Structure–Property Relationship of Low-Dimensional Layered

Jun 13, 2018 - We report the growth of layered GaSexTe1–x mesostructures across the whole composition range. ... (7−11) However, these are less co...
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Cite This: Chem. Mater. 2018, 30, 4226−4232

Structure−Property Relationship of Low-Dimensional Layered GaSexTe1−x Alloys Jose J. Fonseca,*,†,‡,§ Matthew K. Horton,† Kyle Tom,† Jie Yao,† Wladek Walukiewicz,‡ and Oscar D. Dubon*,†,‡ †

Department of Materials Science and Engineering, University of California, Berkeley, California 94720, United States Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States



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S Supporting Information *

ABSTRACT: We report the growth of layered GaSexTe1−x mesostructures across the whole composition range. For compositions up to x = 0.32 (the Te-rich region), mesocrystals form predominantly in the monoclinic structure, similar to naturally occurring GaTe. However, the hexagonal crystal structure, similar to naturally occurring GaSe, begins growing at the x = 0.28 composition and grows almost exclusively in the range of x = 0.32 to pure GaSe, establishing a region of composition where both monoclinic and hexagonal crystals exist. While the optical bandgap of the monoclinic phase increases linearly from 1.65 to 1.77 eV with increasing Se content, the incorporation of Te in the hexagonal phase reduces the optical gap from 2.01 (pure GaSe) to 1.38 eV (x = 0.28). Specifically, a bandgap difference of ∼0.35 eV between monoclinic and hexagonal crystals is observed in the composition range where both crystal structures can be grown. These observations are in good agreement with direct-gap trends calculated by density functional theory, which show a linear dependence on composition for the direct gap of the monoclinic phase and a considerable bowing of the direct gap of the hexagonal phase for Te-rich compositions. Our results show that layered semiconductor alloys are remarkably versatile systems in which electronic properties can be controlled by not only thickness but also structural phase and composition.



INTRODUCTION The emergence of layered materials such as graphene and transition metal dichalcogenides (TMDs) in the few-layer regime has drastically changed electronic materials science and technology. While graphene does not possess an energy bandgap, layered semiconductors such as TMDs do and have been extensively studied as possible substitutes of conventional semiconductors for future applications.1−3 Among the different properties observed for TMDs, the transition from indirect to direct bandgap at the monolayer regime has been their most remarkable one.1,3,4 The precise control and fine-tuning of electronic properties of layered semiconductors has been demonstrated through quantum confinement as well as strain and phase engineering.4−6 This can also be achieved through the alloying of layered semiconductors, the canonical strategy for bandstructure engineering. Some theoretical and experimental studies on TMD alloys, including MoS2(1−x)Se2x and Mo1−xWxS2, have been performed with interesting results.7−11 However, these are less common, particularly for alloy systems where limited miscibility of the constituent compounds makes crystal synthesis challenging. The gallium-monochalcogenide family is composed of the layered semiconductors GaS, GaSe, and GaTe. GaS and GaSe share a hexagonal crystal structure (Figures 1a and c), while © 2018 American Chemical Society

the naturally occurring structural phase of GaTe is monoclinic (Figures 1b and d). Hexagonal gallium monochalcogenide layers are composed of an X−Ga−Ga−X assembly (X = S, Se, or Te) perpendicular to the layer, where for monoclinic GaTe, one out of every three Ga−Ga bond lies parallel to the layer and perpendicular to the b-axis of the unit cell.12−15 GaSe is an indirect semiconductor with a 2.01 eV bandgap and a direct gap about 20 meV larger, typically p-type with a hole concentration and mobility around 1014 to 1015 cm−3 and 10 cm2 V−1 s−1, respectively.13 In contrast, GaTe is a direct semiconductor with a gap of 1.65 eV, also p-type with a hole concentration and mobility around 1016 to 1018 cm−3 and 20 cm2 V−1 s−1, respectively.16,17 However, even though GaTe shows better p-type transport properties, it has been shown that GaTe is sensitive to the environment, modifying its bandstructure.18 Here, we report the growth of GaSe−GaTe alloys to study the relation between composition, crystal structure, and optical properties. Bulk GaSexTe1−x alloys have been previously studied only over a limited composition range due to the limited miscibility Received: January 10, 2018 Revised: June 12, 2018 Published: June 13, 2018 4226

DOI: 10.1021/acs.chemmater.8b00130 Chem. Mater. 2018, 30, 4226−4232

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Chemistry of Materials

due to the higher vapor pressure of Se compared to Te, the growth of the hexagonal phase being preferred over the monoclinic, or a combination of factors. Energy dispersive X-ray spectroscopy (EDS) characterization showed that crystal composition tended to be higher in selenium content to that indicated by the nominal composition for the growth run (based on growth conditions). In addition, within a single growth a spread of compositions was obtained for different crystals, as seen in Table1. The Table 1. Comparison between Nominal Se-Fraction Composition and Actual Composition Range

Figure 1. Top-view of the (a) hexagonal and (b) monoclinic structures with the a- and b-axis in the vertical direction, respectively. Side-view of the (c) hexagonal and (d) monoclinic crystal structures along the a- and b-axis, respectively. The purple spheres represent the gallium atoms, and the orange spheres represent the chalcogen atoms. (e) Schematic of the quartz-tube furnace reactor used for the growth of GaSexTe1−x alloys during Growth Method 1.

nominal composition (x fraction)

actual composition (x fraction)

0 0.03 0.10 0.25 0.50 0.65 0.75 1

0 0.09−0.23 0.20−0.32 0.37−0.49 0.64−0.73 0.82−0.92 0.92−0.96 1

compositional variation was evident even for crystals grown at close proximity on the same substrate, but to a lesser degree. Figures 2a and b show the chemical-analysis mapping obtained

between GaSe and GaTe.12,19−21 Grown by the Bridgman method, bulk ingots were characterized by optical absorption19 and photoluminescence spectroscopy20 as well as Hall effect transport measurements.21 These studies found that in the Terich side of composition, the bandgap increased monotonically with Se content (from 1.67 eV for GaTe to 1.80 eV for x ≈ 0.35) while both the carrier concentration and mobility dropped. In the Se-rich regime, the bandgap decreased with Te content (from 2.01 eV for GaSe to 1.79 eV for x ≈ 0.70), and the resistivity decreased by over an order of magnitude. However, in the 0.35 < x < 0.70 range, the alloy separated into Te-rich and Se-rich phases. Here, we show that by growing mesostructures we are able to produce single-phase crystals along the entire alloy composition range.



RESULTS GaSexTe1−x Growth and Characterization. Eight different nominal compositions of the GaSexTe1−x alloy were grown (x = 0, 0.03, 0.10, 0.25, 0.50, 0.65, 0.75, and 1) in a quartz-tube reactor as detailed in Growth Method 1 and illustrated in Figure 1e. Careful inspection of the grown crystals revealed a variety of crystal morphologies and sizes that can be attributed to different crystal structures and compositions. The morphologies grown ranged from zig-zagged and serrated crystals to triangular crystals and nanowires. The triangular islands observed for the Te-rich compositions have been previously reported during the vapor growth of monoclinic GaTe,17 which could serve as a simple indication of the monoclinic nature of the Te-rich alloy crystals. Similarly, the zig-zagged and serrated crystals have also been observed during the growth of hexagonal GaS and GaSe nanostructures.22,23 The dimensions of the crystals ranged from single-digit micrometers to over 300 μm in length and thicknesses from about 20−100 nm. The larger crystals were generally found in the nominally Se-rich growths, where nucleation at the quartztube’s wall was also observed. The difference in size could be

Figure 2. SEM images and EDS chemical maps of representative (a) triangular crystal with x = 0.32 and (b) serrated crystal with x = 0.65. Thin nanowires can also be seen crossing over the larger crystal in panel a.

by EDS for crystals with x = 0.32 and x = 0.65, respectively. These maps highlight the composition uniformity along the crystals, even for those compositions that reported phase separation in the bulk form.12,19−21 Electron backscattering diffraction (EBSD) analysis confirmed the single-phase nature of the GaSexTe1−x alloy crystals grown along the whole composition range. Figure 3a shows an electron micrograph of a crystal with x = 0.30 and its EBSD pattern in the inset. The corresponding simulated pattern and 4227

DOI: 10.1021/acs.chemmater.8b00130 Chem. Mater. 2018, 30, 4226−4232

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Chemistry of Materials

Figure 3. (a) SEM image of a crystal grown with x = 0.30 with its EBSD pattern shown as an inset. (b) Simulated EBSD pattern for a monoclinic crystal structure oriented as shown by unit cell. Additional morphologies of the grown crystals include: (c) an elongated monoclinic crystal that grew along the b-axis, (d) a zig-zagged hexagonal crystal that grew along the main in-plane axis, and (e) a serrated hexagonal crystal that grew 30° from the main axis.

Figure 4. Selected photoluminescence peaks for (a) monoclinic and (b) hexagonal crystals. (c) The dependence of the PL peak energy on the Se content and crystal structure is plotted, with the addition of the absorption edge data for comparison.

crystals that grew preferentially perpendicular to the b-axis (Figure 3a), and nanowires that grew out of the base of the triangular crystals along the b-axis (Figure 2a). On the other hand, single-phase hexagonal crystals grew for the compositions 0.28 ≤ x ≤ 1. Two main growth modes were observed, zig-zagged and serrated crystals, both with characteristic ≈120° angles indicative of a hexagonal structure.22,23 As seen in Figure 3d, the zig-zagged crystals grew along the main in-plane

unit cell orientation are shown in Figure 3b. Through EBSD, it was possible to determine that the direction normal to the crystal surface corresponded to the direction normal to the layer plane for both monoclinic and hexagonal crystals. Similar to what was reported previously, single-phase monoclinic crystals grew within the range of 0 ≤ x ≤ 0.32.12,19−21 Here, three main growth modes were observed: elongated crystals that grew preferentially along the b-axis (Figure 3c), triangular 4228

DOI: 10.1021/acs.chemmater.8b00130 Chem. Mater. 2018, 30, 4226−4232

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Chemistry of Materials

Figure 5. (a) Scheme of Growth Method 2 for h-GaTe on GaSe flakes. (i) GaSe (red) flakes mechanically exfoliated with tape were (ii) transferred onto a silicon substrate and (iii) inserted in a tube furnace for epitaxial GaTe growth on GaSe by vapor deposition. (iv) Triangular h-GaTe crystals (blue triangles) grown on GaSe surface. (b) SEM image of GaSe flake with triangular and hexagonal islands grown on its surface. Inset: crosssectional schematic of grown h-GaTe on an exfoliated GaSe flake. (c) PL spectrum of panel b, showing a PL peak around 1.44 eV.

unit-cell axis (zigzag) while for the serrated crystals the growth direction was 30° from the axis (armchair, Figure 3e).22,23 The experimental and simulated EBSD pattern for an hexagonal crystal is shown in Supporting Information Figure S1. These results illustrate that single-phase hexagonal crystals were grown in a wider compositional range than previously reported.12,19−21 The hexagonal crystals grown around the lowSe to midrange compositions were considerably smaller than those grown with Se-rich conditions. This difference in crystal size could be attributed to the increase of lattice strain with the addition of the larger Te atoms to the hexagonal structure. Supporting Information Figure S2 shows the effect of the increasing strain on the hexagonal structure through the redshift of the Raman peaks with the addition of Te, as previously reported.24 While a hexagonal GaTe phase has been identified, it is highly unstable quickly reverting back to the monoclinic structure.25−28 Therefore, we speculate that the stress induced by the increasing lattice-strain could be better accommodated in these smaller structures, stabilizing the low-Se-content hexagonal crystals. Interestingly, within the 0.27 < x < 0.35 composition range both monoclinic and hexagonal crystals grew alongside each other with the monoclinic crystals generally growing in larger quantity and size compared to the hexagonal ones, consistent with the previous explanation. Additionally, some mixed-phase crystals were found and can be seen in Supporting Information Figure S3. The simultaneous growth of monoclinic, hexagonal, and even some mixed-phase crystals suggests the energy difference between the two phases to be low; opening the door for possible phase-change studies and applications. While such studies are beyond the scope of this work, a mechanism for the transformation between the phases has been proposed for pure GaTe, which includes an unstable tetragonal intermediate state.28

The photoluminescence (PL) spectra of several GaSexTe1−x crystals throughout the composition range were measured at room temperature. Contrary to what was observed previously in the bulk, we observe single PL peaks for each composition.20 Here, we utilize the PL peak energy as an approximate value to the bandgap energy of the alloys. It is well-known that the free excitonic PL peak in GaTe and GaSe is around 18−20 meV below their bandgap, making the approximation reasonable for the pure compounds.11,29,30 This approximation was also confirmed for the alloy compositions that were grown in bulk.12,19,20 To validate the approximation for the midrange compositions, the optical absorption of selected crystals was measured. Supporting Information Figure S4, shows the optical absorption edge and photoluminescence peak of a crystal with x = 0.48 in composition. This example confirms the validity of the approximation with the absorption edge at around 1.55 eV and the PL peak around 1.53 eV, a difference of just 20 meV. Figures 4a and b show the PL peak for selected compositions with the monoclinic and hexagonal structures, respectively. For the monoclinic crystals (Figure 4a), a monotonic increase of the bandgap is observed, similar to previous findings.12,19,20 At room temperature, the 1.65 eV PL peak of monoclinic GaTe blue-shifts to up to 1.77 eV for x = 0.32 with the addition of Se. In Figure 4b, the PL peak of the hexagonal crystals red-shifts with the addition of Te from 2.01 eV for GaSe to 1.38 eV for x = 0.28. Notably, the hexagonal GaSe0.28Te0.72 1.38 eV bandgap is 0.26 eV below that of monoclinic GaTe and matches the GaAs gap, one of the most commonly used materials in the semiconductor industry. The bandgap dependence on composition is plotted in Figure 4c. The PL peaks’ energies measured for the grown crystals are presented together with the optical absorption edges found previously for bulk alloy samples.19 On the 4229

DOI: 10.1021/acs.chemmater.8b00130 Chem. Mater. 2018, 30, 4226−4232

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Chemistry of Materials monoclinic side, our PL results perfectly agree with the optical absorption data. The linear increase in bandgap with Se content supports the linear trend established by Camassel et al., which suggests pure monoclinic GaSe with a bandgap ≈66 meV larger than its hexagonal form.17 In contrast, the PL peaks of the hexagonal crystals deviate from the suggested linear approximation toward the mid- and low-Se-content regions into an apparent shallow bowing trend. In addition, we note that within the 0.27 < x < 0.35 composition range, the hexagonal bandgap is 0.30−0.35 eV, smaller than its monoclinic counterpart. h-GaTe Growth and Characterization. Detailed computational models can be used to explain the nature of the bowing in the bandgap trend for the hexagonal GaSexTe1−x alloy. However, there is no consensus on the value of the bandgap energy of the elusive hexagonal GaTe (h-GaTe) phase, with experimental results ranging from 1.1−1.65 eV at room temperature.26,27,31 To address this, we attempted the growth of h-GaTe in the furnace tube reactor with a different approach (see Growth Method 2) by utilizing mechanically exfoliated GaSe flakes as epitaxial substrates; a schematic of the process is shown in Figure 5a. The growth of triangular and hexagonal structures on top of the GaSe flake after the h-GaTe growth process is evident in Figure 5b. It is well-documented that the equilateral triangular and hexagonal islands are the equilibrium morphologies typically observed during thin-film growth of hexagonal materials.8,11,22 Supporting Information Figure S5 shows the scanning electron micrographs and height profile of a GaSe flake (substrate) that was mechanically exfoliated and transferred to a Si substrate before and after the h-GaTe growth process. It was noticed that the crystals preferentially grew on the edges of the GaSe flakes. EDS characterization confirmed the growth of dilute-Se hexagonal GaSexTe1−x crystals (Supporting Information Figure S6). Chemical analysis of the crystals in Figure 5b indicated an upper-limit Se content of 5% which includes the Se in the GaSe flake underneath, as illustrated in the inset. Photoluminescence spectroscopy of those crystals measured an emission peak around 1.44 eV, seen in Figure 5c. The energy of 1.44 eV is remarkably close to the bandgap of 1.45 eV reported by Gillan et al. and determined by optical absorption spectroscopy.31 We emphasize that the Se content measured by EDS represents an upper bound on the actual Se content of the grown crystals, as the GaSe substrate underneath will also contribute to the measurement. Density Functional Theory (DFT) Calculations. DFT calculations were performed to explain the observed bandgap dependence on crystal structure and alloy composition. Figure 6a shows calculations performed using the Perdew−Burke− Ernzerhof (PBE) exchange-correlation functional. Notably, the bandgap values are systematically underestimated as expected for the PBE functional. They exhibit a linear increase of the bandgaps for the monoclinic phase at the Te-rich compositions, as experimentally observed. For the hexagonal phase, an apparent linear trend is obtained around the mid- to highselenium compositions with the direct gap slightly above the indirect gap, similar to GaSe.13 For the low-selenium hexagonal compositions (x < 0.30), the bandgaps start deviating from the apparent linear trend, plateauing around the 0.10 < x < 0.20 range. For compositions below x = 0.10, we observe that the indirect gap continues to decrease while the direct gap increases slightly, resulting in a large energy difference between the gaps at the pure h-GaTe point of composition. The

Figure 6. (a) DFT-calculated bandgaps for the GaSexTe1−x alloys using the PBE exchange-correlation functional. (b) Same bandgaps fitted using the experimental bandgaps of all three end points. Experimental PL peak data of single-phase (closed black squares) crystals presented for reference.

increase in energy difference between the indirect and direct gaps is caused by a change in conduction band minimum from the Γ-point to the M-point, as shown in Supporting Information Figure S7. To better visualize the DFT bandgaps, we linearly fitted the calculated values of the three end points− m-GaTe, h-GaTe and GaSe−to their experimental values. Figure 6b shows the calculations fitted by y = 1.740x − 0.0460. This fitting is in good agreement with the experimental PL peaks across the composition range and predicts an indirect bandgap for h-GaTe around 1.28 eV. Supporting Information Figure S7 also shows how the PL peaks of the mixed-phase crystals agree with the linear fitting.



CONCLUSIONS In summary, the growth of micro- and nanostructures of GaSexTe1−x allowed the stable synthesis of single-phase crystals across the composition range. Monoclinic crystals grew within the range of x = 0 to x = 0.32, with the bandgap linearly increasing from 1.65 to 1.77 eV, respectively. Meanwhile, hexagonal crystals were obtained within the 0.28 ≤ x ≤ 1 range with the bandgap decreasing with Te content from 2.01 eV (pure GaSe) to 1.38 eV (x = 0.28) and displaying shallow bandgap-bowing trend. An overlap region within 0.27 < x < 4230

DOI: 10.1021/acs.chemmater.8b00130 Chem. Mater. 2018, 30, 4226−4232

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and a k-point mesh of 500 k-points per reciprocal volume were used for density of states calculations. Geometry optimizations of the relaxed structures were performed using an initial guess with the PBE exchange-correlation functional and lattice parameters obtained by Vegard’s law. For the alloy compositions, a supercell containing a random alloy configuration was used with a (3,3,1) supercell containing 72 atoms in the hexagonal phase (P63/mmc). This approach has been found to be robust even in the case of smaller supercells with less than 0.05 eV difference compared to the more complex quasirandom supercell method.37,38 Here, we performed two separate calculations per alloy content and present averaged results. Crystal structures for the end-points were obtained from the Materials Project,39 and random supercells were constructed with the aid of the Python package pymatgen.40

0.35 was found where single-phase monoclinic and hexagonal crystals grew simultaneously. Dilute-Se hexagonal islands (x ≤ 0.05) were grown; their 1.44 eV photoluminescence peak clarified the range of previously reported hexagonal GaTe bandgaps. DFT calculations support the observed bandgap trends and identify a change in the conduction band minimum around x = 0.15. While further characterization of the optoelectronic properties is still needed, the successful growth of the GaSexTe1−x alloys should motivate the study of similar alloy systems such as GaSxTe1−x and (InSe)x(GaTe)1−x. These systems are expected to exhibit more pronounced bandgap bowing and improved transport properties.32,33





METHODS

ASSOCIATED CONTENT

S Supporting Information *

Growth Method 1: GaSexTe1−x Alloys. Gallium (99.99%, Sigma-Aldrich), selenium (99.999%, Alfa Aesar), and tellurium (99.999%, Alfa Aesar) were placed in an alumina crucible inside a quartz tube reactor. The composition was controlled by changing the selenium-to-tellurium ratio while maintaining the gallium amount in excess (about 3/1 gallium/chalcogenide mole ratio). A Si substrate with 20 nm Au nanoparticles (Sigma-Aldrich) deposited as indicated elsewhere was placed 16−18 cm downstream from the powder crucible.34 While not required, the Au nanoparticles considerably increased the growth yield. Forming gas (4% H2 in N2, premixed) was flowed at a rate of 300 sccm. The H2 gas was crucial to maintain a reductive environment and prevent the growth of large gallium oxide wires, as shown in Supporting Information Figure S8. The powder crucible temperature was increased to 1030 °C at a ramping rate of 20 °C/min and maintained there for 1 h before cooling. The substrate temperature ranged from about 600 to 800 °C with most of the growth occurring near the hotter end (temperature profile of furnace in Supporting Information Figure S9). After growth, crystals were transferred, by physical contact, to clean substrates for characterization. Any potential hazards regarding the use of H2 gas at high temperatures or the formation of toxic hydrogen chalcogenides (H2Se or H2Te) was mitigated by keeping a closed furnace system directly vented into a chemical hood exhaust with a room-temperature water bubble-trap to collect any residual precursors on the carrier gas. Growth Method 2: Hexagonal GaTe. GaTe (99.999%, Alfa Aesar) was placed in a quartz boat inside a quartz tube reactor. GaSe thin crystals were obtained by mechanical exfoliation from a bulk GaSe ingot and transferred onto a Si substrate. The substrate was placed 13−16 cm downstream from the quartz boat. Forming gas (4% H2 in N2) was flowed at a rate of 75 sccm. The quartz boat temperature was increased to 800 °C at a ramping rate of 20 °C/min, and maintained there for 1 h before cooling. The substrate temperature varied from about 600 to 700 °C depending on position. Characterization. Grown crystals were inspected by optical and scanning electron microscopy (SEM, FEI Quanta 3D FEG). The composition and crystal structure were confirmed by EDS and EBSD, respectively. Crystal thickness was measured with an atomic force microscope (AFM). Micro-Raman and microphotoluminescence spectroscopies were performed with a 488 nm laser. The absorption edge was calculated from the transmission and reflection spectra. White light from a quartz tungsten source (LSH-100, Horiba) was reflected by a sapphire beam splitter and focused on the surface of samples by a 40× objective lens. A cutting edge aperture was placed at the image plane behind the beam splitter to select sample area (∼50 μm diameter) from the reflected light. Then, the selected light was focused into a spectrometer (iHR320, Horiba) and normalized to the reflection spectrum of a 100 nm gold film. Transmission measurements were performed with a similar setup but with the light passing through a separate lens that focuses on the sample through the glass substrate before being focused into the spectrometer. Transmission measurements were normalized to the transmission spectrum of glass. DFT Calculations. Calculations are performed using VASP and the plane-augmented wave method, with pseudopotentials treating Ga 3d electrons as valence electrons.35,36 A plane-wave cut off of 520 eV

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b00130. Supplementary optical absorption, PL, Raman, SEM, EDS, EBSD, AFM, and DFT data for single-phase alloys, mixed-phase alloys, and h-GaTe crystals (PDF)



AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Jose J. Fonseca: 0000-0002-7979-4661 Matthew K. Horton: 0000-0001-7777-8871 Present Address §

J.J.F.: U.S. Naval Research Lab, Washington, DC 20375, United States. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS J.J.F. acknowledges support from the National Science Foundation Graduate Research Fellowships Program (Grant DGE-1106400). Experiments were supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the U.S. Department of Energy under Contract DE-AC02-05CH11231. M.K.H. acknowledges the support of the Lindemann Trust Fellowship. The authors gratefully acknowledge Prof. Junqiao Wu, at UC Berkeley, for the access to the micro-Raman/photoluminescence instrument, and H. Ubellacker and K. Vega for initial experiments on the growth of GaTe nanostructures.



REFERENCES

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DOI: 10.1021/acs.chemmater.8b00130 Chem. Mater. 2018, 30, 4226−4232

Article

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DOI: 10.1021/acs.chemmater.8b00130 Chem. Mater. 2018, 30, 4226−4232