## 3 Technology
### Electronics Issues for Time-Gated (TG) Operations  
Unfortunately, fast voltage transitions applied to the detector give rise to spurious feed-through voltage spikes at the avalanche detection electronics [66]. When no current flows within the junction, the SPAD can be modeled as a small capacitance due to the depleted region of the p-n junction [67]. This situation is represented in Figure 7 where the SPAD is surrounded by a typical basic front-end circuit. As shown, the anode voltage changes during the gate transition due to the presence of a voltage divider between the SPAD capacitance and the resulting impedance of the anode-side connections. Then, the high-pass filter of the readout circuit generates the spikes. In slow gate conditions (i.e.,  
Figure 6: Simulations of the relative contrast produced by a 1 cm\({}^{3}\) optical inhomogeneity as a function of depth \(z\) in a tissue-like medium for an ideal time-domain, TD (blue continuous lines) or CW (red dashed lines) system. The detectability region (white zone) is identified by a relative contrast \(>\)1% and a quantum noise \(<\)1%. Reprinted with permission from [61] ©The Optical Society.  
transitions in the nanoseconds range) these spikes force the use of high avalanche detection thresholds to avoid to detect the spike instead of the avalanche [31]. This has the effect of increase the time jitter in time-resolved applications as best timing performance of SPADs are always obtained when sensing the very first part of the avalanche current leading edge [68]. In fast gate conditions (transitions in a range of tens or hundreds of picoseconds) the voltage spikes amplitude can exceed the amplitude of avalanche pulses, thus preventing the photon detection [31] (see Figure 8). The former scenario (slow gate) is typical when gated detection is used to grant the effectiveness of the detector when light is expected. Indeed, in free-running operation a dark count can mask following photons due to the detector dead time (i.e., time needed to quench the avalanche and to restore the operative conditions after each photon detection). Time-gating is therefore important in the case of high dark count rate devices like InGaAs or germanium SPADs [68; 69]. The latter case (fast gate) is of interest in TD-DO as early photons can anticipate late photons of just a fraction of nanosecond [38].  
Figure 8: Gate voltage signal (blue line) provided to the SPAD front-end circuit of Figure 7 and resulting SPAD voltage signal at the positive input of the comparator (red line) without photon detection (**a**) and with a single-photon detection (**b**) [31]. The red arrow indicates the arrival delay of a photon inside the gate. Dummy voltage signal (black line) generated by providing the same gate signal to a capacitor that only mimics the SPAD parasitic behavior, without being able to detect photons. If the dummy signal is provided to the negative input of the comparator of Figure 7: (**a**) SPAD and dummy signal do not cross, thus avoiding triggering the comparator and the following timing electronics when no avalanche occurs; (**b**) the SPAD signal exceeds the dummy signal when the photon is detected, thus forcing the comparator to switch, triggering the following timing electronics. A more detailed discussion of these waveforms can be found in [31; 66].  
Figure 7: Basic electrical circuit of a time-gated (TG) single-photon avalanche diodes (SPADs) [31]. The gate pulse is provided by the voltage pulse generator (V\({}_{\text{G}}\)). The SPAD is reversely biased at a voltage-V\({}_{\text{B}}\). The comparator switches its output (OUT) when the voltage at the positive input exceeds a threshold voltage V\({}_{\text{T}}\). Supposing that no avalanche occurs during the gate-ON time, the positive input of the comparator is reached by 2 voltage spikes due to the application of fast voltage transition at the cathode side of the SPAD, which can trigger the comparator if exceeding V\({}_{\text{T}}\).