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			<titleStmt><title level='a'>Strain-Modulated Exciton Localization and Enhanced Emission in Multilayer GaSe</title></titleStmt>
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				<publisher>American Chemistry Society</publisher>
				<date>07/31/2025</date>
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				<bibl> 
					<idno type="par_id">10625826</idno>
					<idno type="doi">10.1021/acs.jpcc.5c02229</idno>
					<title level='j'>The Journal of Physical Chemistry C</title>
<idno>1932-7447</idno>
<biblScope unit="volume">129</biblScope>
<biblScope unit="issue">30</biblScope>					

					<author>Sinto Varghese</author><author>Bimal Neupane</author><author>Bhojraj Bhandari</author><author>Sicheng Wang</author><author>Yan Jiang</author><author>Roberto Gonzalez_Rodriguez</author><author>Sergiy Krylyuk</author><author>Albert V Davydov</author><author>Yuanxi Wang</author><author>Hao Yan</author><author>Anupama Kaul</author><author>Jingbiao Cui</author><author>Yuankun Lin</author>
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			<abstract><ab><![CDATA[Strain engineering is one of the most effective routes for tuning the electrical and optical properties of two-dimensional layered materials. Besides reproducing the results of other groups on the tunability and photoluminescence (PL) enhancement of free and bound excitons under mechanical deformation or thermal effects, we systematically studied the mechanical strain (wrinkle) and local thermal strain (laser heating) effects on the PL lifetime and polarization in GaSe multilayers and their interplay, revealing their coupled impact on excitonic dynamics. The PL intensity of localized excitons in the wrinkle region of GaSe increases superlinearly with the excitation laser power. The polarization effect has been observed for the bound exciton in GaSe under mechanical strain, but not in GaSe under thermal strain. Fluorescence lifetime imaging (FLIM) measurements reveal strain-tunable lifetimes for both free and bound excitons, and the lifetime of the bound exciton is longer than the free exciton in the mechanical strain region, correlating with the enhanced emission of the bound exciton. These results highlight previously uncharacterized optoelectronic tunability in GaSe and broaden the design space for strain (or thermally)-controlled 2D layered devices.]]></ab></abstract>
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<div xmlns="http://www.tei-c.org/ns/1.0"><head>Introduction</head><p>In recent years, atomically thin layered III-VI metal chalcogenides have gained increased attention owing to their remarkable optical and electronic properties in developing optoelectronic devices. <ref type="bibr">[1]</ref><ref type="bibr">[2]</ref><ref type="bibr">[3]</ref><ref type="bibr">[4]</ref><ref type="bibr">[5]</ref><ref type="bibr">[6]</ref><ref type="bibr">[7]</ref><ref type="bibr">[8]</ref> They exhibit a weakly bonded van der Waals (vdW) <ref type="bibr">9</ref> layered structure, allowing the thickness to be reduced to an atomically thin two-dimensional (2D) crystal with distinctive properties. Mo-and W-based transition metal dichalcogenides (TMDCs) have attracted significant attention due to their thickness-dependent bandgap, ranging within the visible range of the electromagnetic spectrum. <ref type="bibr">10</ref> However, their application has been restricted by the necessity of cryogenic temperatures for operation. <ref type="bibr">[11]</ref><ref type="bibr">[12]</ref><ref type="bibr">[13]</ref> As an alternative, the vdW layered compound GaSe has been utilized in a single-photon emission experiment at room temperature. It possesses a direct bandgap of only 25 meV higher than an indirect bandgap of 2.11 eV, rendering it a functional semiconductor. <ref type="bibr">[14]</ref><ref type="bibr">[15]</ref><ref type="bibr">[16]</ref> There exists a strong intralayer covalent bonding and a weak interlayer vdW bonding, enabling the separation of layers 9 using mechanical exfoliation. A single layer of GaSe with a hexagonal symmetry consists of four (Se-Ga-Ga-Se) atoms in a sequence. <ref type="bibr">17</ref> GaSe exhibits intriguing optical and electrical characteristics, including a strong second harmonic generation, <ref type="bibr">17</ref> a large anisotropic Hall mobility, <ref type="bibr">18,</ref><ref type="bibr">19</ref> a high on/off ratio of field-effect transistors <ref type="bibr">19,</ref><ref type="bibr">20</ref> and improved gas sensitivity. <ref type="bibr">21</ref> Conversely, strain engineering has emerged as one of the most effective routes for regulating and manipulating the electrical and optical properties of layered GaSe, offering an additional degree of freedom. <ref type="bibr">17,</ref><ref type="bibr">[22]</ref><ref type="bibr">[23]</ref><ref type="bibr">[24]</ref><ref type="bibr">[25]</ref><ref type="bibr">[26]</ref> It is found that the potential for mechanically compliant optoelectronics lies in a strain sensor utilizing monolayer GaSe, while suitable strain engineering of multilayer GaSe has the prospect of introducing a new class of three-dimensional topological insulators. <ref type="bibr">17,</ref><ref type="bibr">27</ref> In addition, its application of thermal stresses induced by laser excitation, mechanical strains from wrinkling, or tension strains is recognized for enhancing carrier mobilities in transistors based on TMDCs. This approach not only amplifies photoluminescence and singlephoton emission but also allows for the modulation of the direct bandgap to indirect and vice versa. <ref type="bibr">[28]</ref><ref type="bibr">[29]</ref><ref type="bibr">[30]</ref><ref type="bibr">[31]</ref><ref type="bibr">[32]</ref><ref type="bibr">[33]</ref><ref type="bibr">[34]</ref><ref type="bibr">[35]</ref> While previous studies have explored excitonic PL in strained GaSe, including free exciton (FX) and bound exciton (BX) peak evolution under mechanical deformation or thermal effects, <ref type="bibr">36,</ref><ref type="bibr">37</ref> the roles of PL lifetime, polarization behavior, emission enhancement, and the interplay between mechanical and thermal strain remain less examined. In this work, we report the presence of exciton localization in multilayer GaSe under thermal strain, mechanical strain, or their combination. PL and fluorescence lifetime imaging (FLIM) measurements reveal enhanced PL, polarization effect in the bound exciton emission, and longer PL lifetime in the bound exciton than in free-exciton emission. Density functional theory is used to explain the shift in PL wavelength in GaSe under in-plane, out-of-plane, and volume strains.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Experimental Methods</head><p>Preparation of the Multilayer sample with wrinkle: GaSe single crystals were grown by the vertical Bridgman method using pre-synthesized polycrystalline GaSe charge that was vacuum sealed in a graphitized quartz ampoule. The melt was equilibrated at 990 &#176;C for several hours, and then the ampoule was translated across a temperature gradient at a rate of 0.4 mm/h. The &#61541;-phase of GaSe was confirmed by X-ray diffraction. A thin free-standing layer of GaSe is obtained by lightly pressing the corner of a piece of Scotch tape onto the surface of bulk GaSe, using a sharptipped object like a fine pin, and subsequently peeling off the tape. The obtained free-standing sample is then transferred onto a glass surface by pressing it gently with a polydimethylsiloxane (PDMS) stamp. Wrinkles in GaSe flakes were naturally generated during the transfer process.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Strain modulation in multilayer GaSe by applying high pressure:</head><p>A multilayer GaSe sample was obtained from bulk GaSe through repeated exfoliation with Scotch tape until the target thickness was reached. The sample was then placed on thermal release tape, which was subsequently heated to 100 &#176;C to detach the multilayers. These GaSe flakes were transferred to a diamond anvil cell (DAC) for high-pressure experiments, where hydrostatic pressure was applied using silicon oil as a pressure-transmitting medium by adjusting the DAC screws.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Raman and Photoluminescence Spectra:</head><p>The Raman and the PL measurements were carried out at room temperature using the Renishaw inVia Raman Microscope. A Cobolt Samba 532 nm laser, in conjunction with a 50&#215; objective lens (numerical aperture NA=0.5) positioned at an 8.2 mm working distance, facilitated the experiments. We used a 1800 lines/mm grating for measurements since it covered all the necessary wavelength range. Throughout the measurements, an exposure time of 10 s was maintained. Desired laser powers were realized by combining the neutral density filters and Cobolt Samba's laser power control software. Based on our optical setup, the 1 mW laser power corresponds to 0.59 kWcm -2 . For convenience, we processed all the data in terms of laser power instead of laser intensity.</p><p>We also measured the Raman and PL spectra at room temperature using 473 and 785 nm lasers coupled with a 50&#215; objective lens (NA=0.5).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>FLIM:</head><p>The FLIM and the lifetime histogram on the flat and wrinkle region of the multilayer GaSe sample were studied using a Micro Time 200 time-resolved confocal fluorescence microscope. We used one Pico Second Laser with a wavelength of 405 nm, a repetition rate of 80 MHz, and an average power of 3.84 mW for the PL excitation. The confocal microscope used a 20&#215; objective lens (NA=0.4). The data acquisition and analysis were performed using SymPho-Time 64 software.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Profilometer measurements:</head><p>The height profile of the sample is measured using FILMETRICS Profilm 3D Profilometer. We use the White light interferometry (WLI). The measurement parameter 'envelope peak' was selected under the 'single' tab of 'WLI' settings to characterize the surface profiles. This parameter was chosen to identify the highest points on the surface and analyze their distribution.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>DFT calculations:</head><p>The electronic band structure calculations were performed using densityfunctional theory (DFT), as implemented in the Vienna Ab initio Simulation Package (VASP). <ref type="bibr">38</ref> The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional <ref type="bibr">39</ref> was employed, along with projector augmented wave pseudo-potentials. <ref type="bibr">40</ref> The cutoff for the kinetic energy of plane waves was set to 550 eV. All structures were optimized until the force on each atom was less than 0.01 eV/&#197;. The Brillouin zone was sampled by a &#915;-centered mesh of 12&#215;12&#215;1.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Results:</head><p>A. PL emission from flat GaSe.</p><p>The effect of thermal strain on the PL spectrum in the flat region of a multilayer GaSe sample is first examined. Figure <ref type="figure">1</ref> shows PL spectra under laser powers between 0.2 and 12 mW.</p><p>Under low excitation power (0.025-0.4 mW), the PL spectrum has a dominant peak centered near 2.00 eV (&#8764;620 nm ), commonly attributed to FX emission at the direct band edge of GaSe. <ref type="bibr">41</ref> As the laser power increases above 3 mW, a high-energy shoulder peak (X2) is also strong around 2.02 eV (&#8764;610-612 nm ), which we attribute to the indirect transition of the FX state involving phononassisted processes, consistent with prior reports on strain-modulated GaSe multilayers. <ref type="bibr">42</ref> This spectral splitting into X1 and X2 arises due to a strain-induced exciton funneling effect that alters the electronic band structure. Notably, the energy separation between X1 and X2 is &#8764;25 meV at 6 mW, in agreement with previous studies. <ref type="bibr">36,</ref><ref type="bibr">37</ref> At the laser power of 3 mW, a third peak (XB) also appears strongly around 1.97 eV (&#8764;630 nm), likely arising from BXs trapped in localized states formed by laser-induced thermal strain.</p><p>An example of the peak fitting used to resolve X1, X2, and XB is provided in Figure <ref type="figure">S1</ref>. Each PL component was fitted with a multi-peak Lorentzian approach to accurately account for homogeneous broadening mechanisms arising from the excitonic recombination in layered GaSe, as supported by improved fit quality and established approaches in recent literature. <ref type="bibr">37,</ref><ref type="bibr">42</ref> Similar low-energy BX emission has also been reported in GaSe flakes, <ref type="bibr">42,</ref><ref type="bibr">43</ref> where exciton trapping was attributed to localized states formed by mechanical deformation or intrinsic crystal imperfections, supporting the interpretation that strain-whether thermally or mechanically induced-can give rise to such bound exciton features. Figure <ref type="figure">1b</ref> displays the extracted PL intensities for X1 (blue circles), X2 (green triangles), and XB (red squares) as a function of excitation power. The intensity of X1 increases initially but begins to decrease beyond 3 mW. In contrast, the BX peak (XB) exhibits an increasing trend with increasing laser power up to 9 mW due to higher thermal strain under higher laser excitation powers. Figure <ref type="figure">1c</ref> shows the corresponding peak positions, where all three peaks shift to longer wavelengths as the power increases.</p><p>Temperature-dependent PL spectra were also measured in the same region (Figure <ref type="figure">S2</ref>) to evaluate the extent of thermal strain induced in the sample by laser exposure. Using the temperature-dependent GaSe bandgap change rate from Figure <ref type="figure">S2b</ref>, we can estimate the temperature change of the flat GaSe region to be about 398 K when the sample is under 16 mW laser excitation. Also, Figure <ref type="figure">S2c</ref> presents the temperature-dependent energy shift for the free exciton peak (2.00 eV), where the red circles represent the experimental data, and the blue line corresponds to the theoretical fit. The data were fitted using the least squares method based on the Varshni empirical equation:</p><p>&#119864; &#119892; (0) is the band gap of the GaSe slab at 0 K, while &#120572; and &#120573; are Varshni coefficients, where &#120572; accounts for the electron (or exciton)-phonon interaction and &#120573; is associated with the Debye temperature of the material. <ref type="bibr">36,</ref><ref type="bibr">41,</ref><ref type="bibr">44</ref> The agreement between the measured values and the fitting confirms that the intrinsic band structure response to temperature remains unchanged, even though additional strain-induced features emerge at higher temperatures.</p><p>Shifts of the Raman peaks in the flat region of GaSe with increasing laser power were also studied (Figure <ref type="figure">S3</ref>). Above 12 mW, Raman intensity reached detector saturation. We observed peaks at 133 cm -1 , 212 cm -1 , and 307 cm -1 as shown in Figure <ref type="figure">S3a</ref>. These are consistent with the previous reports and are A1g 1 , E2g 1 , and A1g 2 vibration modes of GaSe, respectively. <ref type="bibr">21,</ref><ref type="bibr">45,</ref><ref type="bibr">46</ref> By increasing the laser power from 0.1 to 9 mW (for the comparison with Figure <ref type="figure">S6</ref>), the A1g 1 , E2g 1 , and A1g 2 peak wavenumbers change by 0.44, 1.64, and 1.64 cm -1 , respectively (Figure <ref type="figure">S3b-d</ref>). For more clarity, the Raman shift with temperature is given in Figure <ref type="figure">S4</ref>. The red shifts of the peaks with increasing laser power (and temperature) <ref type="bibr">42</ref> is due to the thermal expansion of the sample, which also supports our observation about the thermal strain.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>B. PL emission from wrinkled GaSe</head><p>After examining the effect of thermal strain on the PL spectra, the focus was shifted to a wrinkle region exhibiting mechanical strain. The wrinkle is generated by pressing the sample with PDMS during the preparation of the sample. Based on theoretical calculations (discussed later), the strained region was identified to exhibit tensile strain. Figure <ref type="figure">2a</ref> shows the optical image of the sample, where there are two wrinkles. PL was measured from the left wrinkle, highlighted by a dashed blue rectangle in Figure <ref type="figure">2a</ref>. PL measurements on the wrinkle at 1 mW laser give us an additional peak (peak-XB). Note, that 1 mW excitation is below an excitation power that resulted in the appearance of the peak-XB for the flat region of the sample (Figure <ref type="figure">1</ref>). The peak wavelength changes with the strength of strain on the wrinkle. An energy of 1.98 eV, corresponding to the maximum PL intensity, was chosen for PL mapping, as shown in Figure <ref type="figure">2b</ref>. Figure <ref type="figure">2c</ref> illustrates the PL spectra for various positions away from the left edge by distances of 2.5, 3.5, 5, 5.5, 6, 6.5, and 7 &#61549;m along the dashed red line in Figure <ref type="figure">2b</ref>. Changes were observed in both PL intensity and the maximum energy. Peak positions for peak-X1 and the additional peak-XB are plotted as a function of distance from the left edge of the rectangle in Figure <ref type="figure">2d</ref>. An example of peak fitting is given in Figure <ref type="figure">S5</ref>. Our findings revealed that the intensity of peak-XB is more pronounced in the proximity of the wrinkle. There is a deformation of the GaSe crystal caused by the wrinkle. These lattice deformations create local strain fields (mechanical strain) that induce confinement potentials that trap excitons. <ref type="bibr">47</ref> Strain enhanced the PL intensity of peak-X1 by two orders of magnitude and induced peak-XB. The PL enhancement on the wrinkle can be explained based on the funneling effect due to the strain. <ref type="bibr">36,</ref><ref type="bibr">37,</ref><ref type="bibr">48,</ref><ref type="bibr">49</ref> The mechanical strain shifts peak-X1 from 2.01 eV for the unstrained region to 1.99 eV, which corresponds to the maximum strain, whereas peak-XB redshifts from 1.98 to 1.96 eV (Figure <ref type="figure">2d</ref>). The shift is 18 meV for peak-X1 and 26 meV for peak-XB. For a comparison, thermal-induced strain of the flat region of GaSe under 7 mW laser excitation causes a similar shift of 18 meV to peak-X1 (Figure <ref type="figure">1c</ref>). Comparing these results, it is evident that mechanical strain has a less pronounced effect on the free exciton emission.</p><p>Shifts of the Raman peaks on the wrinkle of GaSe with increasing laser power were also studied.</p><p>We observed peaks at 133.2 cm -1 , 211.9 cm -1 , and at 306.7 cm -1 as shown in Figure <ref type="figure">S6a</ref>. By increasing the laser power from 0.1 to 9 mW, the A1g 1 , E2g 1 , and A1g 2 peak wavenumbers change, respectively, by 0.5, 2.3, and 2.2 cm -1 (Figure <ref type="figure">S6b-d</ref>) that is larger compared to the respective shifts of 0.44, 1.64, and 1.64 cm -1 for the flat region. The temperature increase in the wrinkled sample is higher than in the flat one, probably due to the reduced heat transfer to the substrate since the flake is suspended.</p><p>The combined effect of thermal and mechanical strains on the PL of multilayer GaSe was further investigated. To resolve subtle changes in the PL spectra, a region with clear separation between peak-X1 and peak-XB is required for accurate fitting. Additionally, one region with dominant peak-X1 intensity and another where peak-XB dominates are needed to probe areas with different mechanical strains. To achieve this, multilayer GaSe was mechanically squeezed to form a sharp hill, as shown in the SEM image in Figure <ref type="figure">S7a</ref>. Figure <ref type="figure">S7b</ref> and S7c show its optical image from a beam profiler and height profile. As seen from Figure <ref type="figure">S7c</ref>, the graph illustrates an initial rise of 2 &#61549;m over a horizontal distance of 2 &#61549;m, followed by a steeper drop of 4 &#61549;m over the next 2 &#61549;m. Figure <ref type="figure">S7d</ref> and S7e show the PL mapping on the right and left sides of the hill, respectively.</p><p>We selected spot-1 in Figure <ref type="figure">S7d</ref> and spot-2 in Figure <ref type="figure">S7e</ref> for laser power-dependent PL measurements when both thermal and mechanical strains are present. Figure <ref type="figure">3a</ref> shows the evolution of the PL spectra at spot-1 under increasing laser power. For low excitation levels, the peak-XB intensity was lower than the peak-X1 intensity. At high laser powers, the peak-XB surpasses the peak-X1. Clear separation of the two peaks facilitates an accurate fitting to extract peak intensities and positions. Figures <ref type="figure">3b</ref> and <ref type="figure">3c</ref> show the laser powerdependent PL peak intensity and peak position, respectively. From Figure <ref type="figure">3b</ref>, we noticed a linear increase in PL peak intensity for the peak-X1 (blue circles) from 0.25 to 16 mW, whereas the peak-XB (red squares) showed super-linear behavior with increasing laser power. For the peak-XB (localized exciton emission), the enhancement of PL intensity is observed above 6 mW excitation, as indicated by a vertical dotted line. Also, to gain insights into the underlying recombination processes, we plotted the power-dependent intensities and fitted them to the power-law relationship &#119868; &#8764; &#119875; &#120572; , as presented in the inset in Figure <ref type="figure">3b</ref>. The &#945; value for peak-XB is 1.8 which indicates that the emission is enhanced or these localized excitons can be related to biexciton recombination under high laser excitation densities. <ref type="bibr">50,</ref><ref type="bibr">51</ref> The PL intensity of peak-XB demonstrates a 1.92-fold enhancement relative to peak-X1 under equivalent increases in laser power. This enhanced emission from peak-XB on the wrinkle is due to the combined effect of both thermal strain from the laser heating and mechanical strain from the wrinkle. The peak position of the peak-X1 (blue circle) changes from 1.99 to 1.97 eV due to the rising laser power up to 6 mW, corresponding to a temperature increase of 48.7 K. Due to the mechanical strain on spot-1, an additional thermal strain caused by the 48.7 K temperature increase can initiate the enhanced emission of localized excitons. For more detailed analysis, the temperature-dependent PL spectrum (Figure <ref type="figure">S8</ref>) and Raman spectrum (Figure <ref type="figure">S9</ref>) from spot 1 are also provided in the Supporting Information.</p><p>Repeatability was examined in a separate series of measurements, as shown in Figure <ref type="figure">S10</ref>.</p><p>At an initial laser power of 1 mW, peak-X1 is higher than peak-XB. When the laser power is increased to 5 mW, peak-XB becomes stronger than peak-X1. However, upon reducing the laser power back to 1 mW, peak-X1 regains its higher intensity relative to peak-XB. Spot-2 is then examined, where peak-XB intensity exceeds that of peak-X1 even at the lowest excitation levels. Figure <ref type="figure">3d</ref> gives the PL spectra taken at low laser powers of 0.03, 0.06, 0.1, 0.2, 0.3, 0.4, and 0.5 mW. Above 0.5 mW, the PL intensity reaches the detector saturation level. At spot-2, the peak-XB has a stronger intensity than peak-X1 under all excitation powers.</p><p>Figure <ref type="figure">3e</ref> shows the laser power-dependent PL peak intensity. We observe the linear growth for peak-X1(blue circles) and peak-XB (red squares) as can be seen from the log-log plot in the inset.</p><p>Here, the &#945; value for peak-XB is 2.1, reaffirming that the observed emission is enhanced (i.e., increasing superlinearly) or these localized excitons can be related to biexciton recombination under high laser excitation densities. <ref type="bibr">50,</ref><ref type="bibr">51</ref> When the laser power is increased from 0.02 to 0.5 mW, the PL intensity of peak-XB exhibits a 2.26-fold enhancement compared to peak-X1 under the same conditions. This can be due to the strain-induced funneling effect, <ref type="bibr">37</ref> where the strain acts as a funnel that drives the exciton migration to spot-2. Figure <ref type="figure">3f</ref> shows the laser power-dependent PL peak positions that do not change with excitation increase.</p><p>FLIM measurements were further conducted on both the flat and wrinkle regions.  XB. Figures <ref type="figure">4a</ref> and <ref type="figure">4b</ref> depict the optical image and lifetime histogram for the strained region using the 600&#177;20 nm filter. In Figure <ref type="figure">4a</ref>, three regions are distinguished by different colors: the top region (violet rectangle) has high strain, the middle region (blue rectangles) is near the hill (or wrinkle), and the red rectangle is for the flat region. Due to different strain levels, the corresponding lifetime histogram of the whole region in Figure <ref type="figure">4b</ref> covers a wide range of lifetime from 0.5 to 1.4 ns. The excitons in the strained top region have longer lifetimes between 1.14 ns and 1.40 ns (violet curve), compared with 0.7-1.2 ns for the middle region (blue curve) and 0.5-0.8 ns for the flat region (red curve) for the free exciton emission at 620 nm. Similar observations were also made for localized exciton emission using the 650&#177;20 nm filter. The image and the lifetime histogram are given in Figures <ref type="figure">4c</ref> and <ref type="figure">4d</ref>, respectively. The data shows a lifetime range of 1.47-2.8 ns on the strained top region (purple color) compared with the 1.06-2.20 ns of the flat region (red curve). Comparing these two histograms, we can see that the lifetime of carriers in the strain region is longer than that in the flat region, and the lifetime of peak-XB is longer than peak-X1 in the corresponding regions. The observed enhanced PL emission and longer PL lifetime in the strain region than the one in the flat region are characteristic of exciton location. <ref type="bibr">52,</ref><ref type="bibr">53</ref> Additionally, Figures <ref type="figure">4e</ref> and <ref type="figure">4f</ref> present the FLIM for non-strained regions using the 600&#177;20 nm and 650&#177;20 nm filters, respectively. The lifetime histogram for these non-strained regions is shown in Figure <ref type="figure">4g</ref>. We see less lifetime event count for peak-XB (black curve) compared with peak-X1 (green curve). However, the carrier lifetime for peak-XB is much longer than peak-X1. In our studies on stimulated emission by defect levels in MoS2 and MoSe2, <ref type="bibr">34,</ref><ref type="bibr">54</ref> the enhanced emission is accompanied by the polarization effect. For the thermal strain-induced localized excitons, we did not observe the polarization effect as seen in Figure <ref type="figure">S12</ref>. We checked the polarization effect for localized exciton emission caused by the mechanical strain (Figure <ref type="figure">5</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Figures 5a and 5b</head><p>present the PL spectra recorded for VV (Vertical, Vertical) and VH (Vertical, Horizontal) polarization arrangements, respectively, at laser powers of 0.5 and 2.5 mW. To evaluate the polarization effect, we calculated the VV/VH ratio for both powers and depicted it in Figure <ref type="figure">5c</ref>. From Figure <ref type="figure">5c</ref>, we observed a consistent value for peak-X1 at both laser powers, indicating its lack of polarization effect. In contrast, peak-XB exhibited a pronounced polarization effect, with a ratio of approximately 25 at 0.5 mW and a ratio of about 40 at 2.5 mW. <ref type="bibr">[55]</ref><ref type="bibr">[56]</ref><ref type="bibr">[57]</ref> The PL intensity in GaSe can be strongly influenced by factors such as crystal orientation, light polarization, and the thickness of the GaSe layers. To rule out such effects in our study, we measured vertically and horizontally polarized PL from the same spot and analyzed their ratio, which revealed distinct polarization behavior for different peaks, indicating intrinsic differences in their origin. The strong polarization dependence observed for the localized exciton emission in mechanically strained regions (Figure <ref type="figure">5</ref>) can be attributed to strain-induced symmetry breaking rather than intrinsic anisotropy of the GaSe crystal. In unstrained or thermally strained regions, where the crystal retains its high-symmetry D3h structure, <ref type="bibr">58</ref> the localized exciton emission does not exhibit significant polarization (Figure <ref type="figure">S12</ref>), indicating that native anisotropy alone is insufficient to produce the observed polarization contrast. Mechanical strain-introduced via wrinkle formation-modifies the local lattice structure and reduces the symmetry, leading to anisotropic optical transitions and alignment of the excitonic dipole. This symmetry lowering is evidenced by the transformation of the fourfold Raman pattern to a twofold response under strain and by the linear polarization of exciton and biexciton emission from strain-localized quantum emitters in multilayer GaSe. <ref type="bibr">59,</ref><ref type="bibr">60</ref> The distinction in polarization behavior between thermally strained and mechanically strained regions supports this interpretation. While GaSe inherently has anisotropic in-plane properties, the pronounced polarization in our measurements is enhanced by localized strain fields that modify exciton confinement and radiative selection rules. If we consider the strain-induced lattice deformation that creates the localized exciton states, a three-level energy system can be formed. Stimulated emission and polarization effects can be explained by that model. However, further theoretical calculations are needed to verify that model.</p><p>Recent studies have shown that strain in multilayer 2D materials plays a significant role in modifying excitonic behavior and carrier dynamics. <ref type="bibr">61,</ref><ref type="bibr">62</ref> In multilayer MoS&#8322; and WSe&#8322;, mechanical strain has been reported to induce exciton drift, trion formation, and bandgap shifts by altering the exciton binding energy and electronic band structure. <ref type="bibr">28,</ref><ref type="bibr">29,</ref><ref type="bibr">63</ref> Strain-induced potential gradients can act as confinement sites, leading to localized exciton emission and enhanced photoluminescence intensity at strained regions. <ref type="bibr">33,</ref><ref type="bibr">47,</ref><ref type="bibr">64</ref> These findings emphasize that strain can activate a variety of excitonic species and modulate emission properties in 2D systems. Our experimental observations on multilayer GaSe under strain conditions similarly show exciton trapping, enhanced PL, and changes in emission energy. To understand the underlying physics behind the excitonic emission from flat and wrinkled GaSe surfaces, we performed a band structure calculation via DFT at different strain levels. We adopted two different approaches: one utilizing bandgap calculations across varying strain levels and the other using phonon-frequency analysis, both aimed at determining the type and magnitude of strain. Our calculation found that applying compressive (tensile) in-plane strain to bulk GaSe led to an increase (decrease) in the band gaps as a function of the applied strain, respectively (Figure <ref type="figure">S13</ref>). On the other hand, applying compressive (tensile) out-of-plane strain to GaSe resulted in a decrease (increase) in band gap, respectively. As an example, shown in Figure <ref type="figure">S14</ref>, both the valence band maximum (VBM) and conduction band minimum (CBM) located at Gamma (&#915;) slightly move toward the Fermi-level, resulting in a decrease in the band gap, when 0.3% in-plane tensile strain is applied to GaSe. Sometimes different ratios of in-plane and out-of-plane strains were applied to explain the experimental data. <ref type="bibr">34</ref> Figure <ref type="figure">6a</ref> shows the band structure of bulk &#120576;-GaSe with 0.5% volume strain (in-plane as well as out-of-plane tensile strain) (dashed red line plot) and without strain (solid black line plot).</p><p>As it is well known that DFT calculations with PBE generally underestimate the band gaps, our focus here is on the change in band gap with increasing volume strain rather than on quantitative values of the actual band gap. In particular, DFT study showed that 0.5% strain reduces the band gap by 0.05 eV. This agrees well with the observed 0.05 eV energy difference of the PL lines from the wrinkled (1.96 eV) and flat areas (2.01 eV) of GaSe in Figure <ref type="figure">2d</ref>. Consistent with earlier studies showing that biaxial strain in multilayer GaSe drives the conduction-band minimum downward while lifting the valence-band maximum at a combined rate of ~0.07-0.20 eV per % strain, <ref type="bibr">48,</ref><ref type="bibr">60,</ref><ref type="bibr">65</ref> this 0.5 % tensile strain therefore creates a ~50 meV type-I potential well more than twice kBT (26 meV) and well above the exciton binding energy((&#8776; 34 meV) <ref type="bibr">41</ref> sufficient to trap excitons stably at room temperature. The CBM is mainly derived from the Ga s orbital, with a minor contribution from the Se s orbital. In contrast, the VBM predominantly arises from Se pz orbitals (see Figure <ref type="figure">S15</ref>). The optical transition from Se pz to Ga s orbital states is dominant when &#119864; &#8407; //&#119888;&#770; , which depends on the direction of vector &#119864; &#8407; of the electro-magnetic wave. <ref type="bibr">66</ref> Our study finds that the orbital contributions to the CBM and VBM remain nearly unchanged between the strained (0.5% volumetric strain) and unstrained cases. Phonon frequencies were also calculated as a function of in-plane biaxial tensile strain. The corresponding vibrations of &#120576;-GaSe from DFT calculations are shown in Figure <ref type="figure">S16</ref>. The shift of the phonon modes with strain obtained from DFT simulation is given in Figure <ref type="figure">S17</ref>. The calculations show the frequency of phonon modes for the strained case is slightly lower than those for the unstrained case. Table <ref type="table">S1</ref> gives the complete data of the shift for each phonon mode from the DFT simulation. This agrees with our experimental observations, where the frequency of phonon modes becomes smaller with higher laser power (higher thermal strain). The frequency is also smaller on the wrinkle compared with the flat surface (higher mechanical strain). The summary of the shift of the phonon modes from the experiment is given in Table <ref type="table">S2</ref>.</p><p>To verify the DFT prediction that applying compressive out-of-plane (in-plane) strain to GaSe resulted in a decrease (an increase) in band gap, we applied hydrostatic pressure on GaSe.</p><p>Because of 2D layered structure and its high in-plane rigidity, the out-of-plane compressive strain plays a dominant role when the GaSe layers were under hydrostatic pressure. Figure <ref type="figure">6b</ref> shows the normalized PL intensity of the sample under different pressures of 0, 0.25, 0.6, and 0.8 GPa. Unlike the several PL peaks (bound and free-exciton peaks in Figures <ref type="figure">1</ref> and <ref type="figure">2</ref>), there is one PL peak in GaSe under a pressure up to 0.6 GPa because of a uniform pressure in the sample. We observed a pressure-induced PL shift in Figure <ref type="figure">6b</ref>, where the PL peak shifted from 2.00 (at 0 GPa) to about 1.95 eV (at 0.6 GPa), in agreement with the DFT prediction. There is an additional peak at 1.90 eV at 0.8 GPa, which we assumed is assigned to a pressure-induced defect peak that will be reported elsewhere. <ref type="bibr">67</ref> </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Conclusion:</head><p>In summary, we have studied the PL of free exciton and bound exciton, their polarization effects, and FLIM in GaSe under mechanical strain, thermal strain, and their combination.</p><p>Advancing from the previous study by other research groups on the tunability of these localized excitons and their assignments of free excitons (X1, X2) and bound exciton (XB), we have revealed other uncharacterized strain-tunable excitonic dynamics. The thermal strain can trigger the bound exciton with no PL polarization effects. The mechanical strain in the wrinkle has resulted in the biexciton-dominated bound exciton with a strong polarization effect. Lifetime image measurement has revealed strain-dependent lifetimes for both free exciton and bound exciton. The lifetime of the bound exciton is longer than the free exciton in the same mechanical strain region of the wrinkle, explaining the PL enhancement of the bound exciton. These results provide further design space for strain-related devices. </p></div>
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