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Document Sample
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
p-contact metallization SiNx passivation
+
p -InP diffused region E
# of trapped i-InP cap
multiplication region
carriers n-InP charge
n-InGaAsP grading
i-InGaAs absorption
primary +
n -InP buffer
avalanche n+-InP substrate
anti-reflection coating n-contact metallization
short hold-off optical input
time 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. 4
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
OLD Performance (1 ns gate duration) NEW Performance (1 ns gate duration)
1E+0
PER DETECTED PHOTON
1E-1
1E-1
Afterpulse Probability
Afterpulse Probability
(per 1 ns gate pulse)
1E-2
1E-2
1E-3
10 MHz
1E-4 5 MHz 1E-3 50 MHz
2 MHz
33 MHz
1E-5 1 MHz
10 MHz
0.5 MHz 1 MHz
1E-6 1E-4
5% 10% 15% 20% 25% 30% 0% 10% 20% 30% 40%
Photon Detection Efficiency Photon Detection Efficiency
• 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
Cova, Lacaita, Ripamonti,
Trigger single-photon avalanches in 1st gate EDL 12, 685 (1991)
Measure probability of afterpulse in 2nd gate at Tn
Use range of Tn to determine dependence of afterpulse probability on
time following primary avalanche
Double-pulse (“pump-probe”) method
T1
probability
Afterpulse
≈
T2
≈
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 2 3 128 1
SPW2011 – June 2011 Princeton Lightwave Inc. 7
FPGA-based afterpulse measurements
Obtain afterpulsing probability data at 5 frequencies for 128 gates
1E-1 1E-1 1E-1
33 MHz 25 MHz 10 MHz
Afterpusle probability
Afterpusle probability
Afterpusle probability
1E-2 1E-2 1E-2
1E-3 1E-3 1E-3
1E-4 1E-4 1E-4
33 MHz 25 MHz 10 MHz
1E-5 1E-5 1E-5
10 100 1000 10 100 1000 10 100 1000
Time following primary avalanche (ns) Time following primary avalanche (ns) Time following primary avalanche (ns)
1E-1
40 MHz 1E-1
Afterpusle probability
1E-2 All frequencies PDE = 20%
1 ns gates
detected photon per gate
Afterpusle probability per
1E-3
1E-2
1E-4
40 MHz APP ~ 1%
1E-5
at 30 ns
10 100 1000
Time following primary avalanche (ns) 1E-3
1E-1
50 MHz 50 MHz
Afterpusle probability
1E-2 40 MHz
1E-4 33 MHz
1E-3
25 MHz
1E-4
50 MHz 10 MHz
1E-5 1E-5
10 100 1000
Time following primary avalanche (ns) 10 100 1000
SPW2011 – June 2011 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
PDE = 20%
1 ns gates
Single exponential curve generally
fits range of ~5X in time
detected photon per gate
Afterpusle probability per
1E-2
1E-3
50 MHz
1E-4 40 MHz
33 MHz
25 MHz
10 MHz
1E-5
10 100 1000
Time following primary avalanche (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 9
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
PDE = 20%
1 ns gates
Single exponential curve generally
fits range of ~5X in time
detected photon per gate
Afterpusle probability per
1E-2
1E-3
50 MHz
1E-4 40 MHz
33 MHz
25 MHz
10 MHz
1E-5
10 100 1000
Time following primary avalanche (ns)
SPW2011 – June 2011 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
PDE = 20%
1 ns gates
Single exponential curve generally
fits range of ~5X in time
detected photon per gate
Afterpusle probability per
1E-2
1E-3
50 MHz
1E-4 40 MHz
33 MHz
25 MHz
10 MHz
1E-5
10 100 1000
Time following primary avalanche (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 11
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
1E-1
PDE = 20%
1 ns gates
detected photon per gate
Afterpusle probability per
1E-2
APP = C1exp(-t/τ1)
τ1 = 30 ns
+ C2exp(-t/τ2)
1E-3 + C3exp(-t/τ3)
τ2 = 120 ns
50 MHz
1E-4 40 MHz
33 MHz τ3 = 600 ns
25 MHz
10 MHz
1E-5
10 100 1000
Time following primary avalanche (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 12
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?
1E-1
PDE ~ 20%
y = 0.52x-1.07 1 ns gates
detected photon per gate
Afterpusle probability per
1E-2
APP = C T-α
1E-3
50 MHz
40 MHz
1E-4
33 MHz
25 MHz
10 MHz
1E-5
10 100 1000
Time following primary avalanche (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 13
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
y = 3.44x-1.03 UVA data
~30% PDE
y= 2.20x-1.05
1E-1 Double-pulse
Afterpulse probability
y = 0.74x-1.09 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. 14
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
y = 2.92x-1.16 NIST data
~15% PDE
1E-1 y = 0.49x-1.21
Double-pulse
Afterpulse Probability
method
1E-2
PLI SPADs
1E-3
1E-4
1.50 ns gate
1E-5 1.00 ns gate y = 0.13x-1.24
0.63 ns gate
0.50 ns gate y = 0.06x-1.25
1E-6
1 10 100 1000
Time following primary avalanche (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 15
Afterpulsing data from Nihon Univ.
Good fit for power law T-α with α = -1.38
data from Naota Namekata, Nihon U.
1
Nihon U. data
Normalized Afterpulse Probability
213 K
Autocorrelation
0.1 test of time-
tagged data
PLI SPADs
0.01 y = 237.66x-1.38
0.001
10 100 1000
Time following primary avalanche (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 16
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
SiNx passivation
p-contact metallization
Ec – 0.37 eV
p+-InP diffused region Electric field Ec – 0.40 eV
i-InP cap
multiplication region Ec – 0.55 eV
n-InP charge
n-InGaAsP grading
i-InGaAs absorption
+
n -InP buffer
n+-InP substrate Early Later Radiation
anti-reflection coating n-contact metallization work work 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. 17
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) δ(R – R0) D(R) “Uniform”
single trap
narrowest widest
distribution R0 R R distribution
D(R) Normal D(R) “Inverse”
D(R) α 1/R
R0 R R
SPW2011 – June 2011 Princeton Lightwave Inc. 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: τmin = 10 ns
Maximum detrapping time: τmax = 10 µs just sample values;
Number of trapped carriers: n=5 can be generalized
Detection efficiency: 20%
SPW2011 – June 2011 Princeton Lightwave Inc. 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
1E+0
Normalized afterpulsing probability
Inverse
1E-1
1E-2 y = 25.23x-1.18
y = 200.93x-2.00 Inverse D(R):
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
10 100 1000 10000
Time following primary avalanche (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 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
R
Inverse distribution not necessarily a unique solution
– 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. 21
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
data from Massimo Ghioni,
-2
Power law Politecnico di Milano
1.E-02
10
Afterpulsing Probability Density (ns-1)
Silicon SPADs
y = 0.21x-1.54
-3 T = -25 C, Pap = 6%
1.E-03
10
Double-pulse
method
-4
1.E-04
10
y = 0.0002e-0.005x
-5 Exponential
1.E-05
10
-6
1.E-06
10
1.E-07-7
10
10 100 1000
Time (ns)
SPW2011 – June 2011 Princeton Lightwave Inc. 22
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
SPW2011 – June 2011 Princeton Lightwave Inc. 23
BACK-UP SLIDES
SPW2011 – June 2011 Princeton Lightwave Inc. 24
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
E
p+-InP diffused region
i-InP cap
multiplication region
n - InP charge
n -InGaAsP grading
i - InGaAs absorption
+
n - InP buffer
+
n - InP substrate Schematic design for
anti-reflection coating n-contact metallization InGaAs/InP SPAD for
1.5 μm photon counting
optical input
SPW2011 – June 2011 Princeton Lightwave Inc. 25
