Single Photon Detector Workshop NIST Gaithersburg Physical Model for Dark Count and the Development of InGaAs/Si Single Photon Detectors Y.-H. Lo, Yimin Kang, Huaxin Lu UC San Diego A. Pauchard, M. Bitter, Z. Pan, R. Dimitrov, S. Hummel Nova Crystals, Inc.
Outline • Physical model for dark count and afterpulsing effect • - critical dependence on device parameters and operational conditions. • - single photon quantum efficiency and the importance of k-factor (electron/hole ionization ratio) • Development of InGaAs/Si APDs
Counting in the Dark Dark count probability: Pd = 1 - e (-Nd*) the probability that there is at least one dark carrier triggering a breakdown when the average effective dark carriers number is Nd* where Nd*= Nd Pa Nd is the number of dark carriers in SPAPD’s gain region within gated pulse duration Pa is the probability of a carrier initiating an avalanche with Geiger mode gain  Dark carrier generation + Avalanche initiation Dark count  R.J. McIntyre, IEEE Transactions on Electron Devices, vol. ED-20, pp.637-641, 1973.
1 t I 2 t t Ntrapped0/td T t 3 4 Four Mechanisms for Dark Carrier Generation Primary dark carrier: IDM -- primary dark current which undergoes the multiplication process Residual primary dark carrier: GB -- gain-bandwidth product of APD M0 -- gain when APD is biased at the DC offset Afterpulse dark carrier: Residual afterpulse dark carrier: td -- detrap time T-- pulse period t*tr -- transit time Ntrapped0 -- trapped carriers per pulse
t Effect of Primary Dark Current on Dark Count Dark count rate is approximately proportional to the primary dark current IDM of APD, provided afterpulse effect is negligible. • voltage pulse width: 2ns • detrap time td : 200ns • pulse repetition rate f: • 100kHz • GB = 30GHz • DC offset gain M0 :5
I t Effects of the DC Bias and the Gain-Bandwidth Product Low DC bias (therefore low DC gain) and large GB product can reduce the dark count rate, but the effect is relatively modest. • voltage pulse width: 2ns • detrap time td : 200ns • pulse repetition rate f: • 100kHz • IDM=0.1pA
Effect of Afterpulse The contribution of afterpulse depends critically on the ratio between the detrap time and the interpulse interval. When td/T > 10%, the afterpulse effect rises sharply. • voltage pulse width: 2ns • single-photon quantum • efficiency: 20% • number of photon per • pulse: 0.1pp • Gain at DC offset M0: 10
Afterpulse Effect (Cont.) The relative importance of afterpulse effect increases with the increasing Geiger mode threshold gain. • Voltage pulse width: 2ns • Single-photon quantum • efficiency: 20% • Number of photon per • pulse: 0.1pp • Gain at DC offset: 10
k=0.002 k=0.02 k=0.002 Photoelectron Detection Probability Breakdown Probability k=0.02 Voltage in excess of Vb ,and is roughly proportional to V/Vb Breakdown Probability – Calculation of Single Photon Quantum Efficiency Low ionization ratio (k-factor) increases the breakdown probability triggered by a single incident photon (i.e. high SPQE) * H. Dautet, et.al., Applied Optics, vol.32, No.21, pp.3894-900 (1993). Mt is the discriminator threshold setting.
Simulated Sub-Geiger Mode APD Impulse Response DC Gain used in this simulation: 6,000 (before breakdown) The Geiger-mode gain (within 2ns pulse window) of InGaAs/Si APD is about 40 times higher than InGaAs/InP APD, manifesting the importance of k-factor. The result indicates that InGaAs/Si APDs can have a much higher single-photon quantum efficiency than InGaAs/InP APDs under the same operation condition.
Summary • To achieve low darkcount and high single-photon quantum efficiency, one likes to have APDs that have • Low primary dark current (< 1pA) • Low trap density in the multiplication region • Short detrap time (< 10% of the interpulse time interval) • Low DC bias (low prepulse gain) and high GB product • Small k-factor (critical to single-photon quantum efficiency) All these lead to the conclusion that Si APDs should have superior performance to InGaAs/InP APDs for single-photon detection.
Large Area, Covalently Bonded InGaAs/Si Structure TEM SEM III-V Si 4x4 cm2 InGaAs/Si wafer
Temperature Dependence of Breakdown Voltage Gsi = 0.026 V/C GSi 4 times smaller than GInP
Excess Noise and k-Factor F (M=10) = 2.2 F (M=50) = 2.8
Summary InGaAs/Si APDs can be fabricated on large area wafers with high process yield. InGaAs/Si has shown high DC gain and normal breakdown behavior. Both the k-factor and the temperature dependence of the breakdown voltage of InGaAs/Si APDs are the same as Si APDs. The temperature dependence of the primary dark current needs to be investigated.