1. What Does SPAD Afterpulsing Actually Tell Us About Defects in InP? Mark Itzler, Mark Entwistle, and Xudong Jiang SPW2011 – June 2011

2. Princeton Lightwave Inc. 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 2

3. Princeton Lightwave Inc. SPW2011 – June 2011 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 Long hold-off time # of trapped carriers primary avalanche afterpulses short hold-off time # of trapped carriers trap sites located in multiplication region EcEc EvEv 3

4. Princeton Lightwave Inc. SPW2011 – June 2011 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 Bethune and Risk, JQE 36, 340 (2000) Cancel transient response synchronous with photon arrival Temporally gate out leading and trailing transients Set threshold for remaining avalanche signal 4

5. Princeton Lightwave Inc. SPW2011 – June 2011 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) Absence of afterpulsing “runaway” indicates higher frequencies can be achieved 5

6. Princeton Lightwave Inc. SPW2011 – June 2011 6 “Double-pulse” afterpulse measurement  Use “time-correlated carrier counting” technique to measure afterpulses  Trigger single-photon avalanches in 1 st gate  Measure probability of afterpulse in 2 nd gate at T n  Use range of T n to determine dependence of afterpulse probability on time following primary avalanche Double-pulse (“pump-probe”) method T1T1 ≈ Cova, Lacaita, Ripamonti, EDL 12, 685 (1991) T2T2 ≈ Afterpulse probability Time T1T1 T2T2

7. Princeton Lightwave Inc. SPW2011 – June 2011 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 7 123456126127128 12 ≈ 50 MHz: 20 ns 25 MHz: 123128 1 ≈ 40 ns

8. Princeton Lightwave Inc. SPW2011 – June 2011 FPGA-based afterpulse measurements  Obtain afterpulsing probability data at 5 frequencies for 128 gates All frequencies 8 50 MHz 40 MHz 33 MHz 25 MHz 10 MHz APP ~ 1% at 30 ns

9. Princeton Lightwave Inc. SPW2011 – June 2011 Legacy approach to afterpulse fitting  Try to fit afterpulse probability (APP) data with exponential fit  Physically motivated by assumption of single dominant trap Single exponential curve generally fits range of ~5X in time APP 1  exp(-t/ τ 1 ) 9

10. Princeton Lightwave Inc. SPW2011 – June 2011 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 Single exponential curve generally fits range of ~5X in time APP 2  exp(-t/ τ 2 ) 10

11. Princeton Lightwave Inc. SPW2011 – June 2011 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 Single exponential curve generally fits range of ~5X in time APP 3  exp(-t/ τ 3 ) 11

12. Princeton Lightwave Inc. SPW2011 – June 2011 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 APP = C 1 exp(-t/ τ 1 ) + C 2 exp(-t/ τ 2 ) + C 3 exp(-t/ τ 3 ) 12

13. Princeton Lightwave Inc. SPW2011 – June 2011 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? APP = C T - α 13

14. Princeton Lightwave Inc. SPW2011 – June 2011 Afterpulsing data from Univ. Virginia  Good fit for power law T - α with α ≈ -1.0 to -1.1 data from Joe Campbell, UVA Double-pulse method PLI SPADs 14

15. Princeton Lightwave Inc. SPW2011 – June 2011 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 Double-pulse method PLI SPADs 15

16. Princeton Lightwave Inc. SPW2011 – June 2011 Afterpulsing data from Nihon Univ.  Good fit for power law T - α with α = -1.38 data from Naota Namekata, Nihon U. Autocorrelation test of time- tagged data PLI SPADs 16

17. Princeton Lightwave Inc. SPW2011 – June 2011 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 E c – 0.24 eV E c – 0.30 eV E c – 0.37 eV E c – 0.40 eV E c – 0.55 eV W. A. Anderson and K. L. Jiao, in “Indium Phosphide and Related Materials: Processing, Technology, and Devices”, A. Katz (ed.) (Artech House, Boston, 1992) Early work Later work Radiation effects 17

18. Princeton Lightwave Inc. SPW2011 – June 2011 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) 18 D(R) R R0R0 R R0R0 R R δ (R – R 0 ) single trap “Uniform” Normal “Inverse” D(R) α 1/R narrowest distribution widest distribution

19. Princeton Lightwave Inc. SPW2011 – June 2011 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 – R 0 ) doesn’t change exponential behavior  “Uniform” and “inverse” distributions can be solved analytically –Require assumptions for a few model parameters Minimum detrapping time: τ min = 10 ns Maximum detrapping time: τ max = 10 µs Number of trapped carriers:n = 5 Detection efficiency:20% 19 just sample values; can be generalized

20. Princeton Lightwave Inc. SPW2011 – June 2011 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 20 Inverse D(R): T - α with 1.05 < α < 1.30 Uniform D(R): T - α with 1.9 < α < 2.1

21. Princeton Lightwave Inc. SPW2011 – June 2011 Insights from modeling of APP  Inverse distribution provides correct power law behavior –More traps with slower release rates D(R) α 1/R –Other distributions considered do not agree with data  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 21 D(R) R A.K. Jonscher, Sol. St. Elec. 33, 139 (1990)

22. Princeton Lightwave Inc. SPW2011 – June 2011 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, Politecnico di Milano Double-pulse method 22 Power law Exponential

23. Princeton Lightwave Inc. SPW2011 – June 2011 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 23

24. Princeton Lightwave Inc. SPW2011 – June 2011 BACK-UP SLIDES 24

25. Princeton Lightwave Inc. SPW2011 – June 2011  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 Electric field engineering in APDs i- n + -InP buffer n-InGaAsP grading n-InP charge i-InP cap SiN x passivation p-contact metallization n + -InP substrate anti-reflection coating n-contact metallization optical input E InGaAs absorption multiplication region p + -InP diffused region Schematic design for InGaAs/InP SPAD for 1.5 μm photon counting 25