## 3 APD Breadboard Design and Implementation
### TIA Results  
The TIA circuit's (Figure 10a) maximum output voltage was limited by the operational amplifier power supply, which was set to \(V_{output\_TIA\_max}\cong\pm 18.0\)V. Using this circuit, the APD was characterized for four different temperatures: \(-23.3\,^{\circ}\)C, \(-19.2\,^{\circ}\)C, \(-3.0\,^{\circ}\)C, and \(18.4\,^{\circ}\)C. The characterizations comprised the measurements of the dark current (DKC) and photocurrent (PHC). For the photocurrent measurements, the APD was exposed to a \(1.55\,\upmu\)m CW diode laser operating at different optical powers: 0.03 mW, 1.30 mW, and 3.00 mW. The laser was positioned in front of the vacuum chamber window, pointing directly at the sensor. Due to the laser's divergence, its distance from the sensor, and its small sensor area, only a small fraction of its power is detected by the sensor. A rough estimation of the optical power reaching the sensor active area can be made knowing that the distance from the center of the laser diode window up to the APD window was 110.8 mm, the laser diode beam divergence (FWHM) is 25\({}^{\circ}\) parallel and 30\({}^{\circ}\) perpendicular, and considering the optical powers for the given wavelength. The total incident power was estimated to be \(4.11\times 10^{-8}\) W, \(1.82\times 10^{-8}\) W, and \(4.11\times 10^{-10}\) W, for 3.00 mW, 1.33 mW, and 0.03 mW, respectively. In the next figures, the measurement results obtained while operating the laser at 1.33 mW are presented. The data using an optical power of 1.33 mW for 4 different temperatures is plotted in Figure 11. The shift of the IV curves is noticeable for the different working temperatures, as the gain increases more significantly at lower bias voltages as temperature decreases. The same analysis was made for an optical power of 3.00 mW and 0.03 mW, with similar behavior being observed. Figure 10: In (**a**) the TIA circuit, with C\({}_{1}\), C\({}_{3}\), and C5 as 82 pF, C2, C4, and C6 as 47 nF, Rp as 32.3 k\(\Omega\), RF as 383.0 k\(\Omega\), and CF as 2.2 pF, and (**b**) the PQC, with RQ as the quenching resistor. The green-shadowed area represents the inside of the chamber. In Figure 11, all the data points end at 4.7 \(\times\) 10\({}^{-5}\) A, which represents the peak current value for each dataset, limited by the chosen operational amplifier and gain. Note that the current produced by the sensor is not exclusively generated by the optical power. Instead, it includes mutually the contributions of the dark current and the photogenerated current, both multiplied by the photodetector gain. For this reason, it is necessary to subtract the photocurrent values from the dark current measurements in order to calculate a \"true\" effective photocurrent. In this way, it was possible to estimate the photocurrent produced by incident optical power alone [27]. This allowed the calculation of the avalanche photodiode gain for the different optical powers and temperatures. The gain was given by the ratio of the effective photocurrent and the primary effective photocurrent. The calculated gain values are strongly dependent on the value of the primary effective photocurrent used. To choose the best primary effective photocurrent, we considered the punch-through current as the primary effective current value, defined as the photocurrent corresponding to gain = 1 when the punch-through voltage is reached. In this condition the layers responsible for the photon detection and triggering the avalanche effect are fully depleted [28]. By plotting the effective current in function of the sensor bias, the punch-through voltage is met when a (first) noticeable increase in the effective photocurrent occurs and a consequent, almost constant, current increase follows, for roughly 1 V to 2 V in the variation of the APD bias.