A single-photon avalanche diode (SPAD)
is a solid-state photodetector in which a
photon-generated carrier (via the internal
photoelectric effect) can trigger a short-duration
but relatively large avalanche current. This
avalanche is created through a mechanism called
impact ionization, whereby carriers (electrons
and/or holes) are accelerated to high kinetic
energies through a large potential gradient
(voltage). If the kinetic energy of a carrier
is sufficient (as a function of the ionization
energy of the bulk material) further carriers
are liberated from the atomic lattice. The
number of carriers thus increases exponentially
from, in some cases, as few as a single carrier.
This mechanism was observed and modeled by
John Townsend for trace-gas vacuum tubes,
becoming known as a Townsend discharge, and
later being attributed to solid-state breakdown
by K. McAfee. This device is able to detect
low-intensity ionizing radiation, including:
gamma, X-ray, beta, and alpha-particle radiation
along with electromagnetic signals in the
UV, Visible and IR (in the optical case this
can be down to the single photon level). SPADs
are also able to distinguish the arrival times
of events (photons) with a timing jitter of
a few tens of picoseconds.
SPADs, like avalanche photodiodes (APDs),
exploit the incident radiation triggered avalanche
current of a p–n junction when reverse biased.
The fundamental difference between SPADs and
APDs is that SPADs are specifically designed
to operate with a reverse-bias voltage well
above the breakdown voltage. This kind of
operation is also called Geiger-mode in the
literature (as opposed to the linear-mode
for the case of an APD). This is in analogy
with the Geiger counter.
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 and optical communications
(particularly quantum key distribution). Notable
companies that have commercialized SPAD technology
include: ST Microelectronics, Tower Jazz,
Phillips and Micro Photon Devices (MPD). The
related technologies of solid-state silicon
photomultipliers (Si-PMs) and multi-pixel
photon counters (MPPCs) have been commercialized
and available through companies such as SensL
(currently part of ON Semiconductor) and Hamamatsu.
== History and technical development ==
The history and development of SPADs and APDs
shares a number of important points with the
development of solid-state technologies such
as diodes and early p–n junction transistors
(particularly war-efforts at Bell Labs). This
history can be traced to the late 1890s and
early 1900s, however suitable references for
the historical development of these devices,
can be found for the years 1900 to 1969 , along
with a number of overview historical and technical
reviews . John Townsend in 1901 and 1903 investigated
the ionisation of trace gases within vacuum
tubes, finding that as the electric potential
increased, gaseous atoms and molecules could
become ionised by the kinetic energy of free
electrons accelerated though the electric
field. The new liberated electrons were then
themselves accelerated by the field, producing
new ionisations once their kinetic energy
has reached sufficient levels. This theory
was later instrumental in the development
of the thyratron and the Geiger-Mueller Tube.
The Townsend Discharge was also instrumental
as a base theory for electron multiplication
phenomena, (both DC and AC), within both Silicon
and Germanium .
However, the major advances in early discovery
and utilisation of the avalanche gain mechanism
were a product of the study of Zener breakdown,
related (avalanche) breakdown mechanisms and
structural defects in early silicon and germanium
transistor and p–n junction devices. 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
the 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, now reaching optical
fill factors of >70%, with >1024 SPADs, with
DCRs < 10Hz and jitter values in the 50ps
region are now available with dead times of
1-2ns. Recent devices have leaveraged 3D-IC
technologies such as through-silicon-vias
(TSVs) to present a high-fill-factor SPAD
optimised top CMOS layer (90nm or 65nm node)
with a dedicated signal processing and readout
CMOS layer (45nm 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.
== Operating principle ==
SPADs are semiconductor devices based on a
p–n junction reverse-biased at a voltage
Va that exceeds breakdown voltage VB of the
junction (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." The current continues until the avalanche
is quenched by lowering the bias voltage VD
down to or below VB: the lower electric field
is no longer able to accelerate carriers to
impact-ionize with lattice atoms, therefore
current ceases. In order to be able to detect
another photon, the bias voltage must be raised
again above breakdown.
"This operation requires a suitable circuit,
which has to:
sense the leading edge of the avalanche current.
generate a standard output pulse synchronous
with the avalanche build-up.
quench the avalanche by lowering the bias
down to the breakdown voltage.
restore the photodiode to the operative level.This
circuit is usually referred to as a quenching
circuit."
=== Passive quenching ===
The simplest quenching circuit is commonly
called Passive Quenching Circuit and comprises
a single resistor in series with the SPAD.
This experimental setup has been employed
since the early studies on the avalanche breakdown
in junctions. The avalanche current self-quenches
simply because it develops a voltage drop
across a high-value ballast load RL (about
100 kΩ or more). After the quenching of the
avalanche current, the SPAD bias VD slowly
recovers to Va, and therefore the detector
is ready to be ignited again. This circuit
mode is therefore called passive quenching
passive reset (PQPR), although an active circuit
element can be used for reset forming a passive
quench active reset (PQAR) circuit mode. A
detailed description of the quenching process
is reported by Zappa et al.
=== Active quenching ===
A more advanced quenching, which was explored
from the 1970s onwards, is a scheme called
active quenching. In this case
a fast discriminator senses the steep onset
of the avalanche current across a 50 Ω resistor
(or integrated transistor) and provides a
digital (CMOS, TTL, ECL, NIM) output pulse,
synchronous with the photon arrival time.
The circuit then quickly reduces the bias
voltage to below breakdown (active quenching),
then relatively quickly returns bias to above
the breakdown voltage ready to sense the next
photon. This mode is called active quench
active reset (AQAR), however depending on
circuit requirements, active quenching passive
reset (AQPR) may be more suitable. AQAR circuits
often allow lower dead times, and significantly
reduced dead time variation.
=== Photon counting and timing ===
The intensity of the signal is obtained by
counting (photon counting) the number of output
pulses within a measurement time slot, while
the time-dependent waveform of the signal
is obtained by measuring the time distribution
of the output pulses (photon timing). The
latter is obtained by means of operating the
Single Photon Avalanche Diode (SPAD) detector
in time-correlated single photon counting
(TCSPC)
=== Saturation ===
While the avalanche recovery circuit is quenching
the avalanche and restoring bias, the SPAD
cannot detect photons. Any photons, (or dark
counts or after-pulses), that reach the detector
during this brief period are not counted.
As the number of photons increases such that
the (statistical) time interval between photons
gets within a factor of ten or so of the avalanche
recovery time, missing counts become statistically
significant and the count rate begins to depart
from a linear relationship with detected light
level. At this point the SPAD begins to saturate.
If the light level were to increase further,
ultimately to the point where the SPAD immediately
avalanches the moment the avalanche recovery
circuit restores bias, the count rate reaches
a maximum defined purely by the avalanche
recovery time in the case of active quenching
(hundred million counts per second or more).
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.
=== Internal noise and afterpulsing ===
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 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).
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.
=== I-V characteristic ===
If a SPAD is observed by an analogue curve-tracer,
it is possible to observe a bifurcation of
the current-voltage characteristics beyond
breakdown, during the voltage sweeps applied
to the device. When the avalanche is triggered,
the SPAD sustains the avalanche current (on-branch),
instead when no carrier has been generated
(by a photon or a thermal generation), no
charge flows through the SPAD (off-branch).
If the SPAD is triggered during a sweep above
breakdown, a transition from the off-branch
to the on-branch can be easily observed (like
a "flickering"). Some authors in the literature
have denoted this phenomenon as bifurcation.
=== Fill factor ===
Arrays of SPADs have been fabricated for some
time, however a critical issue is one of diode
geometry. As SPADs require a guard ring to
prevent premature edge breakdown, the optical
fill factor becomes a product of the diode
shape and size with relation to the guard
rings and inter-diode spacing. The fill factor
of a SPAD array is defined as the ratio of
the optically active area, where photon counts
are detected, to the total area of the array.
However in the literature, fill factors vary
in terms of if the entire planar device (including
readout circuitry and pads) is taken as the
total area or if the functional 'array' only
is taken. Changes in SPAD size can increase
fill factor, however noise may also increase.
Likewise topological shapes such as squares
and rectangles yield high geometrical fill
factors, but lead to increased fields at diode
corners and typically higher dark count rates.
To compromise, squares with sufficiently rounded
edges have been fabricated, i.e. the so-called
super-ellipse, Lamé curve, or the Fermat
shape. This latter nomenclature is common
within the literature, however strictly speaking:
"In particular, when a = b = 1 and n is an
even integer, then it is a Fermat curve of
degree n". Many diodes of the 'Fermat' type
are optimized for both high fill factor and
minimum noise. As such many will have parameters
free of the "a = b = 1 and n is an even integer"
restriction.
== Comparison with APDs ==
Both APDs and SPADs are reverse biased semiconductor
p–n junctions. However, APDs are biased
close to, but not exceeding the breakdown
voltage of the semiconductor. This high electric
field provides an internal multiplication
gain only of the order of few hundreds, since
the avalanche process is not diverging (also
known as run-away avalanche) as in the case
of SPAD avalanche discharges. The resulting
avalanche current intensity is linearly related
to the optical signal intensity. A SPAD, however,
operates with a bias voltage above the breakdown
voltage. Because the device is operating in
this unstable above-breakdown regime, a single
photon (or a single dark-current electron)
can set off a significant avalanche of carriers.
Practically, this means that in an APD, a
single photon produces only tens or few hundreds
of electrons, but in a SPAD a single photon
triggers a current in the milliampere region
(billions of billions of electrons per second)
that can be easily "counted".Therefore, while
the APD is a linear amplifier for the input
optical signal with limited gain, the SPAD
is a trigger device, so the gain concept is
meaningless.
== See also ==
Avalanche photodiode (APD)
p–n junction
Silicon photomultiplier (SiPM)
Oversampled binary image sensor
