## 3 APD Breadboard Design and Implementation
### PQC Results  
When applying and testing the PQC circuit, it was realized that the impact of the quenching resistor value not only applies to the time constant constraints but also to the actual photodiode output voltage magnitude. Low resistor values are better for reaching higher polarizations due to the low drain voltage drop across them, but it also means that  
Figure 14: APD photocurrent for different driving optical powers at \(-\)23.6 \({}^{\circ}\)C. Source bias refers to the APD cathode/anode voltage drop. Figure 15: Logarithmic gain variation as a function of temperature for two different bias voltages. For high bias levels and lower temperatures, a variation of one degree has a significant impact on the gain value. the output voltage values measured (on the red tag indicated in Figure 10b) are very small, thus needing increased readout resolution. For this circuit, various values of quenching resistors were implemented and tested, from megaoahms to a few ohms, to understand the concepts mentioned above. For the results reported here, the laser diode was set to an optical power of 3 mW, and three different quenching resistors, 54.50 k\(\Omega\), 9.79 k\(\Omega\), and 5.5 k\(\Omega\), were used. Due to the oscilloscope resolution, using resistor values below 5 k\(\Omega\) made the reading of the output voltage difficult (in accordance with what was mentioned above), while the maximum safety current value for the photodiode was quickly reached using the same source bias steps as for the other two resistors. Using the mean output voltage measurements, an IV graphic was plotted for the PQC. This was conducted using the same principles employed for the TIA circuit in Figure 11. For better clarity to the reader, only the dark current values and photocurrent values of the 9.79 k\(\Omega\) are shown in Figure 16.  
The four data labels in Figure 16 indicate the bias values for which a current of about 2 mA is reached for the different temperatures and lighting conditions. As shown in this figure, the behavior of the sensor remains comparable to the data obtained when using the TIA circuit (Figure 11). Above that region, the current shows a saturation behavior and varies negligibly even with a bias voltage increase of about 15 V.  
By computing the dark current data for the three resistors used, it was found that the Geiger mode region was well achieved. In fact, all the dark current values retrieved reached near 2 mA, much further than the 100 uA threshold assumed as the frontier between the avalanche and Geiger regions. From the highest resistance to the lowest, for the temperatures of 19.1 \({}^{\circ}\)C and \(-\)23.6 \({}^{\circ}\)C, the breakdown voltage values found are as follows: 63.6 V and 58.6 V; 68.5 V and 64.0 V; 69.3 V and 64.4 V, respectively. With the breakdown voltage data for at least two temperatures, one can then calculate the  
Figure 16: Measured IV curves, using the PQC with the 9.79 k\(\Omega\) resistor, for a mean dark current and a mean photocurrent, with a 3 mW optical power applied on the setup window. Source bias refers to the APD cathode/anode voltage drop. The values indicate the maximum points reached for each dataset. temperature coefficient of breakdown voltage, \(\beta\), uniformly giving 0.11 V/\({}^{\circ}\)C for the three resistors and matching the value provided by the datasheet. To calculate the gain, the primary effective photocurrent was selected by the same method used for the TIA. This, once again, greatly impacts the gain values calculated. Like before, only the data using the 9.79 k\(\Omega\) resistor is plotted for better visualization. A distinct behavior of the one seen in the gain curves extracted with the TIA circuit (Figure 13) can be seen comparing it with the one made by using the PQC (Figure 17), which allowed to push the sensor up to its current limit (i.e., above breakdown voltage). After a certain bias value, highlighted by the data labels, the gain is no longer sustained, behaving erratically even for very small bias variations.