# Geiger-Mode Avalanche Photodiode Arrays Integrated to All-Digital CMOS Circuits
## 5 A Photon-Counting Wavefront Sensor  
Adaptive optics systems for ground-based astronomy and space surveillance require sensors to measure the distortion of a wavefront (from either a bright star or an artificially created beacon) due to atmospheric turbulence. The Shack-Hartmann technique [18] uses arrays of lenslets that focus the light on quad-cell detectors; the displacement of a light spot from the center of a quad cell determines the partition of intensity among the four pixels. This in turn indicates the local wavefront tilt. Lincoln Laboratory has used its CCD imagers to build Shack-Hartmann wavefront sensors. However, in scenarios with weak beacon signals and fast wavefront update rates, the performance of CCDs is limited by readout noise. To address this problem, Lincoln developed Geiger-mode quad-cell arrays, to measure the number of photons from a beacon. Since the quad cell must be responsive to photons incident in between pixels, the low-fill-factor design shown in Figure 8 is not suitable. A high-fill-factor design was devised [19] and its cross section is shown in Figure 12.  
The upper p-type layer is implanted at high energy through an oxide mesa so that the doping profile peaks at a relatively shallow depth (1 \(\upmu\)m) in the center of each diode and deeper (2 \(\upmu\)m) around the periphery and between pixels. The shallow portion of this stepped implant separates the absorber and multiplier portions of each detector. The step lowers the electric field at the periphery of the diode, preventing edge breakdown. The peripheral part of the diode functions as a guard ring, collecting surface-generated dark current without triggering Geiger-mode events. The deep portion of the implant, which is partially undepleted, prevents the guard ring from collecting photoelectrons generated in the absorber; as indicated in the figure, these photoelectrons reach a nearby multiplier region by a combination of diffusion and drift.  
Figure 11: (a) 64 \(\times\) 64-pixel lidar focal plane fabricated by 3D integration of a GMAPD array with two tiers of SOI CMOS circuitry (b) Lidar image of a cone obtained by illumination from a doubled Nd:YAG microchip laser.  
16 \(\times\) 16 and 32 \(\times\) 32-subaperture quad-cell arrays were fabricated and hybridized to readout chips that count the number of detection events with a 10-bit counter in each pixel. The device could be operated with 20-\(\upmu\)s wavefront update latency while introducing no readout noise. Hybridization was accomplished first by bridge bonding and then later on by transfer and bump bonding. Pixel pitch within each quad cell was 50 \(\upmu\)m, with a 200-\(\upmu\)m spacing between subapertures [20].  
To verify the functionality and contiguous spatial response, a focused 5-\(\upmu\)m-diameter spot from a blue (450-nm) LED was raster scanned over the area of a quad cell and, at each 5-\(\upmu\)m step, recording the photon counts from each of the four pixels. Figure 13a is a contour plot of the count rate of the lower right pixel as a function of the position of the light spot. Figure 13b shows the aggregate count rate from all four pixels. This data shows a monotonic transition of detection activity from one pixel to its neighbor as the light spot is being moved across the midpoint. It also shows no droop in the aggregate response in the central region.  
These quad-cell arrays report out raw pixel intensity values, and the wavefront tilt calculation is done off chip. However, one can envision incorporating computational functions such as centroid and tracking into the pixel circuitry.  
Figure 12: High-fill-factor APD design used in quad cells and passive imaging devices.  
Figure 13: (a) Color contour plot of the count rate from the lower right detector as a function of the position of a small light spot raster scanned over the area of the quad cell; (b) Contour plot of the sum of the count rates from all four pixels as a function of light spot position.