Single-photon avalanche diode

thumb|right|upright=1.25|Commercial single-photon avalanche diode module for optical photons

A single-photon avalanche diode (SPAD), also called Geiger-mode avalanche photodiode (G-APD or GM-APD) is a solid-state photodetector within the same family as photodiodes and avalanche photodiodes (APDs), while also being fundamentally linked with basic diode behaviours. As with photodiodes and APDs, a SPAD is based around a semi-conductor p-n junction that can be illuminated with ionizing radiation such as gamma, x-rays, beta and alpha particles along with a wide portion of the electromagnetic spectrum from ultraviolet (UV) through the visible wavelengths and into the infrared (IR).

In a photodiode, with a low reverse bias voltage, the leakage current changes linearly with absorption of photons, i.e. the liberation of current carriers (electrons and/or holes) due to the internal photoelectric effect. However, in a SPAD, germanium on silicon and III-V elements such as InGaAs/InP have been used to fabricate SPADs for the large variety of applications that now utilise the run-away avalanche process. There is much research in this topic with activity implementing SPAD-based systems in CMOS fabrication technologies, and Ge on Si for single-photon detection at short-wave infrared wavelengths suitable for telecommunications applications.

Applications

Since the 1970s, the applications of SPADs have increased significantly. Recent examples of their use include LIDAR, time of flight (ToF) 3D imaging, PET scanning, single-photon experimentation within physics, fluorescence lifetime microscopy, optical communications (particularly quantum key distribution), digital night vision, and ultrahigh sensitivity cameras.

Operation

thumb|upright=1.5|Figure 1 - Thin SPAD cross-section.

Structures

SPADs are semiconductor devices that are based on a p–n junction that is reverse-biased at an operating voltage that exceeds the junction's breakdown voltage (Figure 1). "At this bias, the electric field is so high [higher than 3×105 V/cm] that a single charge carrier injected into the depletion layer can trigger a self-sustaining avalanche. The current rises swiftly [sub-nanosecond rise-time] to a macroscopic steady level in the milliampere range. If the primary carrier is photo-generated, the leading edge of the avalanche pulse marks [with picosecond time jitter] the arrival time of the detected photon."). This can be harmful to the SPAD as it will be experiencing avalanche current nearly continuously. In the passive case, saturation may lead to the count rate decreasing once the maximum is reached. This is called paralysis, whereby a photon arriving as the SPAD is passively recharging, has a lower detection probability, but can extend the dead time. It is worth noting that passive quenching, while simpler to implement in terms of circuitry, incurs a 1/e reduction in maximum counting rates.

Dark count rate (DCR)

Besides photon-generated carriers, thermally-generated carriers (through generation-recombination processes within the semiconductor) can also fire the avalanche process. Therefore, it is possible to observe output pulses when the SPAD is in complete darkness. The resulting average number of counts per second is called dark count rate (DCR) and is the key parameter in defining the detector noise. It is worth noting that the reciprocal of the dark count rate defines the mean time that the SPAD remains biased above breakdown before being triggered by an undesired thermal generation. Therefore, in order to work as a single-photon detector, the SPAD must be able to remain biased above breakdown for a sufficiently long time (e.g., a few milliseconds, corresponding to a count rate well under a thousand counts per second, cps).

Afterpulsing noise

One other effect that can trigger an avalanche is known as afterpulsing. When an avalanche occurs, the PN junction is flooded with charge carriers and trap levels between the valence and conduction band become occupied to a degree that is much greater than that expected in a thermal-equilibrium distribution of charge carriers. After the SPAD has been quenched, there is some probability that a charge carrier in a trap level receives enough energy to free it from the trap and promote it to the conduction band, which triggers a new avalanche. Thus, depending on the quality of the process and exact layers and implants that were used to fabricate the SPAD, a significant number of extra pulses can be developed from a single originating thermal or photo-generation event. The degree of afterpulsing can be quantified by measuring the autocorrelation of the times of arrival between avalanches when a dark count measurement is set up. Thermal generation produces Poissonian statistics with an impulse function autocorrelation, and afterpulsing produces non-Poissonian statistics.

Photon timing and jitter

The leading edge of a SPAD's avalanche breakdown is particularly useful for timing the arrival of photons. This method is useful for 3D imaging, LIDAR and is used heavily in physical measurements relying on time-correlated single photon counting (TCSPC). However, to enable such functionality dedicated circuits such as time-to-digital converters (TDCs) and time-to-analogue (TAC) circuits are required. The measurement of a photon's arrival is complicated by two general processes. The first is the statistical fluctuation in the arrival time of the photon itself, which is a fundamental property of light. The second is the statistical variation in the detection mechanism within the SPAD due to a) depth of photon absorption, b) diffusion time to the active p-n junction, c) the build up statistics of the avalanche and d) the jitter of the detection and timing circuitry.

Optical fill factor

For a single SPAD, the ratio of its optically sensitive area, Aact, to its total area, Atot, is called the fill factor, . As SPADs require a guard ring Here the diode active area may be small or commensurate with the guard ring's area. Likewise, the fabrication process of the SPAD array may put constraints on the separation of one guard ring to another, i.e. the minimum separation of SPADs. This leads to the situation where the area of the array becomes dominated by guard ring and separation regions rather than optically receptive p-n junctions. The fill factor is made worse when circuitry must be included within the array as this adds further separation between optically receptive regions. One method to mitigate this issue is to increase the active area of each SPAD in the array such that guard rings and separation are no longer dominant, however for CMOS integrated SPADs the erroneous detections caused by dark counts increases as the diode size increases.

Geometric improvements

One of the first methods to increase fill factors in arrays of circular SPADs was to offset the alignment of alternate rows such that the curve of one SPAD partially uses the area between the two SPADs on an adjacent row. This was effective but complicated the routing and layout of the array.

To address fill factor limitations within SPAD arrays formed of circular SPADs, other shapes are utilised as these are known to have higher maximum area values within a typically square pixel area and have higher packing ratios. A square SPAD within a square pixel achieves the highest fill factor, however the sharp corners of this geometry are known to cause premature breakdown of the device, despite a guard ring and consequently produce SPADs with high dark count rates. To compromise, square SPADs with sufficiently rounded corners have been fabricated. These are termed Fermat shaped SPADs while the shape itself is a super-ellipse or a Lamé curve. This nomenclature is common in the SPAD literature, however the Fermat curve refers to a special case of the super-ellipse that puts restrictions on the ratio of the shape's length, "a" and width, "b" (they must be the same, a = b = 1) and restricts the degree of the curve "n" to be even integers (2, 4, 6, 8 etc). The degree "n" controls the curvature of the shape's corners. Ideally, to optimise the shape of the diode for both low noise and a high fill factor, the shape's parameters should be free of these restrictions.

To minimise the spacing between SPAD active areas, researchers have removed all active circuitry from the arrays and have also explored the use of NMOS only CMOS SPAD arrays to remove SPAD guard ring to PMOS n-well spacing rules. This is of benefit but is limited by routing distances and congestion into the centre SPADs for larger arrays. The concept has been extended to develop arrays that use clusters of SPADs in so-called mini-SiPM arrangements This removed one of the major guard-ring to guard-ring separation rules and allowed the fill-factor to increase towards 60 or 70%. The n-well and guard ring sharing idea has been crucial in efforts towards lowering pixel pitch and increasing the total number of diodes in the array. Recently SPAD pitches have been reduced to 3.0 um and 2.2 um. By doing so a large optical collection area can be achieved with a smaller SPAD region.

Another concept ported from CMOS image sensor technologies, is the exploration of stacked p-n junctions similar to Foveon sensors. The idea being that higher-energy photons (blue) tend to be absorbed at a short absorption depth, i.e. near the silicon surface.

IC fabrication improvements

With the advancement of 3D IC technologies, i.e. stacking of integrated circuits, the fill factor could be enhanced further by allowing the top die to be optimised for a high fill-factor SPAD array, and the lower die for readout circuits and signal processing. As small dimension, high-speed processes for transistors may require different optimisations than optically sensitive diodes, 3D-ICs allow the layers to be separately optimised.

Pixel-level optical improvements

As with CMOS image sensors micro-lenses can be fabricated on the SPAD pixel array to focus light into the centre of the SPAD. As with a single SPAD, this allows light to only hit the sensitive regions and avoid both the guard ring and any routing that is needed within the array. This has also recently included Fresnel type lenses.

Pixel pitch

The above fill-factor enhancement methods, mostly concentrating on SPAD geometry along with other advancements, have led SPAD arrays to recently push the 1 mega pixel barrier. While this lags CMOS image sensors (with pitches now below 0.8 um), this is a product of both the youth of the research field (with CMOS SPADs introduced in 2003) and the complications of high voltages, avalanche multiplication within the silicon and the required spacing rules.

Comparison with APDs

While both APDs and SPADs are semiconductor p-n junctions that are heavily reverse biased, the principle difference in their properties is derived from their different biasing points upon the reverse I-V characteristic, i.e. the reverse voltage applied to their junction. For optical detection applications, the resulting avalanche and subsequent current in its biasing circuit is linearly related to the optical signal intensity. The APD is therefore useful to achieve moderate up-front amplification of low-intensity optical signals but is often combined with a trans-impedance amplifier (TIA) as the APD's output is a current rather than the voltage of a typical amplifier. The resultant signal is a non-distorted, amplified version of the input, allowing for the measurement of complex processes that modulate the amplitude of the incident light. The internal multiplication gain factors for APDs vary by application, however typical values are of the order of a few hundred. The avalanche of carriers is not divergent in this operating region, while the avalanche present in SPADs quickly builds into a run-away (divergent) condition.

In comparison, SPADs operate at a bias voltage above the breakdown voltage. This is such a highly unstable above-breakdown regime that a single photon or a single dark-current electron can trigger a significant avalanche of carriers. As the device produces a trigger event, the concept of gain is not strictly compatible. However, as the photon detection efficiency (PDE) of SPADs varies with the reverse bias voltage, gain, in a general conceptual sense can be used to distinguish devices that are heavily biased and therefore highly sensitive in comparison to lightly biased and therefore of lower sensitivity. While APDs can amplify an input signal preserving any changes in amplitude, SPADs distort the signal into a series of trigger or pulse events. The output can still be treated as proportional to the input signal intensity, however it is now transformed into the frequency of trigger events, i.e. pulse frequency modulation (PFM). Pulses can be counted These defects were called 'microplasmas' and are critical in the history of APDs and SPADs. Likewise investigation of the light detection properties of p–n junctions is crucial, especially the early 1940s findings of Russel Ohl. Light detection in semiconductors and solids through the internal photoelectric effect is older with Foster Nix pointing to the work of Gudden and Pohl in the 1920s, who use the phrase primary and secondary to distinguish the internal and external photoelectric effects respectively. In the 1950s and 1960s, significant effort was made to reduce the number of microplasma breakdown and noise sources, with artificial microplasmas being fabricated for study. It became clear that the avalanche mechanism could be useful for signal amplification within the diode itself, as both light and alpha particles were used for the study of these devices and breakdown mechanisms.

In the early 2000s, SPADs have been implemented within CMOS processes. This has radically increased their performance (dark count rate, jitter, array pixel pitch, etc.), and has leveraged analog and digital circuits that can be implemented alongside these devices. Notable circuits include photon counting using fast digital counters, photon timing using both time-to-digital converters (TDCs) and time-to-analog converters (TACs), passive quenching circuits using either NMOS or PMOS transistors in place of poly-silicon resistors, active quenching and reset circuits for high counting rates, and many on-chip digital signal processing blocks. Such devices are now reaching optical fill factors of >70%, with >1024 SPADs, with DCRs < 10 Hz, jitter values in the 50ps region, and dead times of 1-2ns. Recent devices leverage 3D-IC technologies such as through-silicon-vias (TSVs) to present a high-fill-factor SPAD optimised top CMOS layer (90 nm or 65 nm node) with a dedicated signal processing and readout CMOS layer (45 nm node). Significant advancements in the noise terms for SPADs have been obtained by silicon process modelling tools such as TCAD, where guard rings, junction depths and device structures and shapes can be optimised prior to validation by experimental SPAD structures.