High-speed Si-Ge avalanche photodiode with a gain-bandwidth product of 7564 GHz

Domain: biology
Published: 2026-03-10
Editorial outcome: major_revision

Abstract
Avalanche photodetectors are renowned for their exceptional sensitivity and high gain-bandwidth product, making them
highly promising for optical communications, quantum technologies, LiDARS, and biosensing. This paper presents a
lateral separate absorption charge multiplication silicon-germanium avalancShe photodiode designed for O-band operation.
The electric field distribution was strategically designed to minimize Edark current and enhance gain. A tapered input
waveguide and a distributed Bragg reflector were integrated to imprRove responsivity. The device achieves a dark current
of only 8.4 μA at 12.5 V reverse bias with an input optical powPer of -24 dBm and demonstrates a record-high gain-
bandwidth product of 7564 GHz. High-speed eye diagram mea surements confirm its support for 100 Gbps NRZ and 200
N
Gbps PAM4 signals, with sensitivities of -17.1 dBm and -9.6 dBm, respectively. Eye diagram validation at 200 Gbps
I
PAM4 was also conducted across eight avalanche photodiodes aligned with an eight-channel dense wavelength division
multiplexing system. E

Introduction
Avalanche photodetectors are highly valued for their high bandwidth, high gain, and compact integration, making them
widely applicable in optical communications, optical interconnects, light detection and ranging (LiDAR) systems,
quantum computing, and biosensing1-3. As artificial intelligence (AI), machine learning, and cloud computing continue
to expand rapidly, the demand for computational power and high-speed data transmission in large-scale data centers and
high-performance computing (HPC) is growing exponentially4-6. This surge has intensified the need for transceivers with
higher bandwidth density. However, current optical link and power budgets are struggling to keep pace with these
escalating demands4. As a pivotal component in optical receivers, APDs play a crucial role in enhancing link performance
by providing internal gain, which helps reduce power consumption and optimize signal integrity. These characteristics
are essential for advancing optical receiver systems toward higher bandwidth and lower power operation7,8.

Gain bandwidth product (GBP) is a key metric in evaluating APD performance in high-speed optical communication
and is strongly influenced by the impact ionization coefficient ratio. While most III-V materials exhibit an impact
ionization coefficient ratio in the range of k ≈ 0.1-19,10 , silicon (Si) stands out with an exceptionally low ratio of k ≈
0.0211,12. However, Si’s cutoff wavelength of 1100 nm limits efficient photo-carrier generation in fiber communication
wavelengths, necessitating alternative materials. Germanium (Ge) is a preferred material for silicon-based PDs due to its
superior absorption efficiency at fiber communication wavelengths and higher carrier mobility compared to Si. However,
the impact ionization coefficient ratio of Ge (k ≈ 1)13,14 is significantly higher, potentially leading to increased noise. To
leverage the high absorption of Ge while benefiting from the low ionization coefficient ratio of Si, researchers have
proposed APDs with separate absorption charge multiplication (SACM) structures15. Fabricated on a standard silicon-
on-insulator (SOI) platform, the Si-Ge APD offers higher gain, excellent sensitivity, and superior integration density,
making it an optimal choice for high-performance optical receivers16,17.

In current SACM structure research, vertical SACM-type APDs require metal electrode deposition on the Ge
surface18,19. However, this approach induces Fermi-level pinning, degrading the ohmic contact and increasing contact
resistance. Additionally, the metal presence on the Ge surface introduces more dangling bonds, leading to higher leakage
current, which in turn reduces device responsivity and increases noise. Moreover, metal contacts facilitate additional
photogenerated carrier recombination, further compromising optoelectronic performance. In contrast, lateral SACM Si-
Ge APDs mitigate these challenges while also simplifying fabrication. Dai et al. proposed a series of lateral SACM Si-
Ge APDs, demonstrating a significant GBP improvement from 615 GHz20 to 1440 GHz21, and later to 3036 GHz22. This
progression has provided valuable insights into GBP enhancement strategies. However, this design still exhibits relatively
high dark current at the operating voltage, which can hinder the achievement of higher sensitivity and gain. A recent
study reported an improved lateral SACM Si-Ge APD with a bandwidth of 53 GHz and a GBP of 1033 GHz23. The high
bandwidth was achieved by incorporating a large inductor (~700 pH) into the APD electrode through inductive peaking.
However, in the SACM structure, the multiplication gain and GBP remain constrained by the Ge-Si doping contact due
to the high dark current resulting from significant tunneling currents at high voltages. Additionally, this approach may
introduce challenges in impedance matching with the transimpedance amplifier S(TIA) and signal transmission. Currently,
researchers continue exploring various strategies to further enhance APSD GBP for higher-speed and higher-gain
detection24. However, achieving a significantly higher GBP remains a crEitical and challenging research direction.

In this work, we present a high-speed Si-Ge APD with a reRcord-breaking GBP of 7564 GHz, which exceeds
previously reported values. Utilizing a lateral SACM structurPe, we design an APD that spatially separates the Ge
absorption region from the doped regions. By minimizing th e electric field in Ge while maintaining efficient carrier
transport and multiplication, the dark current is significantly reduced. To further enhance device responsivity, we
incorporate a tapered waveguide at the front end and a distributed Bragg reflector (DBR) at the rear. Experimental results
show that under a reverse bias voltage of 12.5 V, Ethe APD exhibits a dark current of 8.4 μA and achieves a maximum
GBP of 7564 GHz at an input optical power of L-24 dBm, while maintaining a low effective k value of 0.05. We evaluate
the APD performance for high-speed signals and obtain clear eye diagrams for 64 Gbps and 100 Gbps non-return-to-
zero (NRZ) signals, as well as 128 Gbps and 200 Gbps four-level pulse amplitude modulation (PAM4) signals. The APD
also exhibits high sensitivity, achieving -20.8 dBm and -17.1 dBm for 64 Gbps and 100 Gbps NRZ signals, respectively,
both of which meet the hard-decision forward error correction (HD-FEC) threshold of BER = 3.8×10−3. For 128 Gbps
and 200 Gbps PAM4 signals, the sensitivities are -14.2 dBm and -9.6 dBm, respectively, both within the HD-FEC limit.
Furthermore, we perform high-speed eye diagram measurements for 200 Gbps PAM4 signals across eight APDs, each
tuned to the specific wavelengths required for eight-channel dense wavelength division multiplexing (DWDM). This
manuscript represents a substantial extension of our previous OFC work25, expanding the study from a single-channel
device to an eight-channel APD array, and providing detailed design and analysis, along with a further systematic
investigation of excess-noise characteristics. These remarkable results highlight the immense potential of this APD for
applications in optical communications, quantum technology, LiDAR, and beyond.

Results
Device Structure and Design
Figure 1(a) presents a three-dimensional (3D) schematic of the lateral p+-i-p-n+ doped SACM Si-Ge APD, incorporating
a DBR at the rear to enhance device responsivity. The design process begins with optimizing the electric field distribution
to achieve high performance. Figure 1(b) illustrates the cross-sectional doping profile of the Si-Ge APD, featuring a non-
contact design between the Ge region and the Si-doped areas to effectively control the electric field within the Ge. To
quantitatively describe this non-contact design strategy, we optimize the doping positions on the rib waveguide, denoted
as Wp and ΔW, respectively. Additionally, thicker metal interconnects are employed to further enhance device
performance. The Ge absorption region dimensions are 9.1 μm (length) × 0.5 μm (width) × 0.26 μm (height). Given Ge's
high impact ionization coefficient, optimization efforts focus on the doping regions adjacent to the Ge layer, specifically
adjusting the widths of Wp and ΔW. The primary goal is to maximize ionization within Si while suppressing ionization
in Ge, requiring the electric field strength in Si to exceed 3×10⁷ V/m, while ensuring it remains below 2×10⁷ V/m in
Ge26,27. Additionally, to facilitate efficient carrier transport at saturation velocity within Ge, the electric field in Ge is
designed to exceed 1×10⁶ V/m 28.

The electric field design begins with optimizing the multiplication region doping width Wp to maintain a high
electric field within the multiplication region while preventing its extension into the absorption region. Figure 1(c) depicts
the electric field distribution along the black cutline of the ridge waveguide in Figure 1(b) under varying Wp conditions.
As the Wp increases, the electric field strength in the multiplication region rises, but the high electric field region
gradually shifts toward the absorption region, potentially increasing the electric field in Ge and degrading device
performance. To balance these effects, Wp is set at 225 nm. Next, ΔW is optimized to confine the electric field effectively
within the charge region. Figure 1(d) illustrates the electric field distribution along the black cutline of the ridge
waveguide in Figure 1(b) under different p+ doping width conditions, with anS inset providing a magnified view of the
localized region. If the doping position is too far from the Ge layer, the eSlectric field is not fully confined within the
charge region, potentially inducing additional current in the Si-doped arEea and increasing the device's shot noise. Based
on the above considerations, i.e., to ensure effective confinement ofR the optical field, ΔW is set to 110 nm.

To further enhance performance, graded doping is emploPyed to reduce resistance and capacitance. The p-type
doping concentrations are set at 7.1 × 1019 cm-3 (p++), 5.3 × 1018 cm-3 (p+), and 2.1 × 1017 cm-3 (p), while the n-type
doping concentrations are set at 1.0 × 1020 cm-3 (n++) and 1.0 × 1019 cm-3 (n+), respectively. Additionally, a lateral
structure is adopted to minimize light absorption by metal electrodes and reduce dark current caused by defects near the
heterojunction under breakdown voltage conditioEns. The inset in Figure 1(b) presents the simulated cross-sectional
electric field results under a reverse bias of 12.L5 V, confirming effective electric field confinement. Through optimized
doping position and concentration, together with precise control of Wp and ΔW enabled by the non-contact design, the
high electric field is effectively confined within the Si multiplication region, while the Ge absorption region is maintained
at a relatively low electric field, thereby achieving precise electric-field engineering. Under this field configuration,
avalanche multiplication is dominated by an electron-driven quasi-unipolar mechanism, in which impact ionization in Si
is maximized whereas ionization in Ge is strongly suppressed. As a result, the excess noise is effectively reduced and the
overall device performance is significantly enhanced.

The APD couples O-band optical signals from the Si waveguide into Ge. To mitigate coupling loss caused by abrupt
width changes between the Si and Ge waveguides, a tapered waveguide is employed. Traditionally, increasing Ge volume
has been a primary method for enhancing responsivity. However, as the volume of Ge increases, the carrier transit time
is prolonged, reducing the response speed and adversely impacting the device's electrical performance. To address this
issue, we integrate a DBR at the rear and incorporated a tapered waveguide at the front to confine more light within the
absorption region, thereby enabling secondary light absorption and improving overall responsivity.

The DBR structure in this device is a first-order DBR, chosen for its low scattering losses and high reflectivity. As
depicted in Figure 1(e), when the number of grating periods reaches five, the reflectivity exceeds 90%, effectively
reflecting light at the tail. The inset in Figure 1(e) illustrates that, with five grating periods, the operational wavelength
range extends from 1100 nm to 1700 nm, perfectly covering the O-band. Figure 2 presents 3D finite-difference time-
domain (FDTD) simulation results for two APD structures. The evanescently coupled optical field distributions for APDs
without and with a DBR are shown in Figures 2(a) and (c), respectively. In the absence of a DBR, significant light leakage
occurs at the end of the APD. In contrast, incorporating a DBR significantly reduces this leakage by reflecting the
unabsorbed light back into the Ge region, thereby enhancing responsivity. To fully utilize this reflective effect, the Ge
length is optimized to 9.1 μm (see Supplementary Note 1), rather than 9.0 μm or 9.2 μm, as this specific length allows
more unabsorbed light to be reflected and reabsorbed during a second pass. However, standing waves are observed in
the field distribution, mainly due to mode mismatch between the Si waveguide and Ge layer as well as reflections from
the rear DBR. Simulations indicate that the optical return loss (ORL) of this device is -22.5 dB (see Supplementary Note
2). To further verify the effect of the DBR, top-view field distributions in Figures 2(b) and 2(d) show that the inclusion
of the DBR significantly increases the optical intensity in the Ge absorption region. The inclusion of a five-period DBR
at the rear enhances the overall light confinement within the Ge layer. Additionally, a front-end tapered waveguide is
employed to minimize input reflection losses. As a result, the device's responsivity improves by 35%.

Static Measurements
Figure 3(a) shows the I-V characteristics of the fabricated Si-Ge APD under various bias voltages, both with and without
incident light, with optical power ranging from -26 dBm to -12 dBm. The grating couplers (GCs) used in this work are
characterized using a test structure consisting of a pair of GCs connected by a short straight waveguide. The measured
insertion loss is 6.0 dB/facet at 1310 nm. At a reverse bias of 3.5 V, the APD exShibits an optical internal responsivity of
0.75 A/W at unit gain, determined by comparison with a reference p-i-n PSD fabricated on the same chip and sharing
identical structural parameters (see Supplementary Note 3), includingE Ge volume, waveguide dimensions, and GC
design2,20,22,29. The responsivity of our designed APD at 1310 nm is lRower than the theoretical value (1.06 A/W) because,
to accommodate the bandwidth limitations imposed by a largeP Ge volume, part of the responsivity is intentionally
sacrificed. The dark current initially increases gradually and th en rises sharply as the voltage approaches breakdown. At
a reverse bias voltage of 12.5 V, the dark current remains low at 8.4 μA, allowing the device to achieve exceptionally
high multiplication gain. The breakdown voltage of the Si-Ge APD is 13 V, corresponding to a dark current of 100 μA20.
High multiplication gain enables high-sensitiviEty data reception in optical systems. Figure 3(b) illustrates the
multiplication gain at reverse bias voltages ranLging from 9 V to 13.5 V for incident optical power levels between -26
dBm and -12 dBm. The avalanche multiplication gain G(V) is defined as the difference between the photocurrent (I )
p
and the dark current (I ) at a given bias voltage, normalized to the corresponding value at the unity gain point V : G(V)=
d T 0
(Ip(V) − Id(V))⁄(Ip(V0) − Id(V0)) 23. The gain increases monotonically as the incident optical power decreases,
reaching its maximum at a reverse bias of 12.5 V. However, with further increases in reverse bias, the gain starts to
decrease due to the dark current rising more rapidly than the photocurrent.

Small-Signal Measurements
To characterize the optoelectronic (OE) bandwidth of the APD through small-signal measurements, the test setup is
illustrated in Figure 4(a). The optical signal emitted by the O-band laser is first directed into a lightwave component
analyzer (LCA), then sequentially passes through a handheld variable optical attenuator (VOA) and a polarization
controller (PC), before being vertically coupled into the device under test (DUT) via a GC. Figures 4(c) and 4(d) show
the physical photograph and a cross-sectional scanning electron microscope (SEM) image of the APD, respectively. The
photocurrent generated by the APD is routed back to the LCA through a bias-tee to measure the bandwidth. As shown in
Figure 3(c), when the input optical power is -24 dBm, the APD exhibits a 3-dB OE bandwidth of 8 GHz at a reverse bias
of 7 V, primarily due to incomplete depletion of the Ge absorption region. As the reverse bias voltage increases, the 3 dB
OE bandwidth gradually increases, reaching a maximum of 31 GHz at a reverse bias voltage of 12.5 V. However, with
further increases in reverse bias, the 3 dB OE bandwidth starts to decrease, primarily due to the dominance of the
avalanche buildup time in the frequency response of the APD. The inset of Figure 3(c) shows the variation of the 3-dB
OE bandwidth under input optical powers ranging from -26 dBm to -12 dBm at a fixed reverse bias voltage of 12.5 V.
As the input optical power decreases, the bandwidth gradually reduces. At -26 dBm, the bandwidth is 30 GHz,
representing a 16.6% reduction compared to -12 dBm. This behavior arises because, at lower input optical powers, the
generation and collection of photogenerated carriers slow down, limiting the APD response speed and consequently
reducing the 3-dB bandwidth. Figure 3(d) illustrates the multiplication gain and GBP characteristics at reverse bias
voltages of 9 V, 10 V, 11 V, 12 V, and 12.5 V, corresponding to five different multiplication gain points for input optical
power levels ranging from -12 dBm to -24 dBm. At an input power of -16 dBm and a reverse bias of 12.5 V, the APD
achieves a multiplication gain of 73 and a 3 dB OE bandwidth of 36 GHz, corresponding to a maximum GBP of 2628
GHz. When the input power is reduced to -24 dBm at the same 12.5 V reverse bias, the GBP of the APD increases to
7564 GHz. The inset of Figure 3(d) shows the trends of gain and bandwidth at an input optical power of -24 dBm. Both
metrics increase with bias voltage until peaking, after which they decline. This degradation is attibuted to excessive noise
and prolonged avalanche build-up time at high voltages, which deteriorate the APD’s performance.

Noise Measurement
For APDs, the sensitivity and signal-to-noise ratio primarily benefit from multiplication gain, although the shot
noise current is also amplified. To characterize and analyze the device noise, Swe employed a noise analyzer. The shot
noise current is given by: I
{2
shot}
= 2 q M2( I
photo
+ I
dark
) F(M) Δf, whSere q denotes the electron charge, M is the
multiplication gain, F(M) represents the excess noise factor, Δf is the oEperating bandwidth, I
photo
is the photocurrent at
unity gain, and I
dark
is the dark current at unity gain. The excess noRise factor of an APD can be expressed as: F(M) =
k⋅M+(1−k)⋅(2−1/M) , where k = β⁄α is the impacPt ionization coefficient ratio, with α and β being the
electron and hole ionization coefficients in the multiplication region. To evaluate the APD excess noise, we measured
and plotted F(M) as a function of multiplication gain M. The excess-noise factor F and the corresponding effective k
value were extracted at low multiplication gain, where the fitting is more reliable and less affected by measurement-
chain noise. For comparison, theoretical excess noEise factors are calculated using the local-field model for k values in
the range of 0.03-0.20, as shown in Figure 3(eL) 30. Although the GBP is evaluated at higher multiplication gain, prior
studies indicate that for APDs employing thin multiplication regions and electron-dominated avalanche multiplication,
the effective k factor does not vary sign I ificantly with the multiplication gain M31,32,33,34,35. At 1310 nm, the extracted
effective k value is approximately 0.05, which is close to that of Si (k ≈ 0.02), confirming that avalanche multiplication
predominantly occurs in the Si region of our APD. This value is also significantly lower than that of Ge APDs (k ≈ 0.2-
0.5) and conventional III-V APDs (k ≈ 0.1-1)2,36,37,38,39. Previous studies have shown that as the k value decreases, the
GBP of APDs increases2,5,13,40. This clear trend indicates that a lower k value effectively suppresses excess noise under
high multiplication gain, which is critical for achieving higher GBP in APDs41.

Eye Diagram and Bit Error Rate Measurements
To assess the signal reception quality, an eye diagram measurement was conducted. Figure 4(b) shows the
experimental setup for measuring the APD eye diagram and bit error rate (BER). An O-band tunable laser was used as
the optical source. The optical signal first passed through a PC and was then modulated by a thin-film lithium niobate
(TFLN) Mach-Zehnder modulator (MZM), which was driven by an amplified high-speed electrical signal. After a second
PC for polarization adjustment, the modulated optical signal was vertically coupled into the DUT via a GC. The
photocurrent generated by the APD was directed through a bias-tee to an oscilloscope for eye diagram and TDECQ
analysis, and then sent to a BER tester to assess the APD’s sensitivity.

The eye diagram measurements were conducted with an input optical power of -16 dBm and a reverse bias voltage
of 12.5 V, with no TIA connected to the APD. Figures 5(a) and 5(b) present the eye diagrams measured at data rates of
64 Gbps NRZ and 100 Gbps NRZ, with signal-to-noise ratios (SNRs) of 8.26 dB and 6.08 dB, respectively. Figures 5(c)
and 5(d) show the eye diagrams for data rates of 128 Gbps PAM4 and 200 Gbps PAM4, with PAM4 transmitter and
dispersion eye closure quaternary (TDECQ) values of 1.88 dB and 3.23 dB, respectively.

To evaluate the sensitivity of the APD, BER tests were conducted. The upper partion of Figure 5(e) shows the BER
performance for NRZ signals at 64 Gbps and 100 Gbps with a reverse bias voltage of 12.5 V. The corresponding
sensitivities at the HD-FEC threshold were measured as -20.8 dBm and -17.1 dBm, respectively. The lower partion of
Figure 5(e) illustrates the sensitivities for PAM4 signals at 100 Gbps and 200 Gbps under the same bias voltage, with
sensitivies of -14.2 dBm and -9.6 dBm, respectively, at the HD-FEC threshold. These results highlight the APD’s strong
competitiveness for high-bandwidth and energy-efficient data transmission applications.

Wavelength Division Multiplexing Measurements
Finally, to demonstrate the WDM capability and channel uniformity of the proposed device, we employed an eight-
channel APD array (Figure 6(a)) in combination with an external DWDM demultiplexer with a channel spacing of 200
GHz (≈1.14 nm in the O-band). In the present proof-of-concept experiment, the demultiplexed channels were
characterized sequentially. The demultiplexed wavelengths of λ₁ = 1305.92 nm, λ₂ = 1307.06 nm, λ₃ = 1308.20 nm, λ₄ =
1309.34 nm, λ₅ = 1310.48 nm, λ₆ = 1311.62 nm, λ₇ = 1312.76 nm, and λ₈ = 1313.90 nm were successfully detected.
Owing to the narrow wavelength span (<10 nm) of the eight DWDM chanSnels, the measured responsivity shows
negligible wavelength dependence. Clear eye diagrams were obtained for aSll eight channels at a data rate of 200 Gbps
PAM4, as shown in Figure 6(b), demonstrating the broadband capabilityE and good uniformity of the APD array.

Methods
Device Fabrication
The APD was fabricated on a 130-nm SOI platform, and a schematic cross-section of the device is shown in Fig. 1b. The
Si waveguide was formed by etching the 220-nm-thick top Si layer, with an etch depth of 70 nm as shown in the figure.
After waveguide etching, ion implantation was peErformed to dope the Si waveguide. Subsequently, a 260-nm-thick Ge
absorption layer was epitaxially grown on the Ldoped Si waveguide. Tungsten was then used to form ohmic contacts to
the heavily doped regions, followed by copper metallization for vias and interconnects. Finally, an Al layer was deposited
to form the contact pads.

Eye Diagram Measurements
The experimental setup for the eye-diagram measurement is shown in Fig. 4b. During the measurements, the frequency
response of the test link was calibrated and compensated using a Keysight M8194A arbitrary waveform generator (AWG),
resulting in a relatively flat frequency response of the entire electrical-optical-electrical link within a 40 GHz bandwidth
and effectively minimizing the influence of external link components. A PRBS-11 data pattern (211-1 bits) generated by
the AWG was used for all eye-diagram measurements.

The measurement setup employed a full high-speed Radio Frequency (RF) chain, including RF probes, RF cables,
bias-tees, TFLN MZMs, and RF amplifiers, all with bandwidths exceeding 67 GHz. No TIA was integrated after the
APD, and no external digital signal processing (DSP) or offline equalization was applied. Only the built-in real-time
forward equalization (5 taps) and filtering functions of the sampling oscilloscope were enabled during the measurements.
These signal-processing functions effectively compensate for frequency roll-off and mitigate inter-symbol interference,
thereby providing effective system bandwidth for the successful reception of 200 Gbps PAM-4 signals and enabling clear
eye openings, despite the intrinsic small-signal 3-dB bandwidth of the APD being below 40 GHz.

Multiplication Gain
The avalanche gain of the APD was extracted from current–voltage measurements under optical power. The avalanche
multiplication gain G(V) was defined as the difference between the photocurrent (I ) and the dark current (I ) at a given
p d
bias voltage, normalized to the corresponding value at the unity gain point V : G(V)=
0
(Ip(V) − Id(V))⁄(Ip(V0) − Id(V0)).

Data Availability
The Source Data underlying the figures of this study are available at https://doi.org/10.6084/m9.figshare.31288600.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is an interesting paper. The authors report a Ge-Si avalanche photodiode (APD) having a separate absorption, charge, and multiplication (SACM) structure. This lateral structure is similar to those reported in references 21-23. A novel feature of the present work is that the authors use a graded waveguide at the device input and a Bragg grating at the output to improve responsivity. The authors claim a record gain-bandwidth product > 8700. The receiver measurements are impressive. However, two major issues should be addressed before I can recommend publication. 1. Measurements of the gain bandwidth product require accurately determining the unity gain point. That the authors have accomplished this is doubtful. They state that the unity gain point occurs at a bias of 3.5 V. First, there is no indication of how this is determined. It certainly is not obvious from the photocurrent curves. While the photocurrent curves continue to increase with higher bias from that point, there is no proof that the authors are not observing a combination of increased responsivity from increasing the field in the Ge absorber and increasing impact ionization. It is frequently observed, however, that in APDs the low-bias portion of the photocurrent increases linearly with voltage due to the penetration of the depletion region into the photo-generation region [M. H. Woods, et al., IEEE Solid-State Electron., vol. 16, pp. 381–394.] This reduces the distance that photo-generated minority carriers travel before entering the depletion region and thus increases the injected minority carrier diffusion current. For example, it was found that the low-bias electron injection photocurrent curves in InP APDs consisted of an exponential voltage-dependent portion followed by a linear region [L. W. Cook, et al., Gallium Arsenide Related Compounds, pp. 281–286, 1981 and G. E. Bulman, et al., Solid-State Electron., vol. 25, no. 12, pp. 1189–1200, 1982]. When describing their bandwidth measurements, the authors in the present work note that the absorber is not fully depleted at 7 V bias. The most straightforward method to determine the gain at low bias is to measure the noise and carry out a two-parameter fit to k and gain. At present, the authors’ designations of gain and gain-bandwidth product are not credible. 2. The authors note that using the back grating and tapered input increases the responsivity by 35%. They also quote a unity gain responsivity of 0.75 A/W. It is difficult to believe that this is the external responsivity. What is the estimated input coupling efficiency? If these APDs are to be implemented in practical systems, knowing how much light is lost to input coupling is important. As an extreme example, a detector with an internal quantum efficiency of 100% and an input coupling efficiency of – 10 dB is not very useful.", "reviewer_2": "This paper presents a lateral separate absorption charge multiplication (SACM) silicon-germanium (SiGe) APD designed for operation in the O-band, demonstrating a dark current of ~8.4 μA at 12.5 V and a high GBP of 8784 GHz as well as high bit rate data receiving. Indeed, high GBP APD is really important and attractive for various applications. More efforts should be made to enhance the device performance when possible. There are some comments below to be addressed before it can be re-considered. 1. This paper utilizes the lateral separate absorption charge multiplication (SACM) structure (Fig. 1a and 1b). The reviewer noticed that the structure in Fig. 1b is exactly the same as that proposed in ref. 20-Optica 9, 762-769, 2022 (Fig. 1b, see below). The authors just made a left-right flip. When describing the device structure in the manuscript, the authors should cite ref. 20 and tell that they are exactly the same. Fig. 1b from this manuscript submitted to NC. Fig. 1b from ref. 20 (Optica 9, 762-769, 2022). 2. Actually, Ge has very high absorption coefficient in the O-band. Light can be absorbed completely almost when the length is 8-9μm, as demonstrated previously. Figure 1(f) shows the simulated light propagation in the structures with and without a reflector. However, the authors should give the results about the light absorption in the Ge/Si active region, and compare the difference between the designs with and without the reflector. 3. The authors should label the light propagation direction in Fig. 1(f) to be clarified. From Fig. 1(f), light is reflected back and there are notable interference patterns even in the passive input section, indicating that some light is reflected back to the input port. Such kind of reflection is detrimental for the optical link. This reflection should be double-checked. Basically speaking, it is expected to have very complete light absorption because of the light absorption is enhanced by the forward and backward propagation. 4. The authors claimed “The APD couples O-band optical signals from the Si waveguide into Ge, but conventional coupling efficiency is relatively low”. What is “conventional”? Please clarify it. As demonstrated in Fig. 1(a), there is no special structure for the connection between the passive silicon waveguide and the Ge/Si active region. 5. More details should be given for the experimental results. For example, what is the optical power for Fig. 2(c). The frequency response would become different when operating at different optical powers. Basically, when the optical power decreases, the 3-dB bandwidth might be reduced. Please show the measured 3-dB bandwidths for the cases with different powers. 6. The authors claimed “At a reverse bias of 3.5 V, the APD exhibits an optical responsivity of 0.75 A/W at unit gain, determined by comparing its responsivity to that of a reference p-i-n PD on the same chip”. Since the authors have added reflector at the rear to enhance the light absorption, please explain why the responsivity of the reference p-i-n PD is as low as 0.75 A/W, which is far less than those reported previously (e.g., 0.9~1.0A/W). 7. What is the efficiency for the fiber-chip coupling? It is one of the key for evaluating the responsivity of the PD/APD. Please check how accurately can the coupling efficiency be measured? 8. Could the author explain the strategy for reducing the dark current? Also please give an analysis about the noise. 9. The data about the GBP at the optical power of -12, -14 dBm should be given in Fig. 2(d). 10. About the bandwidths in Fig. 2(c). It can be seen that the bandwidths for the bias voltages of 9, 10, 11V are almost the same but as low as ~18 GHz. When the bias voltage increases to 12V, the 3-dB bandwidth increases rapidly to ~25 GHz. Please give an explanation about this. 11. Please show the result of the measured 3-dB bandwidth as the gain varies. 12. Please comment the polarization dependence of the present APD, which would be important for a receiver. 13. The authors claimed “At an input power of -16 dBm and a reverse bias of 12.5 V, the APD achieves a multiplication gain of 73 and a 3 dB OE bandwidth of 36 GHz, corresponding to a maximum GBP of 2628 GHz. When the input power is reduced to -24 dBm at the same 12.5 V reverse bias, the GBP of the APD increases to 8784 GHz”. Here, the authors assumed that the 3-dB bandwidth remains 36 GHz when the power decreases to -24 dBm (as shown in Table 1). Please measure the 3-dB bandwidth when the power decreases to -24 dBm. Otherwise, the GBP up to 8784 GHz should be updated with the updated bandwidth. 14. The authors claimed “we utilized an eight-channel APD array, with a channel spacing of 200 GHz …”. However, what the authors demonstrated is the chip with eight APDs without any wavelength-division-multiplexing devices. Each APD has its ow grating couplers. The channel spacing of 200 GHz is meaningless."}, "author_response": "Reply to Reviewers Comments\nManuscript ID: NCOMMS-25-17798\nTitle: A High-Speed Si-Ge Avalanche Photodiode with a Gain-Bandwidth Product\nof 7564 GHz\nOn behalf of all the authors, I would like to extend our sincere thanks to the\nreviewers for their constructive and insightful comments on our manuscript. These\nsuggestions have been highly valuable and have played an important role in improving\nthe overall quality of our work. In response to the reviewers’ feedback, we have\nthoroughly revised the manuscript and incorporated additional data to strengthen the\nvalidity of our results. Additionally, we have streamlined the abstract to better align\nwith the journal's requirements. We now submitting a revised version of the manuscript\nthat reflects all the reviewers’ recommendations.\nAs detailed below, we have provided a point-by-point response to each of the\nreviewers’ comments and suggestions. For ease of communication, the reviewers’\ncomments are presented in bold black, while our responses are shown in blue. The\ncorresponding revisions in the manuscript are marked in red. References cited in the\nresponse are formatted in black italics.\nOnce again, we sincerely appreciate your positive evaluation and the valuable\nsuggestions that have contributed to enhancing the quality of our manuscript.\nReviewer 1\n1. Measurements of the gain bandwidth product require accurately determining\nthe unity gain point. That the authors have accomplished this is doubtful. They\nstate that the unity gain point occurs at a bias of 3.5 V. First, there is no indication\nof how this is determined. It certainly is not obvious from the photocurrent curves.\nWhile the photocurrent curves continue to increase with higher bias from that\npoint, there is no proof that the authors are not observing a combination of\nincreased responsivity from increasing the field in the Ge absorber and increasing\nimpact ionization. It is frequently observed, however, that in APDs the low-bias\nportion of the photocurrent increases linearly with voltage due to the penetration\nof the depletion region into the photo-generation region [M. H. Woods, et al., IEEE\nSolid-State Electron., vol. 16, pp. 381–394.] This reduces the distance that photo-\ngenerated minority carriers travel before entering the depletion region and thus\nincreases the injected minority carrier diffusion current. For example, it was\nfound that the low-bias electron injection photocurrent curves in InP APDs\nconsisted of an exponential voltage-dependent portion followed by a linear region\n[L. W. Cook, et al., Gallium Arsenide Related Compounds, pp. 281–286, 1981 and\nG. E. Bulman, et al., Solid-State Electron., vol. 25, no. 12, pp. 1189–1200, 1982].\nWhen describing their bandwidth measurements, the authors in the present work\nnote that the absorber is not fully depleted at 7 V bias. The most straightforward\nmethod to determine the gain at low bias is to measure the noise and carry out a\ntwo-parameter fit to k and gain. At present, the authors’ designations of gain and\ngain-bandwidth product are not credible.\nResponse:\nWe are deeply appreciative of your attention to our work and the valuable feedback\nyou have provided. The method you suggested for determining the unit multiplication\npoint by measuring noise is indeed viable. However, it necessitates the use of a noise\nfigure analyzer. Regrettably, our laboratory does not currently possess this instrument,\nand thus, we are unable to conduct the relevant experiments.\nAs you have pointed out, under low bias conditions, the junction region may not\nbe fully depleted, and the quantum efficiency may not reach saturation. Therefore, the\nincrease in photocurrent I with bias voltage could be attributed to the combined\nph\nincrease in both quantum efficiency and gain G, making it challenging to distinguish\nbetween these two mechanisms. Hence, accurately determining the unit gain point in\nan APD is of paramount importance.\nTo our knowledge, in the current Si-Ge material system, in addition to the method\nyou mentioned for determining the unit multiplication point, there are two other\nmethods. The first method involves estimating the unit gain point by measuring the\npoint where the second derivative of the photocurrent with respect to bias becomes zero\n[1, 2]. We measured the photocurrent at an input optical power of -12 dBm and\nperformed local amplification, with the results shown in Figure 1. From the figure, it\ncan be observed that the unit multiplication point is reached at a voltage of 3.5 V.\nThe second method is the one we employed in our initial draft: determining the\nunit multiplication point by comparing the responsivity of a PIN PD fabricated on the\nsame die and sharing identical structural parameters (such as the length, width, and\nthickness of the Ge absorption region, as well as the length and width of the Si\nwaveguide). Currently, this method has been widely accepted and recognized by many\nprior works, including Nature Photonics [3, 4], Optica [5], Optical Fiber\nCommunication Conference (OFC) [6], and European Conference on Optical\nCommunication (ECOC) [7].\nThis method is considered reliable because the responsivity of the PD is primarily\ndetermined by the length of the Ge region and the coupling area. Although doping can\ninfluence responsivity to some extent, the two devices in our comparison share exactly\nthe same heavily doped regions (in terms of concentration, area, and spacing). The only\ndifference lies in the lightly doped region, where n-type doping is replaced by p-type\ndoping. However, the influence of light doping on responsivity is minimal. Under such\nconditions, the responsivity measured from the PIN device is nearly identical to the\ninitial responsivity of the APD.\nTherefore, we believe that this method provides a reliable means of characterizing\nAPD performance. Notably, the method adopted in our initial draft is consistent with\nthose used in previous studies, suggesting that applying consistent testing and\ncharacterization methods for gain-bandwidth product comparisons is reasonable.\nFurthermore, a comparison of results from both methods yielded the same unit gain\npoint of 3.5 V, which supports the validity of our characterization approach.\nOn the other hand, to address your questions regarding gain measurement, we have\nsupplemented more detailed experimental testing and calculation methods. In the\nexperiment, we used experimental equipment such as a source meter, a probe station, a\ntunable laser, and a variable optical attenuator, with the experimental setup shown in\nFigure 2. We measured the photocurrent Iph at 1310 nm for received optical powers\nranging from -26 to -12 dBm, and simultaneously measured the dark current Id in the\nabsence of optical input. Subsequently, we calculated the multiplication gain G(V)\naccording to the following formula, that is, the ratio of the net photocurrent (Iph−Id) at\nbias V to the net photocurrent measured at the unit gain point of V :\n𝐼𝐼𝑝𝑝ℎ(𝑉𝑉)−𝐼𝐼𝑑𝑑(𝑉𝑉)\nThe gain calculation method we e𝐼𝐼m𝑝𝑝ℎp(𝑉𝑉lo0)y−e𝐼𝐼d𝑑𝑑 (𝑉𝑉i0s) widely used at present, and this\nmethod has also been used to calculate gain in numerous papers [6,8,9].\nFigure 1 shows the empirical estimation of the unit gain point, with the blue triangle\nindicating the position where the second derivative is zero.\nFigure 2 illustrates the experimental setup for the photocurrent measurement.\nreference\n1. Meier, H. T. J. Design, characterization and simulation of avalanche photodiodes. Ph.D. thesis,\nETH Zurich (2011).\n2. Lumerical. Avalanche photodetector. https://support.lumerical.com/hc/en-\nus/articles/360042454814-Avalanche-photodetector.\n3. Shi, Y. et al. Avalanche photodiode with ultrahigh gain–bandwidth product of 1,033 GHz. Nat.\nPhoton. 18, 610-616 (2024).\n4. Kang, Y. et al. Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–\nbandwidth product. Nat. Photon. 3, 59–63 (2008).\n5. Xiang, Y. et al. High speed waveguide ge/si avalanche photodiode with a gain-bandwidth product\nof 615 GHz. Optica 9, 762-769 (2022).\n6. Shi, Y. et al. Ultrafast 67 GHz Waveguide-Coupled Silicon-Germanium Avalanche Photodiode,\nin Optical Fiber Communications Conference and Exhibition (OFC), (2024).\n7. Cao, H. et al. Ultrahigh gain-bandwidth product Ge/Si avalanche photodetector assisted by\nnonuniform electric field distribution, in European Conference on Optical Communications\n(ECOC), (2024).\n8. Salih, Y. et al. Integrated avalanche photodetectors for visible light. Nat. Commun. 12, 1-8 (2021).\n9. Huang, Z. et al. 25 Gbps low-voltage waveguide Si–Ge avalanche photodiode. Optica 3, 793-798\n(2016).\nManuscript revision:\nWe have added an explanation in the first paragraph of Section 3, “Experimental\nResults”. The revised content is as follows:\nThe GC used in this work were characterized using a test structure consisting of a pair\nof GCs connected by a short straight waveguide. The measured insertion loss was 6.0\ndB/facet at 1310 nm. At a reverse bias of 3.5 V, the APD exhibits an optical internal\nresponsivity of 0.75 A/W at unit gain, determined by comparison with a reference p-i-\nn PD fabricated on the same chip and sharing identical structural parameters, including\nGe volume, waveguide dimensions, and GC design2,20,22,28.\nThe avalanche multiplication gain G(V) is defined as the difference between the\nphotocurrent (I ) and the dark current (I ) at a given bias voltage, normalized to the\np d\ncorresponding value at the unity gain point V : G(V)= (I (V) - I (V))/ (I (V ) - I (V ))23.\n0 p d p 0 d 0\nin Optical Fiber Communications Conference and Exhibition (OFC), (2024).\n2. The authors note that using the back grating and tapered input increases the\nresponsivity by 35%. They also quote a unity gain responsivity of 0.75 A/W. It is\ndifficult to believe that this is the external responsivity. What is the estimated input\ncoupling efficiency? If these APDs are to be implemented in practical systems,\nknowing how much light is lost to input coupling is important. As an extreme\nexample, a detector with an internal quantum efficiency of 100% and an input\ncoupling efficiency of - 10 dB is not very useful.\nResponse:\nWe are extremely grateful for your valuable feedback, which has been instrumental\nin enhancing the readability of our manuscript. We sincerely apologize for any\nconfusion caused by our imprecise description. The value of 0.75 A/W represents the\ninternal responsivity, which is acceptable within the range of internal responsivity. In\ncontrast, the external responsivity is 0.17 A/W, and the primary reason for the currently\nlow external responsivity is the relatively high insertion loss from the GC. The\nmeasured grating coupling loss is 6.0 dB/facet, and the detailed testing method is\ndescribed in the third paragraph. The internal responsivity of the APD presented in our\nmanuscript was obtained after calibrating for grating coupler loss.\nWe have taken note of your comment regarding the significance of coupling\nefficiency when applying APDs in practical systems. We fully acknowledge the crucial\nimpact of coupling efficiency on practical applications. However, in this paper, our\nprimary focus is on optimizing the design of a high-performance APD device. In future\nwork, we plan to develop and optimize lower-loss GCs to achieve an APD with high\nexternal responsivity.\nAs illustrated in Figure 3, the testing scheme for the GC is designed to accurately\nmeasure the coupling efficiency of the GC. Two GCs on the chip are connected via a\nstraight waveguide only 700 μm in length. At the O-band, the propagation loss of a 380\nnm-wide waveguide is approximately 2.5 dB/cm, which is negligible. Prior to testing,\nthe optical link, including components such as connecting fibers and polarization\ncontrollers, was calibrated. The measured insertion loss at 1310 nm was 6.0 dB/facet.\nFigure 3: Microscope image of the GC.\nManuscript revision:\nWe have added an explanation in the first paragraph of Section 3, “Experimental\nResults”. The revised content is as follows:\nThe GC used in this work were characterized using a test structure consisting of a pair\nof GCs connected by a short straight waveguide. The measured insertion loss was 6.0\ndB/facet at 1310 nm. At a reverse bias of 3.5 V, the APD exhibits an optical internal\nresponsivity of 0.75 A/W at unit gain, determined by comparison with a reference p-i-\nn PD fabricated on the same chip and sharing identical structural parameters, including\nGe volume, waveguide dimensions, and GC design2,20,22,28.\nReviewer 2\n1. This paper utilizes the lateral separate absorption charge multiplication (SACM)\nstructure (Fig. 1a and 1b). The reviewer noticed that the structure in Fig. 1b is\nexactly the same as that proposed in ref. 20-Optica 9, 762-769, 2022 (Fig. 1b, see\nbelow). The authors just made a left-right flip. When describing the device\nstructure in the manuscript, the authors should cite ref. 20 and tell that they are\nexactly the same.\nResponse:\nWe are extremely grateful for your thorough review of our paper and the valuable\ncomments you have provided. Regarding the issue you raised about the structural\nsimilarity between Figure 1b and the figure in Reference 20, although they may appear\nsimilar at first glance, there are actually some key differences in our design. The\nstructure in Figure 1b is not a simple left-right inversion.\nThe PIPN structure is a high-performance design that separates the absorption and\nmultiplication regions, which is widely recognized. In this paper, we have adopted a\ndifferent design strategy with the primary objective of developing a high-gain APD\ncapable of detecting low optical power. To achieve this, we focused on reducing the\nelectric field in the Ge absorption region to suppress device noise and thereby enhance\ngain performance.\nTo this end, we have optimized the following aspects: 1. The position of the p-type\ndoping region was adjusted to avoid direct contact with the Ge absorption layer,\nallowing for better control of the electric field distribution. 2. The area of the heavily\ndoped region was optimized to increase its contact with the metal electrode, effectively\nreducing the series resistance of the device. 3. The M2 metal layer was employed for\ninterconnection. Due to the greater thickness of the copper in M2, it provides lower\nresistance, which significantly improves the performance of the device.\nThese points represent the main distinctions between our structure and the one\nillustrated in Reference [20]. Through these critical design optimizations, we have\nsignificantly improved device performance. To more clearly highlight these differences,\nwe have redrawn the schematic, as shown in Figure 1. Therefore, citing Reference [20]\nfor this figure may not be necessary.\nFigure 1 Cross-sectional view of the doping distribution within the Si-Ge APD, with\nan inset showing the simulated electric field distribution under a reverse bias of 12.5 V\nManuscript revision:\nWe have added an explanation in the first paragraph of Section 2, \"Design\". The revised\ncontent is as follows:\nFigure 1(b) illustrates the cross-sectional doping profile of the Si-Ge APD, featuring a\nnon-contact design between the Ge region and the Si-doped areas to effectively control\nthe electric field within the Ge. Additionally, thicker metal interconnects are employed\nto further enhance device performance. The Ge absorption region dimensions are 9.1\nμm (length) × 0.5 μm (width) × 0.26 μm (height).\n2. Actually, Ge has very high absorption coefficient in the O-band. Light can be\nabsorbed completely almost when the length is 8-9μm, as demonstrated previously.\nFigure 1(f) shows the simulated light propagation in the structures with and\nwithout a reflector. However, the authors should give the results about the light\nabsorption in the Ge/Si active region, and compare the difference between the\ndesigns with and without the reflector.\nResponse:\nThe reported high-responsivity Si-Ge PDs mainly benefit from the relatively large\nvolume of Ge used. As shown in Table 1 below, in References 1 and 2, the larger volume\nof Ge leads to higher responsivity. Additionally, the responsivity in the C-band is\ninherently higher than that in the O-band, as explained in our response to Question 6.\nIn Reference 3, a high responsivity is achieved with a smaller volume of Ge due to the\noptimization of a novel waveguide structure with a lateral reach-through (RT) design,\nwhich, however, does not have universal applicability. Reference 4 employs a\nconventional waveguide with a responsivity of 0.64 A/W, which is a more typical value.\nReference 5, to enhance the bandwidth, a shorter Ge region was utilized, which resulted\nin a responsivity of only 0.27 A/W.\nThe APD described in our manuscript uses a relatively thin Ge layer, only 260 nm\nthick, and a relatively short length of 9.1 μm, which reasonably results in a lower\nresponsivity. Figure 2 shows the responsivity for different Ge lengths obtained using\n3D-FDTD simulations (with the Ge width and thickness consistent with those in the\nmanuscript). When the Ge length exceeds 26.7 μm, the light absorption rate surpasses\n90%, and it is challenging for Ge to achieve 100% absorption due to light leakage into\nthe silica cladding. The rationale behind choosing a smaller Ge volume is to reduce the\ntransit time of photogenerated carriers in Ge, as well as to lower its capacitance.\nAdditionally, to maximize the reflection of light after evanescent coupling, the Ge\nlength was optimized to allow unabsorbed light to couple into the Si waveguide. This\nresidual light is then reflected by the rear DBR, enabling secondary absorption in the\nGe region.\nFigure 2: Relationship between the absorption rate of light evanesce ntly coupled from\nthe Si waveguide into Ge and the length of Ge.\nTable 1: Relationship between PD responsivity and Ge dimensions.\nReference Responsivity Ge dimensions λ\n1 0.95 A/W L:8μm W:5μm H:400nm 1550nm\n2 0.95 A/W L:8μm W:5μm H:500nm 1550nm\n3 0.93 A/W L:5μm W:0.5μm H:260nm 1310nm\n4 0.64 A/W L:14.2μm W:0.5μm H: / 1310nm\n5 0.27 A/W L:5μm W:0.5μm H: / 1550nm\nFollowing your suggestion, we have included a simulation diagram of the active\nregion in our manuscript. Figure 3 shows the cross-sectional distribution of the optical\nfield in the active region of the APD. The top image depicts the optical field distribution\nwithout a reflective grating at the end, while the bottom image shows the distribution\nafter adding a Bragg reflection grating at the end. We can clearly observe a significant\nincrease in the optical field intensity, and the interference patterns formed by the\nreflected unabsorbed light at the end are more pronounced.\nFigure 3: Top-view of the Ge absorption region.\nReference\n1. Shi, Y. et al. 103 GHz germanium-on-silicon photodiode enabled by an optimized U-shaped\nelectrode. Photonics Research. 12, 1-6 (2024).\n2. Jiang, Z. et al. High-power Si-Ge photodiode assisted by doping regulation. Opt Express.\n29,7389-7307 (2021).\n3. Xiang, Y. et al. High speed waveguide ge/si avalanche photodiode with a gain-bandwidth product\nof 615 GHz. Optica 9, 762-769 (2022).\n4. Srinivasan, S. A. et al. 27 Ghz silicon-contacted waveguide-coupled Ge/Si Avalanche Photodiode.\nJ. Lightwave Technol. 38, 3044–3050 (2020)\n5.Zou, M. et al. 135 GHz Waveguide-Coupled Germanium Photodiode. In proceedings Optical\nFiber Communication Conference (OFC), 1-3 (2025).\nManuscript revision:\nWe have added a new figure at the end of the second paragraph in Section 2, \"Design\",\nalong with additional text in the fifth paragraph. The revised content is as follows:\nFigure 2 presents 3D finite-difference time-domain (FDTD) simulation results for two\nAPD structures. The evanescently coupled optical field distributions for APDs without\nand with a DBR are shown in Figures 2(a) and (c), respectively. In the absence of a\nDBR, significant light leakage occurs at the end of the APD. In contrast, incorporating\na DBR significantly reduces this leakage by reflecting the unabsorbed light back into\nthe Ge region, thereby enhancing responsivity. To fully utilize this reflective effect, the\nGe length was optimized to 9.1 μm, rather than 9.0 μm or 9.2 μm, as this specific length\nallows more unabsorbed light to be reflected and reabsorbed during a second pass. Top-\nview field distributions in Figures 2(b) and (d) further confirm that the optical intensity\nin the Ge absorption region increases markedly with the DBR. The inclusion of a five-\nperiod DBR at the rear enhances the overall light confinement within the Ge layer.\nAdditionally, a front-end tapered waveguide was employed to minimize input reflection\nlosses. As a result, the device's responsivity improves by 35%.\nFig. 2: 3D-FDTD simulation diagram of the Si-Ge APD. Cross-sectional view of optical field distributions: (a)\nwithout DBR and (c) with DBR; Top-view of optical field distributions in the Ge absorption region: (b) without\nDBR and (d) with DBR.\n3. The authors should label the light propagation direction in Fig. 1(f) to be\nclarified. From Fig. 1(f), light is reflected back and there are notable interference\npatterns even in the passive input section, indicating that some light is reflected\nback to the input port. Such kind of reflection is detrimental for the optical link.\nThis reflection should be double-checked. Basically speaking, it is expected to have\nvery complete light absorption because of the light absorption is enhanced by the\nforward and backward propagation.\nResponse:\nWe sincerely appreciate your careful review of our manuscript and the valuable\ncomments you provided. Regarding the issue you raised about the direction of light\npropagation, we have made the necessary corrections in the revised manuscript. The\nupdated results are shown in Figures 4(a) and 4(c), where the Ge absorption region is\nhighlighted with a red dashed box, as also indicated in the revised text.\nRegarding the interference issue you mentioned, it is primarily caused by reflected\nwaves and is, to some extent, unavoidable. In the case of this APD, there are two main\ncontributing factors:\n1. Mode mismatch: The PD employs evanescent coupling from a Si waveguide\ninto the Ge absorption layer. Due to the difference in effective refractive indices\nbetween the Si waveguide and the Ge-covered region, mode mismatch occurs, resulting\nin back-reflection. To address this issue, Global Foundries proposed an innovative\nsolution at the 2025 OFC Conference by optimizing the geometry of the Ge region to\nredirect the reflected light away from the incident Si waveguide, thereby reducing\noptical return losses (ORL) [1].\n2. Reflection from the DBR: The inclusion of a DBR at the end of the APD reflects\nthe portion of light that is not fully absorbed during the first pass, allowing for\nsecondary absorption. However, since Ge cannot absorb all the incident light\ncompletely, a small portion is inevitably reflected, resulting in optical reflections. A\ncase study on the Ansys official website also explains this phenomenon [2], attributing\nit to diffraction in the Si waveguide and coupling between multiple optical modes,\nwhich together contribute to the observed back-reflection.\nThe two mechanisms discussed above represent the primary sources of optical\ninterference in the detector. The resulting standing waves are mainly confined to the\ndetector structure and the incident silicon waveguide.\n1. The photodetector operates as an intensity detector, primarily responding to\noptical power through variations in photocurrent. Therefore, as long as the incident light\nis absorbed by the Ge layer, effective detection can be achieved.\n2. At the Si waveguide input, this phenomenon is known as ORL. Excessive ORL\ncan compromise the stability of the transmitter-side laser, potentially causing shifts in\nthe central wavelength and fluctuations in output power, thereby increasing the bit error\nrate (BER) of the system [4]. To mitigate these effects, the IEEE 802.3 standard imposes\nstrict ORL requirements, specifying a maximum receiver-side reflectance of -12 dB [5].\n3D-FDTD simulations of the APD structure revealed that the reflected optical\npower is less than 0.56%, corresponding to an ORL of -22.5 dB. This value is well\nbelow the threshold specified by the relevant standards, indicating that the device meets\nthe requirements for use in optical communication systems.\nDuring testing, an 8° angled fiber-to-GC coupling configuration was employed to\neffectively prevent reflected light in the Si waveguide from coupling back into the\noptical fiber probe through the GC, thereby protecting the laser source from potential\ndamage. In practice, the device exhibited sufficiently low ORL, with no observable\nadverse effects. Both small- and large-signal measurements were successful performed.\nAdditionally, a review of related studies on PDs revealed that optical back\nreflections were present in many simulation results, though this phenomenon has\nreceived limited attention. In future work, minimizing the ORL of the device will be a\nkey design objective.\nFigure 4: 3D-FDTD simulation diagram of the Si-Ge APD. Cross-sectional view of\noptical field distributions: (a) without DBR and (c) with DBR; Top-view of optical\nfield distributions in the Ge absorption region: (b) without DBR and (d) with DBR.\nreference\n1. Bian, Y. et al. Monolithically integrated high-performance Ge-on-Si PIN photodetectors with\nnearly 60 GHz EO bandwidth, 0.95 A/W responsivity, <30 nA dark current and -36 dB optical return\nloss enabled by Ge shape optimization. In proceedings Optical Fiber Communication Conference\n(OFC), 1-3 (2025).\n2. Lumerical. Germanium-on-Silicon lateral photodetector https://optics.ansys.com/hc/en-\nus/articles/360042828913-Germanium-on-Silicon-lateral-photodetector\n3. Sun, W. et al. Ultralow-LO-Power Silicon Photonic Coherent Receiver with Balanced Ge/Si\nAvalanche Photodiodes. ACS Photonics. 12, 1793-1801 (2025).\n4. Noutsios, P. et al. Optical return loss measurements and simulation of an arbitrary array of\nconcatenated reflective elements on field-installed optical links. Journal of Lightwave Technology.\n24, 1697-1702 (2006).\n5. ieee802.org/3/db/public/November-08-November-17-2021/murty_3db_01_111121.pdf\nManuscript revision:\nWe have added a new figure at the end of the second paragraph in Section 2, \"Design\",\nand have completed the revisions. The revised content is as follows:\nFig. 2: 3D-FDTD simulation diagram of the Si-Ge APD. Cross-sectional view of optical field distributions: (a)\nwithout DBR and (c) with DBR; Top-view of optical field distributions in the Ge absorption region: (b) without\nDBR and (d) with DBR.\nFigure 2 presents 3D finite-difference time-domain (FDTD) simulation results for two\nAPD structures. The evanescently coupled optical field distributions for APDs without\nand with a DBR are shown in Figures 2(a) and (c), respectively. In the absence of a\nDBR, significant light leakage occurs at the end of the APD. In contrast, incorporating\na DBR significantly reduces this leakage by reflecting the unabsorbed light back into\nthe Ge region, thereby enhancing responsivity. To fully utilize this reflective effect, the\nGe length was optimized to 9.1 μm, rather than 9.0 μm or 9.2 μm, as this specific length\nallows more unabsorbed light to be reflected and reabsorbed during a second pass. Top-\nview field distributions in Figures 2(b) and (d) further confirm that the optical intensity\nin the Ge absorption region increases markedly with the DBR. The inclusion of a five-\nperiod DBR at the rear enhances the overall light confinement within the Ge layer.\nAdditionally, a front-end tapered waveguide was employed to minimize input reflection\nlosses. As a result, the device's responsivity improves by 35%.\n4. The authors claimed “The APD couples O-band optical signals from the Si\nwaveguide into Ge, but conventional coupling efficiency is relatively low”. What\nis “conventional”? Please clarify it. As demonstrated in Fig. 1(a), there is no special\nstructure for the connection between the passive silicon waveguide and the Ge/Si\nactive region.\nResponse:\nThank you for pointing out the ambiguous description here. We sincerely\napologize for this oversight in our writing. We intended to explain that we inserted a\ntapered waveguide between two Si waveguides of different widths. Compared to a\ndirect connection using a straight waveguide, a tapered waveguide with gradually\nvarying width helps reduce additional loss caused by abrupt width transitions and the\nassociated refractive index mismatch between waveguides of different widths.\nThe introduction of a tapered waveguide is essential because, in the O-band, the\ntypical width of Si waveguides used for optical transmission ranges from 380 nm to\n410 nm. In contrast, due to standard fabrication constraints, the Ge generally requires a\nwidth exceeding 500 nm, and the process mandates that the Si waveguide fully\nencapsulate the Ge region. Consequently, the Si waveguide beneath the Ge must have\na width of at least over 500 nm. This significant width mismatch between the two\nwaveguides makes a direct connection via a straight waveguide impractical, as it would\ncause severe mode mismatch and refractive index discontinuity, resulting in increased\ncoupling loss.\nManuscript revision:\nWe have made revisions to the fifth paragraph in Section 2, \"Design\". The revised\ncontent is as follows:\nTo mitigate coupling loss caused by abrupt width changes between the Si and Ge\nwaveguides, a tapered waveguide was employed.\n5. More details should be given for the experimental results. For example, what is\nthe optical power for Fig. 2(c). The frequency response would become different\nwhen operating at different optical powers. Basically, when the optical power\ndecreases, the 3-dB bandwidth might be reduced. Please show the measured 3-dB\nbandwidths for the cases with different powers.\nResponse:\nWe are extremely grateful for your valuable feedback and for pointing out the\noversights in our work. As you correctly pointed out, the 3-dB OE bandwidth of the\nAPD does indeed decrease with a reduction in input optical power. In our tests, we\nlimited the current through the APD to within 1 mA to prevent excessive heat generation,\nwhich could damage the internal structure of the APD and potentially lead to junction\nbreakdown. When the input optical power is excessively high, the bandwidth also\ndecreases. We believe this is due to a significant space-charge effect that occurs at high\ninput powers, which in turn reduces the 3-dB OE bandwidth. As the optical power is\nreduced to a more reasonable level, the 3-dB OE bandwidth increases again. However,\nwhen the input optical power is further decreased, the generation and collection of\nphotogenerated carriers slow down, reducing the device's response speed and\nconsequently lowering the 3-dB OE bandwidth. Figure 5 shows the 3-dB OE bandwidth\nmeasured under a bias voltage of 12.5 V for input optical powers ranging from -26 dBm\nto -12 dBm, with a bandwidth reduction of 16.6%. We have promptly updated the GBP\nof the APD in both the text and the figures, as shown in Figure 7.\nFigure 5: 3-dB OE bandwidth of the APD at different input optical powers under a\nbias voltage of -12.5 V.\nManuscript revision:\nWe have made revisions to the second paragraph in Section 3, \"Design\", primarily\nfocusing on the content related to Figures 3(c) and 3(d). We have also updated Figure\n3 and its caption in the manuscript. The revised content is as follows:\nThe inset of Figure 3(c) shows the variation of the 3-dB OE bandwidth under input\noptical powers ranging from -26 dBm to -12 dBm at a fixed reverse bias voltage of 12.5\nV. As the input optical power decreases, the bandwidth gradually reduces. At -26 dBm,\nthe bandwidth is 30 GHz, representing a 16.6% reduction compared to -12 dBm. Figure\n3(d) illustrates the multiplication gain and GBP characteristics for input optical power\nlevels ranging from -12 dBm to -24 dBm. At an input power of -16 dBm and a reverse\nbias of 12.5 V, the APD achieves a multiplication gain of 73 and a 3 dB OE bandwidth\nof 36 GHz, corresponding to a maximum GBP of 2628 GHz. When the input power is\nreduced to -24 dBm at the same 12.5 V reverse bias, the GBP of the APD increases to\noptical power of -16 dBm. Both metrics increase with bias voltage until peaking, after\nwhich they decline. This degradation is attibuted to excessive noise and prolonged\navalanche build-up time at high voltages, which deteriorate the APD’s performance.\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under an\ninput optical power of -16 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under various bias\nvoltages and optical input powers. The inset shows the relationship between bandwidth and gain of the APD at an\ninput optical power of -16 dBm.\n6. The authors claimed “At a reverse bias of 3.5 V, the APD exhibits an optical\nresponsivity of 0.75 A/W at unit gain, determined by comparing its responsivity to\nthat of a reference p-i-n PD on the same chip”. Since the authors have added\nreflector at the rear to enhance the light absorption, please explain why the\nresponsivity of the reference p-i-n PD is as low as 0.75 A/W, which is far less than\nthose reported previously (e.g., 0.9~1.0A/W).\nResponse:\nThank you for your valuable comments. As partially addressed in our response to\nComment 2, we would like to provide a more detailed explanation here. After\nthoroughly reviewing the relevant literature, we found that the responsivity of PDs\noperating in the O-band typically ranges from 0.55 to 0.95 A/W [1–3]. The higher\nresponsivity you mentioned is likely associated with PDs operating in the C-band.\nTheoretically, the responsivity R of a photodetector can be calculated using the\nfollowing expression:\nR=\n𝑞𝑞𝑞𝑞\nwhere η is the quantum efficiency, q𝜂𝜂 iℎs𝑐𝑐 the electron charge, λ is the operating\nwavelength, h is Planck’s constant, and c is the speed of light. Under ideal conditions\nwith η=1, the maximum responsivity is approximately 1.06 A/W at 1310 nm (O-band)\nand 1.25 A/W at 1550 nm (C-band). Therefore, in the C-band, a total absorption rate of\njust over 72% is sufficient to achieve a responsivity greater than 0.9 A/W, whereas\nunder the same conditions, the O-band responsivity is limited to about 0.76 A/W.\nAlthough the quantum efficiency η varies with wavelength, it can be approximated\nas η=1- , where L is the length of the absorption layer and α is the absorption\ncoefficien−t𝛼𝛼 𝛼𝛼of the material. Since the absorption coefficient of Ge does not differ\n𝑒𝑒\nsignificantly between the O-band and C-band, we initially assumed η to be nearly\nidentical across the two bands. As a result, achieving responsivity above 0.9 A/W is\nrelatively straightforward in the C-band. However, in the O-band, doing so typically\nrequires a larger Ge volume, which may adversely affect the bandwidth characteristics\nof the device.\nThe exceptionally high responsivity reported in reference [20] is primarily\nattributed to their use of a novel waveguide design incorporating a resonant tunneling\n(RT) structure, which enables more efficient coupling of light into the Ge region.\nRegarding Comment 2, we simulated the absorption characteristics for different\nGe lengths and found that only when the Ge length exceeds 26.7 µm does the absorption\nrate surpass 90%. Although we introduced a DBR at the end of the waveguide to\nenhance absorption, the Ge region in our device is relatively short and has a small\nthickness and width. In the manuscript, we reported the responsivity measured in the\nO-band. Due to limitations of the designed O-band GC, we were unable to measure the\nresponsivity in the C-band. However, simulations with a laser wavelength of 1550 nm\nindicate approximately 10% increase in responsivity.\nreference\n1. Srinivasan, S. A. et al. 27 Ghz silicon-contacted waveguide-coupled Ge/Si Avalanche Photodiode.\nJ. Lightwave Technol. 38, 3044–3050 (2020).\n2. Kang, Y. et al. Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–\nbandwidth product. Nat. Photon. 3, 59–63 (2008).\n3. Shi, B. et al. 106 Gb/s normal-incidence Ge/Si avalanche photodiode with high sensitivity. In\nproceedings Optical Fiber Communication Conference (OFC), 1-3 (2020).\nManuscript revision:\nWe have added an explanation in the first paragraph of Section 3, “Experimental\nResults”. The revised content is as follows:\nThe GC used in this work were characterized using a test structure consisting of a pair\nof GCs connected by a short straight waveguide. The measured insertion loss was 6.0\ndB/facet at 1310 nm. At a reverse bias of 3.5 V, the APD exhibits an optical internal\nresponsivity of 0.75 A/W at unit gain, determined by comparison with a reference p-i-\nn PD fabricated on the same chip and sharing identical structural parameters, including\nGe volume, waveguide dimensions, and GC design2,20,22,28.\n7. What is the efficiency for the fiber-chip coupling? It is one of the key for\nevaluating the responsivity of the PD/APD. Please check how accurately can the\ncoupling efficiency be measured?\nResponse:\nTo accurately measure the coupling efficiency from fiber to chip, we designed a\nconfiguration where two GCs on the chip are connected via a straight waveguide, as\nshown in Figure 6. The waveguide length used for the connection is only 700 μm. At\nthe O-band, the propagation loss of a 380 nm-wide waveguide is approximately 2.5\ndB/cm, which is negligible. Prior to testing, the optical link, including components such\nas connecting fibers and polarization controllers, was calibrated. The measured\ninsertion loss at 1310 nm was 6.0 dB/facet.\nFigure 6: Microscope image of the grating coupler.\nManuscript revision:\nWe have added an explanation in the first paragraph of Section 3, “Experimental\nResults”. The revised content is as follows:\nThe GC used in this work were characterized using a test structure consisting of a pair\nof GCs connected by a short straight waveguide. The measured insertion loss was 6.0\ndB/facet at 1310 nm. At a reverse bias of 3.5 V, the APD exhibits an optical internal\nresponsivity of 0.75 A/W at unit gain, determined by comparison with a reference p-i-\nn PD fabricated on the same chip and sharing identical structural parameters, including\nGe volume, waveguide dimensions, and GC design2,20,22,28.\n8. Could the author explain the strategy for reducing the dark current? Also please\ngive an analysis about the noise.\nResponse:\nIn APDs, the dark current primarily consists of surface leakage current and bulk\ndark current. The bulk dark current, which passes through the high electric field in the\nmultiplication region, is also multiplied. Therefore, to reduce the dark current of an\nAPD, we need to simultaneously reduce both surface leakage current and bulk dark\ncurrent. The main causes of surface leakage current are: 1. Surface defects, such as\ndangling bonds; 2. High electric fields at the device surface, leading to increased\nleakage current. However, compared to bulk dark current, surface leakage current is\nrelatively small because the bulk dark current is multiplied. Thus, to reduce the device's\ndark current, the focus should be on reducing the bulk dark current. By reducing the\ndetector's volume and the ionization coefficient within the detector, the bulk dark\ncurrent can be effectively lowered. Therefore, in the manuscript, we have chosen Ge\nwith the smallest possible volume. Additionally, since Ge has a relatively high impact\nionization coefficient ratio k, we have employed a SACM structure, utilizing Ge for\ndetection and leveraging Si's low impact ionization coefficient ratio for avalanche\nmultiplication in Si. We have properly designed the doping location and concentration\nto keep the electric field in Ge below the ionization threshold, successfully creating an\nAPD with low dark current.\nRegarding noise, the primary sources of noise in APDs are excess noise and\nmultiplication gain, which lead to shot noise. The excess noise factor F is a function of\ngain, F(M)=k M+(1−k) (2−1/M), where k is the impact ionization coefficient ratio and\nM is the multiplication gain [1,2]. The ratio k is determined by k=β/α, where α and β\n⋅ ⋅\nare the electron and hole ionization coefficients of the semiconductor material in the\nmultiplication region [3]. Since Si has a lower k value, we have adopted the SACM\nstructure, which is advantageous for reducing excess noise.\nReference\n1. McIntyre, R. Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices.\nED-13, 164-168 (1966).\n2. Teich, M. et al. Excess noise factors for conventional and superlattice avalanche photodiodes and\nphotomultiplier tubes. IEEE J. Quantum Electron. 22, 1184-1193 (1986).\n3. Campbell, J. et al. Evolution of low-noise avalanche photodetectors. IEEE J. Select. Topics\nQuantum Electron. 28,1-11 (2022).\nManuscript revision:\nIn the manuscript, the third paragraph of Section 4 has been revised. The specific\nmodifications are as follows:\nSi-Ge APDs remain the most widely studied and promising solution for photodetection,\nowing in part to their favorable noise characteristics. In APDs, the dominant noise\nsources include shot noise associated with multiplication gain and excess noise. The\nexcess noise factor F depends on the multiplication gain M and impact ionization\ncoefficient ratio k, and is given by F(M)=k M+(1−k) (2−1/M)29,30. Germanium exhibits\nrelatively high ionization coefficients, whereas silicon has a much lower k value. By\n⋅ ⋅\nemploying the SACM structure, the dark current in Si-Ge APDs can be effectively\nsuppressed31.\n29. McIntyre, R. Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices.\nED-13, 164-168 (1966)\n30. Teich, M. et al. Excess noise factors for conventional and superlattice avalanche photodiodes\nand photomultiplier tubes. IEEE J. Quantum Electron. 22, 1184-1193 (1986).\n31. Campbell, J. et al. Evolution of low-noise avalanche photodetectors. IEEE J. Select. Topics\nQuantum Electron. 28,1-11 (2022).\n9. The data about the GBP at the optical power of -12, -14 dBm should be given in\nFig. 2(d).\nResponse:\nThank you for your meticulous review, which has been of great help in ensuring\nthe completeness of our data. We have tabulated the device data as shown in Figure 7.\nThe corresponding text has also been revised in the manuscript as follows:\nFigure 7: Gain-bandwidth product at different input optical power levels.\nManuscript revision:\nWe have revised Figure 3(d), and have also updated the relevant description in the\nsecond paragraph of Section 3, \"Experimental Results\". The revised content is as\nfollows:\nFigure 3(d) illustrates the multiplication gain and GBP characteristics for input optical\npower levels ranging from -12 dBm to -24 dBm. At an input power of -16 dBm and a\nreverse bias of 12.5 V, the APD achieves a multiplication gain of 73 and a 3 dB OE\nbandwidth of 36 GHz, corresponding to a maximum GBP of 2628 GHz. When the input\npower is reduced to -24 dBm at the same 12.5 V reverse bias, the GBP of the APD\nincreases to 7564 GHz.\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under an\ninput optical power of -16 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under various bias\nvoltages and optical input powers. The inset shows the relationship between bandwidth and gain of the APD at an\ninput optical power of -16 dBm.\n10. About the bandwidths in Fig. 2(c). It can be seen that the bandwidths for the\nbias voltages of 9, 10, 11V are almost the same but as low as ~18 GHz. When the\nbias voltage increases to 12V, the 3-dB bandwidth increases rapidly to ~25 GHz.\nPlease give an explanation about this.\nResponse:\nThank you for your meticulous review. We sincerely apologize for the data misuse\nthat occurred during data processing. We are grateful that you helped us identify this\nissue in a timely manner, and we have already made the necessary corrections.\nFigure 8: 3-dB OE bandwidth of the APD at different voltages.\nManuscript revision:\nWe have revised Figure 3(c) in the manuscript by replacing the image and updating the\nfigure caption. The modifications are as follows:\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under an\ninput optical power of -16 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under various bias\nvoltages and optical input powers. The inset shows the relationship between bandwidth and gain of the APD at an\ninput optical power of -16 dBm.\n11. Please show the result of the measured 3-dB bandwidth as the gain varies.\nResponse:\nWe are extremely grateful for your suggestion, which helps to more completely\ndemonstrate the performance of the device. To maintain consistency with the input\noptical power used for the bandwidth measurement shown in the previous figure, we\nhave selected an input optical power of -16 dBm and plotted the chart showing how the\n3 dB bandwidth varies with gain.\nFigure 9: Relationship between bandwidth and gain of the APD at an input optical\npower of -16 dBm.\nManuscript revision:\nWe have revised Figure 3(d) in the manuscript by replacing the image and updating the\nfigure caption. The modifications are as follows:\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under an\ninput optical power of -16 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under various bias\nvoltages and optical input powers. The inset shows the relationship between bandwidth and gain of the APD at an\ninput optical power of -16 dBm.\nThe inset of Figure 3(d) shows the trends of gain and bandwidth at an input optical\npower of -16 dBm. Both metrics increase with bias voltage until peaking, after which\nthey decline. This degradation is attibuted to excessive noise and prolonged\navalanche build-up time at high voltages, which deteriorate the APD’s performance.\n12. Please comment the polarization dependence of the present APD, which would\nbe important for a receiver.\nResponse:\nThe APD designed in this paper employs a GC for TE polarization mode, which\nprecludes experimental characterization. In the 3D-FDTD simulations, we converted\nthe source mode to TM polarization, resulting in a 20% decrease in responsivity. Figure\n10 shows the optical field distribution in the Ge active region, where it is evident that\nthe mode is not fully confined within the waveguide, with some leakage into the silica\ncladding, thereby reducing the responsivity.\nOur design focuses on the TE mode primarily for its application in wavelength-\ndivision multiplexing (WDM) receivers. Currently, WDM devices fabricated on Si\nphotonics platforms are polarization-sensitive due to the high birefringence of Si\nwaveguides. Therefore, before the light passes through the WDM demultiplexer, the\nmode needs to be pre-aligned to either TE or TM polarization. The TE mode is\npredominantly used on Si photonics platforms because Si waveguides have a stronger\nconfinement capability for this mode.\nThere are two common schemes for WDM receivers. The first scheme, as shown\nin Figure 11 [1], involves coupling both TE and TM polarized light into the photonic\nchip simultaneously. A polarization splitter-rotator (PSR) is then used to separate the\nTE and TM modes and rotate the TM mode to TE mode. The light is subsequently\ndemultiplexed and directed to the detector for further detection. The second scheme, as\nshown in Figure 12 [2], employs a 2D polarization splitting grating coupler to\nefficiently couple light of arbitrary polarization state and convert it entirely into the TE\npolarization mode for transmission through the waveguide. After demultiplexing, the\nlight is detected by the PD.\nAfter these processes, the polarization mode of the light detected by the PD is TE.\nTherefore, our design primarily considers the optimal performance under the TE mode.\nFigure 10: Optical field distribution in the active region under TM-polarized input\nlight.\nFigure 11: WDM receiver based on the use of a PBS and a PR.\nFigure 12: Three-dimensional schematic diagram of the SiPh WDM RX with a PSGC,\ndual-ring filters, delay lines, and bidirectional PDs.\nreference\n1. Dong, P. Silicon Photonic Integrated Circuits for Wavelength-Division Multiplexing Applications.\nIEEE J. Select. Topics Quantum Electron. 22, 370-378 (2016).\n2. Xue, J. et al. A4×112 Gb/s Ultra-Compact Polarization-Insensitive Silicon Photonics WDM\nReceiver With CMOS TIA for Co-Packaged Optics and Optical I/O. J. Lightwave Technol. 42, 6028-6035 (2024).\nManuscript revision:\nIn the manuscript, the third paragraph of Section 4 has been revised. The specific\nmodifications are as follows:\nGiven that most silicon photonic receivers are designed for TE-mode detection32,33, this\nstudy presents a lateral SACM APD specifically optimized for TE-mode detection, achieving a high gain\nof 244 and an OE bandwidth of 31 GHz.\n32. Dong, P. Silicon Photonic Integrated Circuits for Wavelength-Division Multiplexing\nApplications. IEEE J. Select. Topics Quantum Electron. 22, 370-378 (2016).\n33. Xue, J. et al. A4×112 Gb/s Ultra-Compact Polarization-Insensitive Silicon Photonics WDM\nReceiver With CMOS TIA for Co-Packaged Optics and Optical I/O. J. Lightwave Technol. 42,\n6028-6035 (2024).\n13. The authors claimed “At an input power of -16 dBm and a reverse bias of 12.5\nV, the APD achieves a multiplication gain of 73 and a 3 dB OE bandwidth of 36\nGHz, corresponding to a maximum GBP of 2628 GHz. When the input power is\nreduced to -24 dBm at the same 12.5 V reverse bias, the GBP of the APD increases\nto 8784 GHz”. Here, the authors assumed that the 3-dB bandwidth remains 36\nGHz when the power decreases to -24 dBm (as shown in Table 1). Please measure\nthe 3-dB bandwidth when the power decreases to -24 dBm. Otherwise, the GBP\nup to 8784 GHz should be updated with the updated bandwidth.\nResponse:\nWe are extremely grateful for the suggestions from the reviewer. We have actively\nupdated the relevant data in the manuscript. The bandwidth and gain-bandwidth product\ndata have been promptly revised to provide a more accurate gain-bandwidth product,\nenhancing the rigor of the article. The updated maximum gain-bandwidth product is\nManuscript revision:\nWe have updated Figure 3(d) and revised the second paragraph of Section 3 in the\nmanuscript. The modifications are as follows:\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under an\ninput optical power of -16 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under various bias\nvoltages and optical input powers. The inset shows the relationship between bandwidth and gain of the APD at an\ninput optical power of -16 dBm.\nThe inset of Figure 3(c) shows the variation of the 3-dB OE bandwidth under input\noptical powers ranging from -26 dBm to -12 dBm at a fixed reverse bias voltage of 12.5\nV. As the input optical power decreases, the bandwidth gradually reduces. At -26 dBm,\nthe bandwidth is 30 GHz, representing a 16.6% reduction compared to -12 dBm. Figure\n3(d) illustrates the multiplication gain and GBP characteristics for input optical power\nlevels ranging from -12 dBm to -24 dBm. At an input power of -16 dBm and a reverse\nbias of 12.5 V, the APD achieves a multiplication gain of 73 and a 3 dB OE bandwidth\nof 36 GHz, corresponding to a maximum GBP of 2628 GHz. When the input power is\nreduced to -24 dBm at the same 12.5 V reverse bias, the GBP of the APD increases to\noptical power of -16 dBm. Both metrics increase with bias voltage until peaking, after\nwhich they decline. This degradation is attibuted to excessive noise and prolonged\navalanche build-up time at high voltages, which deteriorate the APD’s performance.\n14. The authors claimed “we utilized an eight-channel APD array, with a channel\nspacing of 200 GHz …”. However, what the authors demonstrated is the chip with\neight APDs without any wavelength-division-multiplexing devices. Each APD has\nits ow grating couplers. The channel spacing of 200 GHz is meaningless.\nResponse:\nWe are extremely grateful for the reviewer's suggestions. We have currently used\nan external eight-channel demultiplexer to complete the wavelength-division\nmultiplexing (WDM) verification, with the aim of demonstrating the good stability of\nthe APD across different operating wavelengths. For our next steps, we plan to integrate\nan on-chip demultiplexer for a complete WDM receiver demonstration.\nManuscript revision:\nWe have made revisions to the fifth paragraph in Section 3, \"Experimental Results\".\nThe revised content is as follows:\nFinally, to demonstrate WDM capability, we employed an eight-channel APD array\n(Figure 6(a)) in combination with an external DWDM demultiplexer featuring 200 GHz\nchannel spacing. The demultiplexed wavelengths of λ₁ = 1305.92 nm, λ₂ = 1307.06 nm,\nλ₃ = 1308.20 nm, λ₄ = 1309.34 nm, λ₅ = 1310.48 nm, λ₆ = 1311.62 nm, λ₇ = 1312.76\nnm, and λ₈ = 1313.90 nm were successfully detected, and the resulting 8 × 200 Gbps\nPAM4 signals produced clear eye diagrams, as shown in Figure 6(b)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "As stated in my prior review, the primary claim in this paper is a Ge on Si avalanche photodiode with very high gain-bandwidth product. This requires an accurate determination of the gain, which in turn necessitates knowing the unity gain point accurately. I questioned the authors’ determination of the unity gain point and the response was, “The first method involves estimating the unit gain point by measuring the point where the second derivative of the photocurrent with respect to bias becomes zero [1, 2].” Reference 1 is a PhD dissertation titled, “Design, Characterization and Simulation of Avalanche Photodiodes” by Hektor Meier. There is no mention of this technique to find the unity gain point. The author does describe Monte Carlo simulations of avalanche photodiodes but there is no physical basis provided for the second derivative method. Reference 2 is the website for Lumerical software. The Lumerical model settings uses the second derivative method but there is no explanation for the basis of this approach. Lumerical is a great software tool but it is not trustworthy when applying a general rule to a broad range of materials. The authors also state that, “Currently, this method has been widely accepted and recognized by many prior works, including Nature Photonics [3, 4], Optica [5], Optical Fiber Communication Conference (OFC) [6], and European Conference on Optical Communication (ECOC) [7].” I am familiar with these references and they do not mention the second derivative method for determining the unity gain point. If the authors can provide a sound physical explanation for this gain determination technique, I cannot recommend publication because accurate determination of the gain is essential to their primary claim in this paper.", "reviewer_2": "1. About the reply to comment #1 of the second reviewer. The authors have explained some minor difference between the present design and that in ref. 20 in the response letter. They have added some sentences to describe their structural design: “Figure 1(b) illustrates the cross-sectional doping profile of the Si-Ge APD, featuring a non-contact design between the Ge region and the Si-doped areas to effectively control the electric field within the Ge. Additionally, thicker metal interconnects are employed to further enhance device performance. The Ge absorption region dimensions are 9.1 μm (length) × 0.5 μm (width) × 0.26 μm (height).” However, the reviewer believes that this difference should be clearly described in the manuscript in order to make it clear to the readers. Furthermore, the authors should tell how the difference influences the device performances with some simulation and experimental verifications. For example, the authors only mention “non-contact design” once in the manuscript (page 2). They have never discussed how this design is related with their results. What is the optimal point for the non-contact design? Since this is the main difference, it is strongly suggested to have more details about it in the manuscript. 2. About EO responses at different optical powers. The experimental results in Fig. 3 only gave the measured OE responses of the APD at various reverse bias voltages under an input optical power of -16 dBm. However, the highest GBP was achieved at the optical power of -24 dBm. It is definitely necessary to show the measured EO responses at -24 dBm. More discussions should be given about the bandwidth reduction as the optical power decreases. 3. The GBP is the most important result considered in this paper. The authors should give more details in Fig. 3(d). For example, all data for different voltages should be given so that the readers can better understand the results. 4. The authors mentioned “To fully utilize this reflective effect, the Ge length was optimized to 9.1 μm, rather than 9.0 μm or 9.2 μm, as this specific length allows more unabsorbed light to be reflected and reabsorbed during a second pass.” Please show the simulation result on how the light absorption depends on the length. It means that the fabrication should be very accurate. How about the fabrication precision? Furthermore, if the light absorption is so sensitive to the length, would it also very sensitive to the cross-sectional dimensions (like the width, the thickness)? 5. About grating couplers. Grating couplers are playing an important role for evaluating the responsivity of the present APDs. The authors should give more results about the characterization of multiple GCs on the same chip, to show the uniformity in the wafer scale, so that it is reasonable to use the data from the reference devices. 6. About the responsivity. The authors mentioned “At a reverse bias of 3.5 V, the APD exhibits an optical internal responsivity of 0.75 A/W at unit gain, determined by comparison with a reference p-i-n PD fabricated on the same chip and sharing identical structural parameters, including Ge volume, waveguide dimensions, and GC design2,20,22,28”. In this design, the Ge thickness is chosen as 260 nm, which might be beneficial to enhance the device performance (e.g., bandwidth), as claimed by the authors (“The rationale behind choosing a smaller Ge volume is to reduce the transit time of photogenerated carriers in Ge, as well as to lower its capacitance). However, such a design lowers the light absorption in Ge. As the authors claimed, the Ge length should exceed 26.7 μm to achieve >90% light absorption. In this paper, the authors have chosen the length as 9.1 μm with the assistance of reflector. As a result, the responsivity is still relatively low (i.e., 0.75 A/W), much lower than the theoretical value of 1.06 A/W. Therefore, the authors should clarify that the GBP was achieved with a relatively low responsivity and also explain the reason in the revised manuscript (to response the second reviewer’s previous comment 6). Otherwise, if they extend the absorption length to achieve a higher responsivity, the bandwidth would be reduced and the GBP will also be reduced. 7. About the reflection (the second reviewer’s previous comment 3). The authors have given some explanation about the reflection. However, they should mention this in the revised manuscript to make everything clear, which is helpful for the readers. They should also tell how much the reflection is. 8. In addition, the authors mentioned that “an 8° angled fiber-to-GC coupling configuration was employed to effectively prevent reflected light in the Si waveguide from coupling back into the optical fiber probe through the GC, thereby protecting the laser source from potential damage.” One should realize that such 8° angled structures are not helpful to lower the reflected light from the rear grating. 9. About the previous comment “8. Could the author explain the strategy for reducing the dark current? Also please give an analysis about the noise.” The authors did not give the strategy for reducing the dark current in the revised manuscript. They should add it. Also, they just gave some general comments on the noise, while more results about the noise analysis should be given numerically or experimentally (experimental data are preferred). 10. About the previous comment “12. Please comment the polarization dependence of the present APD, which would be important for a receiver”. The authors have given a figure (Fig. 12) to show how polarization-insensitivity is achieved with the help of PSGCs. However, the present APD in this paper does not work bi-directionally because of the introduction of the rear reflectors."}, "author_response": "Reply to Reviewers Comments\nManuscript ID: NCOMMS-25-17798A\nTitle: A High-Speed Si-Ge Avalanche Photodiode with a Gain-Bandwidth Product\nof 7564 GHz\nOn behalf of all the authors, I would like to extend our sincere thanks to the\nreviewers for their constructive and insightful comments on our manuscript. These\nsuggestions have been highly valuable and have played an important role in improving\nthe overall quality of our work. In response to the reviewers’ feedback, we have\nthoroughly revised the manuscript and incorporated additional data to strengthen the\nvalidity of our results. In addition, we have provided supplementary information to\nfacilitate readers’ understanding and interpretation of the manuscript. We are now\nsubmitting a revised version of the manuscript that reflects all the reviewers’\nrecommendations.\nAs detailed below, we have provided a point-by-point response to each of the\nreviewers’ comments and suggestions. For ease of communication, the reviewers’\ncomments are presented in bold black, while our responses are shown in blue. The\ncorresponding revisions in the manuscript are marked in red. References cited in the\nresponse are formatted in black italics.\nOnce again, we sincerely appreciate your positive evaluation and the valuable\nsuggestions that have contributed to enhancing the quality of our manuscript.\nReviewer 1\n1. As stated in my prior review, the primary claim in this paper is a Ge on Si\navalanche photodiode with very high gain-bandwidth product. This requires an\naccurate determination of the gain, which in turn necessitates knowing the unity\ngain point accurately. I questioned the authors’ determination of the unity gain\npoint and the response was, “The first method involves estimating the unit gain\npoint by measuring the point where the second derivative of the photocurrent with\nrespect to bias becomes zero [1, 2].” Reference 1 is a PhD dissertation titled,\n“Design, Characterization and Simulation of Avalanche Photodiodes” by Hektor\nMeier. There is no mention of this technique to find the unity gain point. The\nauthor does describe Monte Carlo simulations of avalanche photodiodes but there\nis no physical basis provided for the second derivative method. Reference 2 is the\nwebsite for Lumerical software. The Lumerical model settings uses the second\nderivative method but there is no explanation for the basis of this approach.\nLumerical is a great software tool but it is not trustworthy when applying a general\nrule to a broad range of materials.\nThe authors also state that, “Currently, this method has been widely accepted and\nrecognized by many prior works, including Nature Photonics [3, 4], Optica [5],\nOptical Fiber Communication Conference (OFC) [6], and European Conference\non Optical Communication (ECOC) [7].” I am familiar with these references and\nthey do not mention the second derivative method for determining the unity gain\npoint. If the authors can provide a sound physical explanation for this gain\ndetermination technique, I cannot recommend publication because accurate\ndetermination of the gain is essential to their primary claim in this paper.\nResponse:\nWe sincerely appreciate your insightful and constructive comments on our work.\nYour observation is indeed well-founded, as the precise determination of the unity gain\npoint is of critical importance in this study.\nIn this work, the unity gain point was determined by comparing the performance\nof PIN PD with identical structures fabricated on the same chip. This approach is\nconsidered highly reliable, and its underlying rationale has been elaborated in our\nprevious response. Furthermore, this method has been widely acknowledged in the field\nand explicitly adopted in several peer-reviewed journal articles we have cited in our\nmanuscript.\nRegarding the method of determining the unity gain point by identifying the\nvoltage at which the second derivative of the photocurrent with respect to the bias\nvoltage becomes zero, we would like to clarify that in our manuscript this approach is\nprimarily employed as an auxiliary means to further verify the correctness of the unity\ngain point we selected.\nThe applicability of this method arises from the fact that, under optical\nillumination, the current in an APD mainly consists of two components:\n1. In the unity-gain stage, photogenerated carriers are driven by the electric field\nto produce drift current without multiplication.\n2. In the multiplication stage, once the device enters the avalanche region,\nelectrons or holes acquire sufficient energy to initiate impact ionization, thereby\ntriggering the avalanche process and resulting in current multiplication.\nAt low bias voltages, only carrier drift occurs, and the increase in current with bias\nvoltage is relatively slow, corresponding to a negative second derivative of photocurrent\nwith respect to bias voltage. As the voltage further increases and the electric field\nbecomes sufficiently strong, a fraction of the carriers reach the threshold energy for\nimpact ionization, causing a rapid acceleration in the current growth rate. At this critical\npoint, the second derivative of the photocurrent with respect to the bias voltage (i.e.,\nthe photocurrent generation acceleration) reaches zero, indicating that the APD has\nentered the avalanche region.\nTo facilitate a more intuitive understanding of this method for the reviewer, we\nhave included the relevant content from the original referenced manuscripts in our\nresponse (highlighted in bold) along with the corresponding citations.\nThis method was proposed in Section 4.2.1 on page 45 of Hektor Meier’s doctoral\ndissertation “Design, Characterization, and Simulation of Avalanche Photodiodes”,\nwhere a detailed explanation is provided [1]. The specific description is as follows:\nFollowing definitions are used:\n1. The punch-through voltage V is the voltage where the derivative of the\npt\nphoto current with respect to the voltage ∂i /∂V is at its maximum due to the rapid\np\ndepletion of the absorber region.\n2. The voltage for unity gain V > V is the voltage where the second\nm1 pt\nderivative of the photo current with respect to the voltage ∂2i /∂V2 is zero. This\np\nreflects the assumption of a plateau with respect to the applied voltage for which\nthe responsivity remains constant and the multiplication gain is equal to one.\n3. Multiplication gain for a reverse bias voltage V is defined as the ratio\nbetween the photo current measured at V and the photo current measured at V .\nm1\n4. The breakdown voltage V is the voltage where the dark current exceeds\nbr\ni = i + i = 0.1 mA. Above this voltage, the dark current is influenced by the\nd dm du\nseries resistance depending on the dimension of the APD. This definition of the\nbreakdown voltage corresponds to a multiplication gain of several thousand.\nIn the original text, V denotes the punch-through voltage, corresponding to the\npt\ncomplete depletion of the absorber, at which point the photocurrent increases most\nrapidly due to the abrupt extension of the depletion region. V represents the voltage\nm1\nfor unity gain, while V is the breakdown voltage. Here, i is the dark current, i the\nbr d dm\nmultiplied dark current, and i the unmultiplied dark current.\ndu\nFurthermore, the supplementary material of the 2021 paper titled “Integrated\nAvalanche Photodetectors for Visible Light” published in Nature Communications also\nemployed this method to validate the unity gain point [2]. The original text is as follows:\nInstead, we estimate the unity gain point by measuring where the second\nderivative of the photocurrent with respect to bias becomes zero, i.e. 2 / 2 =\nph B\n0. This yields a reasonable transition point between regimes where the increase in\n𝜕𝜕 𝐼𝐼 𝜕𝜕𝜕𝜕\nwith is likely dominated by a saturation in QE (at lower bias) and an increase\nph B\n𝐼𝐼in (at 𝜕𝜕higher bias). For an input optical power of\nopt\n= 30.2 ± 0.2 dBm, we\n𝐺𝐺 𝑃𝑃\nobtain of 1.45 – 1.7 V across all device types (see Supplementary Figure 4).\nug\nFin𝜕𝜕ally, regarding the Lumerical software, we consider it to be a widely used\noptoelectronic simulation platform applicable to various material systems, including Si,\nGe, Ti, SiO₂, Si₃N₄, liquid crystal materials, and III-V semiconductors [3][4]. In relevant\ncase studies, simulations of a APD based on the Si-Ge material system have also been\nconducted [5], with the unity gain points obtained from these simulations showing high\nconsistency with experimental measurements [6].\nBased on the above analysis, we believe that the unity gain point selected in this\nwork is accurate and reasonable. We sincerely appreciate your attention to our study\nand your valuable suggestions.\nreference\n1. Meier, H. T. J. Design, characterization and simulation of avalanche photodiodes. Ph.D. thesis,\nETH Zurich (2011).\n2. Salih, Y. et al. Integrated avalanche photodetectors for visible light. Nat. Commun. 12, 1-8 (2021).\n3. Material Database in FDTD and MODE – Ansys Optics\n4. III-V Semiconductor Optical Material Data Tool – Ansys Optics\n5. https://optics.ansys.com/hc/en-us/articles/360042454814-Avalanche-photodetector\n6. Huang, Z. et al. 25 Gbps low-voltage waveguide Si–Ge avalanche photodiode. Optica 3, 793-798\n(2016).\nManuscript revision:\nWe have added an explanation in “Supplementary Note 3”. The revised content is as\nfollows:\n1. Comparing the responsivity with that of a PIN PD.\nDetermining the unit gain point by comparing the responsivity of a PIN PD\nfabricated on the same die and sharing identical structural parameters (such as the\nlength, width, and thickness of the Ge absorption region, as well as the length and width\nof the Si waveguide). Currently, this method has been widely accepted and recognized\nby many prior works, including Nature Photonics [1, 2], Optica [3], Optical Fiber\nCommunication Conference (OFC) [4], and European Conference on Optical\nCommunication (ECOC) [5].\nThis method is considered reliable because the responsivity of the PD is primarily\ndetermined by the length of the Ge region and the coupling area. Although doping can\ninfluence responsivity to some extent, the two devices in our comparison share exactly\nthe same heavily doped regions (in terms of concentration, area, and spacing). The only\ndifference lies in the lightly doped region, where n-type doping is replaced by p-type\ndoping. However, the influence of light doping on responsivity is minimal. Under such\nconditions, the responsivity measured from the PIN device is nearly identical to the\ninitial responsivity of the APD.\n2. Second derivative of the photocurrent with respect to the bias voltage becomes\nzero.\nRegarding the method of determining the unity gain point by identifying the\nvoltage at which the second derivative of the photocurrent with respect to the bias\nvoltage becomes zero [6,7], we would like to clarify that in our manuscript this\napproach is primarily employed as an auxiliary means to further verify the correctness\nof the unity gain point we selected.\nThe applicability of this method arises from the fact that, under optical\nillumination, the current in an APD mainly consists of two components:\n1. In the unity-gain stage, photogenerated carriers are driven by the electric field\nto produce drift current without multiplication.\n2. In the multiplication stage, once the device enters the avalanche region,\nelectrons or holes acquire sufficient energy to initiate impact ionization, thereby\ntriggering the avalanche process and resulting in current multiplication.\nAt low bias voltages, only carrier drift occurs, and the increase in current with bias\nvoltage is relatively slow, corresponding to a negative second derivative of photocurrent\nwith respect to bias voltage. As the voltage further increases and the electric field\nbecomes sufficiently strong, a fraction of the carriers reach the threshold energy for\nimpact ionization, causing a rapid acceleration in the current growth rate. At this critical\npoint, the second derivative of the photocurrent with respect to the bias voltage (i.e.,\nthe photocurrent generation acceleration) reaches zero, indicating that the APD has\nentered the avalanche region.\nBoth methods can be used to determine the unity-gain point. In this work, we\ndetermined the unity-gain point by comparing the responsivity of a PIN PD with that\nof an identically structured device fabricated on the same chip, and further verified the\nresult using the method in which the second derivative of the photocurrent with respect\nto the bias voltage becomes zero.\nreference\n1. Shi, Y. et al. Avalanche photodiode with ultrahigh gain–bandwidth product of 1,033 GHz. Nat.\nPhoton. 18, 610-616 (2024).\n2. Kang, Y. et al. Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–\nbandwidth product. Nat. Photon. 3, 59–63 (2008).\n3. Xiang, Y. et al. High speed waveguide ge/si avalanche photodiode with a gain-bandwidth product\nof 615 GHz. Optica 9, 762-769 (2022).\n4. Shi, Y. et al. Ultrafast 67 GHz Waveguide-Coupled Silicon-Germanium Avalanche Photodiode,\nin Optical Fiber Communications Conference and Exhibition (OFC), (2024).\n5. Cao, H. et al. Ultrahigh gain-bandwidth product Ge/Si avalanche photodetector assisted by\nnonuniform electric field distribution, in European Conference on Optical Communications\n(ECOC), (2024).\n6. Meier, H. T. J. Design, characterization and simulation of avalanche photodiodes. Ph.D. thesis,\nETH Zurich (2011).\n7. Salih, Y. et al. Integrated avalanche photodetectors for visible light. Nat. Commun. 12, 1-8 (2021).\nReviewer 2\n1. About the reply to comment #1 of the second reviewer. The authors have\nexplained some minor difference between the present design and that in ref. 20 in\nthe response letter. They have added some sentences to describe their structural\ndesign: “Figure 1(b) illustrates the cross-sectional doping profile of the Si-Ge APD,\nfeaturing a non-contact design between the Ge region and the Si-doped areas to\neffectively control the electric field within the Ge. Additionally, thicker metal\ninterconnects are employed to further enhance device performance. The Ge\nabsorption region dimensions are 9.1 μm (length) × 0.5 μm (width) × 0.26 μm\n(height).” However, the reviewer believes that this difference should be clearly\ndescribed in the manuscript in order to make it clear to the readers. Furthermore,\nthe authors should tell how the difference influences the device performances with\nsome simulation and experimental verifications. For example, the authors only\nmention “non-contact design” once in the manuscript (page 2). They have never\ndiscussed how this design is related with their results. What is the optimal point\nfor the non-contact design? Since this is the main difference, it is strongly\nsuggested to have more details about it in the manuscript.\nWe sincerely thank the reviewer for the detailed suggestions regarding the design\ndifferences. Concerning the non-contact doping structure shown in Figure 1(b), we have\nprovided a more detailed description on page 3, Figure 1(d). As illustrated in Figure\n1(b), the left end of the Ge strip is set 120 nm away from the left end of the rib\nwaveguide to avoid excessive fabrication errors due to overly small dimensions. By\ntuning ΔW from 70 nm to 150 nm, the spacing between the P+ doping region and the\nGe can be precisely controlled. When ΔW is set to 110 nm, the electric field is better\nconfined within the Ge, while the field intensity inside the Ge remains as low as\npossible. This optimized design helps achieve better control of the electric field within\nthe Ge and also contributes to reducing the device’s dark current. The same method is\napplied symmetrically on the left side. In the design section of the manuscript, we used\nthe first two paragraphs to describe the details of this non-contact design strategy.\nManuscript revision:\nWe have added an explanation in the second paragraph of Section 2, “Design”. The\nrevised content is as follows:\nFigure 1(a) presents a three-dimensional (3D) schematic of the lateral p+-i-p-n+\ndoped SACM Si-Ge APD, incorporating a DBR at the rear to enhance device\nresponsivity. The design process began with optimizing the electric field distribution to\nachieve high performance. Figure 1(b) illustrates the cross-sectional doping profile of\nthe Si-Ge APD, featuring a non-contact design between the Ge region and the Si-doped\nareas to effectively control the electric field within the Ge. To quantitatively describe\nthis non-contact design strategy, we optimized the doping positions on the rib\nwaveguide, denoted as Wp and ΔW, respectively. Additionally, thicker metal\ninterconnects are employed to further enhance device performance. The Ge absorption\nregion dimensions are 9.1 μm (length) × 0.5 μm (width) × 0.26 μm (height). Given Ge's\nhigh impact ionization coefficient, optimization efforts focused on the doping regions\nadjacent to the Ge layer, specifically adjusting the widths of Wp and ΔW. The primary\ngoal was to maximize ionization within Si while suppressing ionization in Ge, requiring\nthe electric field strength in Si to exceed 3×10⁷ V/m, while ensuring it remains below\n2×10⁷ V/m in Ge25,26. Additionally, to facilitate efficient carrier transport at saturation\nvelocity within Ge, the electric field in Ge was designed to exceed 1×10⁶ V/m27.\n2. About EO responses at different optical powers. The experimental results in\nFig. 3 only gave the measured OE responses of the APD at various reverse bias\nvoltages under an input optical power of -16 dBm. However, the highest GBP was\nachieved at the optical power of -24 dBm. It is definitely necessary to show the\nmeasured EO responses at -24 dBm. More discussions should be given about the\nbandwidth reduction as the optical power decreases.\nWe sincerely thank the reviewer for this valuable suggestion, which helps us\nimprove the consistency of the manuscript. We have replaced the original bandwidth\nfigure with the one measured at an input optical power of -24 dBm under different bias\nvoltages and revised the corresponding descriptions accordingly. In addition, we have\nadded a discussion in the manuscript regarding the observed bandwidth reduction with\ndecreasing input optical power.\nManuscript revision:\nWe have made revisions to the second paragraph in Section 3, \"Experimental results\",\nprimarily focusing on the content related to Figures 3(c) and 3(d). We have also updated\nFigure 3 and its caption in the manuscript. The revised content is as follows:\nTo characterize the optoelectronic (OE) bandwidth of the APD through small-\nsignal measurements, the test setup is illustrated in Figure 4(a). The optical signal\nemitted by the O-band laser is first directed into a lightwave component analyzer (LCA),\nthen sequentially passes through a handheld variable optical attenuator (VOA) and a\npolarization controller (PC), before being vertically coupled into the device under test\n(DUT) via a grating coupler(GC). Figures 4(c) and 4(d) show the physical photograph\nand a cross-sectional scanning electron microscope (SEM) image of the APD,\nrespectively. The photocurrent generated by the APD is routed back to the LCA through\na bias-tee to measure the bandwidth. As shown in Figure 3(c), when the input optical\npower is -24 dBm, the APD exhibits a 3-dB OE bandwidth of 8 GHz at a reverse bias\nof 7 V, primarily due to incomplete depletion of the Ge absorption region. As the reverse\nbias voltage increases, the 3 dB OE bandwidth gradually increases, reaching a\nmaximum of 31 GHz at a reverse bias voltage of 12.5 V. However, with further\nincreases in reverse bias, the 3 dB OE bandwidth starts to decrease, primarily due to\nthe dominance of the avalanche buildup time in the frequency response of the APD.\nThe inset of Figure 3(c) shows the variation of the 3-dB OE bandwidth under input\noptical powers ranging from -26 dBm to -12 dBm at a fixed reverse bias voltage of 12.5\nV. As the input optical power decreases, the bandwidth gradually reduces. At -26 dBm,\nthe bandwidth is 30 GHz, representing a 16.6% reduction compared to -12 dBm. This\nbehavior arises because, at lower input optical powers, the generation and collection of\nphotogenerated carriers slow down, limiting the APD response speed and consequently\nreducing the 3-dB bandwidth. Figure 3(d) illustrates the multiplication gain and GBP\ncharacteristics at reverse bias voltages of 9 V, 10 V, 11 V, 12 V, and 12.5 V,\ncorresponding to five different multiplication gain points for input optical power levels\nranging from -12 dBm to -24 dBm. At an input power of -16 dBm and a reverse bias of\n12.5 V, the APD achieves a multiplication gain of 73 and a 3 dB OE bandwidth of 36\nGHz, corresponding to a maximum GBP of 2628 GHz. When the input power is\nreduced to -24 dBm at the same 12.5 V reverse bias, the GBP of the APD increases to\noptical power of -24 dBm. Both metrics increase with bias voltage until peaking, after\nwhich they decline. This degradation is attibuted to excessive noise and prolonged\navalanche build-up time at high voltages, which deteriorate the APD’s performance.\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various reverse bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under\nan input optical power of -24 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under reverse\nbias voltages of 9 V, 10 V, 11 V, 12 V, and 12.5 V for various input optical power levels. The inset shows the\nrelationship between bandwidth and gain of the APD at an input optical power of -24 dBm. (e) Measured excess\nnoise factor versus multiplication gain for the APD.\n3. The GBP is the most important result considered in this paper. The authors\nshould give more details in Fig. 3(d). For example, all data for different voltages\nshould be given so that the readers can better understand the results.\nWe greatly appreciate the reviewer’s emphasis on the importance of Figure 1(d).\nWe have supplemented the figure caption with details corresponding to the different\nbias voltages to better assist readers in understanding the figure.\nTo further facilitate the reviewer’s understanding, we have added auxiliary lines\nin Figure 1(b), where L1 to L7 indicate the responses at input optical powers of -12\ndBm, -14 dBm, -16 dBm, -18 dBm, -20 dBm, -22 dBm, and -24 dBm under different\nbias voltages.\nThe specific voltages shown in Figure 1(d) are extracted from Figure 1(b). In\nFigure 1(d), we plotted the data measured at five voltages: 9 V, 10 V, 11 V, 12 V, and\n12.5 V. We did not include 13 V and 13.5 V because the GBP reaches its maximum at\n12.5 V, as shown in Figure 1(b). This selection makes the figure clearer and easier for\nreaders to interpret.\nFig. 1: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various reverse bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under\nan input optical power of -24 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under reverse\nbias voltages of 9 V, 10 V, 11 V, 12 V, and 12.5 V for various input optical power levels. The inset shows the\nrelationship between bandwidth and gain of the APD at an input optical power of -24 dBm. (e) Measured excess\nnoise factor versus multiplication gain for the APD.\nManuscript revision:\nWe have made revisions to the second paragraph in Section 3, \"Experimental results\",\nprimarily focusing on the content related to Figure 3(d). We have also updated Figure\n3 and its caption in the manuscript. The revised content is as follows:\nFigure 3(d) illustrates the multiplication gain and GBP characteristics at reverse\nbias voltages of 9 V, 10 V, 11 V, 12 V, and 12.5 V, corresponding to five different\nmultiplication gain points for input optical power levels ranging from -12 dBm to -24\ndBm. At an input power of -16 dBm and a reverse bias of 12.5 V, the APD achieves a\nmultiplication gain of 73 and a 3 dB OE bandwidth of 36 GHz, corresponding to a\nmaximum GBP of 2628 GHz. When the input power is reduced to -24 dBm at the same\n12.5 V reverse bias, the GBP of the APD increases to 7564 GHz. The inset of Figure\n3(d) shows the trends of gain and bandwidth at an input optical power of -24 dBm. Both\nmetrics increase with bias voltage until peaking, after which they decline. This\ndegradation is attibuted to excessive noise and prolonged avalanche build-up time at\nhigh voltages, which deteriorate the APD’s performance.\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various reverse bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under\nan input optical power of -24 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under reverse\nbias voltages of 9 V, 10 V, 11 V, 12 V, and 12.5 V for various input optical power levels. The inset shows the\nrelationship between bandwidth and gain of the APD at an input optical power of -24 dBm. (e) Measured excess\nnoise factor versus multiplication gain for the APD.\n4. The authors mentioned “To fully utilize this reflective effect, the Ge length was\noptimized to 9.1 μm, rather than 9.0 μm or 9.2 μm, as this specific length allows\nmore unabsorbed light to be reflected and reabsorbed during a second pass.”\nPlease show the simulation result on how the light absorption depends on the\nlength. It means that the fabrication should be very accurate. How about the\nfabrication precision? Furthermore, if the light absorption is so sensitive to the\nlength, would it also very sensitive to the cross-sectional dimensions (like the width,\nthe thickness)?\nWe sincerely thank the reviewer for the valuable suggestion, to which we have\nalso provided a simulation-based response. In a conventional PD (without a reflector at\nthe end), the absorption efficiency of Ge increases monotonically with length. However,\nwhen a DBR is introduced at the end, the absorption efficiency of Ge no longer\nincreases simply with length; instead, it is influenced by both the coupling of the\nevanescent wave and the position of the DBR. The key point is that when the Ge volume\nis relatively small, the absorption efficiency is low, and secondary reflection is required\nto enhance the responsivity. A higher responsivity is achieved only when a sufficient\namount of light is reflected. This effect is mainly determined by the length and thickness\nof the Ge, and we will provide a detailed analysis of these factors separately.\nFirst, we performed simulations to analyze the absorption of Ge with different\nthicknesses, and the results are shown in Figure 2. It can be clearly observed that the\noverall trend is that a thicker Ge layer leads to higher responsivity, while local\nenhancements in absorption appear at certain specific thicknesses. Several\nrepresentative points were selected for detailed discussion. Figure 2(a) illustrates the\nabsorption for different Ge thicknesses under the same length condition. To more\nintuitively present the optical field distribution at these points, seven typical positions\nare marked in Figure 2(a). At points b, c, and d, the increase in absorption gradually\nslows down. This is because, although increasing the Ge thickness enhances absorption,\nthe amount of light reflected back by the DBR decreases, thus reducing the growth rate\nof responsivity. At point e, the absorption improvement induced by increasing Ge\nthickness is insufficient to compensate for the reduced reflection from the DBR,\nresulting in a lower absorption compared to point d. To further visualize the optical field\ndistribution, points f, g, and h were analyzed. At point g, more light is clearly reflected\nby the DBR; while points f and h show nearly identical DBR reflections, the greater\nthickness of the Ge layer at point h yields stronger intrinsic absorption, leading to higher\noverall absorption than at point f.\nFigure 2(a) shows the absorption for different Ge thicknesses under the same\nlength condition, while Figure 2(b)-(h) present the corresponding optical field\ndistributions at the selected points. The red arrows indicate the direction of input light,\nand the DBR is located at the right end.\nRegarding the Ge length, we kept the thickness fixed at 260 nm, and the simulated\nstructure is shown in Figure 3. The red dashed line in Figure 3(a) represents the fitted\ntrend curve, which more intuitively illustrates the variation of responsivity with length.\nFour representative points were selected for analysis, where b and d correspond to\nrelatively low absorption, while c and e correspond to relatively high absorption. By\nexamining the optical field distributions at points b, c, d, and e, it is evident that the\nabsorption of Ge is higher when the evanescent wave is fully coupled from Ge into Si.\nFigure 3(a) shows the absorption for different Ge length under the same high\ncondition, while Figure 2(b)-(e) present the corresponding optical field distributions at\nthe selected points. The red arrows indicate the direction of input light, and the DBR is\nlocated at the right end.\nWith the incorporation of a rear DBR, the enhancement of the Ge absorption relies\non selecting an optimal combination of thickness and length. In the design, both the\nheight and length of the Ge layer were optimized to allow more light to enter the DBR\nand be reflected back into the Ge, thereby maximizing absorption.\nRegarding fabrication tolerance, the adopted platform is a 130-nm process.\nSimulations show that near the maximum absorption point, length variations within\n±200 nm cause only negligible changes in absorption, indicating that the design does\nnot impose stringent requirements on process accuracy and can be readily achieved with\ncurrent fabrication capabilities. Of course, although slight deviations in length have\nminimal impact, during the design process we still chose the peak position, and thus\nselected 9.1 μm.\nManuscript revision:\nWe have added an explanation in the fifth paragraph of Section 2, “Design”. The revised\ncontent is as follows:\nIn contrast, incorporating a DBR significantly reduces this leakage by reflecting the\nunabsorbed light back into the Ge region, thereby enhancing responsivity. To fully utilize this\nreflective effect, the Ge length was optimized to 9.1 μm (see Supplementary Note 1), rather than\n9.0 μm or 9.2 μm, as this specific length allows more unabsorbed light to be reflected and reabsorbed\nduring a second pass. However, standing waves are observed in the field distribution, mainly due to\nmode mismatch between the Si waveguide and Ge layer as well as reflections from the rear DBR.\nSimulations indicate that the optical return loss (ORL) of this device is -22.5 dB (see Supplementary\nNote 2). To further verify the effect of the DBR, top-view field distributions in Figures 2(b) and 2(d)\nshow that the inclusion of the DBR significantly increases the optical intensity in the Ge absorption\nregion. The inclusion of a five-period DBR at the rear enhances the overall light confinement within\nthe Ge layer. Additionally, a front-end tapered waveguide was employed to minimize input reflection\nlosses. As a result, the device's responsivity improves by 35%.\n5. About grating couplers. Grating couplers are playing an important role for\nevaluating the responsivity of the present APDs. The authors should give more\nresults about the characterization of multiple GCs on the same chip, to show the\nuniformity in the wafer scale, so that it is reasonable to use the data from the\nreference devices.\nWe sincerely appreciate the reviewer’s valuable suggestion regarding the\nuniformity of the grating couplers. In this work, the fabrication was carried out using a\nMulti-Project Wafer (MPW) process, wherein one designated block was allocated,\nyielding a total of 20 individual chips. We performed characterization tests on the GCs\nacross these 20 chips using the measurement method described in our previous response.\nTo minimize potential errors caused by variations in coupling conditions during testing,\nall 20 chips were placed on the testing stage simultaneously. The stage was moved while\nkeeping the GC fixture fixed, thereby ensuring maximal consistency of the testing setup.\nThe results demonstrate good uniformity in coupling loss among the GCs, with only\nminor variation observed. The coupling loss for the majority of the chips was\napproximately 6.0 dB/facet.\nTable 1. Summary of GC Characterization Results\nCoupling loss of the GC at 1310 nm\n#1 #2 #3 #4 #5 #6 #7 #8 #9 #10\n6.1 6.0 5.8 5.8 6.0 6.0 6.0 6.0 6.0 6.2\ndB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet\n#11 #12 #13 #14 #15 #16 #17 #18 #19 #20\n6.0 6.0 6.0 6.0 6.0 6.0 6.2 6.0 5.8 6.1\ndB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet dB/facet\nTherefore, we believe that using the GC data from the reference devices for\nresponsivity calculation is both reasonable and valid. We sincerely thank you again for\nyour valuable suggestion, which has significantly enhanced the rigor of our work.\nManuscript revision:\nRegarding this comment, we have not made any modifications and have retained\nthe descriptions from the previous version.\n6. About the responsivity. The authors mentioned “At a reverse bias of 3.5 V, the\nAPD exhibits an optical internal responsivity of 0.75 A/W at unit gain, determined\nby comparison with a reference p-i-n PD fabricated on the same chip and sharing\nidentical structural parameters, including Ge volume, waveguide dimensions, and\nGC design2,20,22,28”. In this design, the Ge thickness is chosen as 260 nm, which\nmight be beneficial to enhance the device performance (e.g., bandwidth), as\nclaimed by the authors (“The rationale behind choosing a smaller Ge volume is to\nreduce the transit time of photogenerated carriers in Ge, as well as to lower its\ncapacitance). However, such a design lowers the light absorption in Ge. As the\nauthors claimed, the Ge length should exceed 26.7 μm to achieve >90% light\nabsorption. In this paper, the authors have chosen the length as 9.1 μm with the\nassistance of reflector. As a result, the responsivity is still relatively low (i.e., 0.75\nA/W), much lower than the theoretical value of 1.06 A/W. Therefore, the authors\nshould clarify that the GBP was achieved with a relatively low responsivity and\nalso explain the reason in the revised manuscript (to response the second\nreviewer’s previous comment 6). Otherwise, if they extend the absorption length\nto achieve a higher responsivity, the bandwidth would be reduced and the GBP\nwill also be reduced.\nWe sincerely appreciate your suggestion and fully agree with your viewpoint.\nIndeed, using a larger Ge volume would impose limitations on the APD’s bandwidth.\nTherefore, during the design optimization process, we chose a smaller Ge volume to\nminimize its impact on bandwidth. At the same time, to avoid excessively low\nresponsivity, we incorporated a DBR at the rear of the device to maximize light\nabsorption.\nThe relatively low responsivity of the APD is primarily due to the small Ge volume\nused. Moreover, although a DBR was added at the rear, it cannot guarantee complete\nreflection of all incident light back into the absorption region. In the optimization, we\nindeed sacrificed part of the responsivity in exchange for higher device bandwidth.\nNevertheless, we believe that although the responsivity is lower than the theoretical\nvalue, it remains reasonable for an O-band detector and can be considered at a moderate\nlevel.\nManuscript revision:\nWe have added an explanation in the first paragraph of Section 3, “Experimental\nResults”. The revised content is as follows:\nFigure 3(a) shows the I-V characteristics of the fabricated Si-Ge APD under various bias\nvoltages, both with and without incident light, with optical power ranging from -26 dBm to -12 dBm.\nThe GC used in this work were characterized using a test structure consisting of a pair of GCs\nconnected by a short straight waveguide. The measured insertion loss was 6.0 dB/facet at 1310 nm.\nAt a reverse bias of 3.5 V, the APD exhibits an optical internal responsivity of 0.75 A/W at unit gain,\ndetermined by comparison with a reference p-i-n PD fabricated on the same chip and sharing\nidentical structural parameters (see Supplementary Note 3), including Ge volume, waveguide\ndimensions, and GC design2,20,22,28. The responsivity of our designed APD at 1310 nm is lower than\nthe theoretical value (1.06 A/W) because, to accommodate the bandwidth limitations imposed by a\nlarge Ge volume, part of the responsivity was intentionally sacrificed. The dark current initially\nincreases gradually and then rises sharply as the voltage approaches breakdown. At a reverse bias\nvoltage of 12.5 V, the dark current remains low at 8.4 μA, allowing the device to achieve\nexceptionally high multiplication gain. The breakdown voltage of the Si-Ge APD is 13 V,\ncorresponding to a dark current of 100 μA20. High multiplication gain enables high-sensitivity data\nreception in optical systems. Figure 3(b) illustrates the multiplication gain at reverse bias voltages\nranging from 9 V to 13.5 V for incident optical power levels between -26 dBm and -12 dBm. The\navalanche multiplication gain G(V) is defined as the difference between the photocurrent (I ) and\np\nthe dark current (I ) at a given bias voltage, normalized to the corresponding value at the unity gain\nd\npoint V : G(V)= (I (V) - I (V))/ (I (V ) - I (V ))23. The gain increases monotonically as the incident\n0 p d p 0 d 0\noptical power decreases, reaching its maximum at a reverse bias of 12.5 V. However, with further\nincreases in reverse bias, the gain starts to decrease due to the dark current rising more rapidly than\nthe photocurrent.\n7. About the reflection (the second reviewer’s previous comment 3). The authors\nhave given some explanation about the reflection. However, they should mention\nthis in the revised manuscript to make everything clear, which is helpful for the\nreaders. They should also tell how much the reflection is.\nWe sincerely appreciate the reviewer’s valuable comments regarding the reflection\nissue. In the revised manuscript, we include a detailed discussion on the origins of\ndevice reflections and their potential impacts, to help readers better understand this\naspect. In addition, we have supplemented the manuscript with the simulated reflection\nmagnitude of the proposed APD for completeness. We once again thank the reviewer\nfor the meticulous feedback, which is highly beneficial for improving the quality and\nclarity of our work.\nManuscript revision:\nWe have added an explanation in the fifth paragraph of Section 2, “Design”. The revised\ncontent is as follows:\nThe DBR structure in this device is a first-order DBR, chosen for its low scattering losses and\nhigh reflectivity. As depicted in Figure 1(e), when the number of grating periods reaches five, the\nreflectivity exceeds 90%, effectively reflecting light at the tail. The inset in Figure 1(e) illustrates\nthat, with five grating periods, the operational wavelength range extends from 1100 nm to 1700 nm,\nperfectly covering the O-band. Figure 2 presents 3D finite-difference time-domain (FDTD)\nsimulation results for two APD structures. The evanescently coupled optical field distributions for\nAPDs without and with a DBR are shown in Figures 2(a) and (c), respectively. In the absence of a\nDBR, significant light leakage occurs at the end of the APD. In contrast, incorporating a DBR\nsignificantly reduces this leakage by reflecting the unabsorbed light back into the Ge region, thereby\nenhancing responsivity. To fully utilize this reflective effect, the Ge length was optimized to 9.1 μm\n(see Supplementary Note 1), rather than 9.0 μm or 9.2 μm, as this specific length allows more\nunabsorbed light to be reflected and reabsorbed during a second pass. However, standing waves\nappear in the field distribution, primarily due to mode mismatch between the Si waveguide and Ge\nlayer, as well as reflections from the rear DBR. Simulation results indicate that the optical return\nloss (ORL) of this device is -22.5 dB (see Supplementary Note 2). To further verify the effect of the\nDBR, top-view field distributions in Figures 2(b) and 2(d) show that the presence of the DBR\nsignificantly increases the optical intensity in the Ge absorption region. The inclusion of a five-\nperiod DBR at the rear enhances the overall light confinement within the Ge layer. Additionally, a\nfront-end tapered waveguide was employed to minimize input reflection losses. As a result, the\ndevice's responsivity improves by 35%.\n8. In addition, the authors mentioned that “an 8° angled fiber-to-GC coupling\nconfiguration was employed to effectively prevent reflected light in the Si\nwaveguide from coupling back into the optical fiber probe through the GC,\nthereby protecting the laser source from potential damage.” One should realize\nthat such 8° angled structures are not helpful to lower the reflected light from the\nrear grating.\nWe sincerely appreciate your valuable suggestion and fully concur with your\nperspective. In our testing process, the use of an 8°-angled fiber-to-grating coupler\nconfiguration indeed cannot reduce the intrinsic back reflection of the APD itself. We\nacknowledge that our previous description lacked sufficient rigor and clarity. Our\nintended meaning was that, compared with perfectly vertical coupling, the angled\ncoupling configuration can effectively prevent light from being reflected by the chip’s\nsurface back into the optical fiber probe due to mirror-like reflections, thereby reducing\nthe portion of back reflection originating from this mechanism [1].\nreference\n1. Cheng, L. et al. Grating couplers on silicon photonics: design principles, emerging trends and\npractical issues. Micromachines. 11, 1-25 (2020).\nManuscript revision:\nRegarding this comment, we have not made any modifications and have retained\nthe descriptions from the previous version.\n9. About the previous comment “8. Could the author explain the strategy for\nreducing the dark current? Also please give an analysis about the noise.” The\nauthors did not give the strategy for reducing the dark current in the revised\nmanuscript. They should add it. Also, they just gave some general comments on\nthe noise, while more results about the noise analysis should be given numerically\nor experimentally (experimental data are preferred).\nWe sincerely appreciate the reviewers for their careful evaluation of our\nmanuscript and their valuable suggestions. As mentioned in our previous responses, in\nAPDs, the bulk dark current is multiplied by the gain and thus constitutes the dominant\ncomponent of the overall dark current. Therefore, the key strategy is to suppress the\nbulk dark current. In this work, we adopted the following approaches: (1) minimizing\nthe Ge volume as much as possible; (2) employing non-contact doping to Ge in order\nto optimize the electric field distribution within the Ge layer; and (3) utilizing a SACM\nstructure, where Si—with its favorable ionization coefficient ratio—is used for\nmultiplication, while Ge serves as the absorption medium. These constitute the methods\nimplemented in this study to reduce the dark current.\nFor APDs, the sensitivity and signal-to-noise ratio primarily benefit from\nmultiplication gain, although the shot noise current is also amplified. To characterize\nand analyze the device noise, we employed a noise analyzer. The shot noise current is\ngiven by:\n2 2\nwhere q denotes 𝐼𝐼t{h𝑠𝑠eℎ 𝑜𝑜e𝑜𝑜l}ec=tr o2n 𝑞𝑞 c h𝑀𝑀arge 𝐼𝐼,𝑝𝑝 Mℎ𝑜𝑜 𝑜𝑜i𝑜𝑜s t+he 𝐼𝐼 m𝑑𝑑𝑑𝑑u𝑑𝑑l𝑑𝑑tip𝐹𝐹li(c𝑀𝑀at)io𝛥𝛥n𝛥𝛥 gain, F(M) represents\nthe excess noise factor, Δf is the operating bandwidth, I is the photocurrent at unity\nphoto\ngain, and I is the dark current at unity gain.\ndark\nThe excess noise factor of an APD can be expressed as:：\nwhere k=β/α is the𝐹𝐹 i(m𝑀𝑀p)ac=t i𝑘𝑘on⋅i𝑀𝑀za+tio(n1 c−oe𝑘𝑘ff)ic⋅i(e2nt− ra1ti/o𝑀𝑀, w)ith α and β being the\nelectron and hole ionization coefficients in the multiplication region [1-3].\nFig. 4 Measured excess noise factor versus multiplication gain for the APD.\nTo evaluate the APD excess noise, we measured and plotted F(M) as a function of\nmultiplication gain M. For comparison, theoretical excess noise factors were calculated\nusing the local-field model for k values in the range of 0.03-0.20, as shown in Figure 4\n[4]. At 1310 nm, the extracted effective k value is approximately 0.05, which is close\nto that of Si (k≈0.02), confirming that avalanche multiplication predominantly occurs\nin the Si region of our APD. This value is also significantly lower than that of Ge APDs\n(k≈0.2-0.5) and conventional III-V APDs (k≈0.1-1) [5-9].\nRegarding strategies for reducing dark current, we have discussed this in the\n“Design” section of the manuscript, and it is also addressed in the “Discussion” section.\nIn the revised manuscript, the primary modifications focus on the analysis of noise.\nReference\n1. McIntyre, R. Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices.\nED-13, 164-168 (1966).\n2. Teich, M. et al. Excess noise factors for conventional and superlattice avalanche photodiodes and\nphotomultiplier tubes. IEEE J. Quantum Electron. 22, 1184-1193 (1986).\n3. Campbell, J. et al. Evolution of low-noise avalanche photodetectors. IEEE J. Select. Topics\nQuantum Electron. 28,1-11 (2022).\n4. Mcintyre, R. J. Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices\nED-13, 164–168 (1966).\n5. Kang, Y. Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain– bandwidth\nproduct. Nat. Photon. 3, 59-63 (2009).\n6. Huang, Z. 25 Gbps low-voltage waveguide si–ge avalanche photodiode. Optica 3, 793-798 (2016).\n7. Wang, B. A low-voltage si-ge avalanche photodiode for high-speed and energy efficient silicon\nphotonic links. Journal of Lightwave Technology. 38, 3156-3162 (2020).\n8.Chen, H. High sensitivity 10gb/s si photonic receiver based on a low-voltage waveguide-coupled\nge avalanche photodetector. Optics Express. 23, 815-822 (2015).\n9.Virot, L. Germanium avalanche receiver for low power interconnects. Nat. Commun. 4,1-6 (2014).\nManuscript revision:\nWe have made revisions to the fourth paragraph in Section 1, \"Introduction\", added the\nthird paragraph in Section 3, \"Experimental Results\", revised the first and second\nparagraphs in Section 4, \"Discussion\", and also made modifications to Table 1. The\nrevised content is as follows:\nIntroduction\nIn this paper, we present a high-speed Si-Ge APD with a record-breaking GBP of 7564 GHz,\nsurpassing the highest previously reported value. Utilizing a lateral SACM structure, we designed\nan APD that spatially separates the Ge absorption region from the doped regions. By minimizing\nthe electric field in Ge while maintaining efficient carrier transport and multiplication, we\nsignificantly reduced dark current. To further enhance device responsivity, we incorporated a\ntapered waveguide at the front end and a distributed Bragg reflector (DBR) at the rear. Experimental\nresults show that under a reverse bias voltage of 12.5 V, the APD exhibits an ultra-low dark current\nof 8.4 μA, and achieves a maximum GBP of 7564 GHz at an input optical power of -24 dBm, while\nmaintaining a low effective k value of 0.05. We evaluated the APD’s performance for high-speed\nsignals, achieving clear eye diagrams for 64 Gbps and 100 Gbps non-return-to-zero (NRZ) signals,\nas well as 128 Gbps and 200 Gbps four-level pulse amplitude modulation (PAM4) signals. The APD\ndemonstrated excellent sensitivity, reaching -20.8 dBm and -17.1 dBm at 64 Gbps and 100 Gbps\nNRZ signals, respectively, meeting the hard-decision forward error correction (HD-FEC) threshold.\nFor 128 Gbps and 200 Gbps PAM4 signals, the sensitivities were -14.2 dBm and -9.6 dBm,\nrespectively, also within the HD-FEC limit. Furthermore, we conducted high-speed eye diagram\nvalidation for 200 Gbps PAM4 signals across eight APDs, each tuned to the specific wavelengths\nrequired for eight-channel dense wavelength division multiplexing (DWDM). These remarkable\nresults highlight the immense potential of this APD for applications in optical communications,\nquantum technology, LiDAR, and beyond.\nExperimental results\nFig. 3: (a) Measured IV curves with different input optical powers; (b) The dependence of gain on input optical\npower at various reverse bias voltages; (c) Measured OE responses of the APD at various reverse bias voltages under\nan input optical power of -24 dBm. The inset shows the 3-dB OE bandwidth of the APD for input optical powers\nranging from -26 dBm to -12 dBm at a reverse bias voltage of 12.5 V; (d) Measured GBP of the APD under reverse\nbias voltages of 9 V, 10 V, 11 V, 12 V, and 12.5 V, as well as at different input optical powers. The inset shows the\nrelationship between bandwidth and gain of the APD at an input optical power of -24 dBm. (e) Measured excess\nnoise factor versus multiplication gain for the APD.\nFor APDs, the sensitivity and signal-to-noise ratio primarily benefit from multiplication gain,\nalthough the shot noise current is also amplified. To characterize and analyze the device noise, we\nemployed a noise analyzer. The shot noise current is given by:\n2 2\n, where q denotes the electron charge, M is the multiplic𝐼𝐼a{𝑠𝑠tiℎo𝑜𝑜n𝑜𝑜} g=ain 2, F𝑞𝑞( M𝑀𝑀) re 𝐼𝐼p𝑝𝑝rℎe𝑜𝑜s𝑜𝑜e𝑜𝑜n+ts\nt\n𝐼𝐼\nh𝑑𝑑e𝑑𝑑 𝑑𝑑e𝑑𝑑x\n\nc e\n𝐹𝐹\ns(s\n𝑀𝑀\nn)o i\n𝛥𝛥\nse\n𝛥𝛥\nfactor, Δf is the operating bandwidth, I\nphoto\nis the photocurrent at unity gain, and\nI is the dark current at unity gain. The excess noise factor of an APD can be expressed as:\ndark\n, where k=β/α is the impact ionization coefficient ratio, with\nα\n𝐹𝐹\n(a\n𝑀𝑀\nnd) β\n=\nb\n𝑘𝑘\nei\n⋅\nng\n𝑀𝑀\nth\n+\ne (e\n1\nle\n−\nctr\n𝑘𝑘\no)n\n⋅\na\n(\n2\nn\n−\nd\n1\nho\n/\nle\n𝑀𝑀\nio\n)\nnization coefficients in the multiplication region. To evaluate\nthe APD excess noise, we measured and plotted F(M) as a function of multiplication gain M. For\ncomparison, theoretical excess noise factors were calculated using the local-field model for k values\nin the range of 0.03-0.20, as shown in Figure 3(e) 29. At 1310 nm, the extracted effective k value is\napproximately 0.05, which is close to that of Si (k ≈ 0.02), confirming that avalanche multiplication\npredominantly occurs in the Si region of our APD. This value is also significantly lower than that\nof Ge APDs (k ≈ 0.2-0.5) and conventional III-V APDs (k ≈ 0.1-1)2,30,31,32,33.\n2. Kang, Y. et al. Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–\nbandwidth product. Nat. Photon. 3, 59-63 (2009).\n29. McIntyre, R. Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices.\nED-13, 164-168 (1966).\n30. Huang, Z. et al. 25 Gbps low-voltage waveguide si–ge avalanche photodiode. Optica. 3, 793-\n798 (2016).\n31. Wang, B. et al. A low-voltage si-ge avalanche photodiode for high-speed and energy efficient\nsilicon photonic links. J. Lightwave Technol. 38, 3156-3162 (2020).\n32. Chen, H. et al. High sensitivity 10gb/s si photonic receiver based on a low-voltage waveguide-\ncoupled ge avalanche photodetector. Opt. Express. 23, 815-822 (2015).\n33. Bai, X. et al. Development of low excess noise SWIR APDs. In Proc. Infrared Technology and\nApplications XXXVIII, (2012).\nDiscussion\nTable 1 provides an overview of state-of-the-art Ge APDs and Si-Ge APDs, which primarily operate\nin the O-band and C-band wavelength ranges. Earlier studies proposed using the Ge region as the\nmultiplication region and integrating all PN junctions within the Ge of the APD5. However, this\napproach suffered from excessive light absorption by dopants, resulting in insufficient responsivity.\nTo address this limitation, researchers developed a vertically structured Ge APD with simultaneous\nSi-Ge doping, effectively reducing doping-induced absorption and enhancing responsivity24.\nDespite these improvements, Ge APDs still face inherent challenges. When Ge is used as the\navalanche region, its high impact ionization coefficient ratio k leads to increased noise, dark current\nand a limited GBP, thereby constraining the viability of Ge APDs as a mainstream solution5.\nIn contrast, Si-Ge APDs exhibit a lower effective impact ionization coefficient ratio k. A\nreduced k is critical for minimizing the excess noise, thereby significantly improving the GBP and\nsensitivity2,13. In SACM-structured Si-Ge APDs, the engineered electric field distribution confines\nthe multiplication region primarily to the Si layer, further reducing the effective k value and\neffectively suppressing noise. Based on the electric field orientation, SACM Si-Ge APDs can be\nclassified into vertical and lateral configurations. The vertical SACM Si-Ge APD has undergone\nsubstantial advancements through continuous optimization, achieving a relatively low avalanche\nvoltage, which is beneficial for APD applications6,13,14. However, its GBP remains modest, and its\nfabrication process is more complex. Additionally, direct contact between Ge and the electrode can\ndegrade device performance. In contrast, the lateral SACM Si-Ge APD features a simpler fabrication\nprocess, eliminating Ge-electrode contact and thereby preventing responsivity and bandwidth\ndegradation7,20-23. Through ongoing research efforts, the GBP of lateral SACM Si-Ge APD has been\nsignificantly improved while maintaining a bias voltage below 15 V, further enhancing their\npotential for practical applications.\n10. About the previous comment “12. Please comment the polarization\ndependence of the present APD, which would be important for a receiver”. The\nauthors have given a figure (Fig. 12) to show how polarization-insensitivity is\nachieved with the help of PSGCs. However, the present APD in this paper does not\nwork bi-directionally because of the introduction of the rear reflectors.\nWe sincerely thank the reviewer for the valuable suggestion. As you correctly\npointed out, the present APD does not support bi-directional light incidence and\ntherefore cannot be directly employed in such a system. However, this functionality\ncould be achieved through certain system-level optimizations.\nOne possible approach, as illustrated in Figure 5 and reported by NVIDIA in the\ndemonstrates that a unidirectional PD can indeed be used for such applications. The\nmain idea is to employ a cascaded Mach-Zehnder interferometer (MZI) structure to\ncombine two TE-mode inputs into a single path, which is then directed into the PD for\nmeasurement [2][3]. Using this structure eliminates the need for a APD that supports\nbidirectional incidence.\nFig. 5. Active polarization-tracking microring receiver architecture.\nreference\n1. Nandish, M. et al. Overcoming challenges of co-integrated optics to advance accelerated\ncomputing. in 2025 IEEE 75th Electronic Components and Technology Conference (ECTC). (2025).\n2. Madsen, C. K. et al. Reset-free integrated polarization controller using phase shifters. IEEE\nJournal of Selected Topics in Quantum Electronics. 11, 431-438 (2005).\n3. Nespola, A. et al. Proof of concept of polarization-multiplexed PAM using a compact Si-Ph device.\nIEEE Photonics Technology Letters. 31, 62-65 (2019).\nManuscript revision:\nWe have revised the third paragraph in Section 4, \" Discussion,\". The revised content\nis as follows:\nGiven that most silicon photonic receivers are designed for TE-mode detection34,35,36, this study\npresents a lateral SACM APD specifically optimized for TE-mode detection, achieving a high gain\nof 244 and an OE bandwidth of 31 GHz.\n36. Nandish, M. et al. Overcoming challenges of co-integrated optics to advance accelerated\ncomputing. in 2025 IEEE 75th Electronic Components and Technology Conference (ECTC).\n(2025)."}, {"round": 3, "reviewer_comments": {"reviewer_3": "This manuscript describes a Si/Ge APD aiming to achieve a high GBP and to demonstrate high-symbol-rate eye diagrams. While the topic is important, several issues remain unclear, and the current version does not provide sufficient evidence to support the main claims. 1. This submission appears closely related to the authors’ OFC 2025 paper (M4K.5). If this is an extended version, it should be clearly stated, and the differences must be explained. 2.The main new element seems to be the 8-channel array, but key points are missing: whether the channels were operated simultaneously, the level of crosstalk, and any wavelength dependence across the O-band. These aspects should be clarified. 3. The TDECQ values in Fig. 5 appear low. It is also unclear why the eyes open despite the device bandwidth (30–35 GHz) being lower than the Nyquist rate for 100-GBaud PAM-4. The manuscript should state whether any equalization or signal processing was used. 4. The manuscript suggests that the non-contact design drastically improves performance, but the mechanism and effect are not clearly explained. If the excess-noise factor corresponds to k ≈ 0.05, the authors should discuss with such as simulations whether such a value reasonably leads to a GBP above 7000 GHz. 5. In Fig. 3, F is extracted at low M that do not match the operating point used for the GBP measurement. k should be evaluated at the relevant M to support the argument."}, "author_response": "Reply to Reviewers Comments\nManuscript ID: NCOMMS-25-17798B\nTitle: A High-Speed Si-Ge Avalanche Photodiode with a Gain-Bandwidth Product\nof 7564 GHz\nOn behalf of all the authors, I would like to extend our sincere thanks to the\nreviewers for their constructive and insightful comments on our manuscript. These\nsuggestions have been highly valuable and have played an important role in improving\nthe overall quality of our work. In response to the reviewers’ feedback, we have\nthoroughly revised the manuscript and incorporated additional data to strengthen the\nvalidity of our results. We are now submitting a revised version of the manuscript that\nreflects all the reviewers’ recommendations.\nAs detailed below, we have provided a point-by-point response to each of the\nreviewers’ comments and suggestions. For ease of communication, the reviewers’\ncomments are presented in bold black, while our responses are shown in blue. The\ncorresponding revisions in the manuscript are marked in red. References cited in the\nresponse are formatted in black italics.\nOnce again, we sincerely appreciate your positive evaluation and the valuable\nsuggestions that have contributed to enhancing the quality of our manuscript.\nReviewer 3\n1. This submission appears closely related to the authors’ OFC 2025 paper\n(M4K.5). If this is an extended version, it should be clearly stated, and the\ndifferences must be explained.\nWe sincerely thank the reviewer for this important comment. We clarify that this\nmanuscript represents a substantial extension of our previously published OFC 2025\npaper (M4K.5) [1], which has now been explicitly cited in the revised manuscript. The\nrelationship between the two works is clearly stated.\nCompared with the OFC paper, the present manuscript introduces several\nsignificant advances:\na) Extension from a single-channel device to an eight-channel Si/Ge APD array,\nwith a systematic evaluation of its performance in dense wavelength-division\nmultiplexing systems;\nb) Gain–bandwidth product analysis exceeding 7000 GHz, including discussions\nof excess noise measurements and underlying physical mechanisms;\nc) Demonstration of PAM-4 signal transmission at data rates up to 200 Gbps;\nd) Refined descriptions of the experimental setup to enhance reproducibility;\ne) Systematic analysis of APD bandwidth dependence on input optical power and\nnoise characteristics;\nf) Extended discussion of the reflection properties of Bragg gratings and their\nimpact on system performance.\nThese clarifications and the main differences relative to the OFC paper have been\nincorporated into the revised manuscript.\nReference\n1. Cheng, C. et al. A 112 Gbps silicon-germanium avalanche photodiode with ultra-\nhigh gain-bandwidth product. In 2025 Optical Fiber Communications Conference and\nExhibition (OFC), 1−3(2025).\nManuscript revision:\nWe have added an explanation in the second paragraph of Section 4, “Introduction”.\nThe revised content is as follows:\nIn this paper, we present a high-speed Si-Ge APD with a record-breaking GBP of 7564 GHz,\nsurpassing the highest previously reported value. Utilizing a lateral SACM structure, we designed\nan APD that spatially separates the Ge absorption region from the doped regions. By minimizing\nthe electric field in Ge while maintaining efficient carrier transport and multiplication, we\nsignificantly reduced dark current. To further enhance device responsivity, we incorporated a\ntapered waveguide at the front end and a distributed Bragg reflector (DBR) at the rear. Experimental\nresults show that under a reverse bias voltage of 12.5 V, the APD exhibits an ultra-low dark current\nof 8.4 μA, and achieves a maximum GBP of 7564 GHz at an input optical power of -24 dBm, while\nmaintaining a low effective k value of 0.05. We evaluated the APD’s performance for high-speed\nsignals, achieving clear eye diagrams for 64 Gbps and 100 Gbps non-return-to-zero (NRZ) signals,\nas well as 128 Gbps and 200 Gbps four-level pulse amplitude modulation (PAM4) signals. The APD\ndemonstrated excellent sensitivity, reaching -20.8 dBm and -17.1 dBm at 64 Gbps and 100 Gbps\nNRZ signals, respectively, meeting the hard-decision forward error correction (HD-FEC) threshold.\nFor 128 Gbps and 200 Gbps PAM4 signals, the sensitivities were -14.2 dBm and -9.6 dBm,\nrespectively, also within the HD-FEC limit. Furthermore, we conducted high-speed eye diagram\nvalidation for 200 Gbps PAM4 signals across eight APDs, each tuned to the specific wavelengths\nrequired for eight-channel dense wavelength division multiplexing (DWDM). This manuscript\nrepresents a substantial extension of our previous OFC work25, expanding the study from a single-\nchannel device to an eight-channel APD array, and providing detailed design and analysis, along\nwith a further systematic investigation of excess-noise characteristics. These remarkable results\nhighlight the immense potential of this APD for applications in optical communications, quantum\ntechnology, LiDAR, and beyond.\n25. Cheng, C. et al. A 112 Gbps silicon-germanium avalanche photodiode with ultra-high gain-bandwidth\nproduct. In 2025 Optical Fiber Communications Conference and Exhibition (OFC),\n1−3(2025).\n2. The main new element seems to be the 8-channel array, but key points are\nmissing: whether the channels were operated simultaneously, the level of crosstalk,\nand any wavelength dependence across the O-band. These aspects should be\nclarified.\nWe sincerely thank the reviewer for this helpful comment and agree that these\npoints require further clarification. In the revised manuscript, we have added the\nfollowing explanations regarding the eight-channel array:\na) Channel operation: In the eye-diagram measurements, each of the eight\nchannels was characterized sequentially rather than simultaneously. The array\narchitecture itself, however, inherently supports multi-channel operation. In\nfuture chip designs, grating couplers will be arranged at a standard 127-µm pitch\nand integrated with on-chip transimpedance amplifiers (TIAs), enabling\nsimultaneous eight-channel operation.\nb) Crosstalk: A commercial eight-channel dense wavelength-division multiplexer\n(DWDM) was employed, which is a mature technology and effectively\nsuppresses optical crosstalk. In addition, adjacent APD channels are physically\nseparated and electrically isolated, resulting in negligible electrical crosstalk.\nc) Wavelength dependence: The eight DWDM channels cover a total wavelength\nrange of less than 10 nm, over which the APD responsivity remains nearly\nconstant. The measured responsivity among the eight detectors shows negligible\nchannel-to-channel variation, indicating minimal wavelength dependence.\nThese clarifications have now been explicitly included in the revised manuscript.\nManuscript revision:\nWe have added an explanation in the seventh paragraph of Section 3, “Experimental\nresults”. The revised content is as follows:\nFinally, to demonstrate the WDM capability and channel uniformity of the proposed device,\nwe employed an eight-channel APD array (Figure 6(a)) in combination with an external DWDM\ndemultiplexer with a channel spacing of 200 GHz (≈1.14 nm in the O-band). In the present proof-\nof-concept experiment, the demultiplexed channels were characterized sequentially. The\ndemultiplexed wavelengths of λ₁ = 1305.92 nm, λ₂ = 1307.06 nm, λ₃ = 1308.20 nm, λ₄ = 1309.34\nnm, λ₅ = 1310.48 nm, λ₆ = 1311.62 nm, λ₇ = 1312.76 nm, and λ₈ = 1313.90 nm were successfully\ndetected. Owing to the narrow wavelength span (<10 nm) of the eight DWDM channels, the\nmeasured responsivity shows negligible wavelength dependence. Clear eye diagrams were obtained\nfor all eight channels at a data rate of 200 Gbps PAM4, as shown in Figure 6(b), demonstrating the\nbroadband capability and good uniformity of the APD array.\n3. The TDECQ values in Fig. 5 appear low. It is also unclear why the eyes open\ndespite the device bandwidth (30–35 GHz) being lower than the Nyquist rate for\n100-GBaud PAM-4. The manuscript should state whether any equalization or\nsignal processing was used.\nWe sincerely thank the reviewer for this valuable and insightful comment. In\npractical experimental conditions, an open eye diagram does not necessarily require\nstrict satisfaction of the Nyquist criterion, mainly for the following reasons:\na) For the APD eye-diagram measurements, a complete high-speed electro-optical\ntest setup was employed, including radio frequency (RF) probes, RF cables,\nbias-tees, thin-film lithium niobate (TFLN) modulators, and RF amplifiers, all\nwith bandwidths exceeding 67 GHz. The optical signal was generated by a\nKeysight M8194A arbitrary waveform generator (AWG) and measured using a\nKeysight 86100D sampling oscilloscope, which supports full-link calibration\n[1]. During the experiment, the entire electrical-optical-electrical test link was\ncalibrated to 40 GHz to ensure that the measurement results were not limited by\nthe external link bandwidth.\nb) During the measurements, built-in real-time forward equalization (5 taps) and\nfiltering functions of the Keysight sampling oscilloscope were enabled, in line\nwith IEEE 802.3 testing standards [2]. While the intrinsic bandwidth of the APD\nremains unchanged, the use of 5-tap feed-forward equalization effectively\ncompensates for frequency roll-off and mitigates inter-symbol interference,\nthereby providing sufficient effective system bandwidth for the successful\nreception of 200 Gb/s PAM-4 signals and contributing to the observed open eye\ndiagrams [3].\nRegarding signal processing, no external digital signal processing (DSP) or offline\nequalization was applied. All eye diagrams presented in the manuscript were obtained\nafter completing the system calibration. Under these conditions, the measured TDECQ\nvalues primarily reflect the system-level performance of the full test link under finite\nbandwidth, influenced by all components in the chain, rather than being solely\ndetermined by the intrinsic performance of the APD. This measurement scheme is\nconsistent with commonly used system-level characterization methods for high-speed\noptoelectronic devices.\nThese clarifications have been further incorporated into the revised manuscript.\nReference\n1. https://www.keysight.com/us/en/assets/7018-06341/data-sheets/5992-3361.pdf.\n2. https://www.ieee802.org/3/dj/public/25_01/ghiasi_3dj_01_2501.pdf.\n3. Zhou, H. et al. Recent advances in equalization technologies for short-reach optical\nlinks based on PAM4 modulation: a review. Appl. Sci. 9, (2019).\nManuscript revision:\nWe have added an explanation in the Fourth paragraph of Section 3, “Experimental\nresults”. The revised content is as follows:\nTo assess the signal reception quality, an eye-diagram measurement was conducted. During\nperforming the test, the frequency response of the test link was calibrated and compensated using a\nKeysight M8194A arbitrary waveform generator (AWG), resulting in a relatively flat frequency\nresponse of the entire electrical-optical-electrical link within a 40 GHz bandwidth, thereby\neffectively reducing the influence of external link components on the measurement results. Figure\n4(b) shows the experimental setup for measuring the APD eye diagram and bit error rate (BER). An\nO-band tunable laser was used as the optical source. The optical signal first passed through a PC\nand was then modulated by a thin-film lithium niobate (TFLN) Mach-Zehnder modulator (MZM),\nwhich was driven by an amplified high-speed electrical signal. After a second PC for polarization\nadjustment, the modulated optical signal was vertically coupled into the DUT via a GC. The\nphotocurrent generated by the APD is directed through a bias-tee to an oscilloscope for eye diagram\nand TDECQ analysis, and then sent to a BER tester to assess the APD’s sensitivity. The\nmeasurement setup employed a full high-speed RF chain, including Radio Frequency (RF) probes,\nRF cables, bias-tees, TFLN MZMs, and RF amplifiers, all with bandwidths exceeding 67 GHz. No\ntransimpedance amplifier (TIA) was integrated after the APD, and no external digital signal\nprocessing (DSP) or offline equalization was applied. Only the built-in real-time forward\nequalization (5 taps) and filtering functions of the sampling oscilloscope were enabled during the\nmeasurements. These signal-processing functions effectively compensate for frequency roll-off and\nmitigate inter-symbol interference, thereby providing sufficient effective system bandwidth for the\nsuccessful reception of 200 Gb/s PAM-4 signals and enabling clear eye openings, despite the\nintrinsic small-signal 3-dB bandwidth of the APD being below 40 GHz.\n4. The manuscript suggests that the non-contact design drastically improves\nperformance, but the mechanism and effect are not clearly explained. If the excess-\nnoise factor corresponds to k ≈ 0.05, the authors should discuss with such as\nsimulations whether such a value reasonably leads to a GBP above 7000 GHz.\nWe sincerely thank the reviewer for raising this important question. The non-\ncontact design adopted in this work achieves effective spatial separation between the\nGe absorption region and the Si-doped multiplication region by optimizing the\nparameters Wp and ΔW, thereby enabling precise control of the electric-field\ndistribution. In this architecture, the high electric field is predominantly confined to the\nSi multiplication region, while a relatively low electric field is maintained in the Ge\nabsorption region.\nBecause the high electric field is concentrated in the Si region, the avalanche\nmultiplication process is predominantly electron-initiated, while hole-initiated\nmultiplication in the Ge region is effectively suppressed. This quasi-unipolar avalanche\nmechanism maximizes impact ionization in Si while minimizing ionization in Ge,\nthereby significantly reducing the excess noise.\nThe performance advantage of APDs strongly depends on achieving a sufficiently\nhigh gain–bandwidth product (GBP), which is closely related to the excess noise.\nFactors that reduce excess noise often also lead to a higher GBP. Since the excess-noise\nfactor is determined by the k value, APDs with lower k are more likely to achieve higher\nGBPs, a trend that has been consistently reported in the literature [1-3].\nIn our design, a thin multiplication-region APD is employed, which is favorable\nfor achieving a low k value. Previous studies have shown the following correlation\nbetween k and GBP: for k ≈ 0.4-0.5, GBP < 100 GHz [4,5]; for k ≈ 0.09, GBP ≈\nThis clear trend indicates that APDs with lower k values can achieve substantially\nhigher GBPs. Therefore, by designing our device to have an even lower k, it is\nreasonable to expect a further enhancement in GBP.\nThe simulated electric-field distributions shown in Fig. 1(c) and Fig. 1(d) further\nconfirm that the high electric field is effectively confined within the Si multiplication\nregion, while the Ge absorption region remains at a relatively low electric-field level.\nThese results provide direct physical evidence that the non-contact design supports the\nsimultaneous realization of low excess noise and high GBP.\nIn summary, through deliberate electric-field engineering and a non-contact\nstructural design, the device achieves electron-dominated avalanche multiplication, a\nlow effective k value, and a high GBP. These points have now been further clarified in\nthe revised manuscript.\nReference\n1. Campbell, J. Recent advances in telecommunications avalanche photodiodes. J.\nLightwave Technol 25, 109-121 (2007).\n2. Campbell, J. Recent advances in avalanche photodiodes. J. Lightwave Technol 34,\n278-285 (2016).\n3. Yuan, Y. et al. Avalanche photodiodes on silicon photonics. J. Semicond. 43, 1-13\n(2022).\n4. Amiento, C. Impact ionization in (100)-,(110)-, and (111)-oriented InP avalanche\nphotodiodes. Appl. Phys. Lett. 43, 333–335, (1983).\n5. Cook, L. Electron and hole ionization coefficients in InP determined by\nphotomultiplication measurements. Appl. Phys. Lett., 40, 589–591, (1982).\n6. Kang, Y. et al. Monolithic germanium/silicon avalanche photodiodes with 340 ghz\ngain–bandwidth product. Nat. Photon. 3, 59–63 (2008).\n7. Wang, B. et al. 64 gb/s low-voltage waveguide si-ge avalanche photodiodes with\ndistributed bragg reflectors. Photonics Res. 8,1118-1123 (2020).\n8. Shi, Y. et al. Ultrafast avalanche photodiode exceeding 100 GHz bandwidth. Nat. Commun.16,\n(2025).\nManuscript revision:\nWe have added an explanation in the third paragraph of Section 2, “Design”, added the\nthird paragraph in Section 3, \"Experimental Results\", and added the second paragraph\nin Section 4, \"Discussion\". The revised content is as follows:\nTo further enhance performance, graded doping was employed to reduce resistance and\ncapacitance. The p-type doping concentrations were set at 7.1 × 10^19 cm^-3 (p++), 5.3 × 10^18\ncm^-3 (p+), and 2.1 × 10^17 cm^-3 (p), while the n-type doping concentrations were set at 1.0 ×\n10^20 cm^-3 (n++) and 1.0 × 10^19 cm^-3 (n+), respectively. Additionally, a lateral structure was\nadopted to minimize light absorption by metal electrodes and reduce dark current caused by defects\nnear the heterojunction under breakdown voltage conditions. The inset in Figure 1(b) presents the\nsimulated cross-sectional electric field results under a reverse bias of 12.5 V, confirming effective\nelectric field confinement. Through optimized doping position and concentration, together with\nprecise control of Wp and ΔW enabled by the non-contact design, the high electric field is effectively\nconfined within the Si multiplication region, while the Ge absorption region is maintained at a\nrelatively low electric field, thereby achieving precise electric-field engineering. Under this field\nconfiguration, avalanche multiplication is dominated by an electron-driven quasi-unipolar\nmechanism, in which impact ionization in Si is maximized whereas ionization in Ge is strongly\nsuppressed. As a result, the excess noise is effectively reduced and the overall device performance\nis significantly enhanced.\nAt 1310 nm, the extracted effective k value is approximately 0.05, which is close to that of Si\n(k ≈ 0.02), confirming that avalanche multiplication predominantly occurs in the Si region of our\nAPD. This value is also significantly lower than that of Ge APDs (k ≈ 0.2-0.5) and conventional III-\nV APDs (k ≈ 0.1-1) 2,36,37,38,39. Previous studies have shown that as the k value decreases, the GBP\nof APDs increases2,5,13,40. This clear trend indicates that a lower k value effectively suppresses\nexcess noise under high multiplication gain, which is critical for achieving higher GBP in APDs41.\nIn contrast, Si-Ge APDs exhibit a lower effective impact ionization coefficient ratio k. As\nshown in Table 1, a reduced k value is critical for minimizing the excess noise under high\nmultiplication gain, thereby significantly improving the GBP2,5,13,40. In SACM-structured Si-Ge\nAPDs, the engineered electric field distribution confines the multiplication region primarily to the\nSi layer, further reducing the effective k value and effectively suppressing noise.\nTable 1. Summary of the state-of-the-art Ge APDs and Si-Ge APDs\n40. Shi, Y. et al. Ultrafast avalanche photodiode exceeding 100 GHz bandwidth. Nat. Commun.16,\n(2025).\n41. Yuan, Y. et al. Avalanche photodiodes on silicon photonics. J. Semicond. 43, 1-13 (2022).\n5. In Fig. 3, F is extracted at low M that do not match the operating point used\nfor the GBP measurement. k should be evaluated at the relevant M to support the\nargument.\nWe thank the reviewer for this important and technically insightful comment. We\nagree that clarification is necessary regarding the extraction conditions of the excess\nnoise factor F and the corresponding k value in Fig. 3, and their relation to the operating\npoint at which the GBP is evaluated.\nIn this work, the k value is extracted under low multiplication gain (M) conditions.\nThis approach is primarily motivated by the dead-space effect in thin-multiplication-\nregion APDs. Owing to the different dead-space lengths of electrons and holes,\nelectrons can more readily accumulate sufficient energy within the limited\nmultiplication region to initiate impact ionization, whereas hole ionization is strongly\nsuppressed by the longer dead space and the associated energy accumulation\nrequirements [1,2]. Early theoretical analyses, supported by experimental verification,\nhave demonstrated that in thin multiplication-region APDs with electron-dominated\navalanche multiplication, the k factor remains nearly constant [3]. Consequently, even\nat higher multiplication gains, the avalanche process is still primarily electron-initiated,\nresulting in only a weak dependence of the effective k factor on M. These expressions\nhave been confirmed experimentally by Melchior and Lynch [4], Baertsch [5,6],\nand\nMcintype [3,7] and others.\nMoreover, at high multiplication gain, both the dark current and noise from the\nmeasurement chain are significantly amplified, which can compromise the accurate\nextraction of the excess noise factor F and obscure the intrinsic avalanche noise\ncharacteristics of the device. Therefore, characterizing the k value under low-gain\nconditions is a commonly adopted and more reliable approach in APD noise analysis,\nas evidenced by multiple prior studies that have employed the same experimental\nstrategy [8-11].\nIt should be further emphasized that the GBP reported in this work is directly\nmeasured at a high multiplication gain (M) operating point and is not inferred from the\nk value. The k value obtained at low M is primarily used to characterize the intrinsic\navalanche noise of the device and to provide a physical explanation for why the APD\ncan maintain low excess noise and achieve high GBP under high-gain operation.\nReference\n1.Wang, B. & Mu J. High-speed si-ge avalanche photodiodes. PhotoniX 3, 1-22 (2022).\n2. Yuan, Y. et al. Avalanche photodiodes on silicon photonics. J. Semicond. 43, 1-13\n(2022).\n3. Mcintyre, R. The Distribution of gains in uniformly multiplying avalanche\nphotodiodes: theory. IEEE Trans. Electron Devices, ED-19, 703-713, 1972.\n4. Melchior, H. et al. Signal and noise response of high speed germanium avalanche\nphotodiodes. IEEE Trans. Electron Devices, ED-13, 829-838, 1966.\n5. Baertsch, R. Noise and ionization rate measurements in silicon photodiodes. IEEE\nTrans. Electron Devices, ED-13, 987-987, (1966).\n6. Baertsch, R. Noise and multiplication measurements in InSb avalanche photodiodes.\nJ. Appl. Phys. 38, 4267–4274 (1967).\n7. Mcintyre, R. The Distribution of gains in uniformly multiplying avalanche\nphotodiodes: experimental. IEEE Trans. Electron Devices, ED-19, 713-718, 1972.\n8. Virot, L. et al. Germanium avalanche receiver for low power interconnects. Nat.\nCommun. 5, 1-6 (2014).\n9. Kang, Y. et al. Monolithic germanium/silicon avalanche photodiodes with 340 ghz\ngain–bandwidth product. Nat. Photon. 3, 59–63 (2008).\n10.Jones, A. et al. Low-noise high-temperature AlInAsSb/GaSb avalanche photodiodes\nfor 2-μm applications. Nat. Photon. 14, 559-563 (2020).\n11. Assefa, S. et al. Reinventing germanium avalanche photodetector for nanophotonic\non-chip optical interconnects. Nat. 464, 80-84 (2010).\nManuscript revision:\nWe have made revisions to the third paragraph in Section 3, \"Experimental Results\",\nThe revised content is as follows:\nFor APDs, the sensitivity and signal-to-noise ratio primarily benefit from multiplication gain,\nalthough the shot noise current is also amplified. To characterize and analyze the device noise, we\nemployed a noise analyzer. The shot noise current is given by:\n, where q denotes the electron charge, M is the multiplica2tion gain, F(M)2 represents\n𝐼𝐼{𝑠𝑠ℎ𝑜𝑜𝑜𝑜} = 2 𝑞𝑞 𝑀𝑀  𝐼𝐼𝑝𝑝ℎ𝑜𝑜𝑜𝑜𝑜𝑜+\nthe excess noise factor, Δf is the operating bandwidth, I is the photocurrent at unity gain, and\n𝐼𝐼𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐹𝐹(𝑀𝑀) 𝛥𝛥𝛥𝛥 photo\nI is the dark current at unity gain. The excess noise factor of an APD can be expressed as:\ndark\n, where k = β/α is the impact ionization coefficient ratio,\nwith α and β being the electron and hole ionization coefficients in the multiplication region. To\n𝐹𝐹(𝑀𝑀) = 𝑘𝑘⋅𝑀𝑀+(1−𝑘𝑘)⋅(2−1/𝑀𝑀)\nevaluate the APD excess noise, we measured and plotted F(M) as a function of multiplication gain\nM. The excess-noise factor F and the corresponding effective k value were extracted at low\nmultiplication gain, where the fitting is more reliable and less affected by measurement-chain noise.\nFor comparison, theoretical excess noise factors were calculated using the local-field model for k\nvalues in the range of 0.03-0.20, as shown in Figure 3(e)30. Although the GBP is evaluated at higher\nmultiplication gain, prior studies indicate that for APDs employing thin multiplication regions and\nelectron-dominated avalanche multiplication, the effective k factor does not vary significantly with\nthe multiplication gain M31,32,33,34,35. At 1310 nm, the extracted effective k value is approximately\n0.05, which is close to that of Si (k ≈ 0.02), confirming that avalanche multiplication predominantly\noccurs in the Si region of our APD. This value is also significantly lower than that of Ge APDs (k ≈\n0.2-0.5) and conventional III-V APDs (k ≈ 0.1-1)2,36,37,38,39. Previous studies have shown that as the\nk value decreases, the GBP of APDs increases2,5,13,40. This clear trend indicates that a lower k value\neffectively suppresses excess noise under high multiplication gain, which is critical for achieving\nhigher GBP in APDs41.\n31. Melchior, H. et al. Signal and noise response of high speed germanium avalanche photodiodes.\nIEEE Trans. Electron Devices, ED-13, 829-838 (1966).\n32. Baertsch, R. Noise and ionization rate measurements in silicon photodiodes. IEEE Trans.\nElectron Devices, ED-13, 987-987 (1966).\n33. Baertsch, R. Noise and multiplication measurements in InSb avalanche photodiodes. J. Appl.\nPhys. 38, 4267–4274 (1967).\n34. Mcintyre, R. The distribution of gains in uniformly multiplying avalanche photodiodes: theory.\nIEEE Trans. Electron Devices, ED-19, 703-713 (1972).\n35. Mcintyre, R. The distribution of gains in uniformly multiplying avalanche photodiodes:\nexperimental. IEEE Trans. Electron Devices, ED-19, 713-718 (1972).\n40. Shi, Y. et al. Ultrafast avalanche photodiode exceeding 100 GHz bandwidth. Nat. Commun.16,\n(2025).\n41. Yuan, Y. et al. Avalanche photodiodes on silicon photonics. J. Semicond. 43, 1-13 (2022)."}, {"round": 4, "reviewer_comments": {"reviewer_3": "The manuscript is much improved, and the authors have addressed the main comments. To make the eye-diagram results easier to understand and reproduce, please add a few missing measurement details in the main text. In particular, please specify the data pattern used for the eye measurements (including the PRBS type/order and the pattern length) and state the target BER/SER used for the PAM4 evaluation. These details are needed to interpret the PAM4 eye (and TDECQ) results properly."}, "author_response": "Reply to Reviewers Comments\nManuscript ID: NCOMMS-25-17798C\nTitle: A High-Speed Si-Ge Avalanche Photodiode with a Gain-Bandwidth Product\nof 7564 GHz\nOn behalf of all the authors, we sincerely thank the reviewer for their constructive\nand insightful comments on our manuscript. These suggestions have been invaluable in\nimproving the overall quality of our work. In response to the reviewer’s feedback, we\nhave carefully revised the manuscript. We are now submitting a revised version of the\nmanuscript that reflects all the reviewers’ recommendations.\nAs detailed below, we have provided a point-by-point response to each of the\nreviewers’ comments and suggestions. For ease of communication, the reviewers’\ncomments are presented in bold black, while our responses are shown in blue. The\ncorresponding revisions in the manuscript are marked in red.\nOnce again, we sincerely appreciate your positive evaluation and the valuable\nsuggestions that have contributed to enhancing the quality of our manuscript.\nReviewer 3\n1. To make the eye-diagram results easier to understand and reproduce, please\nadd a few missing measurement details in the main text. In particular, please\nspecify the data pattern used for the eye measurements (including the PRBS\ntype/order and the pattern length) and state the target BER/SER used for the\nPAM4 evaluation. These details are needed to interpret the PAM4 eye (and\nTDECQ) results properly.\nWe sincerely thank the reviewer for the valuable comments regarding the\nmeasurement details and the reproducibility of the results. We fully agree that the data\npattern used in the eye-diagram measurements and the performance evaluation\nthresholds are critical for the correct interpretation of the results.\nIn the revised manuscript, we have added and clarified the relevant measurement\ndetails in the main text. Specifically, the eye-diagram measurements were performed\nusing a PRBS-11 pattern (211-1 bits) generated by an arbitrary waveform generator.\nUnder these conditions, the measured TDECQ values for the eye diagrams at data rates\nof 128 Gbps and 200 Gbps PAM-4 were 1.88 dB and 3.23 dB, respectively, as indicated\nin Fig. 5.\nIn addition, the performance of the signals was evaluated based on the hard-\ndecision forward error correction (HD-FEC) threshold (BER = 3.8×10−3). This\nevaluation criterion has been explicitly indicated in both the main text and Fig. 5 to\nfacilitate proper interpretation.\nManuscript revision:\nWe have added an explanation in the fourth paragraph of Section 3, “Experimental\nresults”, added the fourth paragraph in Section 1, \"Introduction\". In addition, Figure 5\nin Section 3 has been updated. The revised content is as follows:\nSection 3, “Experimental results”\nTo assess the signal reception quality, an eye diagram measurement was conducted. During the\nmeasurements, the frequency response of the test link was calibrated and compensated using a\nKeysight M8194A arbitrary waveform generator (AWG), resulting in a relatively flat frequency\nresponse of the entire electrical-optical-electrical link within a 40 GHz bandwidth and effectively\nminimizing the influence of external link components. A PRBS-11 data pattern (211-1 bits) generated\nby the AWG was used for all eye-diagram measurements. Figure 4(b) shows the experimental setup\nfor measuring the APD eye diagram and bit error rate (BER). An O-band tunable laser was used as\nthe optical source. The optical signal first passed through a PC and was then modulated by a thin-\nfilm lithium niobate (TFLN) Mach-Zehnder modulator (MZM), which was driven by an amplified\nhigh-speed electrical signal. After a second PC for polarization adjustment, the modulated optical\nsignal was vertically coupled into the DUT via a GC. The photocurrent generated by the APD is\ndirected through a bias-tee to an oscilloscope for eye diagram and TDECQ analysis, and then sent\nto a BER tester to assess the APD’s sensitivity. The measurement setup employed a full high-speed\nRF chain, including Radio Frequency (RF) probes, RF cables, bias-tees, TFLN MZMs, and RF\namplifiers, all with bandwidths exceeding 67 GHz. No transimpedance amplifier (TIA) was\nintegrated after the APD, and no external digital signal processing (DSP) or offline equalization was\napplied. Only the built-in real-time forward equalization (5 taps) and filtering functions of the\nsampling oscilloscope were enabled during the measurements. These signal-processing functions\neffectively compensate for frequency roll-off and mitigate inter-symbol interference, thereby\nproviding effective system bandwidth for the successful reception of 200 Gbps PAM-4 signals and\nenabling clear eye openings, despite the intrinsic small-signal 3-dB bandwidth of the APD being\nbelow 40 GHz.\nSection 1, \"Introduction\"\nIn this paper, we present a high-speed Si-Ge APD with a record-breaking GBP of 7564 GHz,\nsurpassing the highest previously reported value. Utilizing a lateral SACM structure, we designed\nan APD that spatially separates the Ge absorption region from the doped regions. By minimizing\nthe electric field in Ge while maintaining efficient carrier transport and multiplication, we\nsignificantly reduced dark current. To further enhance device responsivity, we incorporated a\ntapered waveguide at the front end and a distributed Bragg reflector (DBR) at the rear. Experimental\nresults show that under a reverse bias voltage of 12.5 V, the APD exhibits an ultra-low dark current\nof 8.4 μA, and achieves a maximum GBP of 7564 GHz at an input optical power of -24 dBm, while\nmaintaining a low effective k value of 0.05. We evaluated the APD’s performance for high-speed\nsignals, achieving clear eye diagrams for 64 Gbps and 100 Gbps non-return-to-zero (NRZ) signals,\nas well as 128 Gbps and 200 Gbps four-level pulse amplitude modulation (PAM4) signals. The APD\ndemonstrated excellent sensitivity, achieving -20.8 dBm and -17.1 dBm for 64 Gbps and 100 Gbps\nNRZ signals, respectively, which meet the hard-decision forward error correction (HD-FEC)\nthreshold of BER = 3.8×10−3. For 128 Gbps and 200 Gbps PAM4 signals, the sensitivities were -\n14.2 dBm and -9.6 dBm, respectively, also within the HD-FEC limit. Furthermore, we conducted\nhigh-speed eye diagram validation for 200 Gbps PAM4 signals across eight APDs, each tuned to\nthe specific wavelengths required for eight-channel dense wavelength division multiplexing\n(DWDM). This manuscript represents a substantial extension of our previous OFC work25,\nexpanding the study from a single-channel device to an eight-channel APD array, and providing\ndetailed design and analysis, along with a further systematic investigation of excess-noise\ncharacteristics. These remarkable results highlight the immense potential of this APD for\napplications in optical communications, quantum technology, LiDAR, and beyond.\nFig. 5: Eye diagrams measured at an input optical power of -16 dBm for data rates of (a) 64 Gbps NRZ, (b) 100\nGbps NRZ, (c) 128 Gbps PAM4, and (d) 200 Gbps PAM4; (e) Measured BERs at a reverse bias voltage of 12.5V\nfor NRZ and PAM4 signals."}, {"round": 5, "reviewer_comments": {"reviewer_3": "The authors have fully satisfied my request by clearly specifying the data patterns used for the eye diagram measurements and the performance evaluation criteria for PAM4. These additions have improved the clarity of the measurement results. Therefore, I recommend publication of the revised version."}, "author_response": "Reply\nOn behalf of all the authors, we sincerely thank you for your positive evaluation\nand valuable suggestions on our manuscript, which have greatly contributed to\nimproving its quality."}]

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