Silicon single-photon avalanche diodes with nano-structured light trapping

Silicon single-photon avalanche detectors are becoming increasingly significant in research and in practical applications due to their high signal-to-noise ratio, complementary metal oxide semiconductor compatibility, room temperature operation, and cost-effectiveness. However, there is a trade-off in current silicon single-photon avalanche detectors, especially in the near infrared regime. Thick-junction devices have decent photon detection efficiency but poor timing jitter, while thin-junction devices have good timing jitter but poor efficiency. Here, we demonstrate a light-trapping, thin-junction Si single-photon avalanche diode that breaks this trade-off, by diffracting the incident photons into the horizontal waveguide mode, thus significantly increasing the absorption length. The photon detection efficiency has a 2.5-fold improvement in the near infrared regime, while the timing jitter remains 25 ps. The result provides a practical and complementary metal oxide semiconductor compatible method to improve the performance of single-photon avalanche detectors, image sensor arrays, and silicon photomultipliers over a broad spectral range.

oxidation. Due to dopant diffusion, after the thermal oxidation at 1000 • C, there is a higher doping in intrinsic region. So the depletion width decreases, which reduces the SPAD breakdown voltage.
Supplementary Note 1 | Nano-structure reflection measurement Inverse pyramid nano-texturing could be treated as a two dimensional grating, so in reflection measurement, it is expected to have a resonance valley in the spectrum. As in Supplementary   Figure 3(a), with photon injection angle shifts, the resonance valley has a clear shift. Across the spectrum, reflection is below 10 % when θ is between 0 • and 30 • . This shows that surface texturing serves as an anti-reflection layer. In comparison between control and light-trapping SPAD as in Supplementary Figure 3(b), the control SPAD has higher reflection as well as sharp resonances, suggesting a strong vertical resonance between SOI substrate and top surface. Light-trapping SPAD, however, has lower reflection and much weaker resonance, suggesting that photons are coupled to waveguiding mode and are horizontally propagating instead of creating a vertical resonance. will have a fairly decent absorption at different angles of incidence. This is because the nanostructure has been optimized for this wavelength. At different incoming angles, the absorption of 980 nm wavelength remains above 50 % of normal EQE and we could further optimize it by changing the nano-structure period and pattern (e.g. from square lattice to hexagonal or more complicated lattice structure). asured results for two wavelengths in two directions.

Supplementary Note 3 | Estimation of the uncertainty of the Photon Detection Efficiency
We derived the uncertainties of each measurement steps to calculate the final uncertainty of the PDE. The PDE of a SPAD can be calculated by the formula, − 1 µ ln 1−P 1 1−P 0 , where P 1 denotes the probability of detecting an avalanche signal per gate with pulsed illumination; P 0 denotes the probability of detecting an avalanche signal per gate without illumination; and µ denotes the average photon number of each laser pulse. Assuming that all of the uncertainties of the components were independent, the uncertainty of PDE is expressed as: where u denotes the standard deviation of each single variable. Equation (1)  Uncertainty of the Photon Count/Dark Count Probability In a single measurement, we use an ultra wide band digital oscilloscope to randomly sample the output signal of the SPAD. At each gate sampled, we check whether an avalanche pulse is detected in that gate. When a total of C t gates are checked and in which C p 1 avalanche pulses are found under illumination or C p 0 avalanche pulses are found without illumination, then P 1 and P 0 can be calculated by P 1 = C p 1 /C t and P 0 = C p 0 /C t respectively. The C t is constant in our measurements. The C p 1 obeys a binomial distribution, therefore the uncertainty of C p 1 is C t P 1 (1 − P 1 ). So the uncertainty of P 1 will be: In the same way, the uncertainty of P 0 will be: Uncertainty of the Average Photon Number The average photon number per pulse is calculated with the following equation, µ = kP , where P denotes the total laser beam power measured by optical power meter and k is a ratio determined by the laser pulse repeat rate, the photon energy, the beam spot size at 13.5% maximum intensity, the active area of our SPADs, and the alignment of SPAD and Gaussian beam center. The laser beam power P is measured by an optical power meter from Thorlabs Inc., PM200, with sensor head S130VC. The datasheets indicate that the measurement uncertainty of S130VC is 3 % and the measurement uncertainty of PM200 is 0.5 % of full scale (97 nW in our experiments). The beam spot size at 13.5% maximum intensity is measured to calculate the intensity at beam center, where our SPAD is placed. Thus the power portion that actually illuminates the SPAD can be calculated. The uncertainty of beam spot size contributes little to the uncertainty of average photon number per pulse. First, the beam spot size at 13.5% maximum intensity is about 3 mm in our experiment, which is significantly large compared to the 20 µm diameter of the SPAD. Second, the beam spot size is measured using a beam profiler (BC-106N), and if we fit the spot image in Matlab we will see the relative uncertainty will be about only 0.2 %. The accuracy of active area of our SPADs is guaranteed by design and fabrication. The wavelength of the laser, which is measured by an optical spectrometer, also has high accuracy.
The laser pulse repetition rate is quite stable and accurate. The significantly large beam spot size reduces the requirement of aligning the SPAD and beam center. So the alignment also contributes little to the uncertainty of average photon number per pulse. Also the not so perfect alignment will merely cause under estimation of photon detection efficiency. In summary, the uncertainty of laser beam power is the main part of uncertainty of average photon number per pulse, and k can be treated as constant. Thus the uncertainty of average photon number per pulse is : We can get the uncertainty of Photon Detection Efficiency using equations (1), (2), (3) and (4).

Supplementary Note 4 | Estimation of the Uncertainty of the Full Width Half Maximum of Timing Jitter
The full width half maximum (FWHM) of timing jitter is read out from the histogram of photon arriving time, which is the time from the laser pulse to the time the avalanche signal crosses the threshold. Let C max be the maximal counts of the histogram. Draw a 0.5C max horizontal line, which will cross the distribution on both left and right of the peak. The distance between the two cross points can be read out as FWHM. But the time bin is 5 ps, and the statistical fluctuation of counts on each bin is quite large, so some fitting is needed to get a more accurate read out of FWHM. It's hard to find a function to describe the whole distribution of photon arriving time detected by SPAD, so global fitting is not feasible. Instead, we choose a local fitting method.
Several data points near the two cross points are chose manually and fitted by a linear function t = a + bc separately, in which c is counts of photon arriving at t, and a, b are the coefficients to be fitted. The fitting result contains a 1 , b 1 with uncertainty u a 1 , u b 1 for the left cross point and a 2 , b 2 with uncertainty u a 2 , u b 2 for the right cross point. New cross points are calculated based on the fitting result, and a more accurate FWHM can be calculated. Let c 1 = c 2 = 0.5C max , and uncertainty u c 1 = u c 2 = √ 0.5C max , the uncertainty of FWHM will be: = (u a 1 ) 2 + (0.5C max u b 1 ) 2 + (b 1 u c 1 ) 2 + (u a 2 ) 2 + (0.5C max u b 2 ) 2 + (b 2 u c 2 ) 2 The uncertainty of FWTM and tail can be calculated in the same way.