Avalanche photodiodes (APDs) are widely used to detect low-power optical signals in fibre optic communication¹, sensing², biotechnologies³ and quantum applications⁴. Due to the high internal gain, they provide a 5–10 dB sensitivity improvement compared with conventional p–i–n photodiodes^5,6. In the modern information era, emerging applications such as big data, cloud computing and artificial intelligence have given rise to an expanding demand for data communication capacity at a 60% annual pace⁷. Intense research has focused on upgrading optical communication devices to handle this demand^8,9,10, particularly in hyperscale data centres and high-performance computing, where 800 G/1.6 T optical interconnects are being deployed¹¹. The fast-growing data capacity has made the high-speed performance of APDs a high priority.

To meet the requirements of high sensitivity and high detection speed, APDs need to have both high gain and large bandwidth, and the gain–bandwidth product (GBP) becomes a key metric that must be constantly improved. According to Emmons’ theory¹², the improvement of the GBP requires a proper multiplication material with a low ratio of the impact ionization coefficients of electrons and holes (also known as the k factor). Traditional commercial APDs are based on the group III–V platform, using indium–phosphide (InP, k ≈ 0.4) or indium–aluminium–arsenic (InAlAs, k ≈ 0.2) as multiplication materials to present limited GBPs below 300 GHz (refs. ^13,14,15,16). Recently, several investigations have begun to adopt aluminium–indium–arsenic–antimony (AlInAsSb, k ≈ 0.01–0.05) or aluminium–arsenic–antimony (AlAsSb, k ≈ 0.005) to break through this limitation^2,17,18. A theoretically predicted high GBP of ~400 GHz has been obtained in AlAsSb APDs¹⁷.On the other hand, great efforts have been undertaken to demonstrate enhanced GBPs of ~300–600 GHz by utilizing germanium/silicon (Ge/Si) APDs based on the silicon photonics platform^{19,20,21,22,23}, owing to the very low k factor of ~0.02–0.05 of Si material and the complementary metal–oxide–semiconductor (CMOS)-compatible fabrication. Ge/Si APDs mainly operate in the optical communication band of 1,300–1,600 nm, integrating the advantage of the large absorption coefficient of Ge material²⁴. The separation absorption–charge–multiplication (SACM) structure is very popular to prevent impact ionization in Ge (k ≈ 0.9). In addition to material selection, a thin multiplication region is more beneficial due to the improvement of the certainty of the avalanche process, known as the dead-space effect^25,26. Recently, a very high GBP of 615 GHz was reported due to the relatively narrow multiplication region²³. However, further tightening is difficult, and the consequent large dark current becomes a thorny issue.

The impedance resonance effect is another possibility to further improve the GBP. Under high voltages, the rapidly increased photocurrent shields the electric field in the multiplication region due to the space charge effect, thereby reducing the gain and avalanche build-up time to improve the GBP^27,28. Theoretical research has shown that the multiplication region can be equivalent to an inductor interacting with the capacitance of the APD, resulting in a resonance peak in the impedance and frequency response²⁹. This unconventional phenomenon was observed early in InAlAs APDs³⁰, Si APDs³¹ and Si/SiGe APDs³², respectively. A normal-incidence Ge/Si APD exploiting this effect has been reported to have a GBP of up to 845 GHz (ref. ³³). Nonetheless, the maximum bandwidth is less than 15 GHz due to the efficiency versus speed trade-off in normal-incidence photodiodes. In addition, previously reported resonant APDs lack comprehensive engineering to further explore the potential of this effect. Therefore, a Ge/Si APD with larger GBP and higher bandwidth remains elusive and much desired.

In this Article, we demonstrate a high-speed waveguide-coupled Ge/Si impedance resonance APD with a record GBP over 1 THz. This represents a breakthrough of the GBP from the GHz to THz level for an APD operating at 1,310/1,550 nm. The performance is achieved by introducing an on-electrode spiral inductance to enhance the resonant dynamic with the equivalent inductance inside the multiplication region, as well as precisely shaping the electric field distribution. Thanks to the waveguide-coupled structure, a large bandwidth is ensured under the premise of high optical responsivity. Experimentally, the presented APD has a primary optical responsivity of 0.87 A W⁻¹ at unity gain, a constant large bandwidth of 53 GHz in the gain range of 9–19.5 and an ultrahigh GBP of 1,033 GHz under −8.6 V and at 1,550 nm. We attribute the flat bandwidth feature to the resonance enhancement effect compensating for the avalanche build-up process. For demonstration, open and clear eye diagrams of 112 Gb s⁻¹ on–off keying (OOK) and 200 Gb s⁻¹ four-level pulse amplitude modulation (PAM4) signals are obtained. These bit rates are among the highest speeds for single-wavelength reception enabled by Ge/Si APDs. Furthermore, 800 G reception is demonstrated via four channels. The sensitivities of the presented APD for OOK signals are −14.0 and −11.8 dBm for hard decision forward-error-correction operation at different bit rates of 100 and 112 Gb s⁻¹, while the sensitivities for PAM4 signals are −17.0 and −6.0 dBm at bit rates of 100 and 200 Gb s⁻¹. Thanks to the CMOS-compatible fabrication and good performance, this work provides a solution for low-cost and high-speed photodetectors.

Device structure and design

Figure 1a shows the concept and structure of the proposed impedance resonance APD, consisting of an L-shaped SACM junction and an on-electrode spiral inductor. The waveguide-coupled structure is utilized to decouple the optical absorption length and carrier transit path, ensuring a simultaneous improvement of efficiency and speed. A 20-μm-length Ge film guarantees >90% optical absorption at 1,550 nm. The width and height are 600 and 200 nm, respectively. The simulated optical field distribution and absorption efficiency are given in Supplementary Fig. 1a, and the measured absorption spectral response of the Ge absorber is given in Supplementary Fig. 1b. The cross-section of the junction region is shown in Fig. 1b. A 150-nm-thin intrinsic Si (i-Si) is designed for a large GBP and a low breakdown voltage. The charge layer (p-Si) is p-type doped with a concentration of 5 × 10¹⁷ cm⁻³ and a width of 640 nm, being different from the narrow charge layer of ~100 nm that is conventionally used in the reported lateral multiplication APDs^23,34,35. It can effectively prevent the diffusion from the charge layer to the multiplication region and enables accurate control of the multiplication width and electric field. To validate this, we simulate the electric field deviation under different charge layer width deviations in Supplementary Fig. 2. The wide charge layer shows six fold higher adjusting precision of the electric field than the normal, 100 nm one. To reduce the effective k value of the APD, the electric field in the Ge region should be lower than 1 × 10⁷ V m⁻¹ to prevent any ionization³⁶. Due to the high electric field present in i-Si, a gap of ~40 nm is designed between the intrinsic Ge (i-Ge) and i-Si to suppress the Ge surface electric field. Figure 1c shows the simulated electric field distribution along the dotted red line in Fig. 1b, under different gaps (ΔW). The region of Y = −0.3 to 0.3 μm represents the i-Ge, while the rest is the charge layer and i-Si. It can be found that, when ΔW increases, the electric field at the Ge interface drops below the ionization threshold. When ΔW exceeds 40 nm, the change in the electric field is very small. Therefore, a 40 μm gap is adopted considering a minimum transit time. The influence of electric field engineering is summarized in Fig. 1d. Compared with an unoptimized APD (blue line), Ge surface electric field suppression (red line) prevents the Ge ionization and reduces the effective k factor, thereby improving the GBP. Under the same gain, the bandwidth is also increased. However, the bandwidth still decreases as the gain increases, limited by the avalanche build-up process. The resonance effect is used to further improve the frequency response and the GBP by reducing the avalanche build-up time, obtaining a relatively stable bandwidth with gain.

a, The concept and structure of the device. The Si strip waveguide is designed to be 500 × 220 nm² for a single mode at 1,550 nm and is adiabatically tapered to the junction region of the APD. Si materials heavily doped (p⁺/n⁺) to ~10²⁰ cm⁻³ are ohmically contacted with the aluminium (Al) electrode for a minimum contact resistance. The main part of the junction region is an L-shaped absorption–charge–multiplication layer. The photogenerated carriers converted in the Ge absorption region enter the Si multiplication region under the action of a lateral electric field. b, The two-dimensional (2D) cross-section of the junction region. The L-shaped region is shown in highlight patterns. W_Ge = 600 nm, W_Si = 150 nm, ΔW = 40 nm. c, The simulated electric field distribution in the Ge and Si region under different gaps. The reverse voltage is fixed at −9 V. d, A comparison between different approaches to optimize the performance of the APD. Under low gain, the bandwidth is dominated by the resistance–capacitance (RC) delay and the carrier transit time and hardly varies with gain. Under high gain, the bandwidth begins to decrease due to the time for avalanche build-up. Indeed, Si material has a very low k factor. However, the Ge ionization causes a relatively declined effective k factor (k_eff). Previous methods including Ge ionization suppression and a thin multiplication region, or Ge surface electric field engineering in this work, contribute to a reduced k_eff. These efforts improve the GBP, but the bandwidth reduces under high gain, making it hard for APDs to fulfil both high sensitivity and high speed. We consider and engineer the resonant effect in the avalanche process to achieve a flat feature of the bandwidth versus gain. e, The simulated bandwidth and corresponding GBP with different L_p under a gain of 20. f, A microscopy image of the fabricated APD. The light is fed into the chip by a grating coupler with an optical loss of 4 dB. The junction region and spiral inductor are highlighted in the image.

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We investigate the impedance resonance dynamics based on an equivalent circuit model. When the APD operates under high gain, an electric field opposing the direction of the externally applied electric field is formed between the separated electrons and holes. Therefore, the accumulation of the amplified photocurrent in the multiplication region shields the electric field and weakens the gain. This appears to hinder the change of the photocurrent, and this effect can ultimately be equivalent to an inductance L_m. In the lateral direction, the i-Ge for optical absorption can be equivalent to a plate capacitor C_a. The frequency resonance of the LC circuit can be comprehensively optimized via the on-electrode inductor L_p. Based on the key equivalent elements shown in Fig. 1a, a more complete model including the junction resistance and electrode parasitic capacitance is given in Supplementary Fig. 3. Figure 1e shows the simulated bandwidth and corresponding GBP with different L_p under a gain of 20. We prepare a reference APD with an identical junction region but without an inductor to experimentally extract the equivalent electrical parameters, which are then used to obtain these simulated results. It can be seen from Fig. 1e, when L_p is less than 540 pH, that the bandwidth and GBP increase very slowly, since the L_p is much smaller than the dominant inductance in the multiplication region (L_m ≈ 3.5 nH). The bandwidth is ~25 GHz without an external inductor, and when the L_p is near 540 pH, the maximum bandwidth exceeds 62 GHz, and the GBP can reach 1,200 GHz. At this point, the external inductance complements the internal one and achieves the optimal inductance required to fully resonate with the APD capacitor, resulting in a bandwidth and GBP leap. Continuously increasing L_p reduces the bandwidth in reverse, probably due to the rapidly cut-off mid- and high-frequency components under a relatively large inductance³⁷. In the wide range of 540–1.000 pH, the GBP is enhanced from 500 to over 1,000 GHz. However, in the vicinity of the 540 pH point, the performance is very sensitive to the selected L_p, and we therefore chose a ~700 pH inductance, fabricated through a 1.5 turn 105-μm-diameter circular spiral inductor. The simulated inductance for different sizes is given in Supplementary Fig. 4. Figure 1f shows a microscopy image of the fabricated APD with the on-electrode inductor. The APD is fabricated on a 220 nm silicon-on-insulator platform that is conventionally used for Si photonics. The device is fabricated at Advanced Micro Foundry (AMF). During the fabrication process, we design and define the key parameters for the optical/electrical structures and the doping conditions. All fabrication processes, including the Ge epitaxial growth proprieties and the detailed information, can be found in Methods.

Static response

Firstly, the static performance of the presented APD is measured, referring to d.c. electrical measurements in Methods. Figure 2a shows the dark current and photocurrent when operating at 1,550 nm with different optical powers varying from −17 to −29 dBm. The breakdown voltage is determined to be −8.9 V, according to 1/gain versus voltage curves^38,39 shown in Supplementary Fig. 5c. The low breakdown voltage provides low power consumption and compatibility with the integrated electrical circuit⁴⁰. The measured dark current is ~33 nA at −2 V and reaches 12 μA at −8.0 V (90% of the breakdown voltage). This result is much lower than previously reported dark currents of ~30–100 μA in lateral SACM APDs^23,34,35. The lower dark current is mainly due to the fewer defects and lower electric field at the Ge–Si interface. For comparison, Ge is usually grown inside a Si groove that is etched, resulting in Si lattice disruption and a higher defect density, as well as a larger Ge/Si contact area^23,34,35. On the other hand, our structure utilizes a gap between the intrinsic Ge and intrinsic Si regions to reduce the electric field from a typical value of ~2 × 10⁷ V m⁻¹ (ref. ²³) to <1 × 10⁷ V m⁻¹, showing lower tunnelling dark current components. The good Ge epitaxial growth and resulting low dark current are important to obtain the high sensitivity of the APD. When operating at a higher bias voltage beyond −9 V, the dark current becomes relatively high, mainly resulting from the tunnelling and the internal multiplication.

a, The measured current–voltage characteristic in the dark state and under optical powers of −17 to −29 dBm. The optical power is the light fed into the active region, deducting the optical loss of the grating coupler. b, The measured gain and optical responsivity. The inset shows the optical responsivity near −2 V. c, The measured S₂₁ characteristics from −3 to −9 V. d, The 3 dB bandwidth and corresponding GBP under different gains. The gain and bandwidth are obtained from b and c with voltage increases. The bandwidth and GBP fold back after the maximum gain of 19.6, due to the decreased gain after a voltage of −8.6 V.

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The optical responsivity under unity gain is 0.87 A W⁻¹ at −2 V, which is obtained by comparing the responsivity with the reference p–i–i–n photodiode without the charge layer on the same chip^19,20. The gain and responsivity under other voltages are shown in Fig. 2b. The optical responsivity near −2 V is shown in the inset to Fig. 2b. It is clear that −2 V is the boundary that differentiates the no-gain from the notable-gain areas. This also demonstrates that the unity gain occurs at −2 V. The gain reaches a maximum value at −8.6 V but decreases under higher voltage due to the high photocurrent density inside the junction. As the voltage increases from −8.6 to −9.2 V, both phonon scattering and the space charge effect occur, lowering the gain. This is the origin of the internal resonance phenomenon. The dependence of the gain on the optical power has been further investigated. The gain decreases as the optical power increases, which is also due to the space charge effect. When the reverse bias voltage is low, the gain does not change obviously with the optical power, and the photocurrent appears proportional to the optical power. However, under high voltages, the gain decreases with the optical power due to the space charge effect and the photocurrent becomes not proportional to the optical power⁴¹. In the measured optical power range, the APD achieves a maximum gain of 88 under −29 dBm. The maximum gain is ~116 when the optical power is low enough, as shown in Supplementary Fig. 5. When the optical power is increased to −20 dBm, the gain still reaches 19.5. Meanwhile, the maximum responsivity reaches 17.0 A W⁻¹ with a quantum efficiency of 1,357%. For high-speed applications, a gain of ~10–20 is usually suitable to realize high-sensitivity data reception⁴².

Dynamic response

To characterize the opto-electric bandwidth, the S₂₁ frequency response is measured, referring to the radio-frequency (RF) S parameter measurements in Methods. Figure 2c shows the S₂₁ frequency response of the APD under voltages from −3 to −9 V and an input optical power of −20 dBm. When operating with a bias voltage of −3 V, the presented APD has a 3 dB bandwidth of 1.7 GHz. The limited bandwidth is due to the incomplete depletion of the Ge region^43,44. The bandwidth increases from 1.7 to 46 GHz when increasing the bias voltage from −3 to −7 V, owing to the complete depletion and the minimized junction capacitance. The frequency responses show an obvious resonance phenomenon, with a gain peak appearing at a frequency of 42 GHz. In addition, the bandwidth shows a slight improvement from 46 to 53 GHz and remains unchanged when further increasing the bias voltage to −9 V. This is a result of the comprehensive influence of internal avalanche and impedance resonance under high voltages. The avalanche build-up process reduces the speed of the device, while the resonant effect leads to the bandwidth enhancement⁴⁵. The measured S₂₁ curves with L_p of 0, 300, 500 and 700 pH and corresponding bandwidths are shown in Supplementary Fig. 6. The results are consistent with simulation, verifying the applicability of the model. Figure 2d shows the results for the GBP changing with gain. Under low gain (<6), the GBP is very small since the bandwidth and gain are both low, and it increases almost linearly with the gain within the gain region of 9–19.5. The largest GBP is measured to be 1,033 GHz at −8.6 V (gain 19.5).

High-speed operation

The high-speed reception characteristics of the APD are measured via eye diagrams test, referring to high-speed signal measurements in Methods. The optical signal is converted through the APD without using a trans-impedance amplifier or an electrical amplifier. The APD operates at −8.6 V for maximum gain. In this experiment, post-compensation is used and the digital signals detected from the present APD are captured by a real-time digital storage oscilloscope. Finally, an offline digital signal process is carried out by using a computer to deduct the distortion of the high-speed electrical signals through the cables and the transmitter. As shown in Fig. 3a, we measure the open eye diagrams for 100 and 112 Gb s⁻¹ OOK signals by setting the input optical power as −12 and −8 dBm with signal-to-noise ratio (SNR) of 13.12 and 11.76 dB, respectively. Furthermore, the present APD is used to receive 100 and 200 Gb s⁻¹ PAM4 signals, under input optical power of −12 and −6 dBm with SNR of 19.47 and 18.11 dB. Finally, a four-channel APD array (Fig. 3b) is utilized to receive 4 × 200 Gb s⁻¹ wavelength multiplexing PAM4 signals, resulting in clear eye diagrams as shown in Fig. 3c.

a, The measured eye diagrams of 100 and 112 Gb s⁻¹ OOK and 100 and 200 Gb s⁻¹ PAM4. b, An optical microscopy image of the four-channel APD array. The wavelength multiplexing signals with 3.2 nm wavelength spacing are fed into the chip via edge coupling. c, The measured clear and open eye diagrams of 4 × 200 Gb s⁻¹ PAM4 signals. d, The measured BER results when operating at −8.6 V for the OOK signals of 100 and 112 Gb s⁻¹, the dashed horizontal line is the hard decision forward-error-correction (HD-FEC) threshold. e, The measured BER results when operating at −8.6 V for the PAM4 signals of 100 and 200 Gb s⁻¹, the dashed horizontal line is the HD-FEC threshold.

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The bit error rate (BER) measurement for the APD is provided on the basis of the experimental setup shown in Supplementary Fig. 7. Figure 3d shows the measured results when operating at −8.6 V for the OOK signals at bit rates of 100 and 112 Gb s⁻¹. Correspondingly, the sensitivities are −14.0 and −11.8 dBm at a BER of 3.8 × 10⁻³ for hard decision forward-error-correction operation. We also characterize the APD when receiving 100 and 200 Gb s⁻¹ PAM4 signals, as shown in Fig. 3e. It can be seen that the presented APD has sensitivities of −17.0 and −6.0 dBm, respectively. These results make the APD very competitive to satisfy the demands of applications with large capacity data transmission.

Since Kang et al. realized Ge/Si APDs with a GBP of 340 GHz and proved their advantages compared with InP-based APDs¹⁹, research focused on Ge/Si APDs has emerged in data communication. Table 1 presents a literature overview of state-of-the-art on-chip APDs^{16,17,19,20,22,23,34,46,47}, and Fig. 4 summarizes several works supporting over 50 Gb s⁻¹ using a radar image. In recent years, III–V APDs have used InAlAs as a multiplication material to achieve GBP values of up to 300 GHz, with more than 35 GHz bandwidth and data bit rates up to 100 Gb s⁻¹. However, low gain and high noise factor limit their sensitivities. The Ge/Si schemes benefit from the advantages of such materials and realize GBPs of 300–600 GHz. However, the bandwidth is lower than 30 GHz, being limited by the relatively low mobility of Si and Ge. This work shows an enhanced bandwidth as high as 53 GHz and an ultrahigh GBP of 1,033 GHz, the best among the counterparts. We attribute the good performance to the overall resonance effect in a narrow multiplication region and an on-electrode inductor. Therefore, the highest data reception has been demonstrated. In addition, the APD operates under low voltages below −9 V, being beneficial for low power consumption and electrical circuit integration. The main challenge of Ge/Si APDs is the relatively high dark current, due to the well-known lattice mismatch at the Ge–Si interface. However, careful fabrication processing and device design can minimize the impact.

The performance of APDs supporting >50 Gb s⁻¹ with bandwidth, GBP and bit rate.

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Sensitivity is important for APDs. For a signal at a given bit rate, the sensitivity of an APD is mainly influenced by its bandwidth and excess noise (related to the k factor). Although the k of Si material is considered to be low (~0.02–0.05), experiments have demonstrated that it could become higher when the multiplication region is very thin⁴⁸. This is because k is an exponential function of the electric field and increases with the electric field, while the avalanche electric field is higher for a thin avalanche region^38,48. The influence of k on the sensitivity needs to be considered, and a comprehensive sensitivity simulation under different k factors and bandwidths is shown in Supplementary Fig. 8. The bit rates of 50 and 100 Gb s⁻¹ are selected for the representatives, considering the 53 GHz bandwidth of the APD. The sensitivity degrades rapidly as the bandwidth of the APD decreases, while it degrades slowly as k increases. As a result, although k can be decreased, for instance, by increasing the intrinsic region to form a weaker avalanche electric field, the sensitivity may not be improved significantly since it is also limited by the bandwidth. The resonance effect is beneficial to improve the sensitivity through improving the bandwidth.

In conclusion, we have demonstrated a waveguide-integrated APD with a large bandwidth of 53 GHz and a record GBP above 1 THz, adopting a simple CMOS-compatible fabrication process. The APD supports >200 Gb s⁻¹ data reception per wavelength with high sensitivity and over 800 Gb s⁻¹, compatible with wavelength multiplexing, enabling robust and stable on-chip photodetection. This work is expected to open up a new route towards next-generation optical interconnects.

Device fabrication

The device was fabricated on a silicon-on-insulator wafer with a 220 nm top Si layer, a buried oxide (SiO₂, insulator) layer and a high-resistivity Si substrate, at AMF, Singapore. First, the top Si layer was etched into strip waveguides and Si slabs by 193-nm-deep ultraviolet lithography and Si dry etching. Subsequently, the Si slab was doped using boron with a dose of 1 × 10¹³ cm⁻² and energy of 40 keV for the charge layer. For the ohmic contact on Si, separate masks were used for heavily doped boron and phosphorus implantation. The dopants were activated using rapid thermal annealing at 1,030 °C for 5 s. The high-quality Ge epitaxy was achieved by a two-step low/high-temperature method based on AMF’s standard multi-project-wafer service⁴⁹. The substrate was first kept at 350 °C, and a thin SiGe buffer layer was grown on the Si slab. In the second step, 200 nm of high quality pure Ge was selectively grown on the buffer layer by commercial ultrahigh vacuum chemical vapour deposition at 550 °C with subsequent high-temperature annealing. With stepwise deposition and etching of SiO₂, the first contact hole to the Si contact region and Al metal layer were fabricated. Then, the second contact hole was formed on the first metal layer with a thickness of 2 μm. The second Al metal layer was deposited in the SiO₂ hole to form the spiral inductor and pads. During the fabrication process, we designd and defined the key parameters for the optical and electrical structures and the doping conditions. The Ge epitaxy was based on AMF’s standard multi-project-wafer service. Although the detailed parameters for Ge epitaxial growth cannot be disclosed because of business considerations, the service is publicly available at AMF.

D.c. electrical measurements

The I–V characteristic was measured using a source meter (Keithley 2601B), a probe station and a tunable laser. The photocurrent I_ph was obtained at 1,550 nm under a received optical power from −29 to −17 dBm by extracting the coupling loss of the grating coupler (4 dB). The dark current I_d was measured when no light was input. We then calculated the multiplication gain G(V) as the ratio of the net photocurrent (I_ph − I_d) at bias V to that measured at the unity gain point of −2 V thus

RF S parameter measurements

Small-signal RF measurements were carried out using a 110 GHz light component analyser (Keysight N4372E) in the range from 10 MHz to 60 GHz with a 50 Ω load resistance. The Impedance Standard Substrate (TCS1-100150) was used to calibrate the bias tee, cables and GS microprobe (TP100A) with one-port calibration. A polarization controller was used to optimize the polarization before coupling into the chip. Reverse bias voltages of 0 to −10 V were supplied to the APD by the source meter through a bias tee and GS microprobe.

High-speed signal measurements

The eye diagrams of the APD were measured by using a real-time digital storage oscilloscope with a 256 GSa s⁻¹ sampling rate (Keysight UXR0594AP). An OOK or PAM4 series with a pattern length of 2¹⁵ – 1 was generated by an arbitrary waveform generator (AWG, Keysight M8199A) and amplified by a 45 GHz high speed driver. A 40 GHz Mach–Zehnder modulator was adopted to modulate the continuous-wave light. The optical signal was fed into the APD, and the output RF signal was collected by the oscilloscope.