# Geiger-Mode Avalanche Photodiode Arrays Integrated to All-Digital CMOS Circuits
## 2 Geiger-mode APDs and Photon-to-Digital Conversion  
There are many types of detectors that have single-photon sensitivity, including photomultiplier tubes, image intensifiers, superconducting nanowires, and CCDs with avalanche gain registers [9]. GMAPDs, also known as single-photon avalanche detectors or SPADs [10], have a combination of advantages over these other photon-counting technologies. It is an all-solid-state device technology, scalable to many pixels, capable of room-temperature or thermoelectrically-cooled operation, and as noted already, amenable to on-focal-plane digitization and processing.  
An avalanche photodiode is a _p-n_ junction diode whose doping profile supports high electric fields near the junction at operational bias. A photoelectron or photohole created by the absorption of a photon is accelerated to sufficient energy to initiate a chain of impact ionization events, creating offspring electron-hole pairs and leading to internal gain. Once this avalanche process is underway, there is a competition between carrier generation and carrier extraction. Below the avalanche breakdown voltage, carriers are being extracted faster than they are being generated. The current flow decays, leading to self-termination of the avalanche process. This gives finite gain and therefore produces a photocurrent that is proportional to the intensity of the incident light. This is the traditional mode of operation used in optical communication receivers, known as linear mode. The gain is an increasing function of bias, and there is a random variation of gain that degrades signal-to-noise ratio.  
The APD can also be operated above the avalanche breakdown voltage. When an avalanche starts, carrier generation predominates over extraction leading to exponential growth of the current. This growth is arrested by series resistance (in most cases mediated by space charge buildup). This mode of operation is known as Geiger mode, in which a single photon can initiate an avalanche that is self-sustaining. Of course, the APD must then be reset by reducing the bias to below breakdown long enough to terminate the avalanche, a process known as quenching.  
The physics of Geiger-mode operation lends itself to a startlingly simple way of interfacing the GMAPD to a digital CMOS circuit: a direct connection to the input of a logic element, illustrated in Figure 1. The _p_-side of the APD is tied to a negative bias voltage slightly less in magnitude than the breakdown. The _n_-side is connected to a logic circuit that performs simple voltage sensing. Initially, the n-side of the APD is set to a logic-high voltage by briefly turning on a pull-up transistor. Once armed in this fashion, the APD has a reverse bias several volts above breakdown. When an avalanche is initiated, the APD turns on and then discharges its own parasitic capacitance. Once at or below breakdown, the avalanche terminates, leaving the _n_-side at a voltage close to a logic 0. The APD is effectively a CMOS-compatible digital element. Also, like a CMOS logic element, the APD draws current only when it is switching. This \"photon-to-digital conversion\" scheme has been the basis of all of Lincoln's GMAPD imaging devices, with minor modifications. One can, for example, add a pull-down transistor to speed up the APD discharge, size the transistors in the sensing gate to adjust the triggering threshold, or cascode transistors to augment the voltage swing. Voltage sensing gives more timing latency and timing jitter than current sensing circuits [11]. This drawback has been more than offset by the advantages of the photon-to-digital conversion scheme: simplicity, robustness, and freedom from static power dissipation.