# Geiger-Mode Avalanche Photodiode Arrays Integrated to All-Digital CMOS Circuits
## 1 Introduction  
The MIT Lincoln Laboratory (Lexington, MA, USA) has been a world leader in the development of specialized high-performance charge-coupled-device imagers (CCDs) [1]. CCDs have outstanding performance and support advanced functions such as charge-domain image stabilization, electronic shuttering, and blooming control. The ultimate sensitivity limitation of a CCD is set by the readout noise of the output amplifier that senses the charge packets and converts them to analog voltage levels. The faster the readout rate, the more severe the readout noise penalty. This sensitivity limitation becomes important in photon-starved applications, such as night vision or high-temporal-resolution imaging.  
Interest in such scenarios lead to Lincoln's development of photon-counting image sensors, primarily based on arrays of custom-fabricated Geiger-mode avalanche photodiodes (GMAPDs) integrated with all-digital CMOS readout circuits. The term \"photon counting\" is used broadly here to mean that each photon arrival is digitally recorded by the pixel circuit. The pixel could be designed to either time stamp photons or count them. While the primary focus of this article is silicon GMPDs [2], Lincoln Laboratory has developed GMAPD arrays based on compound semiconductors sensitive at wavelengths ranging from 1.06 \(\upmu\)m [3] to the mid-wave infrared [4].  
The principal advantage of a photon counting image sensor is that it eliminates readout noise. Because digitization occurs within the pixel, there is no analog circuitry in the readout path, and therefore no analog circuit noise. This means that there is no readout noise penalty for operating at high frame rates, using short integration times, or dividing the incoming light into multiple spectral or spatial channels. In-pixel digitization therefore enables high-frame-rate imaging [5; 6], multispectral imaging [7], and spatial oversampling [8].  
A second advantage of a photon-counting image sensor is that it facilitates in-pixel time-to-digital conversion. The ability to digitally time stamp individual photon arrivals is an enabler for exquisitely sensitive lidar imaging systems. The GMAPD arrays can also be used as laser communication receivers in systems with challenging link budgets. Use of pulse-position-modulated formats allows for multiple bits of information to be encoded in a single transmitted photon [8].  
The integration of GMAPDs with digital CMOS can take advantage of Moore's Law scaling and 3D integration to incorporate on-focal-plane processing functions such as imaging stabilization, spatial filtering, change detection, and tracking of objects of interest without mechanical scanning.  
Potential disadvantages of GMAPDs include afterpulsing and crosstalk. Afterpulsing denotes false detection events triggered by carriers generated in previous events. To avoid afterpulsing the avalanche photodiode (APD) must be debiased for a sufficient time after an event to give such residual carriers time to recombine or be collected. Since the APD is unresponsive during this time, this leads to blocking loss and causes the count rate to saturate at high optical fluxes. Crosstalk is mediated by hot-carrier light emission by the avalanche process and is discussed at the end of Section 4.