What Does SPAD Afterpulsing Actually
Tell Us About Defects in InP?
Mark Itzler, Mark Entwistle, and Xudong Jiang
SPW2011 – June 2011
Presentation Outline

50 MHz photon counting with RF matched delay line scheme

Afterpulse probability (APP) dependence on hold-off time

Fitting of APP data

inadequacy of legacy approach assuming one or few traps

new fitting based on broad trap distribution

Implications of APP modeling for trap distributions

Summary
SPW2011 – June 2011
Princeton Lightwave Inc.
2
Afterpulsing: increased DCR at high rate

Single photon detection by avalanche multiplication in SPADs

Avalanche carriers trapped at defects in InP multiplication region

Carrier de-trapping at later times initiates “afterpulse” avalanches

Serious drawback of afterpulsing → limitation on counting rate
SiNx passivation
p-contact metallization
+
E
p -InP diffused region
i-InP cap
# of trapped
carriers
multiplication region
n-InP charge
n-InGaAsP grading
i-InGaAs absorption
primary
avalanche
+
n -InP buffer
+
n -InP substrate
anti-reflection coating
short hold-off
time
n-contact metallization
optical input
afterpulses
trap sites located in
multiplication region
# of trapped
carriers
Ec
Ev
Long hold-off time
SPW2011 – June 2011
Princeton Lightwave Inc.
3
New results for RF delay line circuit

Enhance matched delay line circuit to operate at higher repetition rate
 Inverted and non-inverted RF reflections cancel transients
 Based on existing PLI product platform
Cancel transient response synchronous
with photon arrival
Temporally gate out leading and trailing
transients
Set threshold for remaining avalanche
signal
Bethune and Risk,
JQE 36, 340 (2000)
SPW2011 – June 2011
Princeton Lightwave Inc.
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Matched delay line solution to 50 MHz

Extension of cancellation scheme to higher frequencies
 More precise cancellation for reduced detection threshold → detect smaller avalanches
 Higher speed components to enable 50 MHz board-level operation

Measure cumulative afterpulsing using odd gates “lit”, even gates “dark”
 Take all counts in even gates above dark count background to be afterpulses
1E+0
NEW Performance (1 ns gate duration)
OLD Performance (1 ns gate duration)
1E-1
1E-2
1E-3
10 MHz
5 MHz
2 MHz
1 MHz
0.5 MHz
1E-4
1E-5
PER DETECTED PHOTON
1E-2
1E-3
50 MHz
33 MHz
10 MHz
1 MHz
1E-4
1E-6
5%
•
Afterpulse Probability
Afterpulse Probability
(per 1 ns gate pulse)
1E-1
10%
15%
20%
25%
Photon Detection Efficiency
30%
0%
10%
20%
30%
Photon Detection Efficiency
40%
Absence of afterpulsing “runaway” indicates higher frequencies can be achieved
SPW2011 – June 2011
Princeton Lightwave Inc.
5
“Double-pulse” afterpulse measurement

Use “time-correlated carrier counting” technique to measure afterpulses

Trigger single-photon avalanches in 1st gate

Measure probability of afterpulse in 2nd gate at Tn

Use range of Tn to determine dependence of afterpulse probability on
time following primary avalanche
Cova, Lacaita, Ripamonti,
EDL 12, 685 (1991)
T1
≈
T2
Afterpulse
probability
Double-pulse (“pump-probe”) method
≈
T1
T2
Time
SPW2011 – June 2011
Princeton Lightwave Inc.
6
FPGA-based data acquisition

Use FPGA circuitry to control gating and data collection

Generalize double-pulse method to many gates
 Capture afterpulse counts in up to 128 gates following primary avalanche
 Temporal spacing of gates determined by gate repetition rate

Allows capture of afterpulse count in any gate after avalance
 No need to step gate position as in double-pulse method
1 ns gates
20 ns
≈
50 MHz:
1
2
3
4
5
6
126 127 128
1
2
40 ns
≈
25 MHz:
1
SPW2011 – June 2011
2
3
128
Princeton Lightwave Inc.
1
7
FPGA-based afterpulse measurements
 Obtain afterpulsing probability data at 5 frequencies for 128 gates
1E-2
1E-3
1E-4
33 MHz
1E-5
100
1000
Time following primary avalanche (ns)
1E-1
1E-2
1E-3
1E-4
25 MHz
100
1000
Time following primary avalanche (ns)
1E-1
40 MHz
All frequencies
1E-2
1E-3
1E-4
40 MHz
1E-5
10
100
1000
Time following primary avalanche (ns)
1E-1
50 MHz
1E-2
1E-3
1E-4
1E-1
10 MHz
1E-2
1E-3
1E-4
10 MHz
1E-5
10
Afterpusle probability per
detected photon per gate
Afterpusle probability
25 MHz
1E-5
10
Afterpusle probability
1E-1
Afterpusle probability
33 MHz
Afterpusle probability
Afterpusle probability
1E-1
10
100
1000
Time following primary avalanche (ns)
PDE = 20%
1 ns gates
1E-2
APP ~ 1%
at 30 ns
1E-3
50 MHz
40 MHz
33 MHz
25 MHz
10 MHz
1E-4
50 MHz
1E-5
1E-5
10
100
1000
Time following primary avalanche (ns)
SPW2011 – June 2011
10
100
1000
Time following
primary avalanche (ns)
Princeton Lightwave
Inc.
8
Legacy approach to afterpulse fitting
 Try to fit afterpulse probability (APP) data with exponential fit
 Physically motivated by assumption of single dominant trap
APP1  exp(-t/τ1)
1E-1
Afterpusle probability per
detected photon per gate
PDE = 20%
1 ns gates
Single exponential curve generally
fits range of ~5X in time
1E-2
1E-3
50 MHz
40 MHz
33 MHz
25 MHz
10 MHz
1E-4
1E-5
10
SPW2011 – June 2011
100
1000
Time following primary avalanche (ns)
Princeton Lightwave Inc.
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Legacy approach to afterpulse fitting
 Try to fit afterpulse probability (APP) data with exponentials
 Physically motivated by assumption of single dominant trap
 Single exponential not sufficient; assume second trap
APP2  exp(-t/τ2)
1E-1
Afterpusle probability per
detected photon per gate
PDE = 20%
1 ns gates
Single exponential curve generally
fits range of ~5X in time
1E-2
1E-3
50 MHz
40 MHz
33 MHz
25 MHz
10 MHz
1E-4
1E-5
10
SPW2011 – June 2011
100
1000
Time following primary avalanche (ns)
Princeton Lightwave Inc.
10
Legacy approach to afterpulse fitting
 Try to fit afterpulse probability (APP) data with exponentials
 Physically motivated by assumption of single dominant trap
 Single exponential not sufficient; assume second trap
 Still need third exponential to fit full data set
APP3  exp(-t/τ3)
1E-1
Afterpusle probability per
detected photon per gate
PDE = 20%
1 ns gates
Single exponential curve generally
fits range of ~5X in time
1E-2
1E-3
50 MHz
40 MHz
33 MHz
25 MHz
10 MHz
1E-4
1E-5
10
SPW2011 – June 2011
100
1000
Time following primary avalanche (ns)
Princeton Lightwave Inc.
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Legacy approach to afterpulse fitting
 Can achieve reasonable fit with several exponentials
 …but choice of time constants is completely arbitrary!
→ depends on range of times used in data set
 Our assertion: No physical significance to time constants in fitting
→ simply minimum set of values to fit the data set in question
Afterpusle probability per
detected photon per gate
1E-1
PDE = 20%
1 ns gates
1E-2
APP = C1exp(-t/τ1)
+ C2exp(-t/τ2)
+ C3exp(-t/τ3)
τ1 = 30 ns
1E-3
τ2 = 120 ns
50 MHz
40 MHz
33 MHz
25 MHz
10 MHz
1E-4
1E-5
10
SPW2011 – June 2011
τ3 = 600 ns
100
1000
Time following primary avalanche (ns)
Princeton Lightwave Inc.
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What other functions describe APP?
 Good fit for simple power law T-α with α ≈ -1
→ Is power law behavior found for other afterpulsing measurements?
→ Is the power law functional form physically significant?
Afterpusle probability per
detected photon per gate
1E-1
y = 0.52x-1.07
PDE ~ 20%
1 ns gates
1E-2
APP = C T-α
1E-3
50 MHz
40 MHz
33 MHz
25 MHz
10 MHz
1E-4
1E-5
10
SPW2011 – June 2011
100
1000
Time following primary avalanche (ns)
Princeton Lightwave Inc.
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Afterpulsing data from Univ. Virginia
 Good fit for power law T-α with α ≈ -1.0 to -1.1
data from Joe Campbell, UVA
1E+0
Afterpulse probability
y = 3.44x-1.03
y=
1E-1
2.20x-1.05
UVA data
~30% PDE
y = 0.74x-1.09
Double-pulse
method
PLI SPADs
1E-2
1E-3
3 ns gate
2 ns gate
1 ns gate
1E-4
10
100
1000
Time following primary avalanche (ns)
SPW2011 – June 2011
Princeton Lightwave Inc.
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Afterpulsing data from NIST
 Good fit for power law T-α with α ≈ -1.15 to -1.25
data from Alessandro Restelli
and Josh Bienfang, NIST
1E+0
NIST data
y = 2.92x-1.16
Afterpulse Probability
~15% PDE
y = 0.49x-1.21
1E-1
Double-pulse
method
1E-2
PLI SPADs
1E-3
1E-4
1.50 ns gate
1.00 ns gate
0.63 ns gate
0.50 ns gate
1E-5
1E-6
1
y = 0.13x-1.24
y = 0.06x-1.25
10
100
1000
Time following primary avalanche (ns)
SPW2011 – June 2011
Princeton Lightwave Inc.
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Afterpulsing data from Nihon Univ.
 Good fit for power law T-α with α = -1.38
data from Naota Namekata, Nihon U.
Normalized Afterpulse Probability
1
Nihon U. data
213 K
Autocorrelation
test of timetagged data
0.1
PLI SPADs
y = 237.66x-1.38
0.01
0.001
10
SPW2011 – June 2011
100
1000
Time following primary avalanche (ns)
Princeton Lightwave Inc.
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Literature on InP trap defects
 Literature on defects in InP describes dense spectrum of levels
 Instead of assuming one or a few dominant trap levels:
→ consider implications of a broad distribution for τ
Deep-level traps in
multiplication region
Ec – 0.24 eV
Ec – 0.30 eV
Ec – 0.37 eV
Ec – 0.40 eV
SiNx passivation
p-contact metallization
p+-InP diffused region
Electric field
i-InP cap
Ec – 0.55 eV
multiplication region
n-InP charge
n-InGaAsP grading
i-InGaAs absorption
+
n -InP buffer
+
n -InP substrate
anti-reflection coating
n-contact metallization
Early
work
Later
work
Radiation
effects
optical input
W. A. Anderson and K. L. Jiao, in “Indium Phosphide
and Related Materials: Processing, Technology, and
Devices”, A. Katz (ed.) (Artech House, Boston, 1992)
SPW2011 – June 2011
Princeton Lightwave Inc.
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Implications of trap distribution on APP
 Develop model for APP with distribution of detrap rates R ≡ 1/τ
– APP related to change in trap occupation: dN/dt ~ R exp(-t R)
– Integrate over detrapping rate distribution D(R)
→ APP ~ ∫ dR D(R) R exp(-t R)
D(R)
narrowest
distribution
“Uniform”
R
R0
R
Normal
D(R)
SPW2011 – June 2011
D(R)
δ(R – R0)
single trap
R0
D(R)
R
Princeton Lightwave Inc.
widest
distribution
“Inverse”
D(R) α 1/R
R
18
Implications of trap distribution on APP
 “Single trap” leads to exponential behavior
– Fitting requires multiple exponentials and is arbitrary
 Normal distribution is similar to single trap
– Gaussian broadening of δ(R – R0) doesn’t change exponential behavior
 “Uniform” and “inverse” distributions can be solved analytically
– Require assumptions for a few model parameters
Minimum detrapping time:
Maximum detrapping time:
Number of trapped carriers:
Detection efficiency:
SPW2011 – June 2011
τmin = 10 ns
τmax = 10 µs
n=5
20%
Princeton Lightwave Inc.
just sample values;
can be generalized
19
Modeling results for APP
 APP results for Uniform and Inverse detrap rate distributions D(R)
 APP behavior fit well by T-α for 10 ns to 10 µs
– Value of α depends on model parameter values, but α is well-bounded
Normalized afterpulsing probability
1E+0
Inverse
1E-1
y = 25.23x-1.18
1E-2
Inverse D(R):
y = 200.93x-2.00
1E-3
T-α with 1.05 < α < 1.30
1E-4
Uniform
Uniform D(R):
1E-5
T-α with 1.9 < α < 2.1
1E-6
10
SPW2011 – June 2011
100
1000
Time following primary avalanche (ns)
Princeton Lightwave Inc.
10000
20
Insights from modeling of APP
 Inverse distribution provides correct power law behavior
– More traps with slower release rates D(R) α 1/R
D(R)
– Other distributions considered do not agree with data
 Inverse distribution not necessarily a unique solution
R
– But it provides more accurate description than single trap or uniform
 Slower falloff of APP with hold-off time for Inverse distribution
– Need longer hold-off times to achieve same relative decrease in total AP
 Other possible explanations for power law behavior to explore
– Role of field-assisted detrapping, especially in non-uniform E-field
– Model in literature cites power law behavior for “correlated” detrapping
A. K. Jonscher,
Sol. St. Elec. 33, 139 (1990)
SPW2011 – June 2011
Princeton Lightwave Inc.
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Afterpulsing data on Silicon SPADs
 Neither power law nor exponential provide particularly good fit!
 Nature of defects in Si SPADs may be categorically different than for InP
Afterpulsing Probability Density (ns-1)
-2
1.E-02
10
data from Massimo Ghioni,
Politecnico di Milano
Power law
Silicon SPADs
T = -25 C, Pap = 6%
y = 0.21x-1.54
-3
1.E-03
10
Double-pulse
method
-4
1.E-04
10
-5
1.E-05
10
y = 0.0002e-0.005x
Exponential
-6
1.E-06
10
-7
1.E-07
10
10
100
1000
Time (ns)
SPW2011 – June 2011
Princeton Lightwave Inc.
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Summary
 Reached 50 MHz photon counting with RF matched delay line scheme
 Significant further repetition rate increases should be feasible
 Fitting of APP data with multiple exponentials not physically meaningful
 Extracted detrapping times are arbitrary, depend on hold-off times used
 Literature on defects in InP suggests possibility of broad distribution of defects
 Consistent power law behavior of APP data found by various groups
 APP vs. time T described by T-α with α ~ 1.2 ± 0.2
 Assumption of “inverse” distribution D(R) α 1/R for detrapping rate R
provides best description of data among distributions considered so far
 Not unique, but establishes general behavior
 May be other models that predict power law APP behavior for dominant trap
 Further modeling can predict behavior for different operating conditions
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Princeton Lightwave Inc.
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BACK-UP SLIDES
SPW2011 – June 2011
Princeton Lightwave Inc.
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Electric field engineering in APDs

Vertical structure to realize SAGCM structure for well-designed APD





Multiplication gain: high field for impact ionization
Carrier drift in absorber: low but finite absorber field
Avoid of tunneling in all layers
Eliminate interface carrier pile-up
Control of 3-D electric field distribution to avoid edge breakdown
p-contact metallization SiNx passivation
p+-InP diffused region
E
i-InP cap
multiplication region
n- InP charge
n -InGaAsP grading
i- InGaAs absorption
+
n -InP buffer
+
n -InP substrate
anti-reflection coating
n-contact metallization
optical input
SPW2011 – June 2011
Princeton Lightwave Inc.
Schematic design for
InGaAs/InP SPAD for
1.5 μm photon counting
25