1. Theory

Definition (SPAD): A single-photon avalanche diode is a p-n or p-i-n avalanche diode biased above its breakdown voltage by the excess bias $V_{e x} = V_{bia s} - V_{B D}$ , in the Geiger mode, so that one photogenerated or thermally generated carrier can trigger a self-sustaining avalanche that is counted as one event.
Definition (SiPM): A silicon photomultiplier is a pixelated detector of many microcells of 10 μm to 100 μm, from several hundred to tens of thousands per device, each a SPAD in series with a quenching resistor $R_{q}$ , all connected in parallel to one anode and one cathode, so that the output is the sum of the microcell pulses, with gain $1 0^{5}$ to $1 0^{7}$ .
Silicon SPAD types: A thin-junction diode (50% at 550 nm, 32 ps jitter, up to 160 Mcounts/s), a reach-through diode (more than 60% to 800 nm, jitter above 150 ps, dark counts as low as 25 per second for 180 μm), and a red-enhanced diode (70% at 650 nm).
Infrared SPADs: InGaAs/InP diodes with separate absorption and multiplication regions, gated near 225 K, give more than 30% at 1550 nm, and Ge-on-Si diodes 35% at 1310 nm at 100 K.
Figures of merit: Detection efficiency, dark count rate, afterpulsing probability, dead time, timing jitter and, for the SiPM, gain, crosstalk and the dynamic range set by the number of microcells.
Detection efficiency: It is the product of the reflection, absorption, collection and triggering probabilities, and for the SiPM the product of the quantum efficiency, the geometric fill factor and the Geiger probability.
Noise: Dark counts come from thermally generated carriers, field-enhanced emission and band-to-band tunnelling, and the SiPM adds optical crosstalk and afterpulses, which raise the excess noise factor to about 1.1.

2. Working Principle

Geiger mode: At $V_{bia s} > V_{B D}$ a carrier that enters the multiplication region triggers the avalanche with the probability $P_{G} = 1 - e^{- κ V_{e x}}$ , the current grows until it is limited by the series resistance, and the diode stays on until it is quenched.
Quenching: A resistor of about 100 kΩ (passive) or an active circuit lowers the bias below $V_{B D}$ , which stops the avalanche, and the bias is then restored; the dead time $t_{d}$ is the sum of the sensing, quenching, hold-off and reset times.
Detection: A photon absorbed in the depletion layer, or a carrier that diffuses into it, creates the primary carrier, and the response is counted with the probability $P_{P D P}$ .
Timing: The detection delay has the drift, build-up and propagation components, and the build-up of the avalanche dominates the randomness.
Spurious counts: Dark counts from the generation rate $G_{S R H}$ , afterpulses from carriers trapped in the avalanche and released later (reduced by the hold-off), and in the SiPM crosstalk from photons emitted in an avalanche that trigger a neighbour.
SiPM output: Each fired cell delivers the charge $Q = C_{ce l l} Δ V$ and recharges through $R_{q}$ with $τ_{r ec} = R_{q} C_{ce l l}$ , and the sum of the cells gives an analog signal that is proportional to the number of photons until $N_{f i r e d}$ approaches $N_{t o t}$ .
Temperature: $V_{B D}$ rises with temperature, so that the gain falls at constant bias and a constant $Δ V$ stabilizes it, and the dark count rate roughly doubles every 8 °C.

3. Applications

Quantum photonics: Single-photon counting with SPADs of silicon, InGaAs/InP and Ge-on-Si, where the efficiency, the dark counts and the jitter set the performance.
Transient imaging and time-of-flight: SPAD sensors that record the arrival time of single photons for transient imaging.
Scintillator and Cherenkov readout: SiPMs read the light of scintillators and Cherenkov telescopes in high-energy physics detectors, with the gain of $1 0^{6}$ and a low operating voltage.

Single-Photon Avalanche Diode (SPAD)

Name	Formula	Related Formulae	Variables/Constants
Excess bias and probability that a carrier triggers the avalanche	$V_{e x} = V_{bia s} - V_{B D}, P_{G} = 1 - e^{- κ V_{e x}}$	$P_{t r i g} = P_{t, e} + P_{t, h} - P_{t, e} P_{t, h}$ $P_{P D P} = (1 - R) P_{ab s} P_{co l l} P_{t r i g}$	$V_{B D} : b r e ak d o w n v o l t a g e$ $V_{e x} : e x cess bia s (o v er v o l t a g e)$ $P_{G} : G e i g er (t r i g g er) p r o babi l i t y$ $κ : e m p i r i c a l s l o p e (0.366 V^{- 1} f or t h e d a r k co u n t s an d 0.155 V^{- 1} f or t h e o pt i c a l cr oss t a l k o f o n e S i P M)$ $P_{t, e}, P_{t, h} : t r i g g er in g p r o babi l i t i es o f an e l ec t r o n an d o f a h o l e$ $R : r e f l ec t an ce$ $P_{ab s} : ab sor pt i o n p r o babi l i t y$ $P_{co l l} : co l l ec t i o n p r o babi l i t y (u ni t y in t h e d e pl e t e d r e g i o n, d i f f u s i o n - l imi t e d in t h e n e u t r a l r e g i o n s)$ $P_{P D P} : p h o t o n d e t ec t i o n p r o babi l i t y$ $(f or V_{e x} = 2.8 V t h e tw o s l o p es g i v e 0.64 an d 0.35, co m p u t e d)$
Absorption in a thin depletion layer	$P_{ab s} = 1 - e^{- α d}$	$P_{ab s}^{ma x} = 1 - \frac{1}{1 + 4 n ^{2} α d}$ $P_{d} = P_{ab s} P_{co l l} P_{b}$	$α : ab sor pt i o n coe f f i c i e n t$ $d : d e pl e t i o n t hi c k n ess$ $n : r e f r a c t i v e in d e x$ $P_{ab s}^{ma x} : u pp er l imi t w i t h a p er f ec t l i g h t - t r a pp in g t e x t u r e, ab o u t 4 n^{2} t im es t h e s in g l e p a ss f or α d ≪ 1$ $P_{b} : a v a l an c h e p r o babi l i t y$ $(f or α d = 0.1 an d n = 3.5 (a ss u m e d) t h e s in g l e p a ss i s 9.5% an d t h e l imi t 83%, co m p u t e d; a nan oco n e d es i g n in s im u l a t i o n g a v e ab o u t 60% a t 900 nm w i t h a 3 μ m l a y er a g ain s t ab o u t 20% f or a f l a t f i l m)$
Dark count rate	$G_{S R H} = N_{t r a p} \frac{r _{e} r _{h}}{r _{e} + r _{h}}, DCR = A \int G (x) P_{t r i g} (x) d x$	$r_{e, e f f} = Γ_{e} (F) r_{e}, r_{h, e f f} = Γ_{h} (F) r_{h}$ $DCR = N_{c a r} P_{G}^{D C R} e^{b V_{bia s}}$	$N_{t r a p} : d e n s i t y o f d ee p l e v e l s$ $r_{e}, r_{h} : e l ec t r o n an d h o l e e mi ss i o n r a t es$ $Γ (F) : f i e l d - e nhan ce m e n t f a c t or (P oo l e - F r e nk e l an d p h o n o n - a ss i s t e d t u nn e l l in g)$ $F : e l ec t r i c f i e l d$ $A : a r e a o f t h e m u l t i pl i c a t i o n r e g i o n, ban d - t o - ban d t u nn e l l in g d o mina t es a t l o w t e m p er a t u r e$ $N_{c a r} : n u mb er o f c a r r i er s a v ai l ab l e f or g e n er a t i o n$ $b : e m p i r i c a l e x p o n e n t o f t h e bia s (f i t o f o n e S i P M), t h e D C R o f S i P M s r o ug h l y d o u b l es e v er y 8^{\circ} C, i . e . b y 9% p er^{\circ} C (co m p u t e d)$
Afterpulsing	$P_{a p} = \int_{0}^{\infty} η_{a p} (τ) d τ, η_{a p} (τ) = \sum_{i = 1}^{N} A_{i} e^{- e_{i} τ}$	$P_{a p} (t_{h}) = \sum_{i = 1}^{N} \frac{A _{i}}{e _{i}} e^{- e_{i} t_{h}}$ $p_{a} = r - Δ T f_{D C}$	$τ : t im e b e tw ee n t h e t r a pp in g an d t h e r e l e a se o f a c a r r i er$ $A_{i}, e_{i} : p r e f a c t or an d e mi ss i o n r a t e o f t r a p i$ $t_{h} : h o l d - o f f t im e a f t er t h e q u e n c h (a f t er p u l ses r e l e a se d l a t er t han t_{h} r e main)$ $r : r a t i o o f t h e seco n d a r y e v e n t s d e t ec t e d w i t hin t h e w in d o w Δ T t o t h e d e t ec t e d p h o t o n s$ $f_{D C} : d a r k co u n t r a t e$ $p_{a} : m e a s u r e d a f t er p u l se p r o babi l i t y (0.02% f or Δ T = 500 n s in a coo l e d r e a c h - t h r o ug h d i o d e)$
Dead time and maximum count rate	$t_{d} = t_{se n se} + t_{q u e n c h} + t_{h o l d} + t_{r ese t}$	$m = \frac{n}{1 + n t _{d}}, m_{ma x} = \frac{1}{t _{d}}$ $τ_{q} = R_{q} C_{d}$	$t_{d} : d e a d t im e$ $n : t r u e p h o t o n r a t e$ $m : r a t e co u n t e d f or a n o n - p a r a l y z ab l e d e a d t im e (d er i v e d)$ $R_{q} : q u e n c hin g r es i s t or (ab o u t 100 k Ω f or p a ss i v e q u e n c hin g)$ $C_{d} : d i o d e c a p a c i t an ce$ $(an a c t i v e q u e n c hin g c i r c u i t w i t h a h o l d - o f f e n f or ces t_{h o l d}; t hin s i l i co n d i o d es r e a c h e d 160 M co u n t s / s w i t h l ess t han 5% a f t er p u l s in g an d I n G a A s / I n P w i t h s in u so i d a l g a t in g 650 M co u n t s / s w i t h 1.5%)$
Timing jitter	$T_{d e t} = T_{t r an s i t} + T_{b u i l d} + T_{p r o p}$	$σ_{t} = ⟨ t_{b}^{2} ⟩ - ⟨ t_{b} ⟩^{2}$ $FWHM = 2 2 ln 2 σ_{t}$	$T_{t r an s i t} : d r i f t t im e o f t h e p h o t oe l ec t r o n t o t h e m u l t i pl i c a t i o n r e g i o n$ $T_{b u i l d} : b u i l d - u p t im e o f t h e a v a l an c h e t o t h e t h r es h o l d$ $T_{p r o p} : l a t er a l p r o p a g a t i o n o f t h e a v a l an c h e o v er t h e a r e a$ $t_{b} : b u i l d - u p t im e, t h e j i tt er i s t h e F W H M o f T_{d e t}$ $(r e p or t e d : 32 p s f or a t hin 200 μ m s i l i co n d i o d e, 83 p s f or a r e d - e nhan ce d o n e, m or e t han 150 p s f or r e a c h - t h r o ug h, b e l o w 70 p s g a t e d I n G a A s / I n P an d 175 p s t o 310 p s f or G e - o n - S i)$

Silicon Photomultiplier (SiPM)

Name	Formula	Related Formulae	Variables/Constants
Gain and recovery time of a microcell	$G = \frac{Q}{q} = \frac{( C _{ce l l} + C _{q} ) ( V _{bia s} - V _{B D} )}{q} \approx \frac{C _{ce l l} Δ V}{q}$	$τ_{r ec} = R_{q} C_{ce l l}$ $C_{ce l l} = \frac{ε _{0} ε _{S i} A _{ce l l}}{d}$	$C_{ce l l} : c a p a c i t an ce o f t h e mi cr oce l l$ $C_{q} : p a r a s i t i c c a p a c i t an ce o f t h e q u e n c hin g r es i s t or$ $Δ V : o v er v o l t a g e$ $R_{q} : q u e n c hin g r es i s t or (ab o v e 100 k Ω, u p t o 20 M Ω)$ $τ_{r ec} : r eco v er y t im e$ $A_{ce l l} : a c t i v e a r e a o f t h e ce l l$ $d : d e pl e t i o n w i d t h$ $(a ce l l o f 50 μ m p i t c h w i t h t h e a c t i v e a r e a 0.615 o f t h e p i t c h s q u a r e d an d d = 1.9 μ m g i v es 85 f F, G = 1.5 \times 1 0^{6} a t Δ V = 2.8 V an d τ_{r ec} = 15.5 n s f or R_{q} = 182.9 k Ω, co m p u t e d; t h e g ain d oes n o t d e p e n d o n R_{q})$
Photon detection efficiency of the SiPM	$PDE (λ, Δ V) = QE (λ) ε_{f f} P_{G} (Δ V)$	$P_{G} = 1 - e^{- κ Δ V}$ $I_{S} = \frac{I _{o u t} - I _{d}}{1 + P _{C T} + P _{A P}}$	$QE : q u an t u m e f f i c i e n cy o f t h e ce l l$ $ε_{f f} : g eo m e t r i c f i l l f a c t or (20% t o 30% in o l d er d e v i ces, 50% t o 80% in n e w er o n es)$ $P_{G} : G e i g er p r o babi l i t y$ $I_{o u t} : o u tp u t c u r r e n t$ $I_{d} : d a r k c u r r e n t$ $P_{C T}, P_{A P} : cr oss t a l k an d a f t er p u l se p r o babi l i t i es$ $(o n e H amama t s u d e v i ce ha d a P D E o f 35.5% a t 472 nm an d 2.8 V o v er v o l t a g e, w i t h a p e ak se n s i t i v i t y a t 480 nm)$
Optical crosstalk, afterpulsing and excess noise	$P_{C T} = \frac{ν _{1.5 p e}}{ν _{0.5 p e}}, F \approx \frac{1}{1 - P _{C T}}$	$P_{X T} = G P_{h ν} P_{G}^{X T}, P_{A P} = G P_{t r a p} P_{G}^{A P}$ $A_{A P} = A_{1 p e} (1 - e^{- t / τ_{r ec}})$	$ν_{1.5 p e}, ν_{0.5 p e} : r a t es ab o v e t h e t h r es h o l d s o f 1.5 an d 0.5 p h o t oe l ec t r o n s (t h e s t ai r c a se m e t h o d)$ $F : e x cess n o i se f a c t or (a b r an c hin g es t ima t e, d er i v e d)$ $P_{h ν} : p r o babi l i t y t ha t a p h o t o n e mi tt e d in an a v a l an c h e t r i g g er s a n e i g hb o u r$ $P_{t r a p} : t r a pp in g p r o babi l i t y$ $(m e a s u r e d : P_{C T} = 6.5% a g ain s t 10% o f t h e p r o d u cer, F = 1.07 f r o m t h e f or m u l a an d ab o u t 1.1 in t h e so u r ce; o pt i c a l t r e n c h es l o w er t h e cr oss t a l k f r o m 30% t o 40% t o b e l o w 3%)$
Response and dynamic range	$N_{f i r e d} = N_{t o t} (1 - e^{- N_{p e} / N_{t o t}})$	$N_{p e} = PDE N_{p h} (1 + P_{C T} + P_{A P})$ $S/N = \frac{I _{S}}{i _{d}^{2} + i _{s}^{2}}, i_{d, s} = 2 q G B F I_{d, S}$	$N_{t o t} : n u mb er o f mi cr oce l l s$ $N_{p e} : e f f ec t i v e p h o t oe l ec t r o n s in c l u d in g cr oss t a l k an d a f t er p u l ses$ $N_{p h} : in c i d e n t p h o t o n s, t h e f or m h o l d s f or u ni f or m i l l u mina t i o n an d a l i g h t p u l se t ha t i s s h or t a g ain s t τ_{r ec}$ $B : m e a s u r e m e n t ban d w i d t h$ $I_{d}, I_{S} : d a r k an d s i g na l c u r r e n t s, (f or N_{p e} = N_{t o t} t h e f i r e d f r a c t i o n i s 63%, co m p u t e d; a s ma l l er ce l l or a l a r g er a r e a r ai ses N_{t o t} b u t l o w er s t h e f i l l f a c t or an d t h e P D E)$

Important Questions

Ques: Why must a SPAD be quenched, and what sets its dead time?

Above $V_{B D}$ the avalanche is self-sustaining: the current keeps flowing until the bias across the junction is lowered, so one carrier would trigger an unlimited current and the diode could not detect the next photon. A passive quench uses a series resistor of about 100 kΩ, which lowers the bias as the current flows but recharges slowly, $τ_{q} = R_{q} C_{d}$ , whereas an active quenching circuit can also impose a hold-off time. The dead time is the sum $t_{se n se} + t_{q u e n c h} + t_{h o l d} + t_{r ese t}$ and fixes the maximum rate $1/ t_{d}$ ; the counted rate is $m = n / (1 + n t_{d})$ for a non-paralyzable dead time, so $m = n /2$ at $n t_{d} = 1$ (derived). Thin silicon diodes with active quenching reached 160 Mcounts/s. Reference: Recent advances and future perspectives of single-photon avalanche diodes for quantum photonics applications, arXiv:2010.05613.

Ques: Why does the detection efficiency rise with excess bias and then flatten?

The efficiency is $P_{P D P} = (1 - R) P_{ab s} P_{co l l} P_{t r i g}$ , and only the trigger probability depends on the bias. A carrier in the multiplication region ionizes more as the field rises, so $P_{G} = 1 - e^{- κ V_{e x}}$ approaches 1, and the Hamamatsu note attributes the flattening to phonon scattering. For $V_{e x} = 2.8$ V the fitted slopes of one SiPM, 0.366 V $^{- 1}$ for the dark counts and 0.155 V $^{- 1}$ for the crosstalk, give 0.64 and 0.35 (computed); the source gives no reason for the difference in slope, which may be due to different injection positions. Electrons and holes trigger with different probabilities, $P_{t r i g} = P_{t, e} + P_{t, h} - P_{t, e} P_{t, h}$ . Reference: Recent advances and future perspectives of single-photon avalanche diodes for quantum photonics applications, arXiv:2010.05613; Hamamatsu, What is an SiPM and how does it work? (hub.hamamatsu.com technical note); Characterisation of a large area silicon photomultiplier, arXiv:1810.02275.

Ques: Why do dark counts rise with bias and fall when the diode is cooled?

A deep level of density $N_{t r a p}$ generates carriers at $G_{S R H} = N_{t r a p} r_{e} r_{h} / (r_{e} + r_{h})$ , a high field raises the emission rates by the factor $Γ (F)$ , and a carrier that reaches the multiplication region triggers a count with the probability $P_{t r i g}$ , which itself grows with $V_{e x}$ , so the rate rises faster than the generation. Cooling lowers $r_{e}$ and $r_{h}$ ; at low temperature the band-to-band tunnelling remains. The SiPM review gives a doubling of the rate every 8 °C, i.e. 9% per °C (computed). Thin silicon diodes of 50 μm reach a few counts per second at -20 °C, InGaAs/InP diodes work near 225 K with kilocounts per second, and Ge-on-Si diodes need about 100 K, which a thermoelectric cooler cannot reach. Reference: Recent advances and future perspectives of single-photon avalanche diodes for quantum photonics applications, arXiv:2010.05613; Silicon Photomultipliers for High Energy Physics Detectors, arXiv:1108.3166.

Ques: Why does afterpulsing limit the count rate, and at which excess bias is the low value of the reach-through diode valid?

A carrier trapped during an avalanche is released later with the emission rate $e_{i}$ and can trigger a spurious count, so the probability beyond a hold-off $t_{h}$ is $\sum (A_{i} / e_{i}) e^{- e_{i} t_{h}}$ (derived); a longer hold-off lowers it but also the rate. The silicon reach-through diode gave $p_{a} = 0.02%$ for a window of 500 ns for an excess bias of 10 V in the abstract and 15 V in the conclusion; the waiting-time distributions were taken at 15 V, so 15 V is the more likely, with the abstract probably out of date. InGaAs/InP diodes with sinusoidal gating reached 650 Mcounts/s with 1.5%. Reference: Commercially available Geiger mode single-photon avalanche photodiode with a very low afterpulsing probability, arXiv:1505.04407; Recent advances and future perspectives of single-photon avalanche diodes for quantum photonics applications, arXiv:2010.05613.

Ques: Why does the gain of a SiPM depend on the overvoltage and the cell capacitance but not on the quenching resistor?

The avalanche discharges the capacitance of the cell down to the breakdown voltage, so the charge is $Q = (C_{ce l l} + C_{q}) Δ V$ and the gain is $G = Q / q$ , independent of $R_{q}$ , which only sets how fast the cell recharges, $τ_{r ec} = R_{q} C_{ce l l}$ . A cell of 50 μm pitch with 85 fF at $Δ V = 2.8$ V gives $1.5 \times 1 0^{6}$ , and $R_{q} = 182.9$ kΩ gives 15.5 ns (computed). Because $V_{B D}$ changes with temperature, the gain at constant bias drifts, and holding $Δ V$ constant stabilizes it. The Hamamatsu note writes the gain with $C_{j}$ only and the paper with the extra $C_{q}$ , the difference being small. Reference: Hamamatsu, What is an SiPM and how does it work? (hub.hamamatsu.com technical note); Characterisation of a large area silicon photomultiplier, arXiv:1810.02275.

Ques: What does the response of a SiPM do at high light levels, and what limits its dynamic range?

Each cell fires once per pulse, however many photons reach it, so the number of fired cells follows $N_{f i r e d} = N_{t o t} (1 - e^{- N_{p e} / N_{t o t}})$ , linear only for $N_{p e} ≪ N_{t o t}$ and 63% of the cells at $N_{p e} = N_{t o t}$ (computed). The result holds for uniform illumination and for a pulse short against the recovery time $τ_{r ec}$ of 15 ns to some microseconds, since a cell can fire again after recharging. A larger area or a smaller cell raises $N_{t o t}$ but the smaller cell has a lower fill factor and a lower PDE, so the dynamic range is traded for the efficiency, which is why devices for large photon numbers use many small cells while those for weak light use larger cells with a higher fill factor. Reference: Silicon Photomultipliers for High Energy Physics Detectors, arXiv:1108.3166; Hamamatsu, Main characteristics of SiPMs (shop.hamamatsu.com).

Ques: Why is optical crosstalk the main source of excess noise, and is it 6.5% or 10%?

A photon emitted in an avalanche can trigger a neighbouring cell, so the output pulses come with random extra amplitudes. For a geometric branching with probability $P_{C T}$ the excess noise factor is $F \approx 1/ (1 - P_{C T})$ (derived), which is 1.07 for 6.5% and agrees with the value of about 1.1 of the Hamamatsu note. The measured crosstalk of one device at its operating voltage was 6.5% after the correction for pile-up (below 1%), against 10% of the producer. A producer value is normally a typical or maximum specification, not stated here, so the measured 6.5% is more likely for that unit. Optical trenches reduce the crosstalk from 30% to 40% to below 3%. Reference: Characterisation of a large area silicon photomultiplier, arXiv:1810.02275; Hamamatsu, What is an SiPM and how does it work? (hub.hamamatsu.com technical note); Silicon Photomultipliers for High Energy Physics Detectors, arXiv:1108.3166.

Ques: Which breakdown voltage is right for a SiPM: 54.70 V or the values of the static methods?

The extrapolation of the gain to zero gave $V_{B D} = 54.699$ V, while the static current-voltage methods gave 54.65 V to 55.45 V (spread 0.8 V, computed) and the model 54.799 V. The gain extrapolation uses the definition that matters for the overvoltage, $Δ V = V_{bia s} - V_{B D}$ , and gives a statistical uncertainty of 0.017 V, whereas the static values depend on the derivative chosen, so the dynamic value is the more likely. The spread between the methods also shows that a quoted breakdown voltage must be accompanied by the method used, because the overvoltage, and with it the gain and the efficiency, is referred to it. An error of 0.8 V would matter, since it is 29% of the operating overvoltage of 2.8 V (computed). Reference: Characterisation of a large area silicon photomultiplier, arXiv:1810.02275.

Ques: What sets the timing jitter of a SPAD?

The detection delay is $T_{d e t} = T_{t r an s i t} + T_{b u i l d} + T_{p r o p}$ , and the build-up time of the avalanche to the threshold dominates the randomness. A thin depletion layer gives a short drift and a small jitter, 32 ps for a 200 μm silicon diode, against more than 150 ps for a reach-through diode, which needs a thick layer for the red response; at the same efficiency a flat film with a thicker layer had a jitter about ten times larger than a nanostructured one in simulation, and a 3 μm nanostructured diode reached about 20 ps at 900 nm and 11 V excess. The standard deviation of the build-up time is $σ_{t} = ⟨ t_{b}^{2} ⟩ - ⟨ t_{b} ⟩^{2}$ , and the FWHM is $2 2 ln 2 σ_{t}$ for a Gaussian distribution. Reference: High-efficiency and low-jitter Silicon single-photon avalanche diodes based on nanophotonic absorption enhancement, arXiv:1505.01296; Recent advances and future perspectives of single-photon avalanche diodes for quantum photonics applications, arXiv:2010.05613.

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Single-Photon Avalanche Diode and Silicon Photomultiplier (SPAD, SiPM)