Geiger-Mode APD
SPAD: breakdown voltage, overbias, temperature effects, PDE, and dark count rate.
V_br Shift
+0.00 V
Excess Bias
3.00 V
Trigger Probability
76.2%
PDE
40.0%
Dark Count Rate
1.39e+2 cps
doubles every 6.2 °C at fixed excess bias
Afterpulse Probability
0.410%
Afterpulse Rate (dark)
5.70e-1 cps
Max Count Rate 1/τ
20.0 Mcps
ΔV(T) = ΔV(25 °C) − β·(T − 25 °C); P_t = 1 − exp(−ΔV/V_c); PDE = PDE_max·P_t
DCR = DCR₀ · exp[−(E_a/k_B)(1/T − 1/T₀)] · exp[b(ΔV − ΔV₀)] · P_t(ΔV)/P_t(ΔV₀)
P_ap = η·(ΔV·P_t)/(ΔV₀·P_t₀) · exp(−t_d/τ_trap)
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
The trigger probability P_t = 1 − e^(−ΔV/V_c) is Otte's empirical fit. The dark rate is Arrhenius in T at a fixed excess bias, times Otte's e^(bΔV)·P_t bias dependence, with b held at its 20 °C value (Otte fits 10.1 at −40 °C down to 6.83 at 40 °C). The trapped charge scales with ΔV·P_t, and the trap lifetime is held fixed, though it lengthens on cooling. V_c is held at its 25 °C value while V_br drifts; E_a is fixed (Webster & Henderson measured 293–343 K; at low temperature tunnelling flattens the dark rate). Defaults: one microcell of a Hamamatsu S13360-3050CS, 40.0 % PDE at 3 V. The trap and the 50 ns dead time are illustrative, since a SiPM microcell recharges through its quench resistor instead of a fixed dead time.
- Otte A. N., Garcia D., Nguyen T., Purushotham D. (2017). Characterization of three high efficiency and blue sensitive silicon photomultipliers. Nucl. Instrum. Methods A 846, 106–125. PDE = PDE_max·(1 − e^(−ΔV/a)), eq. 3, with a = α·U_BD and α = 0.0395 at 452 nm (Hamamatsu); dark-rate fit e^(a + b·U_rel)·P_t, eq. 13, b = 8.43 at 20 °C; dark rate doubles every 5.3 °C at fixed overvoltage, −40 to 40 °C. doi:10.1016/j.nima.2016.09.053
- Webster E. A. G., Henderson R. K. (2013). A TCAD and spectroscopy study of dark count mechanisms in single-photon avalanche diodes. IEEE Trans. Electron Devices 60, 4014–4019. Arrhenius activation energies of CMOS SPADs, 293–343 K: 0.85 eV for low-DCR devices, 0.45 eV for field-enhanced E-centre traps. doi:10.1109/TED.2013.2285163
- Cova S., Lacaita A., Ripamonti G. (1991). Trapping phenomena in avalanche photodiodes on nanosecond scale. IEEE Electron Device Lett. 12, 685–687. Afterpulsing from trap release, η·e^(−t/τ), growing with the avalanche charge. doi:10.1109/55.116955
- Hamamatsu Photonics. MPPC S13360 series, datasheet KAPD1052E. S13360-3050CS: V_BR = 53 V, 3 V overvoltage, PDE 40 % at 450 nm, dark count 500 kcps over 3600 pixels, 54 mV/°C. hamamatsu.com