In-plane optical and electrical anisotropy in low-symmetry layered GeS microribbons

Layered group-IV monochalcogenides, including GeS, GeSe, SnS, and SnSe, garner attention because of their anisotropic structures and properties. Here, we report on the growth of GeS microribbons via chemical vapor transport (CVT), which affords each of them with a low-symmetry orthorhombic structure and anisotropic optical and electronic properties. The single-crystalline nature of the GeS microribbon, which has a typical thickness of ~30 nm, is confirmed. Polarized Raman spectra reveal angle-dependent intensities that are attributed to the anisotropic layered structure of GeS microribbons. The photoluminescence (PL) spectra reveal a peak at ~1.66 eV. The angle-dependent PL and anisotropic absorption spectroscopy results provide evidence for a distinct anisotropic optical transition near the energy band edges; this phenomenon is also predicted by our density functional theory (DFT)-based calculations. Strong in-plane direct-current transport anisotropy is observed under dark and white illumination by using back-gate cross-shaped field effect transistors (CSFETs) fabricated with the GeS microribbon; significant gate-tunable conductivity is also confirmed. The strong anisotropy is further confirmed by the DFT-calculated effective mass ratio. Our findings not only support the application of GeS microribbons in anisotropic photoelectronic transistors but also provide more possibilities for other functional device applications. Two-dimensional distorted orthorhombic GeS microribbons has been synthesized applying vapor-liquid-solid and vapor-solid mechanism-based chemical vapor transport. Polarized Raman and photoluminescence characterizations show the significantly angle-dependent intensity and anisotropic optical properties. Additionally, we probed the anisotropic electric properties by fabricating back-gate cross-shaped field effect transistors. In-plane direct current measurement demonstrated the charge carrier transport anisotropy and its anisotropic current ratio can be linearly adjusted by changing the gate voltage under dark and illumination conditions.


Introduction
Germanium sulfide (GeS), which has a distorted orthorhombic crystal structure (Fig. 1a-c) similar to that of black phosphorus and an indirect band gap in the visible range, has garnered interest as a two-dimensional (2D) material owing to its anisotropic properties [1][2][3][4][5][6] . Its anisotropy is attributable to the puckered lattice structure of GeS, which affords it with unique optical properties that enable polarized optical absorption, detection, and photoconductivity 7,8 , as well as unique electronic properties that allow it to have a multiferroic presence with coupled ferroelasticity and ferroelectricity [9][10][11] . GeS is thus expected to have unique applications; for example, it can be advantageous in the fabrication of photovoltaic systems that are based on the shift current 12 . However, most previous studies have focused on the use of DFT calculations to predict the anisotropic photoelectronic properties and piezoelectric effects in monolayer group-IV monochalcogenides; as such, there have been few experimental studies on the anisotropic properties. Thus, the development of diverse, low-symmetry 2D materials, and research on their synthesis, structure, and anisotropy that could promote their applicability, is essential and of considerable scientific significance.
Various methods have been used to prepare GeS flakes and nanowires. The solution process has been applied to the synthesis of a few layers of single-crystal GeS nanosheets; the results revealed good overlap between the narrow band gap and the visible solar spectrum 1 . However, the inevitable contamination of GeS nanosheets has been shown to result in their poor performance in photoelectronic devices. Alternatively, mechanical exfoliation has previously been used to obtain multilayer GeS; the initial photoelectronic characterization results for the fabricated 2D GeS flakes have demonstrated their strongly layer-dependent photoelectronic polarization 13 . However, the controllability of the exfoliation process is very poor, particularly with respect to the size and amount of produced GeS flakes; this lack of controllability limits their applicability in research and industry. The abovementioned studies mainly focused on synthesis and optical anisotropic characterization. As such, high-quality preparation and in-depth research on carrier transport are essential, and such studies should include both experimental and theoretical research. Furthermore, they should focus on investigating the in-plane anisotropy of GeS materials to reveal the properties that are unique to the GeS crystal structure.
Herein, we report the bottom-up growth of high-quality single-crystal GeS microribbons via a low-temperature chemical vapor transport process. The GeS microribbon was synthesized on a SiO 2 /Si substrate using a thin layer of gold as the catalyst. We characterized the morphology, structure, and composition of the synthesized microribbons by using techniques such as scanning electron microscopy (SEM), X-ray diffraction (XRD), and transmission electron microscopy (TEM). Additionally, the results of polarization-dependent Raman spectroscopy and photoluminescence (PL) spectroscopy have provided evidence of anisotropic crystalline orientation and excitation polarization. The PL was confirmed to be strongly related to the direct optical transition, whereas the anisotropic PL was determined to be associated with the anisotropic optical transition near the band edge. Furthermore, the results of the DFT calculations revealed that the optical absorptance and effective mass are anisotropic. Finally, we fabricated CSFETs and evaluated their anisotropic direct-current transport capability, consequently demonstrating that the highest conductance occurs in the armchair direction and that the currents in the armchair and zigzag directions are significantly dependent on the gate voltage. These findings indicate that layered GeS can act as an anisotropic semiconductor. As such, it has considerable potential for photoelectronic applications.

Results and discussion
2D GeS microribbons were synthesized by CVT. Figure  1d shows a schematic of the CVT system. First, the GeS powder was sublimed, and its vapor was carried downstream with Ar gas in a heated tube furnace. The GeS microribbons grew as GeS vapor was deposited onto the surface of the Au-coated SiO 2 /Si substrate by means of the vapor-liquid-solid (VLS) mechanism. However, because the grown GeS microribbons had rectangular cross section and high width-to-thickness ratio, the VLS mechanism in this study is thought to differ from the typical VLS mechanism of nanowire synthesis 14 . We believe that factors such as the temperature, Ar gas flow rate, and GeS vapor concentration, which affect the crystal growth kinetics, may play key roles in determining the morphology and size of the final microribbon. Figure  1e presents the formation of the GeS microribbons. Defects in the interior structure of the nanoscale Au films seem to have caused transgranular fracture or cracking along the grain boundaries. The weak surface of the microstructure led to a localized stress concentration that eventually formed cracks. Au film have much larger surface-to-volume ratio than bulk metal; this means that they also have a larger amplitude of surface lattice vibration and higher Gibbs free energy, which contribute to altering the thermodynamic and thermal properties of the Au film. Increasing the temperature and concentration of GeS vapor was found to cause the Au film to break down into liquid Au droplets. When the temperature was increased to 450°C, the shape of the Au droplets became elliptical, and two or more droplets were observed to have merged to form large cylindrical droplets, as has been previously reported 15 . Furthermore, the continuous transport of a high concentration of GeS vapor supersaturated the GeS-Au alloy liquid, promoting GeS nucleation. Additionally, the amount of precipitated crystal increased because of the presence of crystal nucleates at the liquid/solid interface, causing the interface to shift in the axial direction. A relatively higher temperature was also found to promote the side growth of an orthorhombic-structure GeS crystal; this side growth phenomenon had previously been observed during vaporliquid (VL) deposition 16 . The rate of growth that occurs during the Au-assisted VLS process was observed to be much faster than that of VS side growth; the faster rate may be the reason why the GeS microribbons grew to have rectangular cross section and high width-tothickness ratio 17 .
The chemical composition of the microribbon was analyzed by using energy dispersive spectroscopy (EDS) (Fig. 2a). The elemental mapping results revealed uniform contrast throughout the microribbon, suggesting a homogeneous Ge and S composition. Analysis of the atomic percentage in the embedded table indicated a Ge:S stoichiometric ratio of~1:1. The morphology of the grown GeS microribbons were examined using SEM; the result is shown in Fig. 2b. The bodies and ends were observed to have clear differences in color and topology. Analysis of the SEM and elemental composition results for the ends confirmed the formation of a GeS-Au alloy ( Supplementary Fig. S1, Supporting Information); this finding supports our abovementioned theory regarding the VLS growth mechanism. It is also noteworthy that the sizes of the ribbon-shaped GeS differed, and they were observed to have glossy surface morphologies. The width and length of the microribbons reached tens and hundreds of micrometers, respectively. Through comparison of the widths of the bottom (away from the ends) and top (near the ends) positions of the microribbons, it was found that the width of the bottom position was slightly larger than that of the top position, further verifying the occurrence of the VS mechanism during GeS microribbons synthesis. A typical thickness of the GeS microribbon, as confirmed via atomic force microscopy (AFM), was~30 nm (Fig. 2c). Moreover, thickness distribution is an important factor in evaluating the synthesized GeS microribbons. To quantify the thickness, we measured many GeS microribbons by AFM, as shown in Supplementary Fig. S2. The thickness histogram illustrates that most of the thickness of the GeS microribbons were distributed in the range of 15~90 nm, and a distribution was well-defined with a peak centered at~51.5 nm, with some microribbons as thin as 12 nm. The synthesized GeS microribbons were found to have excellent crystallinity and a single-crystal structure. Analysis of the XRD results ( Fig. 2d) yielded the following lattice constants: a = 10.470 Å, b = 4.297 Å, and c = 3.641 Å, which are consistent with the corresponding values of the bulk GeS material (a = 10.47 Å, b = 4.3 Å, and c = 3.64) 1 . The crystal structure and morphology were further studied using high-resolution TEM (HRTEM) and selected-area electron diffraction (SAED) (Fig. 2e, f). The ripples shown in the HRTEM image may be due to sample crumpling as it was transferred from the substrate to a copper grid or the local thermal strain that was introduced by the bombardment of the electron beam during characterization 18 . The HRTEM image and clear SAED pattern results indicate excellent crystallinity and confirmed the lattice spacing of 0.278 nm, which is associated with the family of crystal planes of orthorhombic GeS. The chemical state and surface composition of single-crystal GeS were determined using X-ray photoelectron spectroscopy (XPS) (Supplementary Fig. S3). The binding energy positions at 29.28, 30.98, and 32.08 eV were assigned to the Ge 3d 5/2 orbital, Ge-S bonding, and Ge 3d photoelectron emissions, respectively 19 . The Ge 3d 5/2 orbital and Ge-S bonds are known to be associated with the oxidation state of Ge 2+ . According to the fitting curves, the Ge 2+ valence state accounts for the main part of the fitting curve, further confirming that Ge largely exists as oxidized Ge 2+ 20 . In addition, the S 2p 3/2 and S 2p 1/2 states at 161.58 and 162.78 eV indicate the presence of S 2− , which is consistent with a previous report 21 .
Polarized Raman-scattering spectroscopy has been proven to be a powerful tool for investigating the anisotropic light-matter interaction and crystal-structure anisotropy of layered materials through the measurement of the periodical variation in intensity in different Raman vibration modes 22 . Such measurements are typically conducted using a rotating polarizer, which is presented along the travel path of the incident laser under the conditions of a fixed sample position and polarized direction of the scattered light. Supplementary Fig. S4 shows an optical image of the GeS microribbon. The optical image clearly illustrates the armchair and zigzag directions along the edges, and the marking of these two directions in the image makes later polarizationdependent analysis more facile. To evaluate the anisotropy of the vibration modes, Raman spectra were obtained under the conditions of rotations that differed relative to the incident polarization axis (Fig. 3a). The spectral results indicate that the distinct peaks at~214, 240, and~272 cm −1 are associated with the B 3g , A 1 g and A 2 g modes, respectively, which is in agreement with the results in a previous report 23 . Additionally, at various thicknesses of GeS, the positions of these Raman peaks do not significantly change with increasing thickness, which suggests that the crystal structure of GeS microribbons does not change at different thicknesses 13 . The Raman intensities above the B 3g , A 1 g and A 2 g modes were plotted in polar coordinates with respect to the angle θ, where θ is the rotated angle of the incident polarization axis with respect to the armchair direction of the GeS microribbon. The results are displayed in Fig. 3b-d. The periodic tracks of polar diagrams were found to be significantly different among the three Raman variation modes, which are strong indicators of the fingerprints of the in-plane anisotropy. The angle-dependent Raman intensity in the B 3g mode was found to have a periodicity of 90°, whereas both the A 1 g and A 2 g modes were found to have a periodic angle of 180°. Furthermore, a phase difference of 90°can be clearly observed between the A 1 g and A 2 g modes. The observed anisotropy of the electronic band structure suggests that GeS possesses anisotropic PL properties. PL characterization was performed to investigate the electronic states of multilayer GeS; the results revealed distinct peaks at~1.67 eV, which had an excitation wavelength of 514 nm in different polarized rotations, as shown in Fig. 3e. The PL intensity at the peak position varied significantly with respect to the GeS thickness. It dramatically increased with increasing thickness, indicating that the PL intensity is a function of the thickness of GeS. However, the peak positions hardly show thicknessdependence 13 . The indirect band gap near 1.68 eV, which was confirmed by diffuse reflectance spectroscopy (DRS) ( Supplementary Fig. S5), was found to be in good agreement with the PL peak. Figure 3f illustrates the polarized intensity of PL at a peak position of 1.67 eV as a function of the angle θ. The experimental results (pink dots) can be fitted to a linear dichroic relation of the polarized light, which is further indicative of the anisotropic characteristics of the PL spectrum of GeS. The double-lobed shapes confirm the periodicity with a range of 180°, and the band-edge emission was fully restrained in the zigzag direction; additionally, the radiation was observed to have the strongest intensity in the polarized armchair direction. The selection law for band-edge PL emission is thought to be determined by the transition-related dipole moment of the multilayered GeS microribbons in the armchair or zigzag direction. The electronegativities of the Ge and S atoms were 2.0 and 2.6, respectively. Their difference of 0.6 satisfies the following condition: 0 < polar covalent bond < 2, which is necessary for the formation of polar covalent bonds in GeS. The Ge(+) → S(−) bond polarity of the up-and-down bond dipole moments may be only in the armchair direction; this property has been reported to induce optical transition polarization dependency, which is associated with variation in the PL intensity from armchair to zigzag direction 24 .
To clarify the electronic properties of GeS, firstprinciples DFT calculations were carried out to determine the band structure and density of states (DOS) of multilayer GeS microribbons. As shown in Fig. 4a, in the electronic band structure, the conduction band minimum (CBM) occurred at the Γ point along the Γ-Y line of the Brillouin zone; alternatively, the valence band maximum (VBM) was very close to the X point along Γ-X, which generated a small energy difference between the direct optical transition I (Γ-Γ dashed green arrow, band gap: 1.74 eV) and indirect optical transition II (X-Γ dashed green arrow, band gap:~1.58 eV) [25][26][27] . Although multilayer GeS is known to be an indirect band gap semiconductor, the energy difference between the direct and indirect band gaps is very small, only~0.16 eV. As shown in the partial DOS diagram, most of the states in the conduction band near the Fermi level were associated with the Ge 4p orbitals. The states in the valence band near the Fermi level were primarily attributed to the S 3p orbitals and their coupling with the Ge 4p and Ge 4 s orbitals, suggesting the occurrence of strong hybridization in the multilayer GeS. For further analysis of the electronic states, the CBM-and VBM-derived partial charge density distributions were calculated; the results are shown in Fig. 4b. It is noteworthy that the CBM-derived densities were found near the Ge atoms, whereas the VBM-derived densities were found closer to the S and Ge atoms; these results are consistent with the abovementioned results of partial DOS analysis.
The Raman spectral results indicated that GeS possesses in-plane crystal anisotropy; thus, its in-plane absorbance in different directions was further investigated. Supplementary Fig. S6a shows the optical absorptance from 0 to 10 eV, and Supplementary Fig.  S6b presents the plot of (αhν) 1/2 as a function of energy. The extrapolated linear fitting line (red dashed line) toward the x-axis indicates a band gap of~1.7 eV, which is close to that observed in a previous study on GeS 7,13,28 . To verify the polarized optical absorption of layered GeS, DFT was used to calculate the optical absorption coefficient (α) using the obtained real (ϵ re (ω)) and imaginary ( ϵ im (ω)) parts of the dielectric function in the armchair (θ = 0°) and zigzag (θ = 90°) directions; the results are shown in Fig. 4c. The calculations were performed in the range of 1.2-2.5 eV, and anisotropic absorption was observed by adjusting the polarization angle from 0°( armchair) to 90°(zigzag). The absorption coefficient was found to be larger in the armchair direction than in the zigzag direction over this wide energy range. Additionally, the absorption spectra were referenced to derive a plot showing the absorption coefficients at 2.13 eV and 2.44 eV in the polar coordinate system shown in Fig. 4d. The double-lobed shapes are clear indicators of the high anisotropy of the optical absorption coefficient in different directions.
A direct-current conductance test was applied to investigate the anisotropic current transport in GeS. Before fabrication of the CSFETs device, the crystalline directions were determined from the optical image. The anisotropic PL intensity at the peak position was strongest in the armchair direction and weakest in the zigzag direction 13,24 . According to the optical image ( Supplementary Fig. S4) and anisotropic PL spectra (Fig. 3e, f), which are in agreement with the previous investigation 13, 24 , the PL intensity is the strongest and weakest when the direction of incident polarized light is parallel to the length direction and width direction of the GeS microribbons, respectively. Thus, the length direction is the armchair direction, and the width direction is the zigzag direction. The metal electrodes were deposited along the length direction and width direction in the GeS microribbon. To this end, a pair of back-gate CSFETs was fabricated; the structural schematic diagram is displayed in Fig. 5a. Au metal electrodes with matching work functions were deposited onto the GeS surface. To minimize the influence of the transistor size difference, the size of the GeS channel in the armchair direction was designed to be the same as that in the zigzag direction. As shown in Fig. 5b, the transfer curves were obtained under dark condition and under the condition of V ds = 5 V. The maximum current value in the armchair direction was much higher than that in the zigzag direction, and both curves indicate typical p-type behavior. Because the material was not intentionally doped to fabricate the CSFETs, the natural p-type behaviors may be related to the presence of Ge vacancies in the synthesized crystal and the high-lying valence band of GeS 29,30 . Low resistance contact strongly influences the charge carrier mobility; thus, output curves were also measured to evaluate the contact resistance, as shown in Supplementary Fig.  S7. The source-drain current I ds varies nearly linearly with the bias V ds in the ±5 V range at different back gate voltages, revealing near-ohmic behavior in the fabricated devices. The carrier mobility of the CSFETs was calculated by solving the equation µ = [L/(WCV ds )]·(dI ds /dV g ), where L and W are the length and width of the GeS channel, respectively, and C is the capacitance at the bottom gate (C = ε 0 ε r /d; ε 0 is the vacuum permittivity, ε r is the relative permittivity, and d is the thickness of the SiO 2 dielectric layer) 31,32 . The carrier mobilities in the armchair (μ a ) and zigzag (μ z ) directions were calculated to be~0.058 cm 2 V −1 s −1 and 0.012 cm 2 V −1 s −1 , respectively, which are~30 times and 10 times higher than the corresponding previously reported values 27 , indicating that the synthesized GeS was not only highly crystalline but also had a low contact resistance in the presence of deposited Au metal. In addition, the anisotropic ratio of the carrier mobilities in the armchair and zigzag directions was observed to bẽ 4.8, which is higher than that of black phosphorous (~1.5) and ReS 2 (~3.1) 33,34 . The charge carrier mobility is known to be largely determined by the presence of defects and trap states on the surface between the SiO 2 dielectric layer and GeS channel. Thus, reducing the number of defect and trap states can considerably improve the performance of CSFET devices [35][36][37][38] . In addition, we have defined the electrical anisotropic ratio Γ a as I a /I z , where I a and I z are the I ds of transfer curves in the armchair and zigzag directions, respectively. The results showing Γ a as a function of the gate voltage (V g ) indicate that the electrical anisotropic ratio can be adjusted by changing V g (inset of Fig. 5b). Interestingly, Γ a increased linearly from~3.3 tõ 7.0 as V g was scanned from 0 to −60 V. To the best of our knowledge, this constitutes the first report of such a significant gate-tunable effect, i.e., a linear increase from low to high V g . Although Γ a was relatively low for small numbers of hole carriers within the range of 0 to −25 V, a remarkable linear increase was observed; it began when V g was increased to~−30 V. This phenomenon may be indicative of better hole collimation under the condition of a larger number of hole carriers; there were preferred paths for the holes when many hole carriers were present. Another possible explanation is that, compared to that observed in the zigzag direction, the lower carrier effective mass in the armchair direction that characterized the band edge resulted in much weaker suppression of source-todrain tunneling 39 .
To analyze the role of anisotropic conductivity in the charge transport in p-type CSFETs, the effective mass of the hole (m h *) was calculated (Methods section). We derived the inverse of the second derivative of the energy-k space relation, E(k), from calculations of the electronic band structure, which were applied under the condition of a parabolic band approximation. According to our calculations, m h * was orientation-dependent at the edges of the valence-band valleys; thus, we obtained 0.28m 0 in the armchair direction and 0.74m 0 in the zigzag direction, where m 0 is the free electron mass. Our results for m h * were found to be in good agreement with the calculated results of previous studies 40,41 . Figure 5c illustrates the responses of the effective masses of holes as a function of the planar crystalline axis angle (θ) in a polar coordinate system. The difference in the values in the x and y directions of a given quantity has been reported to indicate the intrinsic in-plane anisotropic electrical properties of the material 42 .
The CSFETs were also illuminated under white light power~0.48 W (left inset in Fig. 5d); photocurrent generation in the anisotropic direction was also investigated under this condition by measuring the transfer curves, as shown in Fig. 5d. Compared to the results obtained from experiments performed under dark, the photocurrent values were significantly higher in both directions. This result may be due to the mechanism of the photogating effect, which is a photoconductive effect. A pair of electron and hole were generated after photons were absorbed under illumination. One of the electrons or holes in the pairs became trapped in a localized state, which is referred to as localized state electrification. The charged localized state was observed to function similar to the gate voltage, which can affect the carrier concentration of the material and thus alter the conductivity of the material. Because the presence of localized states such as surface states and defects in GeS is inevitable, the photogating effect often dominates the photoelectric response mechanism of CSFETs. Generally, detrapping is a relatively slow process that proceeds after the carrier becomes trapped in a localized state. This process can significantly extend the lifetime of photogenerated carriers, allowing them to achieve high gain and high photoresponsivity. Thus, when the electrons reach the positive electrode and disappear, the trapped positively charged centers (holes) remain in the body. This phenomenon triggers the electrons in the negatively charged electrode to move toward the semiconductor. These electrons move toward the positively charged electrode in the electric field; this process continues until the positively charged centers disappear. This process is equivalent to amplification of the initial photocurrent 43 . We also found the channel current value (V g = −60 V) in the armchair direction to be approximately six times higher than that in the zigzag direction; a similar difference in magnitude was observed under dark condition, indicating similar photoconductive properties in the armchair and zigzag directions under dark and white-light illumination. In addition, the Γ a value (right inset in Fig. 5d) linearly increased from~3.0 to~5.4, yielding a Γ a -V g curve that was relatively gentle compared to that shown in the inset of Fig. 5b; this observation indicates that the gate-tunable effect was relatively weaker under the condition of illumination.

Conclusions
In conclusion, we have successfully applied VLS-and VS-mechanism-based CVT to synthesize high-quality GeS microribbons with anisotropic structures and properties. The elemental and structural characterization results revealed that single-crystal GeS microribbons grew in the 011 Â Ã direction and that these microribbons were 20-150 nm in thickness, several micrometers in width, and hundreds of micrometers in length. Polarized Raman spectroscopy was applied as an effective tool to determine the crystal orientation, and the three expected angledependent vibrational modes, B 3g , A 1 g and A 2 g , were also confirmed in the GeS microribbons. The DRS results and DFT-based band structure calculations revealed an indirect band gap of~1.63 eV, which was consistent with the PL results that indicated a peak at 1.66 eV. The occurrence of an angle-dependent PL peak was further indicative of an anisotropic optical transition near the band edge. We also observed large hole mobilities in the armchair and zigzag directions of~0.058 cm 2 V −1 s −1 and 0.012 cm 2 V −1 s −1 , respectively. In addition, back-gate CSFETs were fabricated to explore the in-plane anisotropic current properties. The current paths in the armchair and zigzag directions revealed significant charge carrier transport anisotropy. Furthermore, we demonstrated that the anisotropic current ratio can be linearly adjusted by changing the gate voltage under dark and white-light illumination conditions. Our research constitutes a meaningful step toward fully understanding the intriguing properties of layered GeS microribbons and this family of layered monochalcogenides.

Synthesis of GeS microribbons
GeS microribbons were synthesized by CVT in a horizontal single-heated-zone tube furnace (S&R Co., Ltd.) with a 2-in quartz tube. GeS powder (10 mg, 99.99% purity, Sigma-Aldrich, USA) located at the center of the heated zone served as the source material. Au film with a thickness of 5 nm (Taewon Scientific Co., Ltd., Republic of Korea) was deposited onto the surface of a rinsed SiO 2 / Si substrate (Namkang Hi-Tech. Co., Ltd., Republic of Korea) using an electron beam evaporator system (Korea Vacuum Tech., Ltd., Republic of Korea). The Au-coated substrate was placed on a quartz boat downstream of the GeS source. The distance between the quartz boat and source was~8 cm. To prevent oxygen contamination, the quartz tube was flushed with pure Ar gas three times before the GeS microribbons growth process was initiated. Then, the Ar carrier gas flow was controlled at 50 sccm, and the air pressure was maintained at~60 Torr. The quartz tube was heated from room temperature to 450°C for 20 min, and the growth process proceeded for 10 min. Finally, the furnace was allowed to naturally cool to room temperature.

Sample preparation
TEM samples were prepared by scratching the synthesized GeS microribbons from the Au-coated SiO 2 /Si substrate and dispersing them in isopropyl alcohol. Then, they were sonicated for 10 s, and the solution was dripped onto TEM grids. The samples were characterized after the alcohol totally vaporized. The samples for optical measurement were prepared by mechanical transfer of flakes onto a bare SiO 2 /Si substrate. The CSFETs were fabricated by applying typical electron-beam lithography techniques. Au metal (80 nm) was deposited as conductive electrodes by using an electron-beam evaporator system.

Characterization
The crystal structure and elemental mappings of the GeS microribbons were analyzed using a JEM-2100Plus TEM system. The morphology and elemental composition were investigated using a 7610f-plus field-emission SEM with an energy dispersive X-ray spectroscopy detector. AFM was conducted on a Park system (NX-10, Republic of Korea) in noncontact mode to measure the thickness and surface morphology. The XRD images were recorded by using a Rigaku X-ray diffractometer with a Cu Kα radiation source. The surface composition and chemical states were determined by XPS (K-alpha). The band gaps, as determined from UV-vis absorption spectra, were recorded on a Varian Technologies Cary 5000 with internal diffuse reflectance accessories, including a 110-mm-diameter integrating sphere. The microribbons were observed on an optical microscope (Olympus BX53, Japan). GeS microribbons growth on the SiO 2 /Si substrates were confirmed by Raman spectroscopy (Thermo Fisher Scientific, DXP, USA) using a system equipped with a 514-nm-wavelength laser as the excitation source. PL analysis was conducted using the same equipment. Polarized Raman and PL spectra were obtained by installing an adjustable polarizer at the entrance of the spectrometer to enable polarized light measurement. Electronic measurements were performed under dark and white light conditions (~0.48 W), achieved via the use of a fluorescent lamp with a probe station that included Keithley 6430 and 2400 source meters.

DFT calculations
The projector augmented wave method, as implemented in the Vienna Ab initio Simulation Package, was employed to perform all DFT calculations [44][45][46] , which were specific to the bulk properties of GeS. The Kohn-Sham orbitals were expanded with a plane-wave basis set, and the kinetic cutoff energy was set to 600 eV. The Brillouin zone was sampled by adopting a Γ-centered kpoint mesh with an equivalent k-spacing of 0.15 Å −1 . The generalized gradient approximation to the exchangecorrelation (xc) functional was used together with vdW corrections via the self-consistent nonlocal vdWcorrection scheme (optB86b) to calculate all structural optimizations 47,48 . The electronic band structures and optical properties were calculated by applying the hybrid DFT xc functional due to Heyd, Scuseria, and Ernzerhof (HSE06) 49 . The effective mass of the holes was determined by fitting the parabolic functions of the VBM as follows: m Ã h ¼ h 2 ð d 2 E K dk 2 Þ À1 . To obtain an estimate of the optical band gap, we calculated the optical absorption coefficient α(ω) under the conditions of the independent particle approximation formalism (i.e., without the excitonic and localized effects) as follows: α ω ð Þ ¼ 2ω c ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ϵ 2 re ω ð Þ þ ϵ 2 im ω ð Þ p À ϵ re ω ð Þ 2 s where c and ω are the speed of light and frequency of the photon, respectively, and ϵ re ω ð Þ and ϵ im ω ð Þ represent the real and imaginary parts of the dielectric function 50 , respectively.