Open Access
Add to BibSonomy
Abstract
We examine gated-Geiger mode operation of an integrated waveguide-coupled Ge-on-Si lateral avalanche photodiode (APD) and demonstrate single photon detection at low dark count for this mode of operation. Our integrated waveguide-coupled APD is fabricated using a selective epitaxial Ge-on-Si growth process resulting in a separate absorption and charge multiplication (SACM) design compatible with our silicon photonics platform. Single photon detection efficiency and dark count rate is measured as a function of temperature in order to understand and optimize performance characteristics in this device. We report single photon detection of 5.27% at 1310 nm and a dark count rate of 534 kHz at 80 K for a Ge-on-Si single photon avalanche diode. Dark count rate is the lowest for a Ge-on-Si single photon detector in this range of temperatures while maintaining competitive detection efficiency. A jitter of 105 ps was measured for this device.
© 2017 Optical Society of America
1. Introduction
Single photon detectors, originating from photomultiplier tubes in the late 1940’s to current solid state semiconductors [1], offer the resolution required for communication beyond the classical limits of typical telecommunication. All forms of avalanche photodiodes rely on the same fundamental process, avalanche multiplication of a single photo-excited carrier into a measurable signal. Superconducting detectors, such as nanowires, have been shown to have the highest single photon detection efficiency (SPDE), in some cases exceeding 90% [2]. III-V single photon avalanche diodes (SPADs) offer the next best SPDE, greater than 45% [3–5]. However, integrating either superconducting or III-V detectors with CMOS photonic circuits would requires additional, and costly, processing. A reasonable approach is to improve CMOS compatible devices performance [6–12].
At the limit of photo-detection, single photon avalanche photodetectors must be able to resolve an incoming signal in the form of a single photon from thermally generated carriers that creates a dark count noise background. Specifically in the near-IR spectrum, applications of SPADs offer improved resolution for quantum key distribution (QKD) [13], 3-D image sensing, and light detection and ranging (LIDAR) [15]. Waveguide-coupling the detectors allows integration with other photonic integratable devices. Ge-on-Si SPADs have so far been fabricated in a vertical manner responsive to surface incident radiation with the first Ge-on-Si photon counter having an SPDE of approximately 0.0017 %, at 1.21 µm [14]. Geiger-mode operated Ge-on-Si APDs have reached 14% SPDE at 1.31 µm and 200 K, however dark count rates (DCR) are as high as 100 MHz have been reported [16]. More recently, Warburton et al. have improved Ge-on-Si SPADs dark count rates to 6 MHz at 100 K [17]. This came at the expense of SPDE, which was only 4%.
In this work, we extend our lateral avalanche photodiode design from linear mode [12, 18, 19] to Geiger-mode operation in a waveguide-coupled Ge on Si avalanche photodiode. Our lateral Geiger mode avalanche photon detectors (Gm-APD) compact areal design results in reducing dark count rate. The waveguide-coupled Gm-APD offers full compatibility with standard silicon photonics processes with addition of a single p-charge implant mask layer. The Gm-APDs were tested through temperature in order to examine the temperature dependence of photon detection efficiency and DCR noise characteristics. The temperature was increased from 4 K to 220 K, for a complete span from low cryogenic temperatures to temperatures achievable with stacked thermo-electric (TEC) coolers.
Figure 1(a) shows a schematic representation of the Ge-on-Si waveguide-coupled Gm-APD. Figure 1(b) shows a processed cross-sectional SEM image of the fabricated waveguide-coupled Gm-APD. Selectively grown Ge acts as a high index optical absorbing material into which light from the waveguide couples. Ge is a CMOS compatible material responsive to telecommunication wavelengths such as 1310 nm and 1550 nm. We have demonstrated PiN photodetectors with similar structure which have a responsivity of 0.8 A/W at 1510 nm [9]. In the APD structure, a Si p-charge layer under the Ge acts as a screening layer to prevent the large electric field in the un-doped Si multiplication region (MR) from penetrating significantly into the absorbing Ge. By separating the absorption and multiplication regions the device takes advantage of the superior impact ionization ratio and hence multiplication characteristics of the silicon. The charge layer is p-doped to provide the proper polarity for a reverse biased avalanche photodiode. Note that the intrinsic multiplication region is on both sides of the charge layer, symmetrically displaced from the center axis.
Fig. 1 (a) Schematic cross-section for lateral separate absorption and charge multiplication APD. The p-charge region and the multiplication regions (MR) in the symmetric Gm-APD are shown. Ge absorber is located above the waveguide feed and p-charge layer extends out from Ge-Si interface. (b) Angled SEM image of Gm-APD with oxide cladding removed. The input waveguide is shown.
Given an applied bias above breakdown for Si, the electric field in the Si “punches” through the p-charge layer into the Ge and causes photo-generated carriers to drift into the Si layer. The carriers are accelerated in the Si multiplication region where they undergo impact ionization. This generates additional carriers which are again accelerated leading to additional impact ionization. This multiplicative ionization of generated carriers is the gain mechanism by which the APD can turn a single photon absorption into a detectable current. For a single photon detector, it is critical to prevent extensive penetration of the electric field into the Ge while keeping the field in the Si above breakdown prior to photo-generated carriers entering the multiplication region. This order of operation will ensure a measurable signal with Geiger mode avalanche operation. However, continued applied bias above breakdown results in substantial current flowing through the device leading to thermal runaway, so the overbias is limited temporally to a gated window, after which the bias is lowered below breakdown. The reduced gated biasing, along with a properly doped charge layer reduces thermally generated carriers in the Ge from causing false avalanche events in between gates, which will have the detrimental effect of increasing the dark count rate.
1.1. Fabrication
The waveguide-coupled lateral APDs utilize a separate absorption region of selective epitaxially grown Ge with a narrow 1 µm width, on a 1.5 µm wide p-implanted charge layer on the Si SOI substrate. Gm-APD’s with symmetric multiplication region (MR) widths of 1.2 µm were examined. It should be noted that the p-doped charge layer extends beyond the footprint of the epitaxial Ge. Previous work on Ge-on-Si APDs operated in linear mode [12] required this positive overlap in order to keep the field in the Si from penetrating directly into the Ge absorption layer. Boron difluoride (BF2) is implanted with 110 keV with a dose of 1.75 × 1012 cm−2 targeting an active p-charge layer density of 1.25 × 1017 cm−3. The Ge contact is formed by BF2 implantation into Ge and activation to a concentration of 1 × 1019 cm−3 to form a top contact. Ti/TiN metal liner is used for ohmic contact to the Ge. The Si contact is fabricated using a heavily doped n+ layer that is formed prior to Ge growth. Figure 1(b) is an angled SEM image of our device illustrating the 15.9 µm device length. Lengths ranging from 8 to 32 µm were tested at a wafer scale, however, the 15.9 µm length APD showed best dark current performance while maintaining high responsivity. Lastly, the n+ Si contacts, through Tungsten vias, are electrically connected to create a symmetric design. Thus the electric field within the germanium is largely vertical, increasing the likelihood that a generated carrier will drift down into the multiplication region, rather than into the sidewall of the germanium.
2. Gated Geiger-mode operation
Gated Geiger-mode operation of an APD is a periodic pulsed biasing method designed to reduce noise by essentially turning the detector off when no signal is expected. In this technique, photon pulses are timed to arrive within a time interval in which the detector is biased above breakdown and hence armed. The absorption of a photon and subsequent transport of an electron to the APDs multiplication region triggers an avalanche of carriers which gives rise to a large current pulse. The runaway avalanche process provides high gain, but if allowed to continue would destroy the APD. The gating process turns off the overbias, hence quenching the avalanche and allowing the detector to be re-armed for the next photon pulse. We characterize this mode of operation by using time correlated single photon counting (TCSPC) electronics.
Figure 2 illustrates the gating sequence for Geiger mode operation. The inset shows the dark IV characteristics of the APD through the breakdown voltage Vbr into the avalanche regime. A DC bias voltage is applied to the detector, which puts it into a low dark current state just below breakdown. A series of periodic AC overbias pulses VAC are applied at a frequency, frep = 1/Trep. The temporal pulse width, Tpulse, is typically kept short to insure that the probability of a dark count is low and the repetition period is long enough to ensure that parasitic false counts from traps do not trigger the avalanche in a process known as afterpulsing. Short photon pulses which arrive within the time-window Tpulse trigger an avalanche signal with some probability. By counting the current signals which exceed a discrimination threshold, we obtain a time-series count of the firing or clicks of the detector. The click statistics of a gated Geiger mode APD will depend on the many parameters shown in figure 2, such as overbias, VEx + Vbr = VDC + VAC, pulse period, and pulse width, and include other device factors like temperature and doping. From these measurements, we can evaluate the detection probability under different detection conditions, such as the percent overbias defined by the ratio VEx/Vbr. In the next subsections, we review the underlying principles needed to extract key metrics for single photon detection using our integrated waveguide-coupled gated Geiger mode APD.
Fig. 2 Illustration of gated Geiger mode operation of the APD. The APD is initially dc biased VDC below the avalanche breakdown voltage Vbr. A periodic series of ac voltage pulses VAC are applied to the APD pushing temporarily the total excess bias, VEx, above the breakdown voltage for the device. A synchronized narrow width optical pulse train is timed to arrive within the over-bias time window triggering avalanche breakdown of the APD and generating a large amplified photocurrent pulse. Inset shows a dark IV characteristic for the APD showing the breakdown voltage.
2.1. Single photons
Single photon detection is the quantum limit of detection since the photon is the fundamental quanta of the electromagnetic field. In order to detect single photons, we need a source of single photons. Coherent states can be generated by a pulsed laser and are quantum optical states that have a natural classical correspondence with the photons electric field amplitude. The photon probability in the number representation for a coherent state is given by
where the average photon occupation is 〈n〉. Eq. (1) is a Poisson distribution for the photon probability and gives the arrival time statistics for a photon stream from a coherent laser source. By suitably attenuating a laser pulse, we can create photon states with average photon number considerably smaller than 1. The average photon number per pulse is given by 〈n〉 = PaveTrepλ/hc, where λ is the wavelength, and Pave is the average optical power. These hattenuated coherent states represent a source of single photons for the gated Geiger mode single photon detection scheme outlined. (See figure 2)2.2. Dark counts and single photon detection efficiency
The quantum efficiency, η, for the absorbing media represents the conversion efficiency of photons into electron-hole pairs and is key to the optoelectronic conversion into photocurrent. Therefore at very low photon flux the absorber under bias acts as a Poissonian source of photocurrent. Explicitly, the average number of carriers generated is related to the average photon number . The induced photocurrent is , where M is the multiplication gain. Gated Geiger mode operation shown in fig. (2) results in large multiplication of the photocurrent (M ≃ 104 or greater) if the detector is triggered in the short time interval when biased above Vbr.
In the dark, thermal and tunneling processes in the semiconductor can create generated carries that trigger the APD avalanche. These so called dark counts give rise to a shot noise Poissonian count profile. Thus, the probability of a dark count is obtained by summing the Poisson distribution over all non-zero generated carriers giving rise to the detector counts. The dark count probability is
The mean number of carriers is related to the short-time window τ, and is given by , where is the average number of carriers, and ρ is the dark count rate or DCR. It is clear that by shortening the over-bias gate length τ, which reduces the time the detector is armed, we can reduce the dark count rate.
The photon detection efficiency can be determined from the click probability when the detector is run under the pulsed illumination shown in Figure 2. It is obvious that a count can be triggered by an arriving photon or a dark count and we assume that the total click probability is Poissonian, such that
where µ is the mean number of carriers generated and pc is click probability. The mean number of carriers can be expressed as the sum of the dark count and the photon detection contribution, such that µ = ζ 〈n〉 + ρτ. The photon detection efficiency in terms of click probability and the dark count probability isThe single photon detection efficiency, or SPDE, corresponds to the detection efficiency ζ when the average photon number per pulse, 〈n〉 ≪ 1. The fractional average photon number guarantees that multi-photon pulses (2 or greater) are highly improbable based on the coherent state Poissonian statistics.
As we will demonstrate in the next section, the dark count probability and the illuminated click probability for the gated Geiger mode detector can be directly measured experimentally by running the detector in the dark and with photon pulses as shown in figure 2. We can therefore determine the derived dark count rate and single photon efficiency for the detector under different operating conditions.
3. Experiment
Figure 3(a) shows the schematic of the gated Geiger mode experimental setup and (b) shows the Gm-APD electrical circuit. The gated Geiger mode pulsed bias scheme of figure 2 is obtained by combining the DC voltage (VDC) from a Keithley 2400 sourcemeter with the AC (VAC) pulses from an Agilent B1110A pulse generator through a high-speed bias-tee. The synchronized optical pulse train is generated from a narrow linewidth pulsed diode laser (PicoHarp PDL-800) operated at 1310 nm. A variable attenuator (EXFO FVA-60B) was used to attenuate the incoming pulsed signal in order to obtain optical power levels corresponding to 〈n〉 ≪ 1.
Fig. 3 (a) Schematic of the gated-Geiger mode single photon measurement setup. Key components shown are a pulsed laser, AC source pulse generator, DC power supply, bias-tee, high-speed oscillloscope, and time correlated single photon counter. The black (red) lines represent electrical (optical) traces. (b) Circuit diagram of the device under test (DUT). The DUT is in a cyrostat for examining Gm-APD performance as a function of temperature.
The device under test (DUT) was maintained in a closed cycle hcryogenic probe station (Montana Instruments) for variation of the device temperature from 4 K to room temperature. The device was wirebonded to a carrier board with high speed SMP connectors. Light was coupled onto the chip using cleaved ultra-high numerical aperture(UHNA) fibers, edge coupled to inverse silicon taper waveguides. A straight through waveguide on the same chip was measured at temperature and used to calibrate the coupling loss for determination of the optical power reaching the detector. In order to calculate the coupling loss, the throughput was measured multiple times, requiring the fiber to be fully retracted, then contact between the fiber and end-fire waveguide was redone. This procedure yielded a coupling loss of 7.11 dB/facet with an uncertainty of ± 0.06 dB. During Geiger mode operation, the amplitude of the signal on the oscilloscope helped in determining if re-optimization of the fiber was necessary, for instance, when the coupled power was low.
The gated Geiger mode signal was observed on a high-speed oscilloscope where the threshold was adjusted above the AC source noise. The trigger threshold of the oscilloscope was adjusted for each DUT in order to trigger on an avalanche within the pulse bias time window. (See Figure 4(a)) Prior to breakdown, the device acts as a capacitive load. The fast rising and falling edge of the AC bias pulse is able to pass through the device, and results in transient spikes, which must be separated from the actual breakdown signal. In our case, this was accomplished by adjusting the threshold of the oscilloscope in order to trigger at a voltage above that of the AV bias feed through. The signal resulting from breakdown of the APD was much higher than this, allowing efficient detection. The oscilloscope provided a synchronized output trigger which was connected to one channel of a PicoHarp 300 (TCSPC).
Fig. 4 (a) Oscilloscope trace of Gm-APD under pulsed single photon illumination. Voltage and time scales are 1 mV/div and 1 ns/div respectively. (b) Histograms for gated Geiger mode single photon detection. Red dots are for pulse illuminated APD with 〈n〉 = 0.1 photons, and black dots are for the APD in the dark. The temporal analysis window τ is shown schematically. The dark count probability is proportional to the cross-hatched area, and detection probability is proportional to the integrated area under the red fit Gaussian.
The TCSPC is used in the experimental configuration to construct an arrival time histogram of APD counts above the threshold relative to the beginning of the AC bias pulse. The overbias pulse is used to start the TCSPC counter where the pulse time window is subdivided into 4 ps bins. A count signal above threshold is recorded and subsequently turns off until the next overbias gate. In this configuration, the total number of counts (Nc) is obtained by summing up the counts in the histogram. The total number of overbias gates (Ng) is given by the total collection time and the repetition rate, Ng = frepTtot. From this data, we can derive the click probabilities for the detector under single photon illumination conditions and in the dark. In the next section, we will demonstrate how analysis of this data gives the SPDE and DCR detector characteristics.
3.1. SPDE and DCR analysis
Figure 4(a) shows the oscilloscope trace illustrating the arrival time variation of the avalanche current pulse generated by the pulsed optical signal. The capacitive feed-throughs are clearly seen and set the scope threshold limit for the triggering. Figure 4(b) contains a light and dark arrival time histogram for our waveguide-coupled Geiger mode APD. The vertical axis gives the number of counts and the horizontal axis the time bins. A Gaussian curve has been fit to the data. Due to the rising and falling edge of the AC bias pulse, it is more convenient to analyze the data over a window shorter than the actual gate pulse, τ shown in figure 4(b). By doing this, the overbias voltage, and therefore the dark count probability and detection efficiency, can be assumed constant. The raw histogram data can be converted into a probability rate by dividing the individual counts per bin nc by NgΔt, where Δt = 4ps is the bin time interval. The probability rate is r(t) = nc (t)/NgΔt. The count probability is then given by
where we are integrating over the small (2 ns) time window shown in figure 4(b). Similarly, we can obtain pd, the dark count probability by integrating the dark rate histogram. From eqs. (2) and (4), we can substitute the extracted probabilities and determine the DCR (ρ), and the SPDE (ζ). SPDE was determined by first subtracting off the counts associated with no light incident on the detector, this is the red hash lines in Fig. 4(b). Then, by fitting a curve to the remaining counts associated with incident photons, we are able to divide the sum total number of photon clicks by the accumulation time, rate of repetition, and average number of incident photons, which is the single photon detection efficiency. In the following section, we will examine these derived single photon detector characteristics as a function of the percent overbias and the temperature of the detector.4. Results
The Gm-APDs were characterized at different over-biases and at temperatures ranging from 5 K to 220 K. At each temperature the devices were allowed to reach equilibrium prior to I-V characterization. Figure 5(a) shows the dark and illuminated IV characteristics for the various temperatures examined in this paper. The IV characteristics show a trend of increasing breakdown voltage as temperature increases. Increasing temperature necessitates higher electric fields in order to reach breakdown because of the increase in carrier cooling caused by phonon scattering [21]. Furthermore, the dark IVs show abrupt transitions from low noise current, <10 pA, to current compliance. This type of behavior suggests that a sufficiently doped charge layer restricts non-photon generated carriers from entering the multiplication region and prematurely setting off an avalanche.
Fig. 5 Temperature dependent Geiger mode characteristics of lateral APD. (a) IV characteristics for multiple temperatures in the dark and under CW laser illumination. (b) DCR vs. excess bias for various temperatures. (Uses same color code as (a)). (c) DCR vs. repetition rate for the gated overbias voltage at 80 K. (d) Single photon detection efficiency (SPDE) and DCR for the Gm-APD measured at 80 K as a function of % overbias. Here the overbias is given by VEx/Vbr in percent.
Next the DCR was measured as a function of the percent overbias (VEx/Vbr) for temperatures of 5, 80, 160, 165, 170, 180, and 220 K, respectively. Figure 5(b) shows that below a nominal temperature of 165 K, the dark count rate is largely unaffected by temperature, but quickly increases above this critical temperature. The gated overbias repetition rate was frep= 2kHz, and the pulse width was fixed at 10 ns for all of the temperatures.
Figure 5(c) shows the dependency of DCR as a function of the frequency of repetition. There is an immediate increase in DCR with increasing repetition rate measured at 80 K. This is more than likely due to the device being operated at such a low temperature that the trapped charge lifetime is likely greater than tens of microseconds [22]. This explains why even at our lowest frequency of repetition, 2 kHz, we see an increase of almost an order of magnitude when the rate is changed to 10 kHz.
Finally, DCR and SPDE were measured for a Gm-APD as a function of excess overbias with the temperature fixed at 80 K. Figure 5(d) shows a Gm-APD’s single photon detection efficiency and dark count rate as a function of excess bias. The integration window τ ≃ 4ns for each SPDE and DCR measurement. The repetition rate for the gate pulses was also held fixed at 2 kHz and VAC was increased. (See figure 3) The Gm-APD achieved 5.27% single photon detection efficiency from a highly attenuated pulsed laser source with 〈n〉 = 0.1 mean photons per pulse. The sub MHz DCR was measured at low excess bias, reaching 534 kHz at the highest detection efficiency. Improving the SPDE is the next step, warranting studies with a 1510 nm pulsed laser for a complete study.
The Gm-APD jitter can be obtained from the single photon histogram of figure 4. The sources of timing jitter are from the pulsed-laser, the gating electronics, and the intrinsic response of the Gm-APD. Here the jitter is
where σHist ≃ FW H M/8 ln(2) was obtained from the histogram FWHM of 116 ps, the laser jitter was measured to be 32 ps, and the electronic jitter was determined to be 31 ps from the hardware specs. Thus, the estimated jitter of the Gm-APD was determined to be 105 ps.5. Conclusions
In this paper, we have described the design, fabrication, and characterization of an integrated waveguide-coupled Ge-on-Si lateral avalanche single photon detector operated in Geiger mode within our Si photonics process. We have demonstrated greater than 5% SPDE operating in the telecom O-band (1310 nm) with the lowest dark current for this temperature range of 534 kHz. An extracted jitter of 105 ps was measured. Furthermore, we find a transition temperature of ≃ 160 K above which the DCR increases dramatically. This work provides a detailed study for dark count rate with dark count probability exceeding previous state of the art Ge on Si SPADs [16, 17] and the first application of a waveguide coupled Ge on Si APD as a single photon detector. Temperature studies were done to illustrate the wide range of operable temperatures the Gm-APD can optimally work at and how little performance suffers at higher temperatures. Our devices have been well characterized with explanation of testing environment and setup.
Future detector designs will include optimization of the p-Si charge layer doping and variation of the Ge epi growth conditions and geometry to increase SPDE for an overall class leading Ge-on-Si single photon detector. The charge layer acts as a scattering and absorbing medium for the photon [23], and as a recombination site for the photo-generated electron. Similarly, within the Ge absorption region, threading misfit dislocations may be trapping the photo-generated charges, thus reducing the probability of it reaching the multiplication region.
Funding
National Nuclear Security Administration contract DE-NA0003525.
Acknowledgments
We would like to thank Nick Boynton and Kate Musick of Sandia Nat. Labs. Funding for this work was provided by Sandia’s Laboratory Directed Research and Development (LDRD) program. Sandia is a multimission laboratory operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the United States Department of Energy’s National Nuclear Security Administration.
References and links
1. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3, 696–705 (2009 [CrossRef] ).
2. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013 [CrossRef] ).
3. B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for 3-D imaging,” Lincoln Lab. J. 13, 335–350 (2002).
4. C. Hu, X. Zheng, J. C. Campbell, B. M. Onat, X. Jiang, and M. A. Itzler, “Characterization of an InGaAs/InP-based single photon avalanche photodiode with gated passive quenching with active reset circuit,” J. Mod. Opt. 13, 1632–3044 (2010).
5. M. Liu, X. Bai, C. Hu, X. Guo, J.C. Campbell, Z. Pan, and M.M. Tashima, “Low dark count rate and high single photon detection efficiency avalanche photodiode in Geiger-mode operation,” IEEE Photon. Technol. Lett. 19, 387–390 (2007 [CrossRef] ).
6. M. R. Watts, J. Sun, C. DeRose, D. C. Trotter, R. W. Young, and G. N. Nielson, “Adiabatic thermo-optic Mach-Zehnder switch,” Opt. Lett. 38, 733–735 (2013 [CrossRef] [PubMed] ).
7. J. A. Cox, A. L. Lentine, D. J. Savignon, R. D. Miller, D. C. Trotter, and A. L. Starbuck, “Very large scale integrated optical interconnects: coherent optical control systems with 3D integration,” in Integrated Photonics Reseach, Silicon and Nanophotonics (2014), pp. IM2A1.
8. J. A. Cox, D. C. Trotter, and A. L. Starbuck, “Integrated control of silicon-photonic micro-resonator wavelength via balanced homodyne locking,” Opt. Express 22, 52–53 (2013).
9. C. T. Derose, D. C. Trotter, W. A. Zortman, A. L. Starbuck, M. Fisher, M. R. Watts, and P. S. Davids, “Ultra compact 45 GHz CMOS compatible Germanium waveguide photodiode with low dark current,” Opt. Express 19, 527–534 (2011 [CrossRef] ).
10. A. L. Lentine, J. A. Cox, W. A. Zortman, and D. J. Savignon, “Electronic interfaces to Silicon photonics,” Proc. SPIE 8989, 89890F (2014 [CrossRef] ).
11. A. L. Lentine and C. T. DeRose, “Challenges in the implementation of dense wavelength division multiplexed (DWDM) optical interconnects using resonant silicon photonics,” Proc. SPIE 9772, 977207 (2016 [CrossRef] ).
12. N. J.D. Martinez, C. T. DeRose, R. W. Brock, A. L. Starbuck, A. T. Pomerene, A. L. Lentine, D. C. Trotter, and P. S. Davids, “High performance waveguide-coupled Ge-on-Si linear mode avalanche photodiodes,” Opt. Express 24, 19072–19081 (2016 [CrossRef] [PubMed] ).
13. X. Jiang, M. Itzler, K. O’Donnell, M. Entwistle, M. Owens, K. Slomkowski, and S. Rangwala, “InP-based single-photon detectors and Geiger-mode APD arrays for quantum communication applications,” IEEE J. Sel. Top. Quantum Electron. 21, 3800112 (2015 [CrossRef] ).
14. A. Y. Loudon, P. A. Hiskett, G. S. Buller, R. T. Carline, D. C. Herbert, W. Y. Leong, and J. G. Rarity, “Enhancement of the infrared detection efficiency of silicon photon-counting avalanche photodiodes by use of silicon germanium absorbing layers,” Opt. Lett. 4, 219–221 (2002 [CrossRef] ).
15. B. Aull, “Geiger-mode avalanche photodiode arrays integrated to all-digital CMOS circuits,” Sensors (16, 495 (2016 [CrossRef] ).
16. Z. Lu, Y. Kang, C. Hu, Q. Zhou, H. Liu, and J.C. Campbell, “Geiger-mode operation of Ge-on-Si avalanche photodiodes,” IEEE J. Quantum Electron. 47, 731–735 (2011 [CrossRef] ).
17. R. Warburton, G. Intermite, M. Myronov, P. Allred, D. Leadley, K. Gallacher, D. Paul, N. Pilgrim, L. Lever, Z. Ikonic, R. Kelsall, E. Huante-Ceron, A. Knights, and G. Buller, “Ge-on-si single-photon avalanche diode detectors: design, modeling, fabrication, and characterization at wavelengths 1310 and 1550 nm,” IEEE Trans. Electron Dev. 60, 3807–3813 (2013 [CrossRef] ).
18. N. Duan, T.-Y. Liow, A. E. Lim, L. Ding, and G. Lo, “High speed waveguide-integrated ge/si avalanche photodetector,” in “Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013,” (Optical Society of America, 2013), p. OM3K.3.
19. S. Zhu, K. W. Ang, S. C. Rustagi, J. Wang, Y. Z. Xiong, G. Q. Lo, and D. L. Kwong, “Waveguided Ge/Si avalanche photodiode with separate vertical SEG-Ge absorption, lateral Si charge, and multiplication configuration,” IEEE Electron. Dev. Lett. 30, 934–936 (2009 [CrossRef] ).
20. J. C. Garrison and R. Y. Chiao, “Quantum Optics,” (Oxford University Press, 2008 [CrossRef] ).
21. D. J. Massey, J. P. David, and G. J. Rees, “Temperature dependence of impact ionization in submicrometer Silicon devices,” IEEE Trans. Electron. Dev. 53, 2328 (2006 [CrossRef] ).
22. R. G. Brown, R. Jones, J. G. Rarity, and K. D. Ridley, “Characterization of silicon avalanche photodiodes for photon correlation measurements. 2: active quenching,” Appl. Opt. 12, 2383–2389 (1987 [CrossRef] ).
23. R. I. Soref and B. R. Bennet, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987 [CrossRef] ).
