## Introduction

Deep-ultraviolet (DUV) photodetectors with an advantage of directly converting UV into an electrical signal have recently attracted much attention, which play a key role in the fields of UV imaging, secure communication, biological detection, military detection, etc1,2,3. Due to the outstanding characteristics of DUV photodetectors, such as high sensitivity, fast response speed, and low dark current4,5,6,7, various wide bandgap semiconductors (AlN, ZnO, GaN, and Ga2O3) have been expanded to DUV fields8,9,10,11. Typically, quasi-two-dimensional (2D) β-Ga2O3 is considered as an ideal candidate for DUV photodetector applications because of its suitable direct bandgap of ~4.90 eV, high breakdown electrical field of ~9 MV/cm, outstanding thermal stability, high adsorption coefficient, etc.12,13,14. However, the current high-performance β-Ga2O3-based UV photodetectors are usually fabricated on rigid substrates, which limit their applications in many novel device concepts such as transparent, wearable, and portable fields15.

It is no doubt that photodetectors based on flexible substrates could meet the growing demands of next-generation optoelectronics with low manufacturing cost, better portability, and light-weight design. Unfortunately, little attention of recent reports has been paid on the flexible β-Ga2O3 DUV photodetectors to date. Sooyeoun et al. fabricated β-Ga2O3 photodiode with graphene electrodes based on polyethylene terephthalate substrate, exhibiting a photo-to-dark current ratio (PDCR) of ~1 × 106% and a responsivity (R) of ~29.8 A/W16; Wang et al. reported flexible graphene/amorphous Ga2O3 van der Waals heterojunction with a PDCR of ~1 × 107% and a R of ~22.75 A/W17; etc. While the performances of the presented flexible β-Ga2O3 DUV photodiodes, especially in terms of R, are not competitive with their rigid devices18. Many strategies have been recently proposed to improve the performance of flexible β-Ga2O3 DUV photodetectors. On one hand, better than the reported photodiodes, the phototransistors, as one kind of three-terminal photodetectors, have showed a significant advantage of the intrinsic current modulation, high intrinsic gain, and low dark current, which have been considered as an alternative solution to further improve the performance of DUV photodetectors19. On the other hand, for the material itself, various affordable and high-quality growth techniques for β-Ga2O3 bulk single crystals have been developed, including edge-defined film-fed growth, the optical floating zone (OFZ), the Czochralski, and so on20.

Herein, the high-quality Ta-doped β-Ga2O3 single crystal has been grown by using an optimized OFZ method. Subsequently, a fully flexible high-performance β-Ga2O3 phototransistor on polyimide (PI) substrate was fabricated. The hexagonal boron nitride (h-BN) is selected as an ideal dielectric due to its large bandgap (5.97 eV), high breakdown field (8–12 MV/cm), atomically flat surface without unnecessary dangling bonds, and high thermal conductivity [1700–2000 W/(m K)]21,22,23. The obtained β-Ga2O3 phototransistor exhibits a high R of 1.32 × 106 A/W, a large detectivity (D*) of 5.68 × 1014 Jones, a great PDCR of 1.10 × 1010%, a high external quantum efficiency (EQE) of 6.60 × 108%, and an ultra-fast response time of ~3.5 ms. Then, the reliability and mechanical flexibility of the fabricated β-Ga2O3 phototransistor were explored. Besides, as a proof-of-concept, the flexible DUV detector arrays based on the present β-Ga2O3 phototransistors, combining with an artificial neural network (ANN), can perform image recognition efficiently and accurately. These results show that high-performance flexible DUV β-Ga2O3 phototransistors have great application potential in future wearable optoelectronics, UV imaging, and artificial intelligence fields.

## Results and discussion

### Material characterizations of Ta-doped β-Ga2O3

To determine the morphology and crystalline phase of the obtained Ta-doped β-Ga2O3 material, the high-resolution transmission electron microscopy (HR-TEM) measurement was conducted. The spacings of lattice fringe shown in Fig. 1a were calculated to be ~0.61 and ~0.58 nm for (200) and (001) atomic planes respectively, which agrees well with the results reported in the literature24. Notably, even with a suitable amount of Ta ion doping, there is almost no obvious lattice damage observed by the HR-TEM, indicating a good crystal quality of β-Ga2O3 material. The selected-area electron diffraction (SAED) pattern in the inset of Fig. 1a further confirms the perfect lattice symmetry and the lattice parameters of exfoliated β-Ga2O3 flakes. Synchrotron-based grazing incidence X-ray diffraction (GIXRD) measurement was used to analyze the fine crystalline structure of the β-Ga2O3 sample. The two-dimensional GIXRD (2D-GIXRD) pattern of Ta-doped β-Ga2O3 is presented in Fig. 1b, which displays the clear and bright diffraction rings. Figure 1c shows the corresponding azimuthally integrated one-dimensional GIXRD (1D-GIXRD) spectrum of Ta-doped β-Ga2O3, demonstrating the typical peaks of β-Ga2O3, which are well consistent with the standard JCPDF (41–1103)25. Notably, as shown in the inset figure, two diffraction peaks located at q ~21.12 nm−1 and 22.49 nm−1, which are assigned to be (400) and (002) planes, show an obvious split in peak shape and a significant increase in peak intensity, implying the Ta5+ doping could effectively occupy the ion vacancies (or substitute Ga3+) and thereby improve the crystalline of the parent β-Ga2O326. Then, the optical transmittance spectrum of Ta-doped β-Ga2O3 bulk single crystal is analyzed in Fig. 1d. In the visible light region of 400–650 nm wavelength, the transmittance value of the current β-Ga2O3 bulk single crystal is ~73%. The cutoff absorption edge is located at ~260 nm. The energy band gap (Eg) of Ta-doped β-Ga2O3 is also determined to be 4.71 eV from reflection electron energy loss spectroscopy (REELS) in the inset of Fig. 1d. Furthermore, the ultraviolet photoelectron spectroscopy (UPS) measurement was employed to investigate the energy level alignment of Ta-doped β-Ga2O3. As displayed in Fig. 1e, the corresponding work function and valence band maximum (EVBM) of the Ta-doped β-Ga2O3 are calculated to be 4.38 and 9.31 eV, respectively. Thus, the Fermi level (EF) of the Ta-doped β-Ga2O3 sample is located at −4.38 eV. The EVBM is located at 4.93 eV below the EF. Combined with the Eg measured from REELS spectrum (4.71 eV for the present Ta-doped β-Ga2O3), the band diagram of Ta-doped β-Ga2O3 is summarized in Fig. 1f. Obviously, the EF of Ta-doped β-Ga2O3 is above the conduction band minimum (ECBM) with 0.22 eV, which would greatly contribute to increase the electron concentration27.

### Interface and electrical properties of the β-Ga2O3 device

Next, a Ta-doped β-Ga2O3 metal insulator semiconductor field effect transistor (MISFET) with h-BN dielectric was fabricated. The β-Ga2O3 and h-BN flakes were mechanically exfoliated and sequentially transferred onto a SiO2/Si substrate. Firstly, the interface properties at Ta-doped β-Ga2O3/ h-BN heterostructure were investigated. Figure 2a shows the cross-sectional HR-TEM image of the stacked Ta-doped β-Ga2O3/h-BN heterostructure on the SiO2/Si substrate. No obvious deformation or fault was observed in each layer and the interface β-Ga2O3/h-BN heterostructure. And from Fig. 2a it can be seen the thickness of exfoliated β-Ga2O3 flake is 165 nm. The HR-TEM image of an enlarged area for the interface of Ta-doped β-Ga2O3/h-BN heterostructure is displayed in Fig. 2b. Note that, the highly crystalline nature of the β-Ga2O3 and h-BN and atomically sharp interface at β-Ga2O3/h-BN heterostructure are evident. In addition, high-magnification cross-sectional HR-TEM images of the h-BN flake and the interface of Ta-doped β-Ga2O3/h-BN heterostructure were shown in Fig. 2c. The displacements of h-BN were calculated to 3.4 Å, which is consistent with the value in the literature28. While the ordered lattice fringe formed at the β-Ga2O3/h-BN interface has a spacing of 4.0 Å, which is slightly larger than that in the bulk of h-BN, which might be attributed to the excessive residual stress at the interface of β-Ga2O3/h-BN29. The corresponding energy band diagram of Ta-doped β-Ga2O3/h-BN heterostructure was established in Supplementary Fig. 1. It can be clearly seen that the β-Ga2O3/h-BN heterostructure system has a staggered band alignment (type II)30. The valence and conduction band offsets (ΔEV and ΔEC) of Ta-doped β-Ga2O3/h-BN heterostructure are 3.42 and 4.68 eV, which could provide a high sufficient barrier height to reduce electron tunneling through the interface due to quantum tunneling effect or thermal fluctuations31. Subsequently, to broaden applications in the emerging area such as wearable and portable electronics and optoelectronics, a flexible β-Ga2O3 phototransistor with h-BN dielectric was fabricated on PI substrate. The PI film was chosen as a flexible substrate due to its capability of withstanding high temperatures up to 350 °C and other advantages such as light-weight, low-cost, soft, and flat surface32,33. The PI substrate used here was spin-coated and cured on the glass film, which corresponds to the optical image (Supplementary Fig. 2). It can be found that the PI film shows high flexibility and foldability. Next, the optical microscopy image of the fabricated β-Ga2O3 transistor is shown in Fig. 2d. The length (L) and width (W) of the β-Ga2O3 channel are ~2.6 and ~2.5 μm in sequence. The measured thicknesses of β-Ga2O3 channel layer and h-BN dielectric layer by atomic force microscope (AFM) are ~199.5 and ~11.3 nm (Supplementary Fig. 3), respectively. Then, the electrical properties of the fabricated flexible β-Ga2O3 transistor were measured and analyzed. Figure 2e displays the transfer curves of the fabricated β-Ga2O3 transistor in log and linear scales under dark condition at Vds = 1 V, which exhibits a high on/off current ratio (Ion/Ioff) of ~108 and a low off-state current (Ioff) of ~10 fA. The threshold voltage (Vth) is extracted as −8.30 V using a linear extrapolation method at Vds = 1 V. The transconductance (gm) as a function of Vg is extracted using $$g_{{{\mathrm{m}}}} = \frac{{\partial I_{{{{\mathrm{ds}}}}}}}{{\partial V_{{{\mathrm{g}}}}}}$$ (Supplementary Fig. 4)34. The maximum value of transconductance (gmax) can reach 0.49 μS at Vg = −6.65 V. The field-effect electron mobility (μfe) is also extracted using the equation of $$\mu _{{{{\mathrm{fe}}}}} = \frac{L}{{W \times C_{{{{\mathrm{ox}}}}} \times V_{{{{\mathrm{ds}}}}}}} \times g_{{{\mathrm{m}}}}$$, where L and W are the length and width of β-Ga2O3 channel, and Cox is the capacitance of gate dielectric per unit area34. Cox is calculated as 3.13 × 10−7 F/cm2, using the formula of $$C_{{{{\mathrm{ox}}}}} = \frac{{\varepsilon _0\varepsilon _{{{\mathrm{r}}}}}}{d}$$ where ε0 is the vacuum permittivity (8.854 × 10−12 F/m), εr is the relative permittivity of h-BN (~4), and d is the dielectric thickness (11.3 nm)34. And the peak value of μfe is calculated to be 1.6 cm2/V·s. Figure 2f shows the output characteristic of β-Ga2O3 transistor where Vg varies from −6 to 2 V with a step of 2 V. The sharp pinch-off and outstanding saturation of current can be clearly observed. These results show that β-Ga2O3 phototransistors have good gate tunability and electrical properties.

### The photoelectrical properties of the β-Ga2O3 device

Subsequently the photoelectrical properties of the fabricated β-Ga2O3 phototransistor were investigated systematically. In general, the photocurrent generation mechanisms are mainly categorized as photoconductive (PC) and photogating (PG) effects for 2D material phototransistors35. In the PC effect, the absorption of photons generates extra free carriers, increasing channel current, and thus the electrical resistance of channel was reduced (Supplementary Fig. 5). While PG effect is a particular example of the PC effect. If the photogenerated holes in n-type transistor are trapped in localized states of which energy near the valence band edge, they can perform as a local gate voltage (ΔVg), effectively modulating the electrical resistance of semiconductor channel (Supplementary Fig. 6)36. It is worth noting that the trapped photocarriers will prolong the lifetime of photogenerated carriers (τphotocarriers), usually leading to a large photoconductive gain (G)37, as detailed in Supplementary Section S1 and Eq. (S1).

To investigate the mechanism of photocurrent generation in β-Ga2O3 channel, we measured Ids-Vg characteristic under a series of illumination Pin at 250 nm excitation wavelength, as shown in Fig. 3a. The UV light source illuminates the surface of the device vertically and covers the entire channel. It is observed that the photocurrent (Iph) of device increases with increasing illumination densities. Then the curves of Iph as a function of Vg were plotted under different illumination Pin at Vds = 1 V in Fig. 3b. Obviously, Iph increases with the optical power. On one hand, this phenomenon is caused by the higher illumination Pin that can excite more photogenerated carriers, in turn, enhancing the PC effect. On the other hand, it is caused by trapping more photogenerated holes, increasing the PG effect mentioned above. But for a fixed power, the photocurrent accesses a maximum value. It is because that the effective modulation of Vg affects PC and PG effects38. Moreover, the generated Iph can be fitted successfully by the empirical Hornbeck-Haynes model (Supplementary Section S1 and Eq. (S2))39. The Pin dependence of Iph curve at a fixed gate voltage of −8 V is presented in Fig. 3c. The bule line is the fitting results according to Supplementary Equation S2, from which $$\eta \frac{{\tau _{{{{\mathrm{photocarriers}}}}}}}{{\tau _{{{{\mathrm{transit}}}}}}}$$ = 8606 and n = 0.79 have been deduced, where η is the efficiency of converting absorbed photons to electrons, τtransit is the transit time of carriers, and n is a phenomenological fitting parameter40. According to the equation of $$\tau _{{{{\mathrm{transit}}}}} = \frac{{L^2}}{{\mu _{{{{\mathrm{fe}}}}}V_{{{{\mathrm{ds}}}}}}}$$, τtransit is calculated to be 42 ns where L = 2.6 μm, Vds = 1 V, and μfe = 1.6 cm2/V·s. According to the transmittance spectrum in Fig. 1d, a reasonable absorption rate of 30% is assumed. Then the values of G and τphotocarriers can be derived to be about 2.8 × 104 and 1.2 ms, respectively. And the bandwidth of a photodetector without gain decay can be roughly defined as $$f_{3 - {{{\mathrm{dB}}}}} = \frac{1}{{2{{{\mathrm{\pi }}}}\tau _{{{{\mathrm{photocarriers}}}}}}}$$. Therefore, the 3-dB bandwidth of the β-Ga2O3 phototransistor is calculated to be ~133 Hz. It is clearly that a larger G will cause a smaller 3-dB bandwidth due to the competing relationship between them. Then, the typical signatures of PC and PG effects are illustrated in Supplementary Section 2. Then Iph-Pin curve at a fixed gate voltage of −8 V is extracted in Fig. 3d. The curve could be well fitted using the formula of Iph Pinα where α is exponent. The obtained value of α is 0.42 in Fig. 3d, smaller than 1, confirming the existence of PG effect in the β-Ga2O3 phototransistor41. Subsequently, the same method was used to extract α under a series of fixed gate voltages and the α-Vg curve was plotted in the inset of Fig. 3d. It reveals that α ranges from 0.71 to 0.1 when Vg changes from −9 to 0 V, indicating that the PG effect has a Vg-dependent relation which is consistent to Supplementary Equation S3. It is also observed that Vth of n-type β-Ga2O3 device shifted in negative direction from −7.50 to −14.50 V, which can be clearly interpreted by PG effect. The dependence of the change of threshold voltage $$\left( {\left| {\Delta V_{{{{\mathrm{th}}}}}} \right|} \right)$$ on Pin was also extracted and plotted in Supplementary Fig. 7. The Vth drifts negatively with increasing Pin. It can be assumed that the local gate electric field formed by trapped holes effectively changes the Fermi level and generates more electrons in β-Ga2O3 channel, causing a stronger PG effect.

The critical parameters including R, D*, PDCR, and EQE are extracted to further evaluate the performances of the fabricated β-Ga2O3 phototransistor42. The R of the β-Ga2O3 phototransistor is extracted firstly (Supplementary Fig. 8) from Fig. 3b using43

$$R = \frac{{I_{{{{\mathrm{ph}}}}}}}{{P_{{{{\mathrm{in}}}}} \times A}}$$
(1)

where A is the active area of the phototransistor. From Eq. (1), it can be found that the R and Iph meet the linear relationship under a fixed Pin. Therefore, the trend of IphVg and RVg curves is the same under a fixed power density. Then the maximum response (Rmax) was extracted from Supplementary Fig. 8 and plotted the corresponding Rmax - Pin curve in Fig. 3e. This result shows Rmax of the β-Ga2O3 phototransistor can reach 1.32 × 106 A/W at a low illumination density of 22 μW/cm2, which is much superior to previous reported β-Ga2O3-based photodetectors under similar power conditions7,44,45. It is also noteworthy that Rmax monotonically decreases with increasing illumination Pin. It is owing to the gradually filled trap states38, which is also related to the multi-faceted generation, separation, and transport processes of photogenerated carriers34. In addition, D* is another photodetector parameter which indicates the signal-to-noise ratio, shot current, considering the thermal, generation-recombination, and background radiations46. Assuming that the shot noise caused by dark current (Idark) is the main noise source of total noise, D* can be given by47

$$D^ \ast = \frac{{RA^{0.5}}}{{(2eI_{{{{\mathrm{dark}}}}})^{0.5}}}$$
(2)

where e is the electron charge (~1.6 × 10−19 C), as displayed in Fig. 3e. It can be seen that the D* reaches the maximum value of 5.68 × 1014 Jones at the illumination Pin of 22 μW/cm2 and maintains the same order of 1014 when a series of power changes, which is comparable to previous reported β-Ga2O3 photodetectors46,48,49. While this method neglected 1/f noise which predominates in the MISFET-based phototransistors50. In order to comprehensively evaluate D*, the low frequency noise measurement is also conducted to extract the D* which was defined as $$D^ \ast = R \times \frac{{\sqrt {AB} }}{{i_{{{\mathrm{N}}}}}} = R \times \frac{{\sqrt A }}{{S_{{{\mathrm{n}}}}}}$$, where R is responsivity, A is the active area of the phototransistor in a unit of cm2, B is the bandwidth, iN is the measured noise current of the phototransistor, and Sn is the noise current density51. The Supplementary Fig. 9a shows that the noise power spectral density for Vg = −8.45, −8.00, −7.60, and −7.35 V, respectively. The Supplementary Fig. 9b shows the noise current density extracted from the Supplementary Fig. 9a at the noise frequency of 100, 101, 102, and 103 Hz. It can be found that Sn increases when the Vg increases under a fixed noise frequency condition. As shown in Supplementary Fig. 10, the extracted D* is 6.55 × 1013 Jones for Vg = −8.45 V under illumination Pin of 22 μW/cm2 condition, which is lower 100 times than that extracted directly using the Idark method (8.65 × 1015 Jones). Note that, this value of 6.55 × 1013 Jones is still very competitive with the reported literature46,48,49. Then, another photodetector parameter, PDCR is given by50

$${\rm{PDCR}} = \frac{{I_{{{{\mathrm{ph}}}}}}}{{I_{{{{\mathrm{dark}}}}}}} \times 100{{{\mathrm{\% }}}}$$
(3)

which is used to evaluate the rejection ability for noise. Obviously, the PDCR exhibits an increasing trend with Pin, as shown in Fig. 3f. In order to eliminate the influence of gate voltage on PDCR, we discussed the PDCR characteristic of the device at Vg = −10 V. The dark current at Vg = −10 V is about 3.18 × 10−8 μA and the Iph under different Pin conditions at Vg = −10 V has been shown in Fig. 3d. The PDCR can reach 5.96 × 109% under 22 μW/cm−2 and increase to 1.10 × 1010% under 207 μW/cm−2. Finally, EQE means the ratio of the number of converting absorbed photons to electrons and the total number of excitation photons, which is extracted from the equation

$${\rm{EQE}} = \left( {\frac{{Rhv}}{e}} \right) \times 100{{{\mathrm{\% }}}}$$
(4)

where h is Planck’s constant (6.626 × 10−34 J s) and υ (=c/λ) is the frequency of incident light48. The EQE of the device decreases gradually with increasing Pin as shown in Fig. 3f. The largest EQE reaches 6.60 × 108% under 22 μW/cm2 of Pin. These results indicate that the obtained β-Ga2O3 phototransistors have outstanding photoelectrical properties.

### The time response and stability properties of the device

To further study the photoresponse properties of the β-Ga2O3 phototransistor, time-dependent measurements on the device under various conditions were conducted. Figure 4a shows the time-dependent properties of the β-Ga2O3 phototransistor under different excitation wavelength. The measurement was carried out at Vg = −8 V and Vds = 1 V with the Pin density of 75 μW/cm2. Then, the rejection ratio is calculated as the ratio of R under 250 nm and visible (410, 532, and 650 nm) light illumination in Fig. 4a. The parameter can show the ratio of single and specific background radiation noise under illumination conditions47. Very clearly, there is almost no photocurrent generation under 410, 532, and 650 nm light exposure. The current of the device is ~1.40 × 10−7 μA under the three visible light illumination while the current of the device is ~2.40 μA under 250 nm light illumination. The rejection ratio of β-Ga2O3 phototransistor between 250 nm/visible light could reach 1.71 × 107, which exhibits high spectral selectivity. It can be confirmed that the obtained β-Ga2O3 phototransistor is much more sensitive to DUV light than the visible and near-IR lights. Besides, from Fig. 4a, a quick rise of Iph as soon as the 250 nm laser is turned on followed by a rapid drop back to initial values when the 250 nm laser is turned off under the chopping effect of the chopper. This implies that the β-Ga2O3 phototransistor can act as a sensitive UV-light-activated switch. To evaluate the repeatability and stability of the device’s optical response characteristic under the excitation of 250 nm laser, time dependence Iph curve was measured for several cycles in Fig. 4b. The illumination light is turned on and off at an interval of 10 s with a period of 20 s. It can be found that the ON-OFF switching behavior can be retained well. To obtain the rise time (τr) and decay time (τd), Fig. 4c shows the enlarged view of the rise and decay edges of the curve in Fig. 4b. The observed switching duration for τr or τd is calculated only to be 3.5 ms, which is much faster than the reported values of other UV photodetectors52,53. While according to the above statement, the response time of device can be further improved if the photogating effect is reduced because there exists a compromise between them. Supplementary Table 1 provides a summary and comparison of key parameters for the reported UV photodetectors based on various materials. By contrast, the maximum R of β-Ga2O3 phototransistor (1.32 × 106 A/W) fabricated in this work is 100 times more sensitive than the traditional material photodetectors (such as GaN (104 A/W), SiC (0.18 A/W), ZnO (12 A/W), and others)54,55,56,57,58,59. In addition, the R of β-Ga2O3 phototransistor is also improved by more than 100 times than the reported the perovskite-based UV photodetectors (BiOBr (1.27 × 104 A/W), Ga2ln4S9 (104 A/W), Sr2Nb3O10 (1.20 × 103), and others)3,60,61,62. Besides, Supplementary Table 2 summaries the photoresponse properties of the fabricated β-Ga2O3 phototransistor and compares some previous works on β-Ga2O3-based photodetectors. These results clearly reveal that the DUV β-Ga2O3 phototransistor fabricated in this work exhibits superior photoelectric performance, outperforming most reported UV photodetectors. The large responsivity stems from a strong PG effect on the β-Ga2O3 channel induced by the localized states in the β-Ga2O3 layer6. Finally, the reliability test of the β-Ga2O3 phototransistor on a flexible PI substrate was carried out. Figure 4d shows the operating platform in the experiment. We bent the device to 60°, 30°, and 0°, respectively. The transfer curves of the device after folding 103 times were shown in Fig. 4e. It is clear that the flexible β-Ga2O3 phototransistor exhibits negligible performance loss. In Fig. 4f, no performance deterioration can be observed even if the device was folded for 104 times at a bending angle of ~0°. It is believed that the proposed flexible β-Ga2O3 phototransistor has great potential in flexible UV image sensing applications due to the outstanding photosensitivity, flexibility, and stability.

### An artificial neural network based on the β-Ga2O3 device

In recent years, the intelligent industry represented by robotics has been so flourishing that researchers are looking forward to developing human-like bionic robots11,63. What’s more, it also hoped that the detection range of the eyes of the bionic robot could exceed that of humans. High-performance flexible UV image sensors based on the fabricated β-Ga2O3 device make it possible for the robot’s UV vision function. To this end, a UV detector array and an ANN are designed to artificially simulate the human vision system, as illustrated in Fig. 5a. The UV detector array composed of 15 × 15 pixels is designed to perceive the image. Images of the letters F, D, and U in Fig. 5b form a database used by artificial neural visual system. Obviously, images of letters formed by UV detector arrays show high contrast because the phototransistors based on β-Ga2O3 can produce a large Iph under DUV light illumination, which makes it easier for robots to recognize and remember them. It is noted that all image signals were normalized. More detailed information is described in Supplementary Note 1. Next, a three-layer ANN was developed for training and recognizing the perceived images. As displayed in Fig. 5c, the three-layer ANN consists of input layer (225 neurons), hidden layer (128 neurons), and output layer (3 neurons). The image-recognition rate of UV detector array is illustrated in Fig. 5d. After 64 training epochs, the corresponding recognition rate could reach 0.99, which shows high image recognition efficiency. To further verify the high image recognition rate of the trained ANN, 90 image examples from above image database, including 30 “F” images, 30 “D” images, 30 “U” images, were chosen to input into the trained ANN. Then the probability for three possibility results was calculated and plotted in Fig. 5e. The results show the trained ANN has great recognition capability. As a result, the flexible UV detector array based on high-performance β-Ga2O3 phototransistors has a promising application in UV photosensitive imaging.

In summary, high performance and flexible DUV Ta-doped β-Ga2O3 phototransistor with the h-BN dielectric has been fabricated on PI substrate. The obtained Ta-doped β-Ga2O3 phototransistor exhibits a high R of 1.32 × 106 A/W, a large D* of 5.68 × 1014 Jones, a great PDCR of 1.10 × 1010%, a high EQE of 6.60 × 108%, and a fast response time of ~3.5 ms. Moreover, the flexible Ta-doped β-Ga2O3 device displays high reliability and mechanical flexibility that can sustain well up to 104 bending cycles. Furthermore, the flexible DUV detector arrays based on high-performance Ta-doped β-Ga2O3 phototransistors, combined with an artificial neural network, can perform image recognition efficiently and accurately. These results show high performance flexible UV Ta-doped β-Ga2O3 phototransistors have great potential for applications in future wearable optoelectronics, UV imaging, and artificial intelligence fields.

## Methods

### Fabrication of the flexible β-Ga2O3 transistor

Ta-doped β-Ga2O3 single crystal was grown by the OFZ technique. First, the β-Ga2O3 (6 N) and Ta2O5 (4 N) powders are mixed fully by the wet ball milling and pressed into a rod by a cold isostatic press. Next, the rod was sintered in air at 1450 °C for 20 h, using <010> oriented crystal as the seed. Finally, the crystal growth starts. The obtained crystals are intact with uniform color. The schematic diagram of the fabrication method of Ta-doped β-Ga2O3 is illustrated in Supplementary Fig. 11.

In this study, the 0.05 mol % Ta-doped β-Ga2O3 singe crystal was chosen due to its suitable active carrier concentration of 1.4 × 1018 cm−3. The fabrication of the flexible β-Ga2O3 phototransistor began by cleaning a glass substrate with isopropyl alcohol, acetone, and DI water, followed by dehydration with a nitrogen spray gun. After that, the soluble PI was deposited by spin-coating at 3000 r/min on the glass substrate and prebaked at 80 °C on a hot plate for 8 min to remove the organic solvent. Then the PI film was fully cured at 280 °C under ambient condition for 60 min. We spin-coated the soluble PI onto the glass substrate, overcoming the problem of plastic shrinkage with the high temperature processes. Next, the mechanically exfoliated β-Ga2O3 flake from the β-Ga2O3 bulk single crystal (the Raman spectrum of β-Ga2O3 flake is displayed in Supplementary Fig. 12) was dry-transferred to the as-fabricated PI substrate. Subsequently, Ti/Al/Ni/Au (20/100/60/80 nm) stack electrodes were deposited as source and drain contract pads via a standard electron-beam lithography, metallization, and lift-off process. The device was then annealed at 350 °C in a high-vacuum furnace with a high pure N2 ambient for 3 h to improve ohmic contacts. Subsequently, the h-BN flake was also obtained by using the mechanical exfoliation method from a BN bulk single crystal (SixCarbon Technology Supplies) and subsequently transferred precisely onto the top of the pre-deposited β-Ga2O3 channel as the gate dielectric utilizing a poly (dimethylsiloxane) transfer method. Finally, the top-gate electrode of Ti/Au (10/70 nm) was patterned and deposited.

### Microscopic and electrical characterizations

The active area of the phototransistor was measured to be ~2.6 × 2.5 μm2 in sequence, which was characterized by the high-precision optical microscope equipment (Olympus BX53M). The high-resolution structural analysis of samples including β-Ga2O3 flakes, h-BN flakes, and the interface of β-Ga2O3/h-BN heterostructure was characterized using HR-TEM (Talos F200X). The morphology and thicknesses of β-Ga2O3 channel and h-BN flakes were measured by AFM (Bruker Dimension Icon). The crystalline structure of β-Ga2O3 samples was investigated by GIXRD which uses X-ray with a wavelength of 0.6887 Å. 2D-GIXRD pattern was obtained by a PILATUS detector at a distance of about 263 mm from the sample, and an exposure time of ~20 s. The optical transmittance characterization of β-Ga2O3 samples was investigated by UV-visible spectrophotometer (UV-3100). The UPS spectrum was acquired using a SPECS PHOIBOS 100 hemispherical analyzer, which was excited by an unfiltered He I (21.20 eV) gas discharge lamp. The electrical and optoelectronic properties of the β-Ga2O3 photodetector were measured with a semiconductor analyzer (Agilent B1500A). The UV source was provided by a deuterium lamp (THORLABS SLS204). Deuterium lamp irradiates directly the device surface through the optical fiber. The optical fiber illuminates the surface of the device vertically and covers the entire β-Ga2O3 channel. The response time was measured by using a chopper (C-995). The calibration of the incident power density is used by an optical power meter (THORLABS S120VC).