A fiber-integrated photodetector combining a semiconductor device with microstructure fiber not only exhibits the advantage of low insertion loss, but also extends the absorption distance of the active layer, showing a “long-range effect” that enhances the device’s responsivity [1]. Therefore, the waveguide-coupled all-fiber-integrated photodetector (AFPD) has potential to simultaneously achieve high responsivity and fast response [2]. Various fiber-integrated photodetectors employing different fiber structures including microfiber [3], photonic crystal fiber [4], and side-polished fiber [1,5,6] have been reported, showcasing improvement in responsivity and response time. Among these works, side-polished fiber provides a large flat surface with an evanescent field, making it an ideal platform for AFPD. However, previous works applied two-dimensional materials and small bias voltages, fabricated by transfer techniques, resulting in limited performance, application, and active layer thickness. The approaches for fast response, high-switch-ratio AFPDs, and the corresponding thickness design of the active layer still need to be explored.

The dual cation perovskite FA0.4MA0.6PbI3 exhibits several advantages including high absorbance, good stability, fewer surface defects, long carrier diffusion distance, and self-assembly in previous studies, rendering them with extensive application potential in the field of photodetection [7–9]. The bandgap and absorption edge of FA0.4MA0.6PbI3 are reported as 1.55 eV and 800 nm, respectively [10], which is close to the low-loss transmission window of multimode fibers (MMFs), indicating its potential for achieving high-performance AFPD. The FA0.4MA0.6PbI3 based metal-semiconductor-metal (MSM) photodetector can be composed solely of perovskite film and interdigital electrodes, providing the advantage of a straightforward device structure. This configuration facilitates the direct deposition of the active layer onto the polished surface of the side-polished MMF (SP-MMF), exhibiting potential for efficient light coupling and light absorption. Therefore, the FA0.4MA0.6PbI3 based MSM photodetector is an ideal device to form AFPD. The direct deposition of the active layer also supports the thickness design based on a thin-film waveguide mechanism. By forming resonance mode, the light field can be enhanced and confined in the active layer, which has potential in improving coupling efficiency and the device’s responsivity [11,12].

In this study, we proposed a waveguide-coupled AFPD based on FA0.4MA0.6PbI3 and designed the thickness of the photodetector’s active layer based on the thin-film waveguide mechanism to optimize its performance. Theoretical analysis and simulation results demonstrate the presence of a strong mode field in the active layer that satisfies the resonance thickness condition, indicating the potential for improving the device’s absorptivity and responsivity. The FA0.4MA0.6PbI3 MSM photodetector is directly deposited and integrated onto the polished surface of SP-MMF, where the transmitted light in the fiber core leaks to the photodetector and induces a photoelectric response. Experimental results indicate that the proposed AFPD achieves a responsivity of 3.2 A/W for 650 nm light with a response time of 8 ms for both rise and fall edges. The proposed AFPD exhibits advantages of high responsivity, short response time, low insertion loss, and all-fiber integration, making it a promising design for the development of high-performance AFPD.

The structure of the proposed AFPD is illustrated in Fig. 1. The MSM photodetector based on FA0.4MA0.6PbI3 is directly integrated onto an SP-MMF. Light transmitted in the fiber core leaks to the active layer of the MSM photodetector through the polished surface, inducing a detection response.

The active layer of AFPD can be considered as a thin-film waveguide, and the proposed photodetector can be simplified to the structure shown in Fig. 2(a). The core diameter and refractive index of SP-MMF are 62.5 μm and 1.472. The cladding diameter is 125 μm with a refractive index of 1.4565. The remaining cladding thickness after polishing is defined as 500 nm, and the thickness of the perovskite film is set to 647 nm with a refractive index of 2.188 [13]. The wavelength used for simulation is 650 nm. As shown in Fig. 2(b), the simulation results demonstrate resonance occurring in the perovskite layer, where constructive interference leads to the formation of strong mode fields. The intensity of the Poynting vector along the positive y-axis direction shown in Fig. 2(a) is illustrated as Fig. 2(c). The result indicates the potential of enhancing the coupling efficiency by confining light into the active layer of the photodetector and forming resonance, consequently improving the device’s responsivity [14].

Since the mode field in the perovskite thin film shown in Fig. 2(b) is distributed near and along the y-axis in Fig. 2(a), the model depicted in Fig. 2(a) can be simplified to the five-layer slab waveguide structure shown in Fig. 3(a). Theoretical analysis and explanations for the resonance thickness conditions of the perovskite film were explored based on this model. The refractive index of air is denoted as n3. The refractive index of FA0.4MA0.6PbI3 is denoted as n4, with a thickness denoted as h4. The refractive index of the remaining cladding of the polished area is denoted as n2, with a thickness denoted as h2. The refractive index of the core is denoted as n1, with a thickness denoted as h1. The refractive indices for air, perovskite, remaining cladding, and fiber core are considered as certain values: n3=1, n4=2.188, n2=1.4565, n1=1.472. The diameter of the core is 62.5 nm, and the thickness of the remaining cladding of the polished area is defined as h2=500nm.

For the model in Fig. 3(a), a strong TE mode is expected to exist in the FA0.4MA0.6PbI3 layer by designing the value of h4, aiming to enhance the material’s light absorption and the device’s responsivity. TE modes in the thin film can only exist in either oscillatory or decay forms. Thus, TE modes must be distributed in oscillatory form as a strong mode field is desired in the FA0.4MA0.6PbI3 layer. Therefore, the following condition needs to be satisfied: n4k0>β>n2k0.(1)

The mode effective refractive index needs to conform to n4>N>n2,(2)where N represents the mode effective refractive index, k0 is the wave number, and β is the propagation constant.

The guided mode of the FA0.4MA0.6PbI3 is physically excited by the evanescent field of the core; the field equation of the Ex component in the remaining cladding layer conforms to decay form with y=h1 as the beginning. The field equations of the Ex component for each layer can be described as the following: Ex={A3e−p3(y−h1−h2−h4),y>h1+h2+h4A4cos(κ4y+φ4),h1+h2<y<h1+h2+h4A2e−p2(y−h1),h1<y<h1+h2A1cos(κ1y+φ1),0<y<h1A5ep2y,y<0.(3)

The details of p3, κ4, p2, and κ1 can be found in Appendix A. According to the second term of Eq. (3), the intensity of the guided mode of the FA0.4MA0.6PbI3 layer primarily depends on the constant coefficient A4. Based on the boundary continuity conditions, Ex and Exdy are continuous at the boundary y=h1+h2. The value of A4 follows the following two equations: A4cos[κ4(h1+h2)+φ4]=A2e−p2h2,(4)A4κ4sin[κ4(h1+h2)+φ4]=A2e−p2h2.(5)

Equations (4) and (5) can be squared and summed to yield A4=A21+p22κ42e−p2h2.(6)

Performing the same process for A2, Eq. (7) can be obtained: A4=A1(1−n42−n12n42−N2)(1+n42−n12n12−n22)e−p2h2.(7)

From Eq. (7), the intensity of the guided mode of the FA0.4MA0.6PbI3 layer depends on N, and the intensity of the TE mode in the film increases as N decreases. Analysis results indicate that by controlling the effective refractive index N, the intensity of the mode field in the FA0.4MA0.6PbI3 layer can be enhanced.

According to the boundary continuity conditions, at y=h1+h2+h4, Eq. (8) can be obtained: arctanp3κ4=κ4(h1+h2+h4)+φ4+m1π.(8)At y=h1+h2, Eq. (9) can be obtained: arctanp2κ4=κ4(h1+h2)+φ4+m2π.(9)

Subtracting Eq. (8) from Eq. (9) and substituting p3, κ4, p2 into the result, the transcendental equation between the film thickness h4 and the effective refractive index N can be obtained: arctanN2−n32n42−N2−arctanN2−n22n42−N2=k0n42−N2h4+niπ.(10)

In Eq. (10), niπ represents the resonance order in the FA0.4MA0.6PbI3 film, where ni=0,1,2,3….

The curve illustrating the relationship between the effective refractive index N and the thickness h4 of the FA0.4MA0.6PbI3 film, as calculated from Eq. (10), is depicted in Fig. 3(b). The flat section denotes the non-resonant range of h4, where the corresponding effective refractive index N fails to satisfy Eq. (2), and TE mode in the film does not meet the criteria for oscillation. According to Eq. (7), as N decreases, the resonance intensity of TE modes in the FA0.4MA0.6PbI3 film increases. Consequently, the dips in Fig. 3(b) depict the strongest resonance thickness conditions for the active layer. The resonance conditions of wavelength are also explored; the related discussion can be found in Appendix B. Additionally, the dips also indicate that the resonance thickness condition should be a series of discrete values; any slight deviation toward larger or smaller values of h4 will result in the decrease of resonance intensity. Related simulation results and discussion can be found in Appendix C as Fig. 12.

The resonance thickness conditions depicted in Fig. 3(b) are validated by the simulation results shown in Fig. 4 [with the third order validated by Figs. 2(b) and 2(c)]. The intensity of the Poynting vector along the y-axis for each thickness condition is shown in Figs. 4(g)–4(l). The simulation results demonstrate that the light energy is enhanced and confined into the perovskite film layer, which satisfied the resonance thickness condition. The resonance orders, as the interference patterns shown in Figs. 4(a)–4(f) and the peaks in Figs. 4(g)–4(l), align consistently with theoretical analysis. With the increase in resonance order, as shown in Fig. 4(m), the calculated resonance thickness conditions show a growing deviation from the values obtained by simulation. This discrepancy may arise from the differences between the slab waveguide model and the cylindrical waveguide structure of fiber.

These resonance thickness conditions and the active layer design method offer promising approaches for enhancing the coupling efficiency between light and the active layer, consequently improving device performance. Further discussion about the enhancement of absorption can be found in Appendix D as Fig. 13. Figure 4 also demonstrates the feasibility of achieving a strong mode field even in a thinned active layer, which presents a potential strategy for meeting the demands of thinning the active layer while maintaining efficient light coupling and absorption for a faster and higher detection response [15,16].

The fabrication process of the proposed AFPD is illustrated in Fig. 5. As shown in Fig. 5(a), the SP-MMF is fixed on a glass substrate and preheated at 155°C for 10 min on a hot plate. The preheating process prevents the incomplete solvent evaporation during deposition and the consequent formation of yellow phase δ-FAPbI3, which possesses poor photoelectric performance [17]. As shown in Figs. 5(b) and 5(c), perovskite thin film is deposited on the polished surface of SP-MMF at 155°C through the blade-coating method, followed by annealing at 150°C for 5 min. The employed precursor solution used a single DMF solvent with a concentration of 40%. During the coating process, as the DMF evaporated, the perovskite crystallized into the α-phase black film, and no yellow phase δ-FAPbI3 was observed. The entire deposition process is completed in air atmosphere at 24°C and 40% RH. Finally, as shown in Fig. 5(d), Ag interdigital electrodes of 100 nm thickness are deposited on the FA0.4MA0.6PbI3 film by thermal evaporation. The schematic and physical images of the fabricated AFPD are shown in Fig. 5(e). The finger width and gap of the electrode mask used during the thermal evaporation process are both 40 μm. The red leaked light in Fig. 5(e) may be caused by the saturation of light absorption in the FA0.4MA0.6PbI3 film and the lack of flatness of the polished surface and the FA0.4MA0.6PbI3 film surface. Microscope images of the polished surface of SP-MMF can be found in Appendix E as Fig. 14.

The overview of the experimental setup is depicted in Fig. 6. A 650 nm laser is utilized as the light source. The 650 nm light is initially transmitted by a single-mode fiber (SMF), and then split equally into two MMFs by a 50:50 coupler. These fibers serve as the experimental and reference paths. The experimental light path consists of the AFPD, a semiconductor analyzer, and an optical power meter (OPM). A portion of the transmitted light leaks through the polished surface of the SP-MMF to the active layer of the AFPD, while the remaining continues to propagate within the fiber. The semiconductor analyzer is used to obtain the I-V curve and photodetection response of the device. The OPM is utilized to measure the transmission power of the experimental light path, which is denoted as OPM1. An MMF of equal length to the experimental light path is utilized in the reference light path to represent the intact transmitted power, which is denoted as OPM2. As shown in Fig. 6(b), two probes of the semiconductor analyzer are connected to the Ag interdigital electrodes of AFPD. The inset image is the corresponding microscope photograph. Figure 6(c) is the enlarged view of the red dotted boxes in Figs. 6(a) and 6(b).

The incident power for a photodetector integrated on fiber can be considered as Eq. (11): Pin=OPM1−OPM2.(11)

Under a certain bias voltage, as the photocurrent for the leakage light is denoted as Iph and the dark current is denoted as Idark, the responsivity R can be described as the following: R=Iph−IdarkOPM1−OPM2.(12)

The external quantum efficiency (EQE) can be obtained from the following equation: EQE=R×hcλq,(13)where h is the Planck constant, c is the vacuum light speed, λ is the wavelength of the incident light, and q is the elementary charge.

Denoting S as the effective irradiation area, the detectivity (D*) can be obtained from the following equation: D*=R2qIdarkS.(14)

The switch ratio (SR) can be obtained from the following equation: SR=IphIdark.(15)

The microscope images of the perovskite thin film deposited on the polished surface by the blade-coating method are shown in Fig. 7(a). The film appears black; no yellow phase δ-FAPbI3 is observed. Figure 7(b) displays an enlarged view of the perovskite film. Defects of the perovskite film can be attributed to the roughness of SP-MMF’s polished surface. The XRD pattern of the FA0.4MA0.6PbI3 film prepared by blade-coating is shown in Fig. 7(c). The characteristic peaks at 2θ=13° and 2θ=14.3° are corresponding to the (001) reflection of PbI2 and the (100) reflection of FA0.4MA0.6PbI3, respectively [18]. No diffraction peak of δ-FAPbI3 is observed in the XRD pattern. The intensity of the diffraction peak of FA0.4MA0.6PbI3 is significantly higher than that of PbI2, indicating that most of the PbI2 has been converted into perovskite and the film possesses high crystallinity. The UV-VIS absorption spectrum shown in Fig. 7(d) indicates that the prepared FA0.4MA0.6PbI3 film possesses an absorption edge reaching 800 nm, which is close to the transmission window of MMF. The images and results shown in Fig. 7 demonstrate the quality of perovskite crystals deposited on the polished surface using the blade-coating method, suggesting potential for achieving a high-performance photodetector.

The band diagram of the deposited MSM photodetector is shown in Fig. 8. The work function of the FA0.4MA0.6PbI3 film is 4.14 eV [19], and the work function of Ag film is 4.26 eV. Under an ideal situation, due to the small difference between the work functions, two back-to-back shallow Schottky junctions, as depicted in Fig. 8(a), are formed in the MSM photodetector. Under a small bias voltage, as shown in Fig. 8(b), the photogenerated electron-hole pairs are separated by the built-in electric field, resulting in a photocurrent. Under a higher bias voltage, as shown in Fig. 8(c), the photodetection response of the device is dominated by the photoconductive effect.

The I-V curves of the device for different powers of 650 nm light are shown in Fig. 9(a), while the enlarged view of the small bias voltage range is depicted in Fig. 9(b). Due to the symmetric structure of the MSM photodetector, the I-V curves exhibit a symmetric distribution concerning the bias voltage. Within the bias range of 0 to 0.1 V, the Schottky junction is under reverse bias, and the device’s current remains relatively unchanged with voltage variations. As the bias exceeds 0.1 V, the device’s current increases rapidly with voltage, indicating a breakdown of the Schottky junction, and the I-V curves align with the photoconductive photodetector. The phenomenon where the lowest current in the device’s I-V curves, corresponding to different incident powers, is not located at V=0 can be attributed to ion migration within the perovskite film [20]. For the same incident power, the photocurrent of the device increases with bias voltage, primarily due to the enhanced ability of the photoconductor to separate photogenerated electron-hole pairs under higher applied bias. Furthermore, as the migration speed of the photogenerated electron rises with bias voltage, its transit time is much shorter than that of photogenerated holes. When photogenerated electrons are rapidly swept out to the electrode, the excess photogenerated holes still remaining in the photodetector will attract electrons back to maintain charge neutrality, resulting in multiple crossings of photogenerated electrons through the photodetector within their lifetime, thereby enhancing the gain of the photodetector. In the experiment, under −3 V bias, the dark current is measured as 16.4 nA. When illuminated by 200 nW 650 nm light, the photocurrent and switch ratio are 0.67 μA and 41, respectively. When the illumination power increased to 48.5 μW, the photocurrent achieved 7.62 μA, which is 465 times greater than the dark current. As shown in Fig. 9(c), the device’s responsivity decreases with increasing light power but increases with higher bias voltage. The former is commonly caused by the light saturation absorption in perovskite film and the enhanced recombination resulting from increased carrier concentration. The latter is attributed to the detector’s enhanced ability to separate photogenerated electron-hole pairs and the raised photoconductive gain. Consequently, the EQE and D* exhibit an increasing tendency with the rise in bias voltage, as shown in Fig. 9(d). In the experiment, under −3 V bias, the device achieves a responsivity of 3.2 A/W to 200 nW 650 nm light, with EQE and D* reaching 607% and 1.63×1010 Jones, respectively.

The result of the response time test is depicted in Fig. 10. In the experiment, pulsed light at different powers was output by a 650 nm laser and utilized as the transmitted light in the fiber. The device’s response time to light pulses of different powers under bias voltages of −1V, −2V, and −3V is illustrated in Figs. 10(a), 10(b), and 10(c), respectively. When the pulsed light leaks through the polished surface of the SP-MMF to the detector, photogenerated carriers will be excited and swept out to the electrodes under the influence of the applied bias, resulting in a photocurrent. In the experiment, the shortest rise time (τon) of the device achieved was 8 ms, and the shortest fall time (τoff) achieved was 3 ms. For different biases, the device exhibits the shortest response time to 2.5 μW 650 nm light. As shown in Fig. 10(d), the shortest overall response time was obtained under −1V bias, with both τon and τoff reaching 8 ms.

The performance comparison between the proposed AFPD and other similar photodetectors is presented in Table 1. The AFPD proposed in this work achieves a larger responsivity attributed to the long-range effect of the fiber-integrated device, which enhances light absorption and responsivity by extending the coupling distance between the material and light field. In comparison to alternative fiber-integrated photodetectors, our work improved the response time and switch ratio to 8 ms and 41 (under similar illumination power). This can be attributed to the direct deposition of FA0.4MA0.6PbI3 film and its high absorbance and long carrier diffusion distance. These advantages are positive for miniaturizing devices, reducing the transit time, and recombination of photogenerated carriers, resulting in better performance. Additionally, responsivity and response time of the proposed AFPD are currently limited by the roughness of the polished-surface of SP-MMF and the subsequent negative impact on the quality of perovskite film [26], which can be enhanced by process improvement.Table 1.

Performance Comparison between the Proposed AFPD and Other Similar Photodetectors

In summary, a waveguide-coupled AFPD based on FA0.4MA0.6PbI3 perovskite has been proposed. The method of optimizing its performance by designing the thickness of the active layer is also explored based on thin-film waveguide theory. Theoretical analysis and simulation results confirm that the presence of a strong mode field in the FA0.4MA0.6PbI3 film satisfied the resonance thickness condition, which has potential to improve both the responsivity and response time of AFPD. Experiment results demonstrate that the device achieved a responsivity of 3.2 A/W to 650 nm light with rise and fall times of 8 ms each. The proposed AFPD offers a promising design for high-performance all-fiber-integrated photodetection, which has potential in compact fiber sensing systems [27,28]. Further performance improvement can be achieved by optimizing the quality of the perovskite film and precisely controlling film thickness to satisfy the resonance condition.

Acknowledgment. The authors would like to thank the associate professor Shishuai Sun for providing us with the instrument for thermal evaporation of Ag film. The authors also would like to thank Dr. Yi Li for the help in simulation.