Gated Avalanche Photodiodes (APDs)

• Gated Avalanche Photodiodes (APDs) are semiconductor detectors that use nanosecond bias gating to enable sensitive single-photon detection with significantly reduced dark noise.
• They employ specialized gating and readout circuitry—such as self-differencing and ultra-narrowband interference—to suppress capacitive transients and achieve timing resolutions below 200 ps at GHz rates.
• Their robust performance in quantum cryptography, photon number resolution, and LIDAR applications highlights their critical role in advanced optical sensing and quantum information protocols.

Gated Avalanche Photodiodes (APDs) are solid-state photon detectors engineered for sensitivity to single photons during periodically applied, nanosecond-to-subnanosecond bias windowing. Leveraging high electric fields induced above the breakdown threshold only during defined “gates,” these devices allow efficient single-photon detection, suppression of dark noise, and exceptional timing performance, underpinned by rapid active or passive quenching. Gated operation is now foundational for high-speed optical quantum information protocols and low-noise photonic instrumentation, with state-of-the-art implementations in both InGaAs/InP (telecom) and silicon (visible/NIR) platforms (Patel et al., 2012, Lunghi et al., 2012, Thomas et al., 2010, Comandar et al., 2014, Fan et al., 2023, Zhengyu et al., 5 Jan 2024).

1. Physical and Operational Principles

The gated mode exploits reverse-biasing the APD just below its breakdown voltage ($V_{\rm br}$), then periodically applying nanosecond-to-subnanosecond high-voltage “gates” ($V_{\rm pulse}$) that exceed $V_{\rm br}$ by a controlled excess bias ($V_{\rm ex}$). During each gate, a single photo-excited carrier may trigger an avalanche multiplication event, yielding macroscopic charge $\mathcal{O}(10–40~\mathrm{fC})$ detectable as a fast, transient current pulse (Patel et al., 2012, Fan et al., 2023, 0807.2320).

Key relationships include:

• Avalanche gain: $M(V_{\rm ex}) \approx \exp[\alpha V_{\rm ex}]$, where $\alpha$ is the ionization coefficient (Yuan et al., 2011).
• Photon detection efficiency per gate: $\eta = P_{\rm abs} \times P_{\rm avalanche}$ (Thomas et al., 2010), with $P_{\rm abs}$ set by absorption, and $P_{\rm avalanche}$ by excess bias and gate width.
• Dark count probability per gate: $P_{\rm d} \sim \mathrm{DCR}\times t_{\rm gate}$, scaling as $\exp(-E_g / kT)$ and strongly reduced by narrow gating and cooling (0807.2320, Lunghi et al., 2012).
• Afterpulsing: $$P_{\rm ap}(t) \propto Q_{\rm av} \exp(-t/\tau_{\rm trap})$$, with $Q_{\rm av}$ the avalanche charge, $t$ the hold-off time, and $\tau_{\rm trap}$ the characteristic trap lifetime (Thomas et al., 2010, Wiechers et al., 2016, Fan et al., 2023).

The temporal gating suppresses events from thermally activated or background-induced carriers, critically reducing the dark noise relative to free-running operation. Gate widths now routinely reach below 500 ps at GHz rates, enabling sub-200 ps timing resolution and minimizing avalanche charge for limited afterpulsing (Comandar et al., 2014, Patel et al., 2012, Fan et al., 2023).

2. Gating and Readout Circuitry

Modern gating implementations use either square-wave, sinusoidal, or custom-shaped voltage pulses with rise/fall times below 100 ps. The gate is often superimposed on a fixed DC bias via a bias-tee, typically with periods $T =$ 0.5–1 ns (1–2 GHz) for InGaAs/InP APDs and durations as short as 150 ps (Patel et al., 2012, Fan et al., 2023, Zhengyu et al., 5 Jan 2024).

Extracting avalanche signals from the dominant capacitive response necessitates specialized readout architectures:

• Self-differencing (SD): The APD output is split, with one path delayed by one or more gate periods before subtraction. This cancels the periodic gate-induced capacitive transients, revealing the stochastic avalanche pulses (Patel et al., 2012, Comandar et al., 2014, 1712.06520).
• Ultra-narrowband interference circuits (UNICs): These are RF interferometers with SAW band-pass filters precisely tuned to the gate frequency. When cascaded, they suppress the capacitive background by >80–160 dB per stage, with minimal distortion to the broadband avalanche signal (Fan et al., 2023, Zhengyu et al., 5 Jan 2024).

Critically, optimized discrimination thresholds—set just above the residual capacitive background—maximize sensitivity while avoiding false triggering (1712.06520, Zhengyu et al., 5 Jan 2024).

3. Noise Sources and Performance Metrics

Gated APDs are constrained by three fundamental noise contributions: dark counts, afterpulsing, and background-induced “charge persistence” (silicon APDs).

• Dark counts ($P_{\rm d}$): Thermally and field-assisted carrier generation, proportional to gate width and exponentially dependent on temperature. Representative values: $P_{\rm d} = 1.8\times10^{-5}$ per 0.5 ns gate at $-30^\circ$C for InGaAs (Patel et al., 2012); $P_{\rm d}=2\times10^{-6}$ per ns in silicon at $-30^\circ$C (Lunghi et al., 2012).
• Afterpulsing ($P_{\rm ap}$): Arises from carrier trapping and release, producing temporally correlated noise in subsequent gates. Ultra-short gates and minimized avalanche charge (as low as $0.035~\mathrm{pC}$ in InGaAs, $<40~\mathrm{fC}$ in UNIC-based designs) can yield $P_{\rm ap}$ below 1% at high detection efficiency, with optimized hold-off times further reducing residual afterpulsing (Fan et al., 2023, Zhengyu et al., 5 Jan 2024, Comandar et al., 2014).
• Charge persistence (Si APDs): Time-dependent afterpulsing in silicon—$P_{\rm cp}(t)=P_0 \exp(-t/\tau_\mathrm{trap})$—important following high-intensity illumination (Lunghi et al., 2012).

Other key performance parameters:

• Detection efficiencies: Up to 73.8% at 600 nm (Si APDs, 500 ps gates) (Thomas et al., 2010); 55% at 1.55 μm (InGaAs/InP, 360 ps gates) (Comandar et al., 2014).
• Maximum count rates: Saturate at $R_{\rm max} = f_{\rm g}$, with up to 1 Gcount/s at 2 GHz (Patel et al., 2012), 700 MC/s at 1.25 GHz (Fan et al., 2023), and 500 MC/s at 1 GHz (Comandar et al., 2014).
• Timing jitter: State-of-the-art SD or UNIC schemes report 120–170 ps FWHM (Patel et al., 2012, Zhengyu et al., 5 Jan 2024, Comandar et al., 2014).

4. Security, Robustness, and Countermeasures

High-rate quantum applications (notably QKD) require detectors robust to manipulation and side-channel attacks:

• Resilience to blinding/brute-force attacks: Gated operation naturally limits exposure to CW blinding—count rates drop only if excess bias is suppressed across the gate, a vulnerability mitigated by minimizing series/bias resistors ($R_{\rm bias}<20~\mathrm{k}\Omega$), and by monitoring DC photocurrent for anomalous increases (e.g., $I_{\rm DC} \gg q\,M\,\eta\,R/f_0$) (Yuan et al., 2011, 1712.06520).
• Optimal discrimination thresholds: Setting the discriminator just above capacitive noise ensures the count rate remains unperturbed up to incident powers >10 mW, unless attack-induced photocurrents cause bias collapse (1712.06520, Yuan et al., 2011).
• Side channels (backflash emission): GHz-gated APDs exhibit reduced backflash–related side-channel leakage, with measured information leakage probabilities $P_L \sim 5 \times 10^{-3}$ (1 GHz) versus $6 \times 10^{-2}$ (MHz) (Koehler-Sidki et al., 2020). At these levels, the impact on the secure QKD key rate is negligible over practical fiber lengths.

5. Advanced Algorithms and Photon Number Resolution

Sub-ns gating enables not only single-photon sensitivity but also photon-number resolution:

• Silicon APDs: By restricting avalanche growth, output pulse heights become proportional to the number of photo-initiated carriers. Gaussian statistics analysis delivers up to four resolvable photon peaks at 600 nm (Thomas et al., 2010). Error rates for 0/1/2-photon events are quantified (e.g., $\varepsilon_1 = 12.2\%$, $\varepsilon_2 = 6.95\%$).
• Afterpulsing estimation and mitigation: Statistical models (SEDF/MEDF) and stepwise algorithms allow post-processing correction of observed count rates to extract genuine signal statistics, crucial for applications operating near saturation or without hardware hold-off (Wiechers et al., 2016). The algorithms have been demonstrated to recover signal even when afterpulsing dominates raw counts.

6. Applications, Integration, and Design Trade-offs

Gated APDs are the enabling technology for high-speed quantum information tasks, quantum random number generation, optical time-domain reflectometry, and single-photon light detection and ranging (LIDAR):

• QKD: 1-GHz-class gated APDs enable system clock rates of $>1~\mathrm{GHz}$ and raw key rates exceeding $1~\mathrm{Gbit/s}$ with $\Delta t < 200~\mathrm{ps}$ jitter, ensuring low quantum bit-error rates for time-bin and phase encoding (Patel et al., 2012, Comandar et al., 2014, Zhengyu et al., 5 Jan 2024). Side-channel robustness (e.g., backflash emission, blinding immunity) is critical and attainable (Koehler-Sidki et al., 2020, Yuan et al., 2011, 1712.06520).
• Photon number resolving (PNR) detection: Si-APD-based fast-gated schemes reach $>70\%$ efficiency, sub-ns gating, and multi-photon resolution (Thomas et al., 2010).
• Fully integrated detectors: Compact UNIC-SPD modules integrate bias, gate generation, capacitive transient rejection, discrimination, and temperature feedback in $$<9~\mathrm{cm} \times 6~\mathrm{cm} \times 2~\mathrm{cm}$$ form factors, supporting up to 220 MHz sustained operation at $<8$ W power (Zhengyu et al., 5 Jan 2024).

Trade-offs are explicit between detection efficiency, dark count and afterpulse rates, duty cycle (short gates result in low “on” time but maximize noise suppression), and complexity of readout electronics. Choice of gating scheme (square, sinusoidal), readout (SD vs UNIC), and dead time/hold-off optimization must be tailored to application-specific requirements (Comandar et al., 2014, Fan et al., 2023, Zhengyu et al., 5 Jan 2024).

7. Comparative Table of Representative Performance Metrics

Device/Group	Gate Rate	$\eta$ (%)	$P_{\rm d}$ (per gate)	$P_{\rm ap}$ (%)	Max Count Rate	Timing Jitter (ps)
InGaAs, SD (Patel et al., 2012)	2 GHz	20	$1.8 \times 10^{-5}$	4.0	$1.0\times10^9$	170
InGaAs, UNIC (Fan et al., 2023)	1.25 GHz	25.3	$<5\times10^{-7}$	0.5	$7.0\times10^8$	—
In/P HP (Comandar et al., 2014)	1 GHz	55	$\sim10^{-4}$	10.2	$5.0\times10^8$	91
Si, Gen. SD (Thomas et al., 2010)	1 GHz	73.8	$<1.1\times10^{-6}$	7.5	$1.0\times10^9$	$\lesssim 50$
Si, Gated (Lunghi et al., 2012)	$10^4$ Hz	45	$4\times10^{-5}$	—	—	—

All parameters reflect single-photon regimes at the specified operational conditions (typically $-30^\circ$C to $+20^\circ$C). Values drawn from cited sources.

---

Gated APDs, as currently realized with advanced gating and readout architectures, represent a mature, high-performance class of photon detectors. Their parameter tunability, robust noise suppression, high timing precision, and demonstrated side-channel resilience render them deterministic tools for next-generation quantum photonic technologies (Patel et al., 2012, Yuan et al., 2011, Lunghi et al., 2012, Thomas et al., 2010, 0807.2320, Wiechers et al., 2016, Fan et al., 2023, Zhengyu et al., 5 Jan 2024, 1712.06520, Comandar et al., 2014, Koehler-Sidki et al., 2020, 0801.3899).