Local avalanche photodetectors driven by lightning-rod effect and surface plasmon excitations

Domain: physics
Published: 2025-12-03
Editorial outcome: major_revision

Abstract
Sensitive avalanche photodetectors (APDs) that operate within the ultraviolet spectrum are critically required for applications in detecting fire and deep-space exploration. However, the development of such devices faces significant challenges, including high avalanche breakdown voltage, the necessity for complex quenching circuits, and thermal runaway associated with Geiger-mode avalanche operation. To mitigate these issues, we report on a 4H-SiC APD design utilizing micro-holes (MHs) structures and Al nano-triangles (NTs) to enhance surface electric field driven by strong localized surface plasmon excitations and lightning-rod effect. The device demonstrates a low avalanche breakdown voltage of approximately 14.5 V, a high detectivity of 2×1013 Jones, a nanosecond-level response time, and repeated stable detections without the requirement of a quenching circuit. Collectively, when compared with the conventional wide-bandgap-based APDs, this device achieves a reduction in avalanche breakdown voltage by an order of magnitude. Consequently, the proposed APD configuration presents a promising candidate for ultraviolet detection and integrated optoelectronic circuits.

Introduction
Avalanche photodetectors (APDs) are widely utilized in various applications, including lidar, chemical sensing, flame detection, ozone-hole sensing, and telecommunications, owing to their intrinsic ultra-high gain, which enables high sensitivity with a range extending from ultraviolet to terahertz1–13. To date, ultraviolet APDs based on wide-bandgap materials as SiC14,15, GaN16–21, Ga2O3 22,23, and ZnO24,25 have shown impressive performance, achieving high gain (>1000) and high response speed (<1μs). These capabilities are largely attributed to their inherent properties, including high avalanche characteristics, low minority carrier lifetime, and intrinsic ultraviolet absorption26. Generally, conventional APDs typically operate in the Geiger mode under 95% of the critical electrical field to achieve high gain. However, several critical limitations arise when operating APDs in this mode. First, the avalanche state increases the risk of device breakdown, necessitating the use of quenching circuits to prevent permanent damage14,15,27–33. This requirement increases considerable complexity in their practical application. Second, the long-term stability and operational life of traditional APDs are compromised due to the stress induced by continuous Geiger-mode operation34. Furthermore, wide-bandgap APDs functioning in Geiger mode require relatively high driving voltages (≥100 V), which make them less suitable for applications that demand lower operational voltages. Therefore, it is critical to develop wide-bandgap APDs capable of achieving high gain at lower voltages for high stability, while eliminating the requirement for quenching circuits. Such advancements could significantly expand the range of APD applications.

An alternative approach to leveraging field enhancement is to construct semiconductor microstructures and metallic nanostructures, which have demonstrated considerable promise in enhancing local electric fields35–40. These enhancements arise from the accumulation of charges in the sharp zones of metallic nanostructures or near the corners of semiconductor microstructures, leading to localized amplification of the electric field41. However, there are relatively few reports on combining the lightning-rod effect with surface plasmon excitations to enhance the electric field to form an avalanche. By incorporating this field enhancement within semiconductor photodetectors, the internal electric field can reach avalanche field intensities (1–3 MV/cm) under lower reverse bias conditions.

In this study, a SiC-based APD design incorporating semiconductor microstructures and metallic nanostructures is presented and demonstrated with lightning-rod effect and surface plasmon excitation mechanisms. This design achieves a low breakdown voltage of 14.5 V with high detectivity of 2×1013 Jones, high gain of 104, and an improved response speed of nanoseconds. These advancements enable scalable and flexible platforms within mature SiC device technology, paving the way for the development of APDs capable of detecting weak signals without Geiger-mode operation. Moreover, the approach has broader implications, potentially influencing the design of wide-bandgap optoelectronic devices, quantum devices, and integrated optoelectronic circuits.

Results
Photoelectrical characterization
The structure of 4H–SiC avalanche photodetectors (APDs) with micro-hole (MH) and aluminum nano-triangles (Al NTs) was illustrated in Fig. 1. For specific details of fabrication, please refer to the Method section. Current-voltage (I–V) characteristics were measured to assess the performance of the proposed APDs. These measurements revealed that the local avalanche effect occurs at a reverse bias of approximately 14.5 V in devices with aluminum NTs in the SiC MHs, as depicted in Fig. 2a. The reduction in avalanche voltage offers significant advantages, particularly in preventing instantaneous breakdown and safeguarding the device from catastrophic damage. In addition, the photocurrent in devices incorporating Al NTs in the MHs was observed to be within the range of 10−5~10−3 A for reverse biases between 20 V and 50 V, compared to devices without Al NTs, which exhibited photocurrents of approximately 10−9~10−8 A. The gain of devices with Al NTs reached 104 within a voltage range of a few tens of volts, whereas the gain in devices without Al NTs was significantly lower, only increasing by 6 times (Figs. 2a, S3). We also tested the dark currents and photocurrents of several devices with 4μm, 8μm and 10μm MHs incorporating Al NTs and calculated their avalanche onset voltages and maximum avalanche gains, with error analysis histograms shown in Fig. 2b. The 4μm MH devices exhibited smaller onset voltage fluctuations overall, while 8μm and 10μm devices showed larger fluctuations, primarily related to Al NTs distribution within the MHs and varying degrees of local avalanche enhancement. Additionally, despite gain fluctuations, 4μm MH devices consistently achieved higher gains than 8μm and 10μm devices, reaching up to 10,556 times, mainly because their lateral region could be fully depleted, creating larger local avalanche regions. However, due to the inability to perfectly control the uniformity of the PS (polystyrene) sphere template arrangement, there may be some variability in the size and spacing of the Al NTs on each device’s surface. Therefore, while each device experiences a local avalanche effect, not many avalanche devices can achieve a gain of 104 as described in Fig. 2b. It can also be observed that not all 4μm devices exhibit an avalanche onset voltage as low as 14.5 V, but they are all below the avalanche voltage of traditional APDs. This is primarily due to the non-uniform distribution of Al NTs. Similarly, the gain of the devices varies from 103 to 104. Detailed photocurrent, gain, and dark current for Al NT devices are provided in Figs. S2–S4.

From the spectral response data, the 4μm MH device without Al NTs showed peak responsivity of 0.133 A/W at 280 nm at 10 V (58.9% External Quantum Efficiency (EQE)) as shown in Fig. S6, while the Al NT-equipped 4μm MH device reached 0.129 A/W (57.2% EQE). 42.8% of the incident photons do not contribute to the generation of photogenerated carriers. This proportion accounts for light reflection, carrier recombination due to defects, and field enhancement. Reflection spectrum testing, as shown in Fig. S13, indicates that the reflectivity at 280 nm is approximately 16.0%. Therefore, the photons contributing to the field enhancement account for less than 26.8%. Similarly, 8μm and 10μm devices with Al NTs exhibited lower EQE values due to partial light reflection by Al NTs. Compared to 4μm devices, the reduced responsivity and EQE in larger MH devices stem from incomplete depletion of lateral electric fields, lowering carrier collection efficiency. Under Al NT and MH-induced local avalanche, the 4μm MH device achieved 3.35×10−4 A photocurrent with EQE of 2,374,473% at 50 V.

Furthermore, device detectivity was evaluated across wavelengths (Fig. 2c). The 4μm MH devices with Al NTs achieved peak detectivity of 2.0×1013 Jones at 280 nm under a reverse bias of 10 V. Notably, detectivity decreased with increasing MH size, which is attributed to in depletion region impairing carrier collection. Regardless of MH size, devices with Al NTs showed lower detectivity than counterparts without Al NTs, as Al NTs both reduce responsivity through light reflection and increase leakage current (Figs. S4, S6). As shown in Fig. S7, the Al NT devices in this work exhibit lower noise characteristics than conventional APDs due to localized avalanche effects.

A comparison of detectivity versus avalanche voltage was conducted to benchmark our devices against existing wide-bandgap semiconductor technology (Fig. 2d). Our APDs demonstrated superior performance, featuring the highest detectivity and the lowest avalanche voltage of 14.5 V. These characteristics underscore the exceptional performance metrics, including low avalanche voltage, high detectivity, and high gain. This balance is particularly advantageous in the realm of micro- and nano-photonics, where surface plasmon excitations in MHs are leveraged in 4H–SiC APDs. Moreover, the stability of the device was evaluated to determine the impact of long-term operation on performance. After 13,000 h (1.5 years) of exposure, multiple I–V measurements showed consistency with the initial curve (Fig. S5). These results indicate that the proposed devices, incorporating Al NTs, exhibit robust and stable operation in the local avalanche state without the need for quenching circuits. In this study, high gain has been achieved in the detectors through stable and repeatable local avalanche at lower voltages, avoiding devastating bulk avalanche breakdown. This approach not only significantly reduces the avalanche voltage but also protects the devices from breakdown, which eliminates the need for a quenching circuit. The long-term stability and repeatability of the devices are demonstrated in Fig. S5.

Lightning-rod effect and surface plasmon simulation
Our previous work investigated the impact of metal holes (MHs) on device performance and conducted a detailed analysis of how MH size affects device performance. Under the condition of maximizing the device’s photocurrent, we determined the optimal MH size to be 4μm. When the MH diameter is less than 4μm, the photocurrent increases with the increase in MH size. However, when the MH size exceeds 4μm, the photocurrent decreases with the increase in MH size42,43. In this study, we further investigated the individual impact of aluminum nanotubes (Al NTs) on device performance by characterizing the photocurrent, dark current, gain, and spectral response of devices incorporating Al NTs but no MHs (Figs. S2–S4, S6). Our results reveal that devices with Al NTs (but no MHs) exhibit no localized avalanche effect. The observed increase in both photocurrent and dark current primarily stems from the strong electric field at the Al NT tips, which effectively elevates the voltage applied to the device’s P+ layer, analogous to enhancing the reverse bias.

The electric field is a crucial factor in determining carrier collection and multiplication within APDs. Therefore, a theoretical simulation based on finite element analysis (FEA) was conducted using TCAD to investigate the electric field distribution in the absence of illumination (Fig. 3a, b). The bulk electric field distribution for the APDs with different MH sizes (Fig. 3a) indicates that a complete depletion layer is formed at the junctions for devices with 4μm MHs and Al NTs. In contrast, the intrinsic i-layer of APDs with 8μm and 10μm MHs and Al NTs is only partially depleted. The undepleted regions serve as recombination centers, resulting in reduced carrier collection during avalanche events, which explain why the APDs with 4μm MHs and Al NTs exhibit superior performance in terms of gain, detectivity, and avalanche voltage (Fig. 2b, c).

Certainly, the operational state of the device varies with different applied voltages, as illustrated in Fig. S8. Under a 5 V bias, the maximum internal electric field reaches 0.4 MV/cm, which is below the threshold for initiating local avalanche. At elevated voltages, the internal electric field intensifies further. With a 40 V reverse bias, the field strength attains 3 MV/cm, thereby extending the avalanche region and amplifying the avalanche effect, consequently increasing the current flow.

The local field enhancement induced by the lightning-rod effect near the corner of MH becomes prominent under different applied voltages. Under dark conditions, the local field enhancement at the edges of the MH, induced by the lightning-rod effect, becomes substantial at different applied voltages. For instance, at a reverse bias of 5 V, electric field aggregation is observed at the tips of the Al NTs near the electrode. However, the electric field intensity reaches only 0.74 MV/cm (Fig. 3b), which remains insufficient to initiate a local avalanche effect within the device. As the reverse bias increases to 15 V, the electric field intensity at the tips of the Al NTs rises to 2.28 MV/cm, causing the internal electric field of the device to reach 1.5 MV/cm (Fig. 3b), which is sufficient to induce a local avalanche effect. With further increases in the reverse bias, the electric field intensity at the tips of the Al NTs continues to strengthen; at 40 V, it reaches a high value of 5.76 MV/cm, which leads to an expanded avalanche region and an increase in avalanche gain. In invariably, the regions where local avalanches occur remain concentrated at the edges of the MHs, as the electric field intensity at the Al NT tips diminishes with distance from the electrodes.

In contrast, for devices without Al NTs, the surface electric field intensity is approximately one-fifth of that observed in devices containing Al NTs. At a 15 V reverse bias, the surface electric field intensity at the edges of the MHs is only 0.41 MV/cm (Fig. S9), with the corresponding internal electric field within the device remaining below 0.4 MV/cm (Fig. S10), which is not adequate to trigger a local avalanche and yield higher gain. These field enhancement effects at the nanotube tips have been corroborated by other studies41.

To further explore the local field enhancement mechanism of Al NTs under illumination, we employed the finite difference time domain (FDTD) method to simulate and validate the field intensity distribution of Al NTs. The spacing between Al NTs was set at 10 nm, 20 nm, 30 nm, and 80 nm, with the side length and thickness of the NTs set at 80 nm and 10 nm, respectively, in alignment with the experimental parameters. It was found that the spacing between adjacent NTs strongly influences the field enhancement (Fig. 3c). Specifically, when the spacing is reduced to less than 10 nm, the plasmon coupling field intensity increases by more than 30-fold. The strong confinement of the enhanced impact ionization at smaller gaps between NTs further extends the local avalanche region, enhancing the performance of the device at the local avalanche state. Although plasmonic coupling between bow-tie structures diminishes as the NT spacing increases from 20 nm to 80 nm, the field intensity remains more than 18 times greater than that of untreated tips. This field intensity is sufficient to cooperate with avalanche multiplication, confirming the effectiveness of the Al NTs surface plasmon excitations in coupling the high local electric field and improving device performance.

To further investigate the internal electric field distribution, we conducted COMSOL simulations on devices with varying Al NT spacings, as illustrated in Figs. S11, S12. The simulation results demonstrate unequivocally that devices incorporating Al NTs produce significantly stronger internal electric fields compared to Al-free devices, achieving a maximum field strength of 4.84 MV/cm at a spacing of 10 nm. Furthermore, the simulations reveal an inverse correlation between Al NT spacing and the maximum internal field strength. As the spacing increases, the field intensity diminishes. This phenomenon can be attributed to the enhanced coupling effects observed in closely spaced Al NTs, which serve to amplify the local electric field. These findings conclusively demonstrate the profound impact of Al NT spacing on device performance.

Response time and band structure
The temporal spectral response of the 4H–SiC APDs was investigated using a 266 nm picosecond laser as the illumination source and an oscilloscope for detection. The rise time (Tr) and fall time (Tf) were defined as the times during which the impulse voltage rises from 10% to 90% and falls from 90% to 10% of the peak value, respectively. Figure 4a and its inset present the photocurrent response at an applied reverse bias of −10 V. The results demonstrate that the APD with Al NTs exhibits superior operational stability and reliability. Additionally, due to the p−i−n vertical structure and the inherently low minority carrier lifetime of the 4H−SiC material, the devices incorporating 4μm MHs and Al NTs achieved a high response speed, with a Tr of 2.2 ns and a Tf of 4.2 ns (Fig. 4a inset). The Tr of the proposed device represents an 82.2% reduction compared to the 12.4 ns response time reported for Ga2O3-based photodetectors23. Furthermore, it was observed that both devices, with and without Al NTs, exhibited longer response times at a reverse bias of 10 V compared to 0 V (Fig. 4b, Fig. S14). Specifically, the Tf of 4.2 ns at 10 V reverse bias was more than twice the 1.9 ns observed at 0 V. First, from the spectral response data, we observe that under 10 V reverse bias, the Al-containing device exhibits greater light reflection, resulting in lower photocurrent compared to the Al-free device. This suggests higher dynamic resistance in the Al-containing device. Following the RC oscillation circuit frequency formula (f = 1/2πRC), the reduced frequency (f) in Al-containing devices consequently yields longer response times (T = 1/f). Additionally, the frequency calculation reveals that total device capacitance impacts response speed. The Al-containing device demonstrates additional parallel capacitance between the device and Al nanoparticles relative to Al-free devices, increasing overall capacitance and consequently response time. Together, these factors account for the prolonged response times observed in Al-containing devices. Additionally, response speed may be influenced by the transit time of carriers, the drift current and the diffusion current within the device. These temporal performance enhancements highlight the strong carrier multiplication induced by the local field enhancement effect and demonstrate voltage-tunable response times in the proposed Al NT-integrated device. The combination of fast temporal response and low operational voltage positions the device as a promising candidate for high-speed ultraviolet (UV) detection applications.

The local avalanche mechanism and carrier transport in UV-illuminated devices are further elucidated through the schematic and band diagrams (Fig. 4c, d). The upper corner region of the device exhibits a higher electric field, corresponding to the local avalanche area. In this region, photogenerated carriers undergo collision ionization, resulting in the generation of electron-hole pairs. These pairs are efficiently separated by the reverse-biased electric field of the pn junction. In contrast to conventional APDs, the collision ionization process in the proposed device is localized to a specific area, while the remainder of the device remains stable. As a result, the photocurrent tends to saturate with increasing reverse bias, indicating that the device operates in a local avalanche state rather than a full avalanche state.

Discussion
This study effectively enhanced the local electric field of 4H–SiC avalanche photodiodes featuring MHs by integrating the lightning rod effect with localized surface plasmon resonance of Al NTs. This approach achieved an unprecedentedly low avalanche initiation voltage of 14.5 V. Notably, these devices can operate in a local avalanche state without requiring quenching circuits, maintaining a high avalanche gain of 104 and demonstrating excellent long-term stability. The concept of local avalanche within 4H–SiC APDs introduces an innovative method for internal electric field regulation in semiconductor devices and holds potential for adaptation to other photodetectors based on wide-bandgap semiconductors. Future directions include optimizing the shape of metal nanostructures, with an emphasis on sharper features and optimized curvature radii, to maximize both the lightning rod effect and surface plasmon resonance, thereby further improving device performance. These findings indicate that 4H–SiC materials and associated technologies constitute a robust and scalable platform for quantum-based light detection and imaging, offering ease of integration and high compatibility with industrial applications.

Methods
The 4H–SiC avalanche photodetectors (APDs) with micro-hole (MH) structures and aluminum nano-triangles (Al NTs) were fabricated into an 8×8 array with dimensions of 2×2 mm2, as illustrated in Fig. 1a. The effective photosensitive area of a single pixel was designed to be 200×200 μm2, as shown in Fig. 1b. The top surface of each device was etched with the MH structure, which serves as a window to enhance ultraviolet (UV) absorption. The MHs were etched through to the intrinsic i-layer with diameters (D) of 4μm, 8μm, and 10μm, respectively. As depicted schematically in Fig. 1c, the APD structure was processed using standard 4H–SiC epitaxial techniques. It consists of a 200 nm thick p-type layer (NA = 1×1019 cm−3), a 3000 nm thick i-layer (NI = 1×1015 cm−3) on a 365 μm thick n+ substrate (ND = 5×1018 cm−3). Notably, in contrast to conventional APD structures, the i-layer of the photodiode in this design is directly exposed to UV light, enabling enhanced UV detection capabilities. The proposed APD design incorporates an array of Al hexagonal NTs within the MHs, positioned on the 4H–SiC i-layer, as shown in Fig. 1d. The diameter (D) of the MHs and the spacing (d) between the NTs were varied from 4μm to 10μm and 10 nm to 80 nm, respectively. The Al NTs were designed with a side length of 80 nm and a thickness of 10 nm. The geometric features of the Al NTs could be precisely controlled using a polystyrene (PS) microsphere template44,45. Further details regarding the fabrication and measurement process are provided as follows.

Devices fabrication
The local avalanche 4H–SiC PDs were fabricated and processed as follows. Firstly, a beveled mesa of the device was processed by photoresist reflow technology to effectively suppress the edge breakdown of the device. Then, a standard photolithography process was applied to obtain the MH array patterns by using AZ5214E positive photoresist. Subsequently, the inductive coupled plasma (ICP) etching was performed with a gas flow rate of 30 sccm (CF4)/5 sccm (O2), MHs with different diameters (4μm, 8μm and 10μm) were etched and the MH spacing was fixed to 5μm. By controlling the etching time, MH with a depth of 220 nm was obtained using an atomic force microscope (AFM). It ensures that the MHs were etched to the i-layer, which allows more UV light to be absorbed directly by the i-layer. Then, a thermally grown SiO2 with a thickness of 45 nm was grown on the surface to restrict the leakage current of the device and suppress the edge breakdown of MHs. Ohmic contact metals on the p+ layer and the backside of n+ substrate was obtained by Ti/Al/Ti/Au (40/60/10/100 nm) and Ti/Ni/Ti/Au (5/200/5/150 nm), respectively, followed by a rapid thermal annealing process of 1000 °C/2 min in Ar ambient. Then, Ti/Au (20/300 nm) were sputtered as wire-bonding pads.

Al nano-triangles (NTs) fabrication
First, the polystyrene (PS) microspheres were mixed with ethanol in a 1:1 ratio and ultrasound ed for 10 min. Secondly, the prepared devices were placed in deionized water, and the water surface was just over the sample, and then the PS microspheres were slowly injected into the surface of the deionized water through the syringe until the PS microspheres were just covered the entire water surface. The deionized water was then slowly pumped down, and the PS microspheres were spread all over the devices surface (Fig. S1a). Finally, a 10 nm thick Al film was prepared by magnetron sputtering method, which was then immersed in tetrahydrofuran to remove the PS microsphere template and form regular Al NTs (Fig. S1b).

Photoelectrical performance measurement
Figure S15a shows a schematic diagram of the device performance measurement system described in the manuscript. The system primarily consists of two integrated parts: the optical path and the electrical circuit. The optical path, which generates and conditions the test light, is composed of a xenon lamp, an optical fiber, and a monochromator. The electrical measurement section is contained within an electromagnetic shielding box and incorporates a probe station connected to a 4200 A-SCS semiconductor parameter analyser. The current-voltage (I–V) characteristics of the semiconductor devices were measured using the source measure units (SMUs) of the analyser.

Prior to device testing, the intensity of the ultraviolet light emitted from the xenon lamp was calibrated. This calibration was performed by integrating a UV-enhanced Si-222 standard photodetector into the system. The UV light signal, after being conditioned by an adjustment objective lens, was focused onto the active surface of the standard photodetector to generate a photocurrent. The calibrated optical power values across the UV wavelength range were then calculated from the known spectral responsivity of the standard detector.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Local Avalanche Photodetectors Driven by Lightning Rod Effect and Surface Plasmon Excitations by Fu et al.\nThe work is interesting and describes the impact of the Lightning Rod Effect and Surface Plasmon Excitations on 4H-SiC;\nhowever, several points require the author's attention for improvement:\n1. Why are the detectivity values very similar at 270 nm excitation for a -10V basis in the 4 µm MH-Al-NTs, while there is\nsignificant variation for the 8 µm and 10 µm samples?\n2. What is the noise level in the fabricated device?\n3. The charge accumulation effect during the Al-Nt process was simulated only at a 15V reverse bias. What is the impact of\nvarying the reverse bias?\n4. Strong carrier multiplication has been reported. The external quantum efficiency (EQE) should be included in the results\nand discussed.", "reviewer_2": "This manuscript presents a novel 4H-SiC avalanche photodetector (APD) designed for ultraviolet detection, addressing key\nchallenges such as high breakdown voltage and the need for complex quenching circuits. By incorporating micro-hole (MH)\nstructures and aluminum nano-triangles (NTs), the device enhances the surface electric field through localized surface\nplasmon excitations and the lightning-rod effect.\nWhile the idea is novel and of interest for the community, the way that the data is currently presented is quite misleading and\nthere are a few technical issues that I would like to point out: I recommend this paper to undergo major revision before being\nfit for publication.\n- in general, the authors fail to clearly explain the different effects of the two design strategies they employed: MH and Al NT.\nThere is no clear discussion of the effect of one vs the other, and most results involve the simultaneous implementation of\nboth strategies. For example, Fig 2c shows a negligible improvement in detectivity granted by the inclusion of Al NT,\ncontrary to what the authors claim across the manuscript. This is perhaps because the Al NT increase both the photocurrent\nand the dark current simultaneously, as noted at line 162-164, with opposing effects on the detectivity. I believe that the\naddition of a detailed and quantitative discussion of each the individual effect of each of the two strategies needs to be\nadded to the manuscript: this can be done for example by merging some of the plots in Fig. 2a and S2.\n- Similarly to what noted above, there seems to be no experimental characterization of what effect the spacing between Al\nNT has on performance, as hinted by the simulations (line 194).\n- I have a particular issue with Fig 2c and 2d. The specific detectivity was invented to express the quality of a specific bulk\nmaterial platform for photodetection, and cannot be freely applied to dimensionally-structured materials without specific\ncaveats [Wang, F., Zhang, T., Xie, R. et al. How to characterize figures of merit of two-dimensional photodetectors. Nat\nCommun 14, 2224 (2023)]. The authors fail to mention what exact numbers were used to calculate the detectivity, in terms of\nresponsivity, dark current and area. In particular, I suspect that the authors assumed an extremely small photosensitive area\nin their calculations, which is a conceptual mistake, as this is equivalent to discarding most of the incident light to be\ndetected. In my opinion, the area used here should be the pitch of one square pixel in Fig. 1a. This will give a real estimation\nof how good the array is at detecting incident light (from the reference above: “for plane array devices, the entire device tiling\nthe plane needs to be regarded as the optical area”). Otherwise, the authors may use a smaller area if they demonstrate a\nmeasurement of the performance of the array with a microns array, which is capable of focusing the incident light onto an\narea smaller than the pixel size. I suggest that the authors specify the numbers used in their calculation, and add other\nperformance metrics, such as internal and external quantum efficiency (the latter based on the total pixel area), which give a\nbetter indication of the useful performance of the detector. This is particularly important as plasmonic enhancement is known\nto introduce additional loss [Khurgin, J. How to deal with the loss in plasmonics and metamaterials. Nature Nanotech 10, 2–\n6 (2015)], and it’s necessary to estimate whether this strategy is worthwhile and provides a net improvement despite the\nplasmonic loss.\n- the authors should provide a clearer explanation of why the presented architecture allows to avoid the need for quenching\ncircuits: is this because the devices are operated at sub-breakdown voltages? If this is the case, what is the advantage\ncompared to operating conventional detectors at sub-breakdown voltages (say devices without Al NT at 50 V)? The\nsentence in lines 113-115 “The reduction in avalanche voltage offers significant advantages, particularly in preventing\ninstantaneous breakdown and safeguarding the device from catastrophic damage” is unclear or misleading: if the avalanche\nvoltage is lower, it is typically easier to trigger breakdown and not harder.\n- the schematic in Fig. 4d is a simple representation of any avalanche process, without and specific relation to the presented\ndevices (e.g. local avalanche, field enhancement), and I believe fails to capture the complex physics in action in these\ndevices. In fact, the incident photons that provide a local field enhancement as shown in Fig. 3c do not contribute to the\nphoto carrier generation. To investigate this, one should put a monitor plane in the FDTD simulation, situated a few 10s nm\ninside the substrate underneath the Al NT, and compare the transmitted number of photons vs the incident ones: this portion\nis the one contributing to photo carrier generation. The authors should implement and discuss this model.\n- The sentence at lines 217-220 “This increase is attributed to the acceleration of photogenerated carriers within the space-\ncharge region at higher reverse bias, necessitating a longer response time. Moreover, both Tr and Tf in devices with Al NTs\nincreased by approximately 10% compared to devices without Al NTs” sounds counter-intuitive, as the higher voltage will\naccelerate charges faster. In fact, I suspect this increase in response time is due to the higher current changing the dynamic\nresistance and hence the RC of the device, as evidenced by the fact that the same increase is also registered for devices\nwith Al NT at the same voltages. If the authors disagree, they should provide an objective argument for their claims.\n- finally, I believe the quality and presentation of the figures graphics can be significantly improved: for starter, the largest\nfonts in several figures are around ten times larger than the smallest in the same figures. Fig. 1a and 1b lack scale bars, and\nsome of the numbers in Fig. 3 are not explained in the caption. The caption of Fig 2b mentions “statistical comparison”,\nbut no statistics is shown or mentioned in the figure itself: I guess the bar plots are the average of some number of devices,\nbut can the authors specify how many devices, how is this average obtained and insert the corresponding error bars? These are\nthe minimum necessary improvements, but there are several more that can be implemented."}, "author_response": "Dear Reviewers:\nThank you for your letter and the reviewers’ comments on our submitted\nmanuscript entitled “Local Avalanche Photodetectors Driven by Lightning-rod\nEffect and Surface Plasmon Excitations”. These comments are very constructive and\nhelpful to our paper and future research. We have studied comments carefully and have\nmade corrections which we hope meet with approval. The detail responses to the\nreviewers’ comments are as follows:\nReviewer #1 (Remarks to the Author):\nLocal Avalanche Photodetectors Driven by Lightning Rod Effect and Surface Plasmon\nExcitations by Fu et al. The work is interesting and describes the impact of the\nLightning Rod Effect and Surface Plasmon Excitations on 4H-SiC; however, several\npoints require the author's attention for improvement:\n1.Why are the detectivity values very similar at 270 nm excitation for a -10V basis in\nthe 4 µm MH-Al-NTs, while there is significant variation for the 8 µm and 10 µm\nsamples?\nAnswer: Thanks for your comments. We have recalculated detectivity based on the\nmeasured dark current and spectral responsivity at a reverse bias of 10 V. The measured\ndark currents are a little bit higher than that at a bias less than 10 V. The detectivity\ncurves have been corrected based on the higher dark current and spectral responsivity\nas follows:\nFig. 2 (c)The corresponding detectivity with the wavelength range from 200 nm to 400 nm\nfor the APDs with and without Al NTs at 10 V reverse bias. The inset shows detectivity from\n260 nm to 300 nm.\nFig.S4 and S6: (a) Spectral response and quantum efficiency graphs of devices with different\nMH diameters (4 μm, 8 μm, and 10 μm). (b) Spectral response and quantum efficiency graphs\nof devices with different MH diameters (4 μm, 8 μm, and 10 μm) with Al NTs under 10 V\nreverse bias. (c) The comparison of dark current for the PDs without Al NTs for different\ndiameters MHs (4 μm, 8 μm and 10 μm). (d) The comparison of dark current for the PDs with\nAl NTs for different diameters MHs (4 μm, 8 μm and 10 μm).\nFirst, the calculation formula for the normalized detectivity (D*) D* = R×\nA\n√ indicates that the detectivity mainly depends on the responsivity and the dark\n2qId\ncurrent density. According to Figure S4 and Figure S6, the detectivities of the devices\nwith different MH sizes under conditions with and without aluminum (Al) has been\nobtained based on the responsivities and dark currents.\nAs illustrated in the attached Figure S8, the 4 μm devices exhibit full depletion of\nthe lateral electric field, whereas the 8 μm and 10 μm devices do not achieve complete\ndepletion. This results in relatively lower responsivity and detectivity for the 8 μm and\n10 μm devices. From the perspective of dark current, as shown in Figure S4, the full\ndepletion of the lateral electric field in the 4 μm devices effectively suppresses both\nsurface and bulk dark currents. In contrast, for the 8 μm and 10 μm devices, the\nincomplete depletion of the electric field leads to increased bulk diffusion current and\nsurface recombination current as the bias voltage increases.\nFurthermore, irrespective of the device's MH size, it is evident that the devices\nwithout Al exhibit higher responsivity and detectivity compared to those with Al. This\nis primarily because localized avalanche breakdown has not yet occurred at a reverse\nbias of 10 V. The presence of Al nanoparticles (Al NTs) increases light reflection to\nsome extent, thereby reducing the incidence efficiency and leading to a decrease in\nphotocurrent. Consequently, the responsivity and detectivity are also reduced. These\nfindings have been discussed in the main text and highlighted accordingly.\nAccording to your comment, we have revised the main text of this section on page\n6 of the manuscript. The revised part is as follow:\n“Furthermore, device detectivity was evaluated across wavelengths (Fig.2(c)). The\n4 μm MH devices with Al NTs achieved peak detectivity of 2.0×1013 Jones at 280 nm\nunder a reverse bias of 10 V. Notably, detectivity decreased with increasing MH size,\nwhich is attributed to indepletion region impairing carrier collection. Regardless of MH\nsize, devices with Al NTs showed lower detectivity than counterparts without Al NTs,\nas Al NTs both reduce responsivity through light reflection and increase leakage current\n(Figs. S4, S6).”\n2.What is the noise level in the fabricated device?\nAnswer: The avalanche noise level depends on the ionization rate ratio (α /α )\nN P\nand the avalanche gain (M). For the case of hole injection, the noise level can be\nexpressed as :\nM-1\nF = M[1-(1-k)( )2]\nM\n1\n≈ kM+(2- )(1-k)\nM\nwhere k=α /α , which remains constant throughout the avalanche region. For SiC\nN P\nmaterial, the impact ionization coefficients of electrons and holes can be expressed as:\n9.96×106 V/cm\nα (E) = 1.69×106 cm-1exp[-( )1.6] (electron)\nN E\n1.07×107 V/cm\nα (E) = 3.32×106 cm-1exp[-( )1.1] (hole)\nP E\nwhere E represents the electric field intensity.\nThe avalanche electric field intensity in conventional SiC APDs is typically 3\nMV/cm. By substituting E=3 MV/cm into the equations above, we calculate that k ≈\n0.032. Consequently, the noise level in conventional devices can be expressed as:\nF = 0.032M-0.968/M+1.936\nFor comparison, the local avalanche electric field intensity in our fabricated device\nis 1.5 MV/cm under a reverse bias of 15 V as shown in Fig. S8. We therefore simulated\nthe local avalanche electric field intensity under different reverse bias conditions. Since\nthe gain is related to the reverse bias (as shown in Fig. 2a), Fig. S7 was obtained by\ncurve fitting.\nFig.S7 Comparison of excess noise factor in the device without MH-Al NTs and the\nfabricated device.\nThe results show that the noise level increases with avalanche gain. The fabricated\ndevice exhibits a lower noise level compared to the device without MH-Al NTs, owing\nto localized avalanche effects.\nAccording to your comment, we have revised the main text of this section on page\n7 of the manuscript. The revised part is as follow:\n“As shown in Fig. S7, the Al NT devices in this work exhibit lower noise\ncharacteristics than conventional APDs due to localized avalanche effects.”\n3.The charge accumulation effect during the Al-Nt process was simulated only at a 15V\nreverse bias. What is the impact of varying the reverse bias?\nAnswer: The application of varying reverse biases to the Al NTs device\nsignificantly alters both the internal electric field distribution and maximum field\nstrength. As discussed in the main text, we have conducted a comprehensive analysis\nof how different reverse biases affect charge accumulation. Figure S8 in the\nsupplementary materials presents detailed electric field distribution diagrams under 5\nV, 15V and 40 V reverse biases, while the main text focuses on the internal electric field\ndistribution at 15 V reverse bias. At this bias voltage, the electric field strength at the\nedge of the MH structures (MHs) reaches 1.5 MV/cm, sufficient to trigger local\navalanche phenomena.\nIn comparison, Figure S8 demonstrates that a 5 V bias generates a maximum\ninternal electric field of only 0.4 MV/cm, below the threshold for local avalanche\ninitiation. As the bias voltage increases, the internal electric field intensifies\nproportionally reaching 3 MV/cm at 40 V reverse bias. This stronger field expands the\navalanche region and enhances the avalanche effect, consequently increasing the\ncurrent flow. Our static-field simulations under various conditions (Fig. 3(b)) confirm\nthat higher applied voltages produce stronger electric fields, thereby increasing the\nprobability of local avalanche occurrences.\nAccording to your comment, we have revised the main text of this section on page\n9 of the manuscript. The revised part is as follow:\n“Certainly, the operational state of the device varies with different applied voltages,\nas illustrated in Figure S8. Under a 5 V bias, the maximum internal electric field reaches\n0.4 MV/cm, which is below the threshold for initiating local avalanche. At elevated\nvoltages, the internal electric field intensifies further. With a 40 V reverse bias, the field\nstrength attains 3 MV/cm, thereby extending the avalanche region and amplifying the\navalanche effect, consequently increasing the current flow.”\nFig.S8. The internal electric field intensity of the devices with MH (4 μm, 8 μm and 10 μm)\nand Al NTs under the charge accumulation effect at the tips of Al NTs was simulated by\napplying (a) 5 V, (b) 15 V, (c) 40 V reverse bias.\n4.Strong carrier multiplication has been reported. The external quantum efficiency\n(EQE) should be included in the results and discussed.\nAnswer: Thank you for your comment. We will include the spectral data for the\ndevice's responsivity and quantum efficiency before local avalanche occurs in the\nsupplement. The spectral response data show that the 4 μm micro-hole device without\nAl NTs achieves the highest responsivity of 0.133 A/W at 280 nm at 10V, corresponding\nto an external quantum efficiency of 58.9% as shown in Fig. S6. Meanwhile, the 4 μm\nMH device with Al NTs shows a maximum responsivity of 0.129 A/W at 280 nm at\n10V, with a corresponding external quantum efficiency of 57.2%. Similarly, the 8 μm\nand 10 μm devices with Al NTs also exhibit lower external quantum efficiency values.\nThis reduction occurs because the aluminum metal partially reflects incident light,\nleading to decreased photocurrent. Compared to the 4 μm devices, the lower\nresponsivity and external quantum efficiency in the 8 μm and 10 μm devices result from\ntheir lateral electric fields not being fully depleted, which reduces carrier collection\nefficiency.\nWhen local avalanche is triggered at 50V by the Al NTs and MHs under light\nexcitation, the 4 μm MH detectors demonstrates significantly enhanced performance\nwith photocurrent reaching 3.35×10-4 A. This corresponds to a responsivity of 5357.4\nA/W and a quantum efficiency of 2,374,473%. We have described these changes in\nexternal quantum efficiency in the main text and highlighted these results.\nAccording to your comment, we have revised the main text of this section on page\n6 of the manuscript. The revised part is as follow:\n“From the spectral response data, the 4 μm MH device without Al NTs showed\npeak responsivity of 0.133 A/W at 280 nm at 10 V (58.9% External Quantum Efficiency\n(EQE)) as shown in Fig. S6, while the Al NT-equipped 4 μm MH device reached 0.129\nA/W (57.2% EQE). 42.8% of the incident photons do not contribute to the generation\nof photogenerated carriers. This proportion accounts for light reflection, carrier\nrecombination due to defects, and field enhancement. Reflection spectrum testing, as\nshown in Fig. S13, indicates that the reflectivity at 280 nm is approximately 16.0%.\nTherefore, the photons contributing to field enhancement account for less than 26.8%.\nSimilarly, 8 μm and 10 μm devices with Al NTs exhibited lower EQE values due to\npartial light reflection by Al NTs. Compared to 4 μm devices, the reduced responsivity\nand EQE in larger MH devices stem from incomplete depletion of lateral electric fields,\nlowering carrier collection efficiency. Under Al NT and MH-induced local avalanche,\nthe 4 μm MH device achieved 3.35×10-4 A photocurrent with EQE of 2,374,473% at\nReviewer #2 (Remarks to the Author):\nThis manuscript presents a novel 4H-SiC avalanche photodetector (APD) designed for\nultraviolet detection, addressing key challenges such as high breakdown voltage and\nthe need for complex quenching circuits. By incorporating micro-hole (MH) structures\nand aluminum nano-triangles (NTs), the device enhances the surface electric field\nthrough localized surface plasmon excitations and the lightning-rod effect.\nWhile the idea is novel and of interest for the community, the way that the data is\ncurrently presented is quite misleading and there are a few technical issues that I would\nlike to point out: I recommend this paper to undergo major revision before being fit for\npublication.\n1. in general, the authors fail to clearly explain the different effects of the two design\nstrategies they employed: MH and Al NT. There is no clear discussion of the effect of\none vs the other, and most results involve the simultaneous implementation of both\nstrategies. For example, Fig 2c shows a negligible improvement in detectivity granted\nby the inclusion of Al NT, contrary to what the authors claim across the manuscript.\nThis is perhaps because the Al NT increase both the photocurrent and the dark current\nsimultaneously, as noted at line 162-164, with opposing effects on the detectivity. I\nbelieve that the addition of a detailed and quantitative discussion of each the individual\neffect of each of the two strategies needs to be added to the manuscript: this can be\ndone for example by merging some of the plots in Fig. 2a and S3.\nAnswer: Thank you for your comment. Firstly, I would like to address your\nconcern regarding the lack of separate discussion about the impact of MH and Al NTs\non device performance in the article. The influence of MH on the performance of\nvertical p-i-n devices has been thoroughly analyzed in our previous work, as referenced\nin the paper \"Local Avalanche Effect of 4H-SiC p-i-n Ultraviolet Photodiodes With\nPeriodic Micro-Hole Arrays\"(ref.44), which we have now included in the references\nsection of the article.\nThe metal-dot (MH) structure was designed to mitigate the ineffective absorption\nof ultraviolet light by the P+ layer, thereby increasing the effective incident ultraviolet\nlight and enhancing both the responsivity and quantum efficiency of the device.\nTheoretically, larger MHs would allow for better ultraviolet light absorption. However,\nin practice, larger MHs result in the partial depletion of the i-layer at the MH sites,\nwhich hinders the collection of photogenerated carriers and leads to a lower\nphotocurrent. Therefore, to maximize the photocurrent of the devices, we determined\nthe optimal MH size to be 4 μm. When the MH diameter is less than 4 μm, the\nphotocurrent increases with the MH size. However, when the MH size exceeds 4 μm,\nthe photocurrent decreases as the MH size increases (ref. 44). Moreover, electric field\nconcentration occurs at the edges of the MHs, leading to a minor localized avalanche\nphenomenon at a reverse bias of 40 V, with a gain of up to 5 times. However, the\nobtained avalanche breakdown voltage remains relatively high, and the avalanche gain\nis small, which does not meet current demands for weak signal detection.\nTo further explore the effects of aluminum nanotubes (Al NTs), we fabricated\ndevices without MHs but incorporated Al NTs, creating a contrast with devices that\nonly have MHs and those that have both MHs and Al NTs. We tested the photocurrent,\ndark current, gain, and spectral response of the devices without MHs but with Al NTs,\nas shown in Figs. S2, S3, S4, and S6. Our results indicate that for devices without MHs\nbut with Al NTs, there was no localized avalanche effect. While both the photocurrent\nand dark current increased, this was primarily due to the high electric field at the tips\nof the Al NTs, which applied a high voltage to the P+ layer of the device, similar to the\neffect of increasing the reverse bias.\nIn this paper, we further investigate the application of MHs, as well as their surface\nplasmonic resonance properties and lightning rod effect, to enhance the localized\navalanche of the device, enabling higher avalanche gain at lower biases. In summary,\nthis study primarily focuses on the impact of Al NTs on device performance based on\nthe MH structure. We have discussed the influence of MHs on device performance in\nthe main text and highlighted this discussion accordingly. Regarding your suggestion\nto merge Figure 2(a) and Figure S3, we selected the best-performing 4 μm devices from\ndifferent types of devices as representatives to showcase their photocurrent, dark\ncurrent, and gain.\nAccording to your comment, we have revised the main text of this section on page\n9 of the manuscript. The revised part is as follow:\n“Our previous work investigated the impact of metal holes (MHs) on device\nperformance and conducted a detailed analysis of how MH size affects device\nperformance. Under the condition of maximizing the device's photocurrent, we\ndetermined the optimal MH size to be 4 μm. When the MH diameter is less than 4 μm,\nthe photocurrent increases with the increase in MH size. However, when the MH size\nexceeds 4 μm, the photocurrent decreases with the increase in MH size44,45. In this study,\nwe further investigated the individual impact of aluminum nanotubes (Al NTs) on\ndevice performance by characterizing the photocurrent, dark current, gain, and spectral\nresponse of devices incorporating Al NTs but no MHs (Figs. S2–S4, S6). Our results\nreveal that devices with Al NTs (but no MHs) exhibit no localized avalanche effect.\nThe observed increase in both photocurrent and dark current primarily stems from the\nstrong electric field at the Al NT tips, which effectively elevates the voltage applied to\nthe device’s P+ layer analogous to enhancing the reverse bias.\nThe electric field is a crucial factor in determining carrier collection and\nmultiplication within APDs. Therefore, a theoretical simulation based on finite element\nanalysis (FEA) was conducted using TCAD to investigate the electric field distribution\nin the absence of illumination (Figs. 3(a) and 3(b)). The bulk electric field distribution\nfor the APDs with different MH sizes (Fig. 3(a)) indicates that a complete depletion\nlayer is formed at the junctions for devices with 4 μm MHs and Al NTs. In contrast, the\nintrinsic i-layer of APDs with 8 μm and 10 μm MHs and Al NTs is only partially\ndepleted. The undepleted regions serve as recombination centers, resulting in reduced\ncarrier collection during avalanche events, which explains why the APDs with 4 μm\nMHs and Al NTs exhibit superior performance in terms of gain, detectivity, and\navalanche voltage (Figs. 2(b) and 2(c)).”\n2. Similarly to what noted above, there seems to be no experimental\ncharacterization of what effect the spacing between Al NT has on performance, as\nhinted by the simulations (line 194).\nAnswer: Thank you for your comment. Controlling the spacing of Al NTs is indeed a\nsapiential idea to study their impact on the avalanche effect. However, there are\nsignificant challenges in achieving uniformly small spacing of Al NTs (several\nnanometers) on the device at the moment.\nFirst, the designed spacing of Al NTs in this study is approximately 80 nm,\nachieved using polystyrene (PS) beads with a diameter of 260 nm, representing the\nsmallest size we can currently achieve with high reproducibility. To obtain uniform\nspacing below 80 nm, smaller PS beads would be required. However, arranging such\nsmaller beads into a single-layer close-packed template poses significant challenges and\nremains practically unattainable at this stage.\nSecond, due to the difficulty in achieving perfect uniformity when arranging PS\nbeads into a single-layer template, the resulting Al NTs exhibit slightly reduced spacing,\nas demonstrated in Fig. 3(c). To further investigate the influence of Al NT spacing on\nthe device's avalanche effect, we employed simulation methods. The results revealed\nthat spacing between Al NTs ranging from 10 to 80 nm can induce resonance effects.\nFurthermore, the lightning-rod effect, as discussed earlier, initiates localized avalanches,\nand the field enhancement caused by resonance between Al NTs further expands the\nlocalized avalanche region.\nIn the future, we plan to explore additional methods to prepare PS bead templates\nwith smaller spacing. While this remains a challenging task, we remain optimistic that,\nthrough continuous efforts and accumulated experience, it will eventually be achievable.\n3. I have a particular issue with Fig 2c and 2d. The specific detectivity was invented to\nexpress the quality of a specific bulk material platform for photodetection, and cannot\nbe freely applied to dimensionally-structured materials without specific caveats [Wang,\nF., Zhang, T., Xie, R. et al. How to characterize figures of merit of two-dimensional\nphotodetectors. Nat Commun 14, 2224 (2023)]. The authors fail to mention what exact\nnumbers were used to calculate the detectivity, in terms of responsivity, dark current\nand area. In particular, I suspect that the authors assumed an extremely small\nphotosensitive area in their calculations, which is a conceptual mistake, as this is\nequivalent to discarding most of the incident light to be detected. In my opinion, the\narea used here should be the pitch of one square pixel in Fig. 1a. This will give a real\nestimation of how good the array is at detecting incident light (from the reference above:\n“for plane array devices, the entire device tiling the plane needs to be regarded as the\noptical area”). Otherwise, the authors may use a smaller area if they demonstrate a\nmeasurement of the performance of the array with MH array, which is capable of\nfocusing the incident light onto an area smaller than the pixel size. I suggest that the\nauthors specify the numbers used in their calculation, and add other performance\nmetrics, such as internal and external quantum efficiency (the latter based on the total\npixel area), which give a better indication of the useful performance of the detector.\nThis is particularly important as plasmonic enhancement is known to introduce\nadditional loss [Khurgin, J. How to deal with the loss in plasmonics and metamaterials.\nNature Nanotech 10, 2–6 (2015)], and it’s necessary to estimate whether this strategy\nis worthwhile and provides a net improvement despite the plasmonic loss.\nFig. 2 (c)The corresponding detectivity with the wavelength range from 200 nm to 400\nnm for the APDs with and without Al NTs at 10 V reverse bias. The inset shows detectivity\nfrom 260 nm to 300 nm.\nAnswer: Thank you for your comment. First, when measuring relatively low dark\ncurrents, there are lots of the fluctuations. At the 10 V point, the value just fluctuated\nbelow 1×10-14 A. We should consider the overall stable trend of the dark current.\nTherefore, we recalculated the detectivity based on the stable dark-current value, as\nshown in the above figure:\nThe specific expression for normalized detectivity is provided in the\nsupplement D* = R×√ A , which represents the photo-detection capability of the\n2qId\noptoelectronic device and is correlated with the device's responsivity, dark current, and\nactive area. In the \"Design and Experiment\" section of the article, the single square\npixel is 200 μm × 200 μm as shown in Figure 1(a), and the dark current I-V curve of\nthe device is shown in Figure S4 in the supplementary material. Moreover, the spectral\nresponse is presented below and has already been incorporated into the supplementary\nmaterial, which includes the device's responsivity and quantum efficiency. In summary,\nwith the photosensitive area, dark current, and responsivity of the device, the detectivity\ncan be obtained in Figures 2(c) and (d).\nFor example, for the 4 μm device at 280 nm at 10V, its responsivity R is 0.129\nA/W, the dark current I is 5.0×10-14 A, and the device area is 200 μm × 200 μm. Thus\nd\nthe normalized detectivity D* is 2.0×1013 Jones. The above-mentioned content has been\npresented in the main text and highlighted.\nFig. S6. Spectral response and quantum efficiency graphs of APD devices with MHs\nwithout Al NTs, with MHs with Al NTs, and without MHs with Al NTs, under 10 V reverse\nbias.\nAccording to your comment, we have revised the main text of this section on page\n6 of the manuscript. The revised part is as follow:\n“From the spectral response data, the 4 μm MH device without Al NTs showed\npeak responsivity of 0.133 A/W at 280 nm at 10 V (58.9% External Quantum Efficiency\n(EQE)) as shown in Fig. S6, while the Al NT-equipped 4 μm MH device reached 0.129\nA/W (57.2% EQE). 42.8% of the incident photons do not contribute to the generation\nof photogenerated carriers. This proportion accounts for light reflection, carrier\nrecombination due to defects, and field enhancement. Reflection spectrum testing, as\nshown in Fig. S13, indicates that the reflectivity at 280 nm is approximately 16.0%.\nTherefore, the photons contributing to field enhancement account for less than 26.8%.\nSimilarly, 8 μm and 10 μm devices with Al NTs exhibited lower EQE values due to\npartial light reflection by Al NTs. Compared to 4 μm devices, the reduced responsivity\nand EQE in larger MH devices stem from incomplete depletion of lateral electric fields,\nlowering carrier collection efficiency. Under Al NT and MH-induced local avalanche,\nthe 4 μm MH device achieved 3.35×10-4 A photocurrent with EQE of 2,374,473% at\nFurthermore, device detectivity was evaluated across wavelengths (Fig.2(c)). The\n4 μm MH devices with Al NTs achieved peak detectivity of 2.0×1013 Jones at 280 nm\nunder a reverse bias of 10 V.”\n4. The authors should provide a clearer explanation of why the presented architecture\nallows to avoid the need for quenching circuits: is this because the devices are operated\nat sub-breakdown voltages? If this is the case, what is the advantage compared to\noperating conventional detectors at sub-breakdown voltages (say devices without Al\nNT at 50 V)? The sentence in lines 113-115 “The reduction in avalanche voltage offers\nsignificant advantages, particularly in preventing instantaneous breakdown and\nsafeguarding the device from catastrophic damage” is unclear or misleading: if the\navalanche voltage is lower, it is typically easier to trigger breakdown and not harder.\nAnswer: Thank you for your insightful comment. The detection of individual\nphotons, which inherently produce weak signals, necessitates the use of APD devices\noperating in Geiger mode. This mode involves applying a high voltage to create an\ninternal electric field near the bulk avalanche breakdown threshold, thereby achieving\nsignificant gain. However, the detectors in Geiger mode requires a quenching circuit to\ndissipate the high electric field to prevent breakdown.\nIn this study, high gain has been achieved in the detectors through stable and\nrepeatable local avalanche at lower voltages avoiding devastating bulk avalanche\nbreakdown. This approach not only significantly reduces the avalanche voltage but also\nprotects the devices from breakdown, which eliminate eliminating the need for a\nquenching circuit. The long-term stability and repeatability of the devices are\ndemonstrated in Fig. S5.\nAccording to your comment, we have revised the main text of this section on page\n7 of the manuscript. The revised part is as follow:\n“In this study, high gain has been achieved in the detectors through stable and\nrepeatable local avalanche at lower voltages avoiding devastating bulk avalanche\nbreakdown. This approach not only significantly reduces the avalanche voltage but also\nprotects the devices from breakdown, which eliminate the need for a quenching circuit.\nThe long-term stability and repeatability of the devices are demonstrated in Fig. S5.”\n5. the schematic in Fig. 4d is a simple representation of any avalanche process, without\nand specific relation to the presented devices (e.g. local avalanche, field enhancement),\nand I believe fails to capture the complex physics in action in these devices. In fact, the\nincident photons that provide a local field enhancement as shown in Fig. 3c do not\ncontribute to the photo carrier generation. To investigate this, one should put a monitor\nplane in the FDTD simulation, situated a few 10s nm inside the substrate underneath\nthe Al NT, and compare the transmitted number of photons vs the incident ones: this\nportion is the one contributing to photo carrier generation. The authors should\nimplement and discuss this model.\nFig.4 (d) band diagram of the APD with MHs and Al NTs under the condition of\nillumination.\nFig. S11. Simulation diagrams of the electric field inside the device under different inter\nspacing(10 nm、20 nm、30 nm and 80 nm) conditions of Al NTs by COMSOL. When the\ninter-spacing between Al NTs is 10 nm, 20 nm, 30 nm, 80 nm, and for the device without Al\nNTs, the maximum electric fields within the devices are 4.84 MV/cm, 3.85 MV/cm, 3.66 MV/cm,\n1.64 MV/cm, and 1.06 MV/cm, respectively.\nAnswer: Thank you for your comment. Below Figure 4(d) illustrates a schematic of\nthe localized avalanche phenomenon, where it can be observed that carrier collision\nionization occurs on both conduction band and valence band. This indicates that\navalanche takes place at the edges of the MHs, whereas the remaining regions remain\nquiet. Figure S11 depicts the effect of varying inter-spacing between Al NTs on the\ninternal electric field of the device simulated by COMSOL. On one hand, it is evident\nthat devices with Al NTs exhibit a significantly stronger internal electric field compared\nto those without Al, with the maximum field strength reaching 4.84 MV/cm at a spacing\nof 10 nm. Additionally, it is observed that the maximum internal electric field within\nthe device increase as the spacing between Al NTs decrease. This increase is primarily\ndue to the enhanced coupling effect that occurs between closely spaced Al NTs, which\nresults in a stronger electric field.\nFig. S12. (a) The distributions of hole and (b) electron concentration within the device at 10V\nreverse bias.\nFig. S13. The reflection spectrum of the device with MH and Al NTs.\nTo better comprehend the carrier concentration within the device, we simulated\nthe spatial distributions of hole and electron concentrations, as illustrated in Fig. S12.\nThe results reveal that in regions with high electric fields, the depletion of the electric\nfield is more pronounced, leading to an increased electron concentration. Furthermore,\nthe contribution of incident photons to carrier generation and field enhancement can\nbe analyzed through photocurrent and quantum efficiency. To elaborate, the\nphotocurrent I is measured as I =7.6×10-9 A (@10 V/280 nm/5.89×10-8 W), with\nph ph\nthe elementary charge q = 1.6×10-19 C, and a quantum efficiency η= 57.2%. Based on\nthese parameters, we can perform the following calculations. First, we calculate the\nnumber of photogenerated carriers produced within 1 second: N = I * t / q = 4.75×1010,\nph\nwhich corresponds to 47.5 billion electron-hole pairs. Subsequently, we determine the\nnumber of incident photons M, where M = N / η = 8.3 × 1010. In summary, 42.8% of\nthe incident photons do not contribute to the generation of photogenerated carriers. This\nproportion accounts for light reflection, carrier recombination due to defects, and field\nenhancement. Reflection spectrum testing, as shown in Fig. S13, indicates that the\nreflectivity at 280 nm is approximately 16.0%. Therefore, the photons contributing to\nfield enhancement account for less than 26.8%, corresponding to fewer than 2.3×1010\nphotons.\nAccording to your comment, we have revised the main text of this section on page\n11 of the manuscript. The revised part is as follow:\n“To further investigate the internal electric field distribution, we conducted\nCOMSOL simulations on devices with varying Al NTs spacings, as illustrated in Fig.\nS11. The simulation results demonstrate unequivocally that devices incorporating Al\nNTs produce significantly stronger internal electric fields compared to Al-free devices,\nachieving a maximum field strength of 4.84 MV/cm at a spacing of 10 nm. Furthermore,\nthe simulations reveal an inverse correlation between Al NT spacing and the maximum\ninternal field strength. As the spacing increases, the field intensity diminishes. This\nphenomenon can be attributed to the enhanced coupling effects observed in closely\nspaced Al NTs, which serve to amplify the local electric field. These findings\nconclusively demonstrate the profound impact of Al NT spacing on device\nperformance.”\nAccording to your comment, we have revised the main text of this section on page\n6 of the manuscript. The revised part is as follow:\n“42.8% of the incident photons do not contribute to the generation of\nphotogenerated carriers. This proportion accounts for light reflection, carrier\nrecombination due to defects, and field enhancement. Reflection spectrum testing, as\nshown in Fig. S13, indicates that the reflectivity at 280 nm is approximately 16.0%.\nTherefore, the photons contributing to field enhancement account for less than 26.8%.”\n6. The sentence at lines 217-220 “This increase is attributed to the acceleration of\nphotogenerated carriers within the space-charge region at higher reverse bias,\nnecessitating a longer response time. Moreover, both Tr and Tf in devices with Al NTs\nincreased by approximately 10% compared to devices without Al NTs” sounds counter-\nintuitive, as the higher voltage will accelerate charges faster. In fact, I suspect this\nincrease in response time is due to the higher current changing the dynamic\nresistance and hence the RC of the device, as evidenced by the fact that the same increase is also registered for devices\nwith Al NT at the same voltages. If the authors disagree, they should provide an objective argument for their claims.\nAnswer: Thank you for your insightful feedback. We agree with your observations\nand would like to provide more detailed explanation.\nFrom the spectral response diagram, it is evident that under a reverse bias of 10 V,\nthe device incorporating Al exhibits higher light reflection compared to the device\nwithout Al. This increased reflection leads to a reduction in photocurrent. Consequently,\nwe can infer that the dynamic resistance of the Al-based device is higher. According to\nthe frequency formula for an RC oscillation circuit, f = 1/2πRC, the frequency f of the\ndevice with Al is lower, which results in a longer response time T = 1/f.\nFurthermore, the overall capacitance of the device plays a crucial role in\ndetermining its response speed. The device with Al introduces an additional parallel\ncapacitance between the device and the Al nanoparticles, which increases the overall\ncapacitance compared to the device without Al. This increase in capacitance further\ncontributes to a longer response time.\nConsidering the both factors—higher dynamic resistance and increased\ncapacitance—we can comprehensively explain why the device with Al exhibits longer\nresponse times.\nAccording to your comment, we have revised the main text of this section on page\n12 of the manuscript. The revised part is as follow:\n“First, from the spectral response data, we observe that under 10 V reverse bias,\nthe Al-containing device exhibits greater light reflection, resulting in lower\nphotocurrent compared to the Al-free device. This suggests higher dynamic resistance\nin the Al-containing device. Following the RC oscillation circuit frequency formula (f\n= 1/2πRC), the reduced frequency (f) in Al-containing devices consequently yields\nlonger response times (T = 1/f). Additionally, the frequency calculation reveals that\ntotal device capacitance impacts response speed. The Al-containing device\ndemonstrates additional parallel capacitance between the device and Al nanoparticles\nrelative to Al-free devices, increasing overall capacitance and consequently response\ntime. Together, these factors account for the prolonged response times observed in Al-\ncontaining devices. Additionally, response speed may be influenced by the transit time\nof carriers, the drift current and the diffusion current within the device.”\n7. finally, I believe the quality and presentation of the figures graphics can be\nsignificantly improved: for starter, the largest fonts in several figures are around ten\ntimes larger than the smallest in the same figures. Fig. 1a and 1b lack scale bars, and\nsome of the numbers in Fig. 3 are not explained in the caption. The caption of Fig 2b\nmentions “statistical comparison”, but no statistics is shown or mentioned in the figure\nitself: I guess the bar plots are the average of some number of devices, but can the\nauthors specify how many devices, how is this average obtained and insert the\ncorresponding error bars? These are the minimum necessary improvements, but there\nare several more that can be implemented.\nAnswer: Thank you for your comment. We have revised all the figure legends\naccording to your request. To be honest, due to the inability to perfectly control the\nuniformity of the PS (polystyrene) sphere template arrangement, there may be some\nvariability in the size and spacing of the Al NTs on each device's surface. Therefore,\nwhile each device experiences a local avalanche effect, not many avalanche devices can\nachieve a gain of 104. For devices with different MH sizes, we tested the photocurrent\nand dark current of over 20 individual devices, and an error analysis histogram is\npresented in Fig. 2(b). It can be observed that not all 4 μm devices exhibit an avalanche\nonset voltage as low as 14.5 V, but they are all below the avalanche voltage of traditional\nAPDs. This is primarily due to the non-uniform distribution of Al NTs. Similarly, the\ngain of the devices varies from 103 to 104. In the future, we will further optimize the\ntechnology to achieve better uniformity.\nAccording to your comment, we have revised the main text of this section on page\n6 of the manuscript. The revised part is as follow:\n“We also tested the dark currents and photocurrents of several devices with 4 μm,\n8 μm and 10 μm MHs incorporating Al NTs and calculated their avalanche onset\nvoltages and maximum avalanche gains, with error analysis histograms shown in Fig.\n2(b). The 4 μm MH devices exhibited smaller onset voltage fluctuations overall, while\n8 μm and 10 μm devices showed larger fluctuations, primarily related to Al NT\ndistribution within the MHs and varying degrees of local avalanche enhancement.\nAdditionally, despite gain fluctuations, 4 μm MH devices consistently achieved higher\ngains than 8 μm and 10 μm devices, reaching up to 10,556 times, mainly because their\nlateral region could be fully depleted, creating larger local avalanche regions.”\nFig. 2 (b) Histograms of error analysis for the avalanche breakdown voltage\n(Va) and gain of APDs with Al NTs and MHs of different diameters (4 μm, 8 μm,\nand 10 μm)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Local Avalanche Photodetectors Driven by the Lightning-Rod Effect and Surface\nPlasmon Excitations by Fu et al.\nThe authors have comprehensively addressed all the concerns raised by the\nreviewers. In light of this, the manuscript may be accepted for publication.", "reviewer_2": "I commend the efforts of the authors and recognize that the quality of the manuscript has substantially improved. However,\nthere is still a key unsolved issue, which I believe to be fundamental to the validity of the manuscript:\n- the main issue is with the answer to point 3 of reviewer#2 which is incomplete at best: the calculations shown are still\nmissing a key factor, which is the incident light power that is used in calculating the responsivity values. Just extracting from\nthe answer to point 5, 58.9 nW is used: is this power entirely focused inside the 4-µm MH or over the entire 200x200 µm\npixel? I suspect that this value is obtained from the light incident over a large area of a few mm beam size, normalized to the\narea of the 4-µm MH (12.6 10^-12 m^2), which is consistent with this number being later used for the EQE calculation.\nThis is a wrong procedure because this area is not the same utilized in the detectivity calculation (i.e. 200x200 µm^2, as\nmentioned by the authors). Since the authors do not provide any details on the experimental setup, it is hard to infer what\nnumbers were used in the calculations. The best practice would be to: 1. Describe the setup (e.g. “a source with __ mW total\npower was focused on a ___ m^2 area, resulting in a power ___ W incident over the 200x200 µm^2 pixel area”); 2. Report\nthe numbers used for both the responsivity and the detectivity calculations.\nOther comments:\n- the discussion and calculations with specific numbers used in the answers to point 2 of reviewer#1 and point 3 and 5 of\nreviewer#2 should be added to the supplementary\n- the following paragraph on the statistics in figure 2(b) should be added to the text or supplementary “To be honest, due to\nthe inability to perfectly control the uniformity of the PS (polystyrene) sphere template arrangement, there may be some\nvariability in the size and spacing of the Al NTs on each device's surface. Therefore, while each device experiences a local\navalanche effect, not many avalanche devices can achieve a gain of 10^4. For devices with different MH sizes, we tested\nthe photocurrent and dark current of over 20 individual devices, and an error analysis histogram is presented in Fig. 2(b). It\ncan be observed that not all 4 μm devices exhibit an avalanche onset voltage as low as 14.5 V, but they are all below the\navalanche voltage of traditional APDs. This is primarily due to the non-uniform distribution of Al NTs. Similarly, the\ngain of the devices varies from 10^3 to 10^4.”"}, "author_response": "Dear Reviewers:\nThank you for your letter and the reviewers’ comments on our submitted\nmanuscript entitled “Local Avalanche Photodetectors Driven by Lightning-rod\nEffect and Surface Plasmon Excitations”. These comments are very constructive\nand helpful to our paper and future research. We have studied comments carefully and\nhave made corrections which we hope meet with approval. The detail responses to the\nreviewers’ comments are as follows:\nReviewer #1 (Remarks to the Author):\nLocal Avalanche Photodetectors Driven by the Lightning-Rod Effect and Surface\nPlasmon Excitations by Fu et al.\nThe authors have comprehensively addressed all the concerns raised by the\nreviewers. In light of this, the manuscript may be accepted for publication.\nAnswer: Thanks for your comments. We are delighted to receive this news and\nsincerely appreciate the time and effort spent by you and the reviewers in evaluating\nour work.\nReviewer #2 (Remarks to the Author):\nI commend the efforts of the authors and recognize that the quality of the\nmanuscript has substantially improved. However, there is still a key unsolved issue,\nwhich I believe to be fundamental to the validity of the manuscript:\n1.the main issue is with the answer to point 3 of reviewer#2 which is incomplete\nat best: the calculations shown are still missing a key factor, which is the incident\nlight power that is used in calculating the responsivity values. Just extracting from the\nanswer to point 5, 58.9 nW is used: is this power entirely focused inside the 4-µm MH\nor over the entire 200x200 µm pixel? I suspect that this value is obtained from the\nlight incident over a large area of a few mm beam size, normalized to the area of the\n4-µm MH (12.6 10^-12 m^2), which is consistent with this number being later used\nfor the EQE calculation. This is a wrong procedure because this area is not the same\nutilized in the detectivity calculation (i.e. 200x200 µm^2, as\nmentioned by the authors). Since the authors do not provide any details on the experimental setup, it is\nhard to infer what numbers were used in the calculations. The best practice would be\nto: 1. Describe the setup (e.g. “a source with __ mW total power was focused on a\n___ m^2 area, resulting in a power ___ W incident over the 200x200 µm^2 pixel\narea”); 2. Report the numbers used for both the responsivity and the detectivity\ncalculations.\nAnswer: Thanks for your comments. In the experiment, a light source with 5.89×10-8\nW total power(@280 nm) was focused on a circular area with a diameter of\napproximately 120 μm, resulting in a power 5.89×10-8 W incident over the 200 µm ×\n200 µm pixel area.\nFigure. S15. (a) shows a schematic diagram of the device performance\nmeasurement system described in the supplementary. The system primarily consists of\ntwo integrated parts: the optical path and the electrical circuit. The optical path,\nwhich generates and conditions the test light, is composed of a xenon lamp, an optical fibre,\nand a monochromator. The electrical measurement section is contained within an\nelectromagnetic shielding box and incorporates a probe station connected to a\n4200A-SCS semiconductor parameter analyser. The current-voltage (I-V)\ncharacteristics of the semiconductor devices were measured using the source measure\nunits (SMUs) of the analyser.\nFig. S15. (a) Schematic diagram of the device performance measurement system. (b)\nFocused light spot on the device photosensitive area (optical microscope image)\nPrior to device testing, the intensity of the ultraviolet light emitted from the\nxenon lamp was calibrated. This calibration was performed by integrating a\nUV-enhanced Si-222 standard photodetector into the system. The UV light signal,\nafter being conditioned by an adjustment objective lens, was focused onto the active\nsurface of the standard photodetector to generate a photocurrent. The calibrated\noptical power values across the UV wavelength range were then calculated from the\nknown spectral responsivity of the standard detector.\nFor instance, at a wavelength of 280 nm, the Si-222 standard photodetector\nexhibits a spectral responsivity of 0.0958 A/W. With an applied bias, a photocurrent of\n5.64×10-9 A was measured, yielding a calibrated optical power of 5.89×10-8 W.\nSubsequently, the fabricated devices were tested. As shown in Figure. S15. (b), the\nlight from the xenon lamp was coupled through the optical fibre and focused into a\ncircular spot with a diameter of approximately 120 μm. This confirms that the total\noptical power of 58.9 nW was illuminated onto the photosensitive area of the device.\nAfter aligning the light spot, the monochromator was set to a wavelength of 280 nm\nfor the measurement, from which the photocurrent-voltage (I-V) curve of the device\nwas obtained. Thus, for the 4 μm device at 280 nm at 10 V, its responsivity R is 0.129\nA/W, the dark current I is 5.0×10-14 A, and the device area is 200 μm × 200 μm. Thus\nd\nthe normalized detectivity D* is 2.0×1013 Jones. The specific calculation procedure is\ndemonstrated by the following formula:\nI 7.6×10-9 A\nph\nR= = =0.129 A/W\nP 5.89×10-8 W\nopt\nA 0.02 cm∙0.02 cm\nD*=R×√ =0.129 A/W∙√ =2.0×1013 Jones\n2qI 2×1.6×10-19 C∙5.0×10-14 A\nd\nAccording to your comment, we have revised the content of this section on page\n11 and page 12 of the supplementary files. The revised part is as follow:\n“In the experiment, a light source with 5.89×10-8 W total power(@280 nm) was\nfocused on a circular area with a diameter of approximately 120 μm, resulting in a\npower 5.89×10-8 W incident over the 200 µm × 200 µm pixel area.\nFigure. S15. (a) shows a schematic diagram of the device performance\nmeasurement system described in the manuscript. The system primarily consists of\ntwo integrated parts: the optical path and the electrical circuit. The optical path,\nwhich generates and conditions the test light, is composed of a xenon lamp, an optical fibre,\nand a monochromator. The electrical measurement section is contained within an\nelectromagnetic shielding box and incorporates a probe station connected to a\n4200A-SCS semiconductor parameter analyser. The current-voltage (I-V)\ncharacteristics of the semiconductor devices were measured using the source measure\nunits (SMUs) of the analyser.\nPrior to device testing, the intensity of the ultraviolet light emitted from the\nxenon lamp was calibrated. This calibration was performed by integrating a\nUV-enhanced Si-222 standard photodetector into the system. The UV light signal,\nafter being conditioned by an adjustment objective lens, was focused onto the active\nsurface of the standard photodetector to generate a photocurrent. The calibrated\noptical power values across the UV wavelength range were then calculated from the\nknown spectral responsivity of the standard detector.\nFor instance, at a wavelength of 280 nm, the Si-222 standard photodetector\nexhibits a spectral responsivity of 0.0958 A/W. With an applied bias, a photocurrent of\n5.64 × 10-9 A was measured, yielding a calibrated optical power of 5.89×10-8 W.\nSubsequently, the fabricated devices were tested. As shown in Figure. S15. (b), the\nlight from the xenon lamp was coupled through the optical fibre and focused into a\ncircular spot with a diameter of approximately 120 μm. This confirms that the total\noptical power of 58.9 nW was illuminated onto the photosensitive area of the device.\nAfter aligning the light spot, the monochromator was set to a wavelength of 280 nm\nfor the measurement, from which the photocurrent-voltage (I-V) curve of the device\nwas obtained. ”\nOther comments:\n2、 the discussion and calculations with specific numbers used in the answers to\npoint 2 of reviewer#1 and point 3 and 5 of reviewer#2 should be added to the\nsupplementary\nAnswer: Thanks for your comments. Based on your comments, we have added\nthe corresponding content to the supplementary files on page 4, page 5, page 6,\npage 9, page 10 respectively. The revised part is as follow:\npoint 2 of reviewer#1\n“The avalanche noise level depends on the ionization rate ratio (α /α ) and the\nN P\navalanche gain (M). For the case of hole injection, the noise level can be expressed as :\nM-1 2\nF=M[1-(1-k)( ) ]\nM\n1\n≈kM+(2- )(1-k)\nM\nwhere k=α /α , which remains constant throughout the avalanche region. For\nN P\nSiC material, the impact ionization coefficients of electrons and holes can be\nexpressed as:\n1.6\n9.96×106 V/cm\nα (E)=1.69×106 cm-1exp[-( ) ] (electron)\nN E\n1.07×107 V/cm 1.1\nα (E)=3.32×106 cm-1exp[-( ) ] (hole)\nP E\nwhere E represents the electric field intensity.\nThe avalanche electric field intensity in conventional SiC APDs is typically 3\nMV/cm. By substituting E=3 MV/cm into the equations above, we calculate that k ≈\n0.032. Consequently, the noise level in conventional devices can be expressed as:\nF=0.032M-0.968/M+1.936\nFor comparison, the local avalanche electric field intensity in our fabricated\ndevice is 1.5 MV/cm under a reverse bias of 15 V as shown in Fig. S8. We therefore\nsimulated the local avalanche electric field intensity under different reverse bias\nconditions. Since the gain is related to the reverse bias (as shown in Fig. 2a), Fig. S7\nwas obtained by curve fitting.\nThe results show that the noise level increases with avalanche gain. The\nfabricated device exhibits a lower noise level compared to the device without MH-Al\nNTs, owing to localized avalanche effects.” on page 5 and page 6 in the\nsupplementary.\npoint 3 of reviewer#2\n“The detectivity of the device shown in Figure 3(c) of the main text is\ncalculated based on the responsivity from the Supplementary Material's Fig. S6 and\nthe dark current from Fig. S4, with the specific calculation method and numerical\ndiscussion as follows:\nThe specific expression for normalized detectivity is provided in the\nsupplement D*=R×√ A , which represents the photo-detection capability of the\n2qId\noptoelectronic device and is correlated with the device's responsivity, dark current,\nand active area. In the \"Design and Experiment\" section of the article, the single\nsquare pixel is 200 μm × 200 μm as shown in Figure 1(a), and the dark current I-V\ncurve of the device is shown in Figure S4 in the supplementary material. Moreover,\nthe spectral response is presented below and has already been incorporated into the\nsupplementary material, which includes the device's responsivity and quantum\nefficiency. In summary, with the photosensitive area, dark current, and responsivity of\nthe device, the detectivity can be obtained in Figures 2(c) and (d).\nFor example, for the 4 μm device at 280 nm at 10 V, its responsivity R is 0.129\nA/W, the dark current I is 5.0×10-14 A, and the device area is 200 μm × 200 μm. Thus\nd\nthe normalized detectivity D* is 2.0×1013 Jones. The specific calculation procedure is\ndemonstrated by the following formula:\nI 7.6×10-9 A\nph\nR= = =0.129 A/W\nP 5.89×10-8 W\nopt\nD*=R×√ A =0.129 A/W∙√ 0.02 cm∙0.02 cm =2.0×1013 Jones” On page 4 and\n2qId 2×1.6×10-19 C∙5.0×10-14 A\npage 5 in the supplementary.\npoint 5 of reviewer#2\n“Below Figure 4(d) illustrates a schematic of the localized avalanche\nphenomenon, where it can be observed that carrier collision ionization occurs on both\nconduction band and valence band. This indicates that avalanche takes place at the\nedges of the MHs, whereas the remaining regions remain quiet. Figure S11 depicts the\neffect of varying inter-spacing between Al NTs on the internal electric field of the\ndevice simulated by COMSOL. On one hand, it is evident that devices with Al NTs\nexhibit a significantly stronger internal electric field compared to those without Al,\nwith the maximum field strength reaching 4.84 MV/cm at a spacing of 10 nm.\nAdditionally, it is observed that the maximum internal electric field within the device\nincrease as the spacing between Al NTs decrease. This increase is primarily due to the\nenhanced coupling effect that occurs between closely spaced Al NTs, which results in\na stronger electric field.\nTo better comprehend the carrier concentration within the device, we simulated\nthe spatial distributions of hole and electron concentrations, as illustrated in Fig. S12.\nThe results reveal that in regions with high electric fields, the depletion of the electric\nfield is more pronounced, leading to an increased electron concentration. Furthermore,\nthe contribution of incident photons to carrier generation and field enhancement can\nbe analyzed through photocurrent and quantum efficiency. To elaborate, the\nphotocurrent Iph is measured as I =7.6×10-9 A (@10 V/280 nm/5.89×10-8 W), with\nph\nthe elementary charge q = 1.6×10-19 C, and a quantum efficiency η= 57.2%. Based on\nthese parameters, we can perform the following calculations. First, we calculate the\nnumber of photogenerated carriers produced within 1 second: N = I * t / q =\nph\n4.75×1010, which corresponds to 47.5 billion electron-hole pairs. Subsequently, we\ndetermine the number of incident photons M, where M = N / η = 8.3 × 1010. In\nsummary, 42.8% of the incident photons do not contribute to the generation of\nphotogenerated carriers. This proportion accounts for light reflection, carrier\nrecombination due to defects, and field enhancement. Reflection spectrum testing, as\nshown in Fig. S13, indicates that the reflectivity at 280 nm is approximately 16.0%.\nTherefore, the photons contributing to field enhancement account for less than 26.8%,\ncorresponding to fewer than 2.3×1010 photons.” on page 9 and page 10 in the\nsupplementary.\n3、 the following paragraph on the statistics in figure 2(b) should be added to the\ntext or supplementary “To be honest, due to the inability to perfectly control the\nuniformity of the PS (polystyrene) sphere template arrangement, there may be some\nvariability in the size and spacing of the Al NTs on each device's surface. Therefore,\nwhile each device experiences a local avalanche effect, not many avalanche devices\ncan achieve a gain of 10^4. For devices with different MH sizes, we tested the\nphotocurrent and dark current of over 20 individual devices, and an error analysis\nhistogram is presented in Fig. 2(b). It can be observed that not all 4 μm devices\nexhibit an avalanche onset voltage as low as 14.5 V, but they are all below the\navalanche voltage of traditional APDs. This is primarily due to the non-uniform\ndistribution of Al NTs. Similarly, the gain of the devices varies from 10^3 to 10^4.”\nAnswer: Thanks for your comments. We have added the following text on page\n6 in the manuscript as suggested. The revised part is as follows:\n“However, to be honest, due to the inability to perfectly control the uniformity of\nthe PS (polystyrene) sphere template arrangement, there may be some variability in\nthe size and spacing of the Al NTs on each device's surface. Therefore, while each\ndevice experiences a local avalanche effect, not many avalanche devices can achieve\na gain of 104 as described in Fig. 2(b). It can also be observed that not all 4 μm\ndevices exhibit an avalanche onset voltage as low as 14.5 V, but they are all below the\navalanche voltage of traditional APDs. This is primarily due to the non-uniform\ndistribution of Al NTs. Similarly, the gain of the devices varies from 103 to 104.”"}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have addressed all points raised and concerns, and I believe the clarity and quality of the manuscript to be\nsubstantially improved: I recommend the manuscript for publication."}, "author_response": ""}]

Decision letter