Download V720 -Testing of Geiger Mode APDs (GmAPs)

TECHNICAL NOTE: V720
Testing of Geiger Mode APDs (GmAPs)
Introduction
This not reviews the processes Voxtel uses to test Geiger Mode Avalanche Photodiodes (APDs)
Background
Dark Count Rate (DCR) and Afterpulsing
GmAPDs suffer two types of spurious detection events: ‘dark’ counts from leakage in the diode junction,
and non-signal counts from stray illumination. Both types of spurious detection event are Poissondistributed and uncorrelated; they can be characterized by their mean rates of occurrence, and those
rates are additive.1 Since the amount of stray light which reaches a GmAPD is a feature of its application
rather than its internal dynamics, here we only concerned ourselves with spurious detection events
from junction leakage.
The DCR of a GmAPD is one of its most important parameters. There is no way to distinguish an
avalanche breakdown event caused by a dark carrier from one caused by a photocarrier, so weak the
optical signal will only be detectible if they boost the rate at which the GmAPD fires above the DCR. Dark
counts also seriously limit the duty cycle of a GmAPD. Once a GmAPD fires, it must be quenched below
Vbr and held off long enough for any traps which were filled during the discharge to release their
carriers. If the overbias is restored before the traps have emptied, the carriers emitted by the traps will
increase the likelihood of a new spurious count – an echo of the detection event that filled the traps in
the first place. This is called ‘afterpulsing’ (Figure 1). A valid signal which arrives during the period of
time that the detector is held off will be missed. Thus, higher DCR means lower detector duty cycle.
The main dark carrier generation processes
active in a GmAPD are thermal (also known as GR), trap release (afterpulsing), trap-assisted
tunneling, and band-to-band tunneling. There is
also a perimeter leakage current associated with
the edge of the device, but to the extent that it
bypasses the multiplying junction, it does not
participate in the generation of dark counts. The
dark carrier generation rate of each of these
mechanisms must be found as a function of
location and time in order to calculate the
instantaneous DCR.
In general, both the carriers generated inside
the depletion region and those carriers which are
Figure 1: An illustration of gated operation of a Geiger
GmAPD, including afterpulsing.
D. G. Fouche, “Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors,” Applied Optics, vol.
42, no. 27, pp. 5388-5398 (2003).
1
generated within one diffusion length of the junction have a reasonable chance of being collected and
contributing to the dark current. Carriers drift across the depletion region according to their charge and
the direction of the electric field. The direction of transport by drift is always from minority side to
majority side (e.g. electrons drift from the p side to the n side, and holes drift in the opposite direction).
Written in discretized form, the DCR is:
G
DCR (t )  ASPAD
dark
(i, t )  Pbe (i)  Pbh (i)
,
where the range of the summation is all elements within one diffusion length of the depletion region,
and:
collection
Gdark(i, t) = GG-R(i) + Gap(i, t) + Gtrap(i) + Gband-to-band(i).
The G-R current is tied to the carrier recombination rate in the vicinity of the junction because the
rate of thermal generation balances the rate of recombination. Recombination rates can be modeled in
varying degrees of detail: a third-order polynomial in carrier concentration is often used to combine
Shockley-Read-Hall (SRH) recombination at traps (linear term), band-to-band recombination (quadratic
term), and Auger recombination (cubic term) into a single expression. The various recombination rates
as a function of location are typically calculated by band edge modelers because they are required for
continuity of the carrier transport equations. As with the electric field profile, Voxtel obtains GG-R(i) as
output from commonly available device modeling software.
Under normal operating conditions, the G-R leakage will be only weakly dependent upon the applied
bias because the width of the depletion region – and hence the volume of collection – will be essentially
constant. The biggest influence on GG-R is the intrinsic carrier concentration, which is a function of alloy
composition and temperature. Generally speaking, dark counts attributable to GG-R originate in the
narrow-gap absorber where the intrinsic carrier concentration is highest, and can be reduced by cooling
or selection of a wider-gap alloy.
Traps contribute to the DCR in three ways. The SRH portion of G-R leakage discussed above is
calculated by the band edge modeler assuming steady state conditions. However, immediately following
Geiger breakdown, the population of filled trap states is larger than its steady state value. Assuming an
excess concentration ΔNt of filled trap states and a characteristic lifetime trap, the generation rate by
trap release at time t after breakdown is:
Gap (i, t ) 
 N t (i )
 trap

t 
exp  
  
 trap  .
The initial excess concentration of filled traps ΔNt can be found by application of the Fermi
distribution, provided the physical concentration of trap states Nt and their energy Et are known:
1
 
 Et  E F   
N t (i )  N t (i ) 1  1  exp 
 
k B T   
 


.
Trap emission is normally modeled as a thermally-excited process that can be characterized by an
activation energy, which is found experimentally. Afterpulsing certainly exhibits such temperaturedependent behavior, but at high electric fields, more than one trap emission mechanism is active. In
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TECHNICAL NOTE: V720 - Page 2
particular, quantum mechanical tunneling out of the trap state is an important field-dependent process
which can affect trap lifetime. Ultimately, a net trap emission rate which reflects both thermal and
tunnel processes running in parallel must be obtained to properly characterize GG-R and Gap.
Generation by trap-assisted tunneling is a two-step process. In the first step, an electron is promoted
out of the valence band and into a mid-gap trap state. This generates a mobile hole in the valence band
and an occupied trap. The second step occurs if the trapped electron manages to tunnel from the trap
state into the conduction band before it recombines with a hole in the valence band. Tunneling
completes the generation of a new electron-hole pair, whereas recombination resets the system to its
original state. The generation rate depends upon the density of trap states (Nt), their occupancy
(determined by their energy Et), and the tunnel lifetime of the trap ( tunnel):
1

 E  EF  
N t (i)  1  exp  t
 
k
T
 B


Gtrap (i) 
 tunnel (i)
.
The trap has a tunnel lifetime because it is technically not a stationary state; rather, it is a resonance
state with a complex energy (the imaginary component means the wave function evolves with time and
‘leaks’ out of the trap potential). Numerical techniques are required to solve for the tunnel lifetime,
which is highly dependent upon the trap depth and applied electric field.2 This is because these two
factors determine the height and width of the potential barrier that separates the trap state from the
conduction band. Generally speaking, tunnel currents have a strong exponential dependence on electric
field (bias). Cooling can reduce tunnel leakage in two ways: by reducing the equilibrium occupancy of
the traps, and through widening of the band gap.
Trap-assisted tunneling complicates the DCR calculation considerably, as the tunnel rate influences
both GG-R and Gap through its impact on trap lifetime and steady state occupancy. Accordingly, a model
for tunnel must be implemented in the band edge modeler in order to obtain accurate simulations. The
technique of Choe et al. outline one relatively simple and rapid computational method.2 The trap can be
modeled as a simple Coulomb potential with a (field-free) bound state energy below the conduction
band. To either side of the trap, the conduction band states vary in energy according to the local electric
field strength (Fi), establishing a triangle barrier between the trap state and conduction band states of
equal and lower energy to one side of the trap. The transfer matrix method outlined by Choe et al. can
be used to solve for the tunnel lifetime through the resulting triangle barrier.
Generation by band-to-band tunneling is very similar to the second step of trap-assisted tunneling.
Two important differences are the density of states that is involved (the density of states at the valence
band edge greatly exceeds the possible density of trap states), and the height of the potential barrier
(the full band gap). Consequently, band-to-band tunneling rates are only significant in narrow-gap
semiconductor alloys, which is why the SACM structure is used to protect narrow-gap NIR absorbers. An
analytic expression for the band-to-band tunneling rate in direct gap semiconductors is commonly used
that depends upon the electric field strength (F), the reduced carrier effective mass ( mr* ) and the
temperature-dependent band gap:Error! Bookmark not defined.
J.-W. Choe, H.-J. Hwang, A. G. U. Perera, S. G. Matsik, and M. H. Francombe, “Resonant tunneling times in superlattice
structures,” Journal of Applied Physics, vol. 79, no. 10, pp. 7510-7513 (1996).
2
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 C2, i (T ) 
Gbandtoband (i)  C1, i (T ) Fi 2 exp 

Fi 

,
where
C1 (T ) 
C 2 (T ) 
q2
 h2
2
2 mr*
E g (T )
;
3
mr*
E g (T ) 2
qh 2
.
temperature trends.
Testing Gm APDs
Count Rate (Hz)
Count Rate (Hz)
‘Free-Run Mode’ Geiger-Mode Testing
Voxtel has developed a TEC-cooled vacuum test chamber to support GmAPD characterization. Test
equipment include a Stanford Research SR620 universal time interval counter used for collecting count
statistics, a pair of temperature-stabilized OZ Optics OZ-2000 fiber-coupled diode lasers emitting at 1064
and 1550 nm to supply the optical signal, and an Avanex PowerLog FA-20 modulator driven by an Avtech
AVM-2-C high speed pulse generator to modulate the illumination; the modulator is stabilized by a YY
Labs Mini-MBC-1 modulator bias controller. Optical power calibration is performed using a Newport
1830C optical power meter with
240 K
a
Newport
818-IG/CM
7
7
10
10
photodiode standard, traceable
0.5 V Dark
0.5 V Light
to the National Institute of
1.0 V Dark
1.0 V Light
Standards and Technology
2.0 V Dark
2.0 V Light
(NIST). We also have the ability
6
6
to take response spectra using a
10
10
Spectral Products CM 110 fibercoupled
monochromator
illuminated by a Spectral
Products
ASBN-W-100-L
5
5
10
10
tungsten-halogen lamp. With
the recent addition of a
Newport
high-speed
photodetector and picosecond
4
4
laser to our test lab, we will
10
10
0
2
4
6
8
10
soon be able to characterize the
Quench Duration (s)
timing jitter of GmAPDs as well.
Figure 2: Example of photon-counting data collected by Voxtel using our
PDE and DCR Measurements
Measuring DCR is very straight- VEA101 instrument. Different curves are for different overbias settings.
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TECHNICAL NOTE: V720 - Page 4
forward, but PDE and afterpulse measurements require some art. Correctly calibrating the optical power
actually delivered to the detector under test (DUT) is the main challenge, because coupling losses into
the test enclosure and any mismatch between the DUT’s active area and the illuminated spot size will
tend to reduce the optical power incident on the DUT.
We solve the calibration problem by a two-step procedure. Prior to testing in the vacuum chamber, a
Cascade Microtech LWP-LEN-MM lightwave probe is used to deliver the optical signal from the fibercoupled monochromator directly to the active area of the DUT. The near field spot size from the
lightwave probe is smaller than the DUT’s active area, so 100% of the optical power is incident on the
DUT. A room temperature photocurrent measurement is obtained from both the DUT and the reference
photodiode. The photocurrent of the reference photodiode can be used to measure the optical power
delivered, and this in turn is used to infer the responsivity of DUT at that single bias condition and
temperature. Next, the DUT is fixtured in the vacuum chamber, and the lightwave probe is switched out
with a fiber collimator. The DUT’s photocurrent is measured a second time inside the vacuum chamber.
Since the responsivity of the DUT at room temperature is already known from the initial measurement
outside the vacuum chamber, the photocurrent measured inside the chamber is actually a calibrated
measurement of the optical power that ultimately reaches the DUT from the fiber collimator. Thus, the
optical power delivered to the DUT is known, and PDE measurements taken at different temperatures
will be properly calibrated. An example of PDE and DCR data taken by Voxtel using this methodology is
shown in Figure 2.
Afterpulse Probability Measurements
Extraction of afterpulse probability from free-run DCR data requires some mathematical manipulation.
Consider a GmAPD characterized by a ‘primary’ dark count rate DCR. In this usage, DCR refers to the rate
of dark counts in an ideal detector that is always active, and which experiences no afterpulsing. DCR is
related to the measured dark count rate (DCRM) – again, without afterpulsing – by subtraction of the
known quench time in free-run mode. Practically, a long quench time (tQ0) is chosen such that
afterpulsing in negligible:
DCR = [1/DCRM – tQ0]-1.
Suppose that for a given quench time, the probability of an afterpulse is characterized by PAP ≤ 1.
Then the rate of ‘secondary’ dark counts is just the product:
[secondary]
DCR × PAP.
However, these secondary dark counts also have a chance of afterpulsing…
[tertiary]
(DCR × PAP) × PAP.
… and so on, ad infinitum. The net dark count rate with afterpulsing included (DCRAP) can be
expressed as a geometric series:

DCRAP = DCR + DCR × PAP + (DCR × PAP) × PAP + … = DCR
P
k
AP
k

DCR
.
1  PAP
Relating DCRAP to the measured value (DCRAP,M) by the procedure described earlier, we have:
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.
Solving for PAP, this is:
Afterpulse Probability
DCR AP  [1 / DCR AP, M
1 Afterpulse Probability
Extracted
DCR [11 / DCR M  t Q 0 ]
 tQ ] 

210 K
1  PAP
1  PAP
1
0.8
1
DCRAP
, M  tQ
.
PAP  1 0.6

1
DCRM  tQ 0
240 K
270 K
290 K
The difficulty in the analysis comes
0.4
from the need to measure the dark
count rate without afterpulsing (DCRM).
0.2
In general, one arrives at this figure by
taking measurements with such a long
0
quench time (tQ0) that afterpulsing is
0
2
4
6
8
10
12
eliminated. So, in the equation above,
Quench Time (s)
DCRM is taken to be a constant at a given
temperature, whereas DCRAP,M varies Figure 3: Afterpulse probability measured at a variety of
with quench time. Voxtel’s test setup temperatures for 0.5 V overbias.
can operate its VX-279 AQC in free-run mode with a maximum quench time of about 10 µs, which is too
short to completely eliminate afterpulsing at the lower end of its temperature range (e.g., 210 K). To
test longer quench times, one must operate in gated mode.
The mathematics of afterpulsing in gated mode is very similar to the treatment for free-run data,
with the caveat that one can measure dark count probability directly, without using the transformations
described above for free-run data. The logic of the geometric series is the same, and afterpulse
probability is equal to:

PDCAP = PDC + PDC × PAP + (PDC × PAP) × PAP + … = PDC
P
k
AP
k

PDC
,
1  PAP
where PDCAP is the measured dark count probability with afterpulsing included and PDC is the dark
count probability without afterpulsing (inferred from measurements taken with a very long quench
time). An example of afterpulse probability measurements made by Voxtel is shown in Figure 3.
Gated-Mode Count Rates
In gated mode, afterpulsing can be characterized using the double-pulse method4. Pairs of two gate
pulses are triggered at a repetition rate well below the rate at which afterpulsing is expected, with light
incident on the APD only during the first gate of each pair. The time delay between the pairs of gate
pulses is then varied, and the number of dark counts occurring only during the second pulse of the pair
is recorded. After subtracting the base dark count rate measured at a very long time delay between
pulses, the probability of an afterpulse can be computed for each value of time delay. Light energy
during the first gate must sufficient to guarantee 100% avalanche probability during this pulse; so long
as this minimum energy is used the results do not vary with the optical energy used.
Since the severity of afterpulsing is a function of the integrated charge flow through the APD during
the avalanche, the specific values of afterpulse probability measured at a given delay value do depend
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upon the duration of the first gate pulse, but the general trends in the data with temperature and excess
bias do not depend on the gate duration.
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