Introduction

SPAD is a semiconductor device operating under reverse bias across a p-n junction, with an operating voltage exceeding the junction’s breakdown voltage (Wikipedia explanation). Under this bias condition, the electric field is sufficiently high that a single charge carrier injected into the depletion region can trigger self-sustaining avalanche multiplication. The current can rapidly rise to the milliampere range. When the primary carrier is generated by a photon-induced pulse current, the leading edge of this pulse indicates the photon arrival time [with picosecond jitter at this point].

SPAD has several critical characteristic parameters, including: bias regions and I-V characteristics, Dark Count Rate (DCR), Jitter, Photon-detection efficiency (PDE), and Afterpulsing. These will be discussed individually below.

Bias Regions and Current-Voltage Characteristics

Semiconductor p-n junctions can operate in different bias regions. For normal diode operation, the device conducts under forward bias conditions with applied forward voltage. When operating under low reverse bias, the p-n junction functions as a unity-gain photodiode. As the reverse bias increases, internal gain can be achieved through carrier multiplication, enabling the photodiode to operate as an Avalanche Photodiode (APD) with stable gain and linear response to optical input signals. However, as the reverse bias continues to increase, the p-n junction breaks down when the electric field strength reaches a critical level. Since this field is induced by the bias across the junction, it is expressed as the breakdown voltage VBD.

SPAD operates under reverse bias with an excess bias voltage Vex above the breakdown voltage, while avoiding excessive overvoltage that could damage the device. Thus, the total bias (VBD+Vex) exceeds the breakdown voltage to such an extent that “under this bias condition, the electric field is extremely high, allowing single charge carriers injected into the depletion region to trigger self-sustaining avalanche multiplication,” known as “Geiger mode” operation. The SPAD’s conduction behavior can be characterized through current-voltage (I-V) measurements.

Dark Count Rate (DCR)

Besides photon-generated carriers, thermally generated carriers (through generation-recombination processes within the semiconductor) can also trigger the avalanche process. Consequently, output pulses can be observed from SPAD even in complete darkness. The average count per second under these conditions is termed the Dark Count Rate (DCR), a key parameter defining detector noise.

Therefore, to function as a single-photon detector, SPAD must maintain bias above breakdown for sufficient duration while exhibiting acceptable noise levels (e.g., below 1000 counts per second, cps).

Jitter

Photon arrival time measurements utilize the leading edge of SPAD breakdown in Geiger mode. The measurement of photon arrival timing involves two primary factors. First is the statistical fluctuation in the photon arrival time itself, which is a fundamental property of light. Second is the statistical variation in the SPAD detection mechanism, which is influenced by four parameters: 1. photon absorption depth, 2. diffusion time to the active p-n junction, 3. avalanche build-up statistics, and 4. detection jitter and timing circuitry.

Photon-Detection Efficiency

PDE represents the probability of incident photons triggering an avalanche at different wavelengths. Beyond the physical phenomena that typically determine semiconductor photodiode performance, additional physical effects are significant in SPADs. The avalanche trigger probability depends on device structure and excess bias voltage (VE) conditions, specifically the difference in reverse bias.

Theoretical and experimental studies demonstrate that this probability initially increases linearly with low VE, then approaches saturation at high VE. 

Afterpulsing

Another phenomenon capable of triggering avalanches is known as afterpulsing. During an avalanche event, the PN junction becomes saturated with charge carriers, and trap states between the valence and conduction bands become occupied to a much greater extent than expected in the thermal equilibrium distribution of charge carriers. After the SPAD is quenched, carriers trapped in these states may receive sufficient energy to be released from the traps and promoted to the conduction band, triggering new avalanches. Thus, different SPAD processes and qualities can generate multiple additional pulses from a single thermally or optically generated event.

For SPAD applications and basic terminology explanations, please refer to the first article (From ADAS Applications to Key Components – The Critical Role of SPAD).