spectra of InSe growth with high In/Se ratios for various deposition times. The vibration modes of γ-InSe appeared on the α-In2Se3 surface after the high In/Se ratio was deposited for 10 min, but when the deposition time reached 50 min, only the γ-InSe vibration signal remained. Figure 3c shows the XRD θ-2θ scans of InSe growth with high In/Se ratios for 10 min to 50 min deposition times. The (002) and (004) γ-InSe diffraction peaks emerged while the deposition time exceeded 10 min, and the peak intensity of γ-InSe gradually increased with the deposition time. In contrast, the peak intensity of α-In2Se3 gradually decreased with the deposition time. When the deposition time reached 50 min, the sample had only γ-InSe peaks. The FWHM of (004) γ-InSe peaks is around 0.36°, and the grain size is estimated as 23.5 nm. The Raman and XRD results show that solid-phase epitaxy on the α-In2Se3 surface effectively grows single-phase γ-InSe. Interestingly, α-In2Se3 also phase transitions to γ-InSe, probably because of the high diffusivity of Indium. Figure 3d presents the RHEED pattern of γ-InSe with high In/Se ratios for 50 min deposition time. The inset of Figure 3d shows the intensity profile of γ-InSe. In addition to showing the stripe pattern of γ-InSe in the RHEED pattern, the ⃑− ⃑ and ⃑− ⃑ spacing of γ-InSe are 672 pixels and 1150 pixels, which is similar to that of α-In2Se3 in Figure 2b. This confirmed the similar lattice spacing of γ-InSe and α-In2Se3. Figure 4a shows the cross-sectional HR-TEM image of γ-InSe with high In/Se ratios for 50 min deposition time. The microstructure of From the above observations, we found that the single-phase α-In 2 Se 3 could rely on simply controlling In/Se ratio, and we noted that the in-plane lattice of γ-InSe (4.01 Å) is close to that of α-In 2 Se 3 (4.03 Å) and has the same space groups. Therefore, we proposed the solid-phase epitaxy method to grow single-phase γ-InSe films, which uses a single crystalline α-In 2 Se 3 film as a template, followed by depositing In and Se sources for γ-InSe crystal growth on the α-In 2 Se 3 and then heating the film to crystallize it. Figure 3a shows the process flow of InSe growth via solid-phase epitaxy. The optimal α-In 2 Se 3 films were achieved with T In set at 740 • C and a growth temperature of 560 • C. Then, the T In and T Se were kept, and the K-cell of the Se shutter was closed to become a high In/Se ratio with deposition times of 10 min to 50 min. Figure 3b presents the Raman spectra of InSe growth with high In/Se ratios for various deposition times. The vibration modes of γ-InSe appeared on the α-In 2 Se 3 surface after the high In/Se ratio was deposited for 10 min, but when the deposition time reached 50 min, only the γ-InSe vibration signal remained. Figure 3c shows the XRD θ-2θ scans of InSe growth with high In/Se ratios for 10 min to 50 min deposition times. The (002) and (004) γ-InSe diffraction peaks emerged while the deposition time exceeded 10 min, and the peak intensity of γ-InSe gradually increased with the deposition time. In contrast, the peak intensity of α-In 2 Se 3 gradually decreased with the deposition time. When the deposition time reached 50 min, the sample had only γ-InSe peaks. The FWHM of (004) γ-InSe peaks is around 0.36 • , and the grain size is estimated as 23.5 nm. The Raman and XRD results show that solid-phase epitaxy on the α-In 2 Se 3 surface effectively grows single-phase γ-InSe. Interestingly, α-In 2 Se 3 also phase transitions to γ-InSe, probably because of the high diffusivity of Indium. Figure 3d presents the RHEED pattern of γ-InSe with high In/Se ratios for 50 min deposition time. The inset of Figure 3d shows the intensity profile of γ-InSe. In addition to showing the stripe pattern of γ-InSe in the RHEED pattern, the a − a and m− m spacing of γ-InSe are 672 pixels and 1150 pixels, which is similar to that of α-In 2 Se 3 in Figure 2b. This confirmed the similar lattice spacing of γ-InSe and α-In 2 Se 3 . Figure 4a shows the cross-sectional HR-TEM image of γ-InSe with high In/Se ratios for 50 min deposition time. The microstructure of γ-InSe exhibited a layered structure and well-defined crystal lattice, in which the monolayer thickness of 0.8 nm is only two-thirds of α-In 2 Se 3 . Even the α-In 2 Se 3 , initially on the sapphire substrate, was transformed into the γ-InSe phase. To verify these local microstructure observations, we utilized GIWAXS measurement to investigate the structure of low-dimension materials and provide information on the structural morphology of an entire sample [31,32]. Figure 4b presents the 2D reciprocal space map of the γ-InSe films via the solid-phase epitaxy. The lateral face of (1010) γ-InSe is at q r = 1.88 Å −1 . Since the γ-InSe is layered in nature and the crystal dimension is confined along the out-of-plane direction, the γ-InSe shows a vertical stripe pattern along the crystal truncation rod (CTR) in reciprocal space. Figure 5 illustrates the growth of γ-InSe via solid-phase epitaxy as a model. The single-phase α-In 2 Se 3 film grown via MBE system at 560 • C, followed by the high In/Se ratio deposition on the α-In 2 Se 3 film, the films underwent a thermodynamic transformation into γ-InSe crystal growth on the α-In 2 Se 3 surface. The formation energy for InSe and In 2 Se 3 are −0.527 and −0.322 eV/atom [33,34]. The practical indium selenide growth requires kinetic considerations such as growth temperature and concentration of sources [22]. During the γ-InSe crystal growth as a function of deposition times, the transformation mechanism involved the α-In 2 Se 3 to the γ-InSe transition, and the whole structure finally became a single-phase γ-InSe structure. γ-InSe exhibited a layered structure and well-defined crystal lattice, in which the monolayer thickness of 0.8 nm is only two-thirds of α-In2Se3. Even the α-In2Se3, initially on the sapphire substrate, was transformed into the γ-InSe phase. To verify these local microstructure observations, we utilized GIWAXS measurement to investigate the structure of low-dimension materials and provide information on the structural morphology of an entire sample [31,32]. Figure 4b presents the 2D reciprocal space map of the γ-InSe films via the solid-phase epitaxy. The lateral face of (101 0) γ-InSe is at qr = 1.88 Å −1 . Since the γ-InSe is layered in nature and the crystal dimension is confined along the out-of-plane direction, the γ-InSe shows a vertical stripe pattern along the crystal truncation rod (CTR) in reciprocal space. Figure 5 illustrates the growth of γ-InSe via solid-phase epitaxy as a model. The single-phase α-In2Se3 film grown via MBE system at 560 °C, followed by the high In/Se ratio deposition on the α-In2Se3 film, the films underwent a thermodynamic transformation into γ-InSe crystal growth on the α-In2Se3 surface. The formation energy for InSe and In2Se3 are −0.527 and −0.322 eV/atom [33,34]. The practical indium selenide growth requires kinetic considerations such as growth temperature and concentration of sources [22]. During the γ-InSe crystal growth as a function of deposition times, the transformation mechanism involved the α-In2Se3 to the γ-InSe transition, and the whole structure finally became a single-phase γ-InSe structure.

Conclusions
This work demonstrated the single-phase γ-InSe epitaxy via solid-phase epitaxy in an MBE system. The α-In2Se3 was first grown on a sapphire substrate by MBE as a template, and then the γ-InSe was formed by depositing In and Se at a high In/Se ratio on the α-In2Se3 films. The growth mechanism of γ-InSe was facilitated by a close in-plane lattice match between the α-In2Se3 and γ-InSe. Raman and XRD measurement revealed that γ-InSe emerged on the α-In2Se3 structure, and the α-In2Se3 phase transformed into γ-InSe during the high In/Se ratio deposition. Furthermore, HR-TEM and GIWAXS measurements showed that the whole structure finally becomes the single-phase 2D γ-InSe structure. The solid-phase epitaxy method opens the door to the development of 2D materials and the possibility of making more 2D materials available for electronic device applications.

Conclusions
This work demonstrated the single-phase γ-InSe epitaxy via solid-phase epitaxy in an MBE system. The α-In2Se3 was first grown on a sapphire substrate by MBE as a template, and then the γ-InSe was formed by depositing In and Se at a high In/Se ratio on the α-In2Se3 films. The growth mechanism of γ-InSe was facilitated by a close in-plane lattice match between the α-In2Se3 and γ-InSe. Raman and XRD measurement revealed that γ-InSe emerged on the α-In2Se3 structure, and the α-In2Se3 phase transformed into γ-InSe during the high In/Se ratio deposition. Furthermore, HR-TEM and GIWAXS measurements showed that the whole structure finally becomes the single-phase 2D γ-InSe structure. The solid-phase epitaxy method opens the door to the development of 2D materials and the possibility of making more 2D materials available for electronic device applications.

Conclusions
This work demonstrated the single-phase γ-InSe epitaxy via solid-phase epitaxy in an MBE system. The α-In 2 Se 3 was first grown on a sapphire substrate by MBE as a template, and then the γ-InSe was formed by depositing In and Se at a high In/Se ratio on the α-In 2 Se 3 films. The growth mechanism of γ-InSe was facilitated by a close in-plane lattice match between the α-In 2 Se 3 and γ-InSe. Raman and XRD measurement revealed that γ-InSe emerged on the α-In 2 Se 3 structure, and the α-In 2 Se 3 phase transformed into γ-InSe during the high In/Se ratio deposition. Furthermore, HR-TEM and GIWAXS measurements showed that the whole structure finally becomes the single-phase 2D γ-InSe structure. The solid-phase epitaxy method opens the door to the development of 2D materials and the possibility of making more 2D materials available for electronic device applications.

Data Availability Statement:
The data presented in this study are available on request from the corresponding authors.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The In/Se ratio is estimated from the vapor pressure and cell temperature. The vapor pressure of In and Se are referenced from Eberl MBE-Komponenten GmbH [35,36], as shown in Figures A1 and A2. The evaporation rate calculation of material is referenced from Andrew Sarangan [37]. The evaporation rate of the material can be written as: Z A is the rate in atoms/cm 2 /s P is the vapor pressure in Torr T is the vapor temperature in Kelvin M is the molar mass The calculated evaporation rate (Z Se(In) ) and In/Se ratio are shown in the table below. The T In was varied at 720 • C, 730 • C, 740 • C, and 750 • C, and T Se was fixed at 198 • C; that In/Se growth ratio was varied from 0.05, 0.06, 0.07, and 0.011. Table A1. The In/Se ratio calculation referenced from the formula of evaporation rate of the materials [37].  Education Sprout Project by the Ministry of Education (MOE) in Taiwan. The authors gratefully acknowledge using the "High-performance low temperature and multi-function X-ray diffractom eter" belonging to the Core Facility Center of National Yang Ming Chiao Tung University.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The In/Se ratio is estimated from the vapor pressure and cell temperature. The vapor pressure of In and Se are referenced from Eberl MBE-Komponenten GmbH [35,36], as shown in Figures A1 and A2. The evaporation rate calculation of material is referenced from Andrew Sarangan [37]. The evaporation rate of the material can be written as: where ZA is the rate in atoms/cm 2 /s P is the vapor pressure in Torr T is the vapor temperature in Kelvin M is the molar mass The calculated evaporation rate (ZSe(In)) and In/Se ratio are shown in the table below The TIn was varied at 720 °C, 730 °C, 740 °C, and 750 °C, and TSe was fixed at 198 °C; tha In/Se growth ratio was varied from 0.05, 0.06, 0.07, and 0.011. Table A1. The In/Se ratio calculation referenced from the formula of evaporation rate of the material [37].