Integrated avalanche photodetectors for visible light

Integrated photodetectors are essential components of scalable photonics platforms for quantum and classical applications. However, most efforts in the development of such devices to date have been focused on infrared telecommunications wavelengths. Here, we report the first monolithically integrated avalanche photodetector (APD) for visible light. Our devices are based on a doped silicon rib waveguide with a novel end-fire input coupling to a silicon nitride waveguide. We demonstrate a high gain-bandwidth product of 234 ± 25 GHz at 20 V reverse bias measured for 685 nm input light, with a low dark current of 0.12 μA. We also observe open eye diagrams at up to 56 Gbps. This performance is very competitive when benchmarked against other integrated APDs operating in the infrared range. With CMOS-compatible fabrication and integrability with silicon photonic platforms, our devices are attractive for sensing, imaging, communications, and quantum applications at visible wavelengths.


Supplementary Note 1. Coupling and Propagation Loss Measurements
We systematically characterized the coupling and propagation losses on our device by performing a series of cutback measurements with test waveguides. In addition to waveguide widths = 750, 900 nm mentioned in the main paper, here we also investigated = 450, 600 nm.
The optical transmission through the device was obtained by measuring the input power A and output power B with a pair of lensed fibers (see Supplementary Figure 1(a)). Using SiN cutback waveguides of various lengths SiN (without the Si rib waveguide), we fitted our results using to obtain the fiber-waveguide coupling loss f-SiN and the SiN waveguide propagation loss coefficient SiN . A representative plot is shown in Supplementary Figure 1(b). Following this, we measured another series of devices that also included Si waveguides of various lengths Si ; fitting our results to we obtained the SiN-Si end-fire coupling loss SiN-Si and the Si waveguide propagation loss coefficient Si . The measured coupling and propagation losses are shown in Supplementary  Figure 1(c). We note that we lack test structures for Si waveguides of width = 750 nm; nonetheless we anticipate that the coupling and propagation losses will not significantly deviate from that of the other widths. The observed fiber-waveguide coupling losses f-SiN agree with our expected values. The slight increase in f-SiN with width is likely due to the larger inverse taper angle, since the taper length and tip width are kept constant for all widths . The end-fire coupling loss SiN-Si is ∼3-4 dB larger than mode-matching calculations, which is attributed to fabrication imperfections resulting in a non-ideal waveguide interface. We also observed decreasing propagation losses with increasing width .
For APD characterization, the total insertion loss into the active device structure (i.e. the Si rib waveguide) is given by where SiN = 0.3125 cm is constant for all characterized devices. For both = 750 nm and 900 nm, this yields total = 7.1± 0.4 dB. We decided to focus on devices with lower insertion loss, and thus only considered devices with these two widths for further characterization in the main paper.

Supplementary Note 2. Electro-optic characterization setup
The schematic of the electro-optic characterization setup is shown in Supplementary Figure 2. Detailed descriptions of the components are found in the Methods section of the main text.  Figure 2. Schematic of the characterization setup. Horizontally polarized (TE) 685 nm light, which can be modulated with an RF signal using an electro-optic modulator (EOM), is coupled to the on-chip SiN waveguide with a lensed fiber. Electrical connections to the devices are made via contact pads on the chip surface using electrical probes. A bias tee separates the AC and DC signals from the APDs. The AC signal is sent either to a network analyzer for bandwidth measurements, or to a sampling oscilloscope for eye diagram measurements. An additional remote sampling head was used at 56 Gbps to obtain a clearer signal.

Supplementary Note 3. Eye diagrams
The reference eye diagrams of the EOM output are shown in Supplementary Figure 3(a). We observe clear, open eyes at up to 56 Gbps, indicating that our measurement system performs well at these bit rates. We are unable to measure at higher bit rates due to our limitations in generating faster bit patterns.
In general, the signal-to-noise ratio (SNR) obtained from the eye diagram increases with the reverse bias B , as the signal amplitude increases with a larger gain. Supplementary Figure 3(b) shows the SNR increase with B for laterally doped devices at 25 Gbps.
The eye diagrams presented in Fig. 5 of the main text show the open eyes at the highest data rate measured for each device. Supplementary Figures 3(c),(d) show additional data obtained at different data rates for lateral and interdigitated devices, respectively. We observe that all devices can be operated at lower data rates with a higher SNR.

Supplementary Note 4. Determination of the unity gain point
To determine the avalanche gain at a particular reverse bias B , the measured photocurrent ph has to be compared to that measured at a low bias voltage ug where avalanche effects are negligible, i.e. the APD exhibits unity gain. We can then attribute any further increase in ph at B > ug solely to the avalanche gain. An implicit assumption here is that the quantum efficiency (QE) -the efficiency of absorbing input photons and converting them into a photocurrent (without multiplication gain) -is saturated and remains essentially constant above ug . However, at a low bias, the junction might not be fully depleted yet, and the QE might not have reached saturation. Thus, the increase of the photocurrent ph with B may be caused by both an increase in the QE and , and it is difficult to distinguish between the two mechanisms. This leads to a difficulty in determining the unity gain bias ug .
In this section, we will present an empirical estimation based on the measured device photocurrent, as well as numerical simulations of the gain and QE. Finally, we analyse our findings and conclude with our choice of ug .
Empirical estimation: 2 nd derivative of the photocurrent with respect to bias Some reports in the literature rely on a bias-independent photocurrent at low B to indicate unity gain [1,2]. However, we do not observe such a feature in our current-voltage measurements (see Fig. 2(a) of main text). Other reports assume full or nearly full depletion at low B [3,4], but it is not obvious that this assumption is valid for our devices: the increase in 3 dB bandwidth with bias up to B ∼ 10 V suggests that the depletion region might still be widening.
Instead, we estimate the unity gain point by measuring where the second derivative of the photocurrent with respect to bias becomes zero [5,6], i.e. 2 ph / B 2 = 0. This yields a reasonable transition point between regimes where the increase in ph with B is likely dominated by a saturation in QE (at lower bias) and an increase in (at higher bias). For an input optical power of opt = 30.2 ± 0.2 dBm, we obtain ug of 1.45 -1.7 V across all device types (see Supplementary Figure 4).

Numerical simulations of gain and quantum efficiency
We simulate the DC electrical performance of laterally doped devices using the ATLAS device simulator (Silvaco Inc.), allowing us to analyze the electric field (an example is shown in Supplementary Figure 5(a)), ionization coefficients, charge carrier drift velocities, etc. Avalanche effects can be simulated by activating the impact ionization model (we choose the Selberherr's model) within ATLAS. By comparing the device photocurrent with and without the impact ionization model, we can extract a simulated value of the gain (see Supplementary Figure 5(b),(c)). The gain increases smoothly with the bias B , and already starts to deviate from unity gain ( = 1) at low bias. The QE can also be obtained by normalizing the simulated photocurrent to the input optical power (see Supplementary Figure 5(c)). While QE does vary with bias, it is already almost saturated at B ∼ 0 V with a high QE of ∼ 0.95. We note that the high doping concentrations lead to large built-in electric fields in the APD even without applied bias, which strongly accelerates the photogenerated charge carriers. Coupled with the small device size, this results in the charge carrier transit time being much shorter than the recombination lifetime. Thus, the photogenerated carriers are efficiently collected by the device before they are lost to recombination.
While it is sufficient to just simulate the 2D cross-section for laterally doped devices, interdigitated devices lack a convenient symmetry axis, and thus require full 3D simulations of the whole device. However, we do not have the required computational resources to perform a thorough quantitative analysis of the gain and QE for the interdigitated devices. Nonetheless, we assume the trends in gain and QE for the interdigitated devices will be similar to that of the lateral devices.

Analysis
Our empirical estimates of the unity gain point yield ug 2 V. This is consistent with our simulation results, which show that QE is already high and that the gain is already increasing even at these low bias voltages. Taking these into account, and to avoid overestimating the avalanche gain and gain-bandwidth product (GBP), we conservatively consider the unity gain point to be ug = 2 V for all devices and input powers opt in our analysis.

Supplementary Note 5. Analysis of simulated electric field profiles
In this section, we will analyze the representative electric field profiles of both laterally doped and interdigitated devices of the same width , and relate their features to the device characteristics we observe in our measurements. The electric field profiles are obtained using the ATLAS device simulator (Silvaco Inc.).
Supplementary Figure 6(a) shows the electric field profile in a laterally doped device, where the high-field regions are found along the p-n + junction within the waveguide core. More detailed simulation results of laterally doped devices can be found in our previous works [7,8]. Supplementary Figure 6(b) shows the electric field profile of an interdigitated device. To reduce computation time, we limited the scale of the device to only two periods of alternating p-n + regions. Nonetheless, we are still able to obtain the necessary features for our analysis. Both figures are simulated at just above the breakdown voltage of the devices.

Peak electric field strengths
We observe that the highest electric field strengths in the interdigitated device are concentrated at the corners of the n + -doped areas, and that their magnitude is significantly higher than that found in the laterally doped device with the same waveguide dimensions. The emergence of these localised high-field regions is likely to have resulted in a lower breakdown voltage br in interdigitated devices. This could also have contributed to the higher dark current observed in interdigitated devices, due to the exponential dependence of the dark carrier generation rate on higher field strengths.

Light absorption in undepleted n + -doped regions
In a p-n + junction, the p-doped regions are fully depleted, but the depletion region only extends minimally into the n + -doped regions due to their higher doping concentration. For the lateral doping profile, there is a large overlap between the depletion region and optical mode over the full length of the Si rib waveguide. However, for the interdigitated design, a significant amount of light absorption occurs in the undepleted n + -doped regions, as input light propagates along the alternating p-and n + -doped "digits".
It is less desirable for light absorption to occur in the undepleted n + regions. Due to the weak electric field strengths, the avalanche multiplication of the photo-generated charge carriers is less efficient compared to the high-field depletion region, and thus it is detrimental to the overall device gain and responsivity. This might explain the slightly lower responsivity observed in = 900 nm interdigitated devices compared to laterally doped devices, though we do not observe a significant difference for = 750 nm devices. The slower charge carrier diffusion in the low-field regions [7] would also contribute to the lower device bandwidth observed in our interdigitated devices. In our devices, input light is first incident on a n + -doped region. This results in an overall slightly higher absorption (a difference of ∼10%) in n + -doped compared to p-doped regions. Thus, the effect of light absorption in the n + -doped regions could be slightly reduced by having input light incident on the opposite end of the Si waveguide, such that the light is first incident on a p-doped region.
The dimensions of the interdigitated doping regions can potentially be optimized, e.g. the pitch and length of each doping region, or to have p-and n + -doped regions of different lengths. However, we foresee a design trade-off as increasing the depletion volume would also likely increase the device capacitance, which could lead to an RC-limited bandwidth.

Charge trapping
Charge trapping can occur as hot carriers are injected into the SiO 2 cladding, and are subsequently trapped at the interface between the n + -doped region and the cladding. The trapped charges would change the electrical field distribution inside the depletion region over time [9]. This effect is likely more severe in interdigitated devices, as the high electric fields occur at the edge of the Si rib waveguide (see Supplementary Figure 6(c)). This could lead to drifts in breakdown voltage and device gain over time, which is discussed in detail in the next section.
A potential mitigating strategy is to include guard-ring structures [10] at the Si-SiO 2 interface. In addition, adopting a shallow etch for the Si rib waveguide would also reduce the interface area for charge trapping.

Supplementary Note 6. Decaying gain and breakdown voltage drifts at high bias
In our devices, the device breakdown voltage br drifts towards higher values over time as a reverse bias voltage B is continuously applied. This is accompanied by an observed decay in the photocurrent and dark current from the onset of applying the reverse bias. Representative measurements based on a = 900 nm laterally doped device are shown in Supplementary  Figure 7(a),(b). The decrease is more pronounced at higher B , with a steep decay in the current at the start before gradually leveling off; while at lower B the decay is much slower.
There is a corresponding decrease in the gain with time, as shown in Supplementary  Figure 7(c). While the effect is minimal at lower B , where decreases by <10% over 10 mins for B <13 V at opt = -25 dBm, the drop in gain increases sharply at high B . The rate of decrease slows down significantly after the first 10 mins, but full stability of is observed only after ∼ 30 mins.
The br drift has been reported in other APDs [11,12]. As discussed above, this effect is likely to be more severe in interdigitated devices. This is consistent with our observation of a larger gain reduction over time for interdigitated devices (comparing Table 1 and Fig. 4 of the main text).
This phenomenon reveals two distinct operating modes for our devices: a gated mode where the APD is operated at high B with high gain, using a reset procedure to circumvent the decay in gain (explained in the following section); and a continuous mode where the APD is either operated at low B , or after the gain has stabilized over some time under a higher B . (a) Photocurrent ph (measured at opt = -25 dBm) and dark current dark at reverse bias B of 14 V and 18 V. Prior to each measurement, the device is reset with the application of a forward bias voltage. (b) The avalanche breakdown voltage br increases upon successive voltage sweeps. Each sweep starts from B = 0 V and is terminated upon the dark current dark reaching the breakdown current of 10 µA. Here, the device is not reset with a forward bias voltage in between runs. (c) Change in gain over time at different B . Here, the reverse bias is continuously applied.