Toward Large-Scale Ga2O3 Membranes via Quasi-Van Der Waals Epitaxy on Epitaxial Graphene Layers

Epitaxial growth using graphene (GR), weakly bonded by van der Waals force, is a subject of interest for fabricating technologically important semiconductor membranes. Such membranes can potentially offer effective cooling and dimensional scale-down for high voltage power devices and deep ultraviolet optoelectronics at a fraction of the bulk-device cost. Here, we report on a large-area β-Ga2O3 nanomembrane spontaneous-exfoliation (1 cm × 1 cm) from layers of compressive-strained epitaxial graphene (EG) grown on SiC, and demonstrated high-responsivity flexible solar-blind photodetectors. The EG was favorably influenced by lattice arrangement of SiC, and thus enabled β-Ga2O3 direct-epitaxy on the EG. The β-Ga2O3 layer was spontaneously exfoliated at the interface of GR owing to its low interfacial toughness by controlling the energy release rate through electroplated Ni layers. The use of GR templates contributes to the seamless exfoliation of the nanomembranes, and the technique is relevant to eventual nanomembrane-based integrated device technology.


INTRODUCTION
The development of large-scale compound semiconductor membranes gives a great opportunity to make unprecedented devices such as ultralightweight, flexible, and vertical devices. 1−3 In addition, multifunctional devices can be achieved through heterogeneous integration by transferring various kinds of membranes on one single chip. 4−6 Despite such advantages, the successful development of membranebased devices has been limited because it is challenging to obtain the large-scale membranes by growing three-dimensional (3D) materials on 3D materials strongly bonded by covalent bonding. Although many attempts to obtain the largescale membranes have been performed by using laser lift-off and chemical lift-off, it also has several drawbacks as it is an extremely expensive process, and there are difficulties in finding proper sacrificial layers. To respond to the challenge, 3D materials growth by using two-dimensional (2D) materials, weakly bonded by van der Waals force, such as graphene (GR) and h-BN can be a good candidate. In other words, the considerably weaker bonding strength at the interface of 2D/ 2D and 3D/2D surfaces alleviates interfacial toughness and allows 3D-materials membranes peeling from the 2D materials. 7−11 However, direct epitaxial growth of 3D materials on 2D materials, especially for GR, is not straightforward owing to its low surface energy. To overcome this hurdle, Chung et al. applied ZnO-coated layers of GR and Chen et al. used GR layers directly grown on sapphire substrates subjected to N 2 plasma treatment for the subsequent growth of group-III-nitride materials. 12−14 Particularly, although Chung et al. demonstrated transferable GaN-based light-emitting diodes by peeling the membranes from the GR layer, the membranes were flake-like. Nevertheless, it is clear that epitaxy using the GR layer offers a great chance to obtain large-scale membranes. Ga 2 O 3 has recently emerged as a promising candidate because it can be used as the absorbing layer in solar-blind photodetectors (PDs) for flame detection, and high-power electronics. 15−17 Among the five phases of Ga 2 O 3 (i.e., α, β, γ, δ, and ε), β-Ga 2 O 3 has been intensively investigated owing to its thermal stability and wide band gap (∼4.9 eV) properties. 15,16 Several studies show β-Ga 2 O 3 grown on various substrates such as sapphire, SiC, GaN, and AlN substrates; however, these bulk substrates restrain the merits of β-Ga 2 O 3 such as inflexibility and a difficulty to fabricate vertical devices. 18−20 In this study, we were able to grow a 201-oriented β-Ga 2 O 3 layer on epitaxial graphene (EG) because the EG directly interacts with SiC substrates. Based on the successful growth of the β-Ga 2 O 3 layer on the EG, we were able to develop a largearea β-Ga 2 O 3 nanomembrane (∼1 cm 2 ) by peeling the β-Ga 2 O 3 layer from the EG through the controlled energy release rate. We then used this nanomembrane to fabricate the flexible and vertical solar-blind PDs, which recorded a responsivity of 151.1 A/W and an improved time response (0.24 s for rise time (τ r ) and 0.48 s for decay time (τ d )). The achieved performance can be attributed to the reduction of transit time of charge carriers owing to the very thin β-Ga 2 O 3 nanomembrane that allowed vertically sandwiched electrodes on both sides. This process not only paves the way for wafer-scale exfoliation for oxide-based materials, but also provides a possibility to develop devices with unprecedented thermal, electrical, and optoelectronic properties based on the membranes.

EXPERIMENTAL SECTION
2.1. Preparation of Epitaxial Graphene. To obtain epitaxial graphene (EG), we prepared a 1 cm × 1 cm Si-faced 6H SiC (0001) cut from two-inch wafers. The organic residue on the substrate was removed with acetone and ethanol, and the metal residue and native oxide were removed with HCl and HF, respectively. We placed the 6H SiC substrates into a graphite box and raised the temperature to 1600°C at a rate of 0.5°C/s in an H 2 atmosphere, and maintained it for 15 min to perform H 2 etching. The pressure automatically vented to remain constant at 550 Torr, whereas it was over 550 Torr throughout the heat treatment process. After H 2 etching, the hydrogen supply was shut-off and Ar was slowly injected. The temperature was increased to 1650°C at a rate of 0.2°C/s and maintained for 15 min to form the EG. The EG was finally obtained by cooling to 1000°C while maintaining the ambient Ar, and naturally cooling to room temperature (RT).
2.2. Growth of β-Ga 2 O 3 by Pulsed Laser Deposition. We attached the EG on SiC (1 cm × 1 cm) to the holder and loaded it into the load lock chamber. After placing the sample in the main chamber, the temperature was raised to 600°C at a rate of 0.5°C/s, and to 800°C at a rate of 0.33°C/s in vacuum at 10 −8 Torr. Once the temperature had reached 800°C, O 2 was injected and stabilized until its partial pressure reached 5 mTorr. The distance between the Ga 2 O 3 target and the substrate was maintained at 80 mm. The frequency of the laser pulse was set to 5 Hz and the energy per a pulse to 300 mJ. We used 20 000 laser pulses to obtain a ∼ 250 nm-thick β-Ga 2 O 3 layer, and used 500 and 2000 laser pulses to investigate the early stage of the growth of β-Ga 2 O 3 on both the EG and SiC. The growth of β-Ga 2 O 3 was completed by lowering the temperature to 200°C at a rate of 0.5°C/s in ambient O 2 , and naturally cooling it to RT in vacuum.
2.3. Electroplating for Deposition of Ni Layers. Prior to the electroplating process, 50 nm-thick layers of Ti and Ni, which served as an adhesive/ohmic and a seed layer, respectively, were deposited on the β-Ga 2 O 3 layers grown on the EG by using e-beam evaporation. The samples were attached to a homemade electroplating jig, and the electrical connection between the samples and the jig was checked with a multimeter. Particles remaining on the surface were removed by using DI rinse, and the jig with the samples was dipped into the electroplating aqueous solution (NiSO 4 ). The jig connected to the sample was connected to the negative electrode, and the counterelectrode was connected to the positive electrode. The current density was controlled by increasing the voltage of the power supply. The residual stress of the Ni layer deposited by electroplating was determined by the temperature of the aqueous solution, the distance between the sample and the counter-electrode, and the current density. 21 We used a solution at a temperature of 55°C, an electrode distance of ∼20 cm, and a current density of 70 mA/cm 2 . The deposition rate of the Ni layer was ∼1.6 μm/min. After the deposition, the aqueous solution remaining on the sample was cleaned with the DI rinse and dried by blowing N 2 .

Residual Stress
Measurements of Ni Layers. The Si substrates were prepared with acetone and ethanol to measure the residual stress of the electroplated Ni layers. The latter were deposited on the Si substrates using the same method of electroplating. After the deposition, two theta scans of X-ray diffraction (XRD) were first performed (Supporting Information (SI) Figure S5a). The Ni layers deposited by electroplating were polycrystalline, and the peaks of the XRD related to the Ni layers were 44.7°for (111), 52.1°for (200), 76.8°for (202), 93.5°for (311), and 99°for (222). Ni (311) was used for stress measurements because of its intense diffraction peak. 22 The measurements of the residual stress using XRD were carried out using two theta/psi scans. 23 In other words, we carried out two theta scans defined in the region close to Ni (311), and psi scans were performed to obtain the results of d-spacing versus sin 2 ψ (SI Figure  S5b−d). Consequently, the residual stress of the Ni layers can be calculated by the following equation: where E, ν, θ 0 , δθ, and ψ are Young's modulus, Poisson's ratio, Bragg angles with stress-free, peak shift, and the difference in angles between the normal of the specimen and that of the plane, respectively. 22 We used 171.1 GPa as the Young's modulus of Ni (311) and 0.3412 as its Poisson's ratio. 22 2.5. β-Ga 2 O 3 Nanomembrane. In general, brittle materials break or spontaneously peel off when the strain exceeds a certain limit due to specific compressive or tensile stresses in the material. By contrast, stress below the limit remains internally condensed. Thus, the residual tensile stress increases the moment, and the force is transmitted downward in case of brittle substrates. In other words, when small cracks appear in part of the substrate, they advanced through mixed modes I and II fracture. 24,25 This crack propagation can be calculated by using the energy release rate through the following formula: where M, E, and I indicate the moment, Young's modulus, and a constant related to the Ni layer, respectively. 25 Furthermore, when multiple layers are formed on the same substrate, there are many interfaces at each layer. They are strongly or weakly bonded with a certain interfacial toughness, and we identify the layer we can use as separation layer by calculating the interfacial toughness of each: v H E where ν, H, σ, and E indicate the Poisson's ratio, thickness, internal residual stress, and Young's modulus of the Ni layer, respectively. 25 Based on the above equation, we obtained an interfacial toughness of 1.71 J/m 2 for spontaneous exfoliation through the thickness and residual stress of the electroplated Ni layers. 2.6. Conventional Lateral Solar-Blind β-Ga 2 O 3 Photodetectors. We grew ∼250 nm-thick β-Ga 2 O 3 layers on bulk SiC substrates. In light of the β-Ga 2 O 3 layers grown on SiC, the positive photoresist (AZ 5214) was coated at 3000 rpm for 30 s and cured at 110°C for 1 min. We then formed mesa patterns by exposing the samples for 50 ms. The mesa structures were formed by developing the samples using a developer (AZ 726MIF) for 40 s and dry etching through inductively coupled plasma etching. We completed the mesa structures of the β-Ga 2 O 3 layers by stripping the rest of the photoresists by acetone. For metallization, the lift-off resist (LOR) was coated at 3000 rpm for 30 s and cured at 110°C for 5 min. Following this, we coated the LOR with AZ 5214 at 3000 rpm for 30 s and cured it at 110°C for 1 min. The sample was exposed for 50 ms, with patterns of two laterally aligned fingers by using a direct writer and were developed for 45 s using AZ 726MIF. Once the pattern had formed, 30 nm-thick Ti and 100 nm-thick Au were deposited by ebeam evaporation, and the photoresist and LOR were removed by acetone and remover PG, respectively, to complete the fabrication of conventional lateral solar-blind PDs.

Flexible Vertical Solar-Blind β-Ga 2 O 3 Photodetectors.
We prepared a β-Ga 2 O 3 nanomembrane consisting of oxidized graphene/∼250 nm-thick β-Ga 2 O 3 /50 nm-thick Ti/50 nm-thick Ni/ ∼40-μm-thick electroplated Ni. We were able to easily control the β-Ga 2 O 3 nanomembrane with a conventional tweezer during the fabrication process owing to the moderately thick Ni layer. We carried out the same fabrication process as in the metallization of lateral solarblind PDs without forming the mesa structures to complete the flexible vertical solar-blind PDs.
2.8. Characterizations. We used Agilent 5500 for atomic force microscopy (AFM) measurements and the free software Gwyddion to process the AFM images. All scanning electron microscopy images were acquired using the Zeiss Merlin. Powder XRD and stress measurements were examined using the Bruker D2 and D8 ADVANCE, respectively, with a Cu Kα (λ = 1.5405 Å) radiation. All materials subjected to XRD were examined using the CrystalDiffract software. For measurements of the Raman spectrum, either a 473 nm Cobolt laser or a 515 nm Ar laser was applied. Lamella for transmission electron microscopy (TEM) was prepared by a focused ion beam through FEI Helios G4. The TEM images and their fast Fourier transforms were obtained by a FEI Titan ST microscope at 300 keV. Crystal models for each material were examined by the CrystalMaker software. Raman mapping was carried out using a 473 nm Cobolt laser. We set 100 μm × 100 μm as the area of the mapping and measured each spectrum in the range from 1200 to 3000 cm −1 . In addition, we extracted the mappings of G, 2D, and 2D/G using ranges of 1570 cm −1 to 1605 cm −1 for G, and 2695 cm −1 to 2775 cm −1 for 2D, and 2D/G, respectively. We conducted X-ray photoelectron spectroscopy measurements for the EG, β-Ga 2 O 3 grown on EG with 500 laser pulses, and β-Ga 2 O 3 grown on EG with 2,000 laser pulses. We used ∼283 eV for SiC, ∼ 284 eV for sp 2 bonding, ∼284.8 eV for sp 3 bonding, ∼286 eV for C−O−C, and ∼288.5 eV for O−CO, as carbon-related binding energy. 26,27 We also investigated the Ga-related binding energy by using ∼1118.7 eV for Ga 2 O 3 . 28 The photoelectrical performance of the fabricated photodetectors was tested using a broadband 500 W mercury−xenon [Hg (Xe)] arc lamp (Newport, 66142). The emitted light passed through a monochromator (Oriel Cornerstone, CS260) equipped with a UV-based diffraction grating (Newport, 74060) before illuminating the sample. The intensity of light was controlled using neutral density (ND) filters and precalibrated using an Si-based photodetector (Newport, 818-UV). The I−V characteristics of the photodetectors were extracted using a four-terminal sensing semiconductor parameter analyzer (Agilent, 4156C).  layers through an e-beam evaporator for Ti and Ni, and electroplating for the Ni stressor, (iv) exfoliation of the β-Ga 2 O 3 layers from the EG via spontaneous exfoliation, and (v) fabrication of flexible, vertical solar-blind PDs. Moreover, the EG on SiC after releasing the β-Ga 2 O 3 layers is reusable by repetitive high-temperature treatment (not shown here). 8 The details of each processes are included in the experimetal section. We used an atomic force microscope (AFM) to investigate the surface of a bare SiC substrate (Figure 1b). Based on AFM analysis, we then formed the EG by using a two-step high-temperature treatment. 29−31 Following that, we observed a terrace-like morphology and grain boundaries in the EG (Figure 1c). We then grew the β-Ga 2 O 3 layer on the bare SiC and the EG by using PLD. Although the β-Ga 2 O 3 layer was grown by causing scratch regions to protrude in the case of the bare SiC, it was grown on over the entire area to fully cover the EG (SI Figures S1 and S2, and Figure 1d). The ∼250 nmthick β-Ga 2 O 3 layers on the bare SiC and EG, grown using 20 000 laser pulses, exhibited surface roughness of 10 and 12 nm, respectively (SI Figure S2c and Figure 1d). We observed no significant differences between the β-Ga 2 O 3 layers grown on SiC and EG based on cross-sectional and surface images obtained using SEM, except for the terrace and grain boundaries on the surface of the EG (SI Figure S3). To investigate changes in the EG due to the growth of the β-Ga 2 O 3 layer, we also prepared three samples of EG on SiC and β-Ga 2 O 3 on EG using 500 and 2000 laser pulses and characterized by X-ray photoelectron spectroscopy (XPS) (SI Figure S1). We observed that β-Ga 2 O 3 layers formed on the surface of the EG at the beginning of the growth, even if the graphene had been deformed. Thus, the successful growth of the β-Ga 2 O 3 can be attributed to the adsorption of oxygen by forming oxygen plasma ambient without damaging the GR.  (Figure 1e). Thus, the β-Ga 2 O 3 on the EG showed similar results, except GR-related peaks at 26.48°, for the β-Ga 2 O 3 on SiC sample. 32 In addition, we also affirmed the existence of β-Ga 2 O 3 layers through Raman spectra ( Figure  1f). However, only one peak located at 200.02 cm −1 for β-Ga 2 O 3 layer due to the background of the Raman spectrum originated from the SiC substrate. 33 However, we were able to clearly identify all peaks associated with β-Ga 2 O 3 in the Raman spectra after the exfoliation of the β-Ga 2 O 3 layer (Figure 3e). We observed blue shifts related to the compressive strain of our EG when initially growing the β-Ga 2 O 3 (Figure 1g and SI Figure S1c). The blue shifts occurred even after the growth of the thin film of the β-Ga 2 O 3 layer. Ni et al. reported that GR formed by the decomposition of SiC through heat treatment is significantly affected by the SiC substrate. 34 Thus, GR can be formed on SiC despite the large difference in lattice constants between the former (2.47 Å) and the latter (3.07 Å) as there were matching points per 13 atoms of GR, known as the carbon mesh. Compressive strain occurred even if the carbon mesh and the SiC had matching lattice points owing to slightly different lattice constants. 34 That is, GR epitaxially grown on SiC was strongly influenced by its lattice in the presence of compressive strain. We confirmed the ∼250 nm-thick β-Ga 2 O 3 layer grown on the EG through low-magnification transmission electron microscopy (TEM) (Figure 2a). In addition, the highmagnification TEM and TEM-energy dispersive X-ray (EDX) clearly showed the β-Ga 2 O 3 layer, the EG, and the SiC layer (Figure 2b,c). The high-magnification TEM image showed that the EG consisted of 20 layers of GR. Although the image showed only a small local area, we confirmed that various distribution of layers of GR were formed in our EG through Raman mapping (SI Figure S7). Three regions corresponding to the β-Ga 2 O 3 , EG, and SiC were investigated by highresolution TEM (HR-TEM) (Figure 2d−f). The displacements of β-Ga 2 O 3 and SiC were 4.69 and 2.59 Å, respectively, almost identical to the respective displacements of bulk β-Ga 2 O 3 (4.68 Å) and SiC (2.54 Å). Although multilayer strainfree GR had a displacement distance of 3.39 Å, GR epitaxially grown on a SiC substrate showed a larger displacement (3.62 Å), which means that the EG exhibited compressive strain as observed in the Raman spectra. Moreover, the fast Fourier transform in various region of the HR-TEM images showed β-Ga 2 O 3 (201), EG (0002), and SiC (0006), respectively (Figures 2g−i). Through systematic examination using AFM, XRD, XPS, Raman, and TEM, we affirmed that the two main factors influencing the growth of β-Ga 2 O 3 on the EG: (i) The Ga 2 O 3 layers can be directly adsorbed on the surface of GR due to the effect of oxygen plasma by using PLD despite the low surface energy of GR, and (ii) unlike GR obtained by the transfer process, GR epitaxially grown on SiC acts as a buffer layer for the growth of β-Ga 2 O 3 by replicating the lattice of the SiC substrate with compressive strain.

RESULTS
3.2. β-Ga 2 O 3 Nanomembranes Obtained via Well-Controlled Ni Stressor. 2D materials formed through the van der Waals force exhibit weak bonding compared with 3D/ 3D materials formed by covalent bonding. The bonding of GR is weak enough to separate its layer using only scotch tape. 35 Although we could also have exfoliated β-Ga 2 O 3 layers grown on EG using only the thermal release tape (TRT), we observed cracks in several areas after the exfoliation (SI Figure S4). In addition, it creates complications and difficulties in handling for scotch tape-based exfoliation method. Thus, even though exfoliation was possible using only the tapeas the interfacial toughness between GR and GR (Γ GR-GR ) is low, 0.45 J/m 2  there were difficulties in terms of realizing high production yield for scalable production. 36 To overcome this drawback, we applied electroplated Ni layers with internal tensile strain to the β-Ga 2 O 3 on the EG for obtaining an exfoliation yield of 100% by controlling the energy release rate (see Experimental Section). This method is easy to implement even in the laboratory and can increase the yield by controlling the internal stress and thickness of the Ni layers. Our structures at the interfaces of the EG showed β-Ga 2 O 3 /EG/SiC corresponding to 3D/2D/3D stacks, which could also be known as the quasivan der Waals epitaxy. The interfacial toughness of the EG and SiC (Γ GR-SiC ) is 0.75 J/m 2 . 37 Comparatively, the interfacial toughness of GR and oxygen (Γ GR-Ga 2 O 3 ) is 1.47 J/m 2 . 38 In other words, by growing the β-Ga 2 O 3 on the EG, we were able to exfoliate β-Ga 2 O 3 layers at the weakest interface (Γ GR-GR ) by controlling the energy release rate via the Ni stressor ( Figure  3a,b). The internal residual stress of the Ni layer used in this work was measured by the XRD stress measurement method (SI Figure S5), where this could be controlled by several factors affecting deposition through electroplating, such as temperature of the aqueous solution, current density, and the distance between the sample and the electrode (see the Experimental Section). In particular, we found a restrictive region where the energy release rate of the Ni stressor was over Γ GR-GR , which is when the β-Ga 2 O 3 layers were exfoliated by using an additional supporting layer, such as TRT. In contrast, spontaneous exfoliation occurred when the energy release rate reached 1.71 J/m 2 without any additional layer (Figure 3c and SI Figure S6). Thus, we were able to exfoliate the β-Ga 2 O 3 layers grown from the EG based on two different methods: (i) by restricting the energy release rate between 0.45 J/m 2 and 1.71 J/m 2 with using TRT, and (ii) through spontaneous exfoliation by increasing the energy release rate to over 1.71 J/ m 2 (SI Figure S6). Furthermore, by directly using the EG, we avoided defects found in conventionally transferred GR, such as polymer residues, wrinkles, and voids. Through XRD measurements before and after the exfoliation, we confirmed that the β-Ga 2 O 3 nanomembranes recorded peaks of 201oriented β-Ga 2 O 3 without any significant changes, except in the XRD peaks of the Ni layer (Figure 3d). Furthermore, although it was difficult to examine peaks related to β-Ga 2 O 3 in the Raman spectra due to the background spectrum originated from the SiC substrates, we clearly observed peaks related to β-Ga 2 O 3 after exfoliation by using the Ni stressor (Figure 3e). We can then determine that the β-Ga 2 O 3 nanomembranes were well exfoliated, with the Ti layer used as adhesive, and Ohmic contact layers and a Ni layer used as a second substrate in cross-sectional focused ion beam (FIB)-TEM images and EDX mapping (Figure 3f). To further examine the state of the GR before/after exfoliation, we performed Raman mapping of the pristine EG on SiC, EG on SiC after exfoliation, and the back side of the β-Ga 2 O 3 nanomembrane (SI Figure S7). The EG showed widely a distributed 2D/G ratio, which means that it was a multilayer GR (SI Figures S7a,d,g). Although most peaks related to G and 2D were similar to those of the pristine GR even after exfoliation, we did not observe any G and 2D peaks in some of the regions, and identified several empty areas in GR based on the nonexistence of 2D/G peaks (SI Figure  S7b,e,h). In addition, although the GR at the back of the nanomembrane was uniformly distributed on the entire surface according to the results of 2D/G, it was oxidized based on a large change in the peak of D. This could be attributed to the fact that the GR at the top of the EG was more strongly attached to the side of β-Ga 2 O 3 owing to the difference in the interfacial toughness (Γ GR-Ga 2 O 3 > Γ GR-SiC > Γ GR-GR ) at the three interfaces of β-Ga 2 O 3 /GR/GR/SiC. In addition, the surfaces of the SiC and the β-Ga 2 O 3 after exfoliation showed a terrace, and the grain boundaries formed on the EG were equal on the side from which the β-Ga 2 O 3 had been removed (SI Figure  S8).
3.3. β-Ga 2 O 3 Nanomembrane-Based Flexible Vertical Solar-Blind Photodetectors. By using the spontaneously exfoliated β-Ga 2 O 3 with the ∼40-μm-thick Ni layer deposited by electroplating, we have also fabricated flexible, and vertical solar-blind PDs with a bending radius of ∼3 mm (Figure 4a). The electroplated Ni layer can be used as the alternative substrate with many advantages such as flexibility in comparison with bulk SiC substrate because the Ni layer is more than five times thinner and excellent electrical, optical, and thermal properties. In addition to membrane-based PDs, we have also fabricated conventional lateral-type solar-blind PDs by using a β-Ga 2 O 3 layer grown on a bulk SiC substrate (SI Figure S9a). We measured the responsivities of the PDs at illumination wavelengths ranging from 230 to 400 nm with the interval of 10 nm (Figure 4b and SI Figure S9b). The responsivity spectrum of both the flexible vertical PDs and the lateral PDs showed photoresponses at 280 nm, with a peak responsivity identified at 250 nm, and decreased toward the 240 nm wavelength. That is, our β-Ga 2 O 3 layers with the nanomembranes and formed on bulk SiC substrates showed the same energy band gap of ∼4.9 eV. However, the peak responsivity at 250 nm was 151.1 A/W for the membranebased vertical PDs and 0.3 A/W for the conventional lateral PDs. Furthermore, they recorded about an order of magnitude differences in current−voltage characteristics at 250 nm (Figure 4c and SI Figure S9c). Although a weak photoresponse is recorded at low voltage that then increases with voltage in conventional lateral PDs, a large photoresponse occurred at low voltage and decreased as voltage increased in the membrane-based vertical PDs. Such results were obtained owing to the different structures of the PDs, defined along the vertical and lateral directions. Due to the distance of the metal fingers, the actual travel distance of the generated carriers in the lateral PDs is 50 μm, which could induce a higher probability of being trapped along the interdigitated metal finger, meanwhile the generated carriers in the vertical PDs is 250 nm, which is almost similar to the diffusion length of the carriers of β-Ga 2 O 3 , and thus the carriers could be efficiently extracted by forming the two metal layers as a sandwiched structure. 39,40 We also investigated the current−voltage characteristics for varying illumination power densities at the illumination wavelength of 250 nm, and noted that the vertical PDs exhibited much higher sensitivity than the lateral PDs, based on the highest (6.43 mW/cm 2 ) and lowest (0.03 mW/ cm 2 ) illumination power densities recorded (Figure 4d and SI Figure S9d). In general, the β-Ga 2 O 3 -based solar-blind PDs exhibited slow time-dependent photoresponse due to traps of Ga + and oxygen vacancy on the surface. 41 We also observed slow time-dependent photoresponses similar to those of current oxide-based PDs, with τ r of 1.26 s and τ d of 3.18 s in our lateral solar-blind PD (SI Figure S9e). 42,43 Moreover, we observed that the charging phenomenon in which the initial dark current was not recovered occurred even though the timedependent photoresponse was measured with a long on/off ratio of 15 s. In contrast, we obtained fast time-dependent photoresponses of 0.28 s for τ r and 0.42 s for τ d , significantly better than those of lateral PDs in case of the vertical PDs ( Figure 4e). Furthermore, the charging phenomenon was absent from the membrane-based vertical PDs. Thus, our flexible, membrane-based vertical solar-blind PDs delivered an outstanding performance in terms of responsivity and timedependent photoresponse compared with conventional lateral PDs grown with a bulk substrate by extremely reducing the travel distance of the generated carriers via very-thin β-Ga 2 O 3 nanomembranes.

CONCLUSIONS
Large-area epitaxial β-Ga 2 O 3 nanomembrane (1 cm × 1 cm) was grown on EG bufferred SiC substrates, and spontaneously exfoliated from the EG, by controlling the energy release rate via an electroplated Ni layer, to realize flexible, vertical-structured solar-blind PDs. The as-fabricated PDs exhibited a higher responsivity, of 151.1 A/W, and faster time-dependent photoresponse (0.28 s for τ r and 0.42 s for τ d ) than the conventional lateral solar-blind PDs on a bulk substrate. This result can be attributed to the significant reduction in the travel distances of the generated carriers, owing to the sandwichstructured vertical PDs of thin β-Ga 2 O 3 . Our results show that EG buffer layers is a suitable template to grow oxide-based materials for producing wafer-scale oxide-based membranes through restrictive or spontaneous exfoliation by using the Ni stressor. This opens new avenues for manufacturing scalable membrane-based high-performance devices for high-power and intergrated photonic devices with unprecedented control over the opto-electrical properties.