## 5 Experimental Results and Discussion
### Characterization of SEB Arrays
#### 5.2.3 Experimental Characterization of SEB Arrays with Different Matching Networks  
In Section 3.2 above, we discussed design choices for building a matching \(\Pi\) network suitable for SEB applications. Figure 6 indicates that a significant boost of sensitivity can be achieved with a simple adjustment of a single capacitor \(C_{IN}\). To verify this, we perform an experiment to compare the response from the same array of 200 SEBs for different values of input capacitance \(C_{IN}\), Figure 14. In this example, the MN is composed of \(L=270\) nH inductor, pad capacitor \(C_{pad}\)-0.55 pF and two selected values of  
Figure 13: Comparison of the performance between two SEB with a nominal number of SEB \(N=40\) (“40 SEB”, here and below marked blue) and \(N=200\) (“200 SEB”, here and below marked red) at \(T=2.8\) K. **(a)** Simplified block diagram of the experiment with 40 SEB and 200 SEB connected to the same resonator and sharing the same ramp voltage \(V_{g}\) while modulated at two different frequencies, \(f_{1}=1.45\) kHz for 40 SEB and \(f_{2}=2.48\) kHz for 200 SEB. MN—matching network operating at 305.7 MHz; circles with “+” sign represent adders; R—reflectometer that includes ultra-high frequency lock-in amplifier by Zurich Instruments (ZI UHF) and SR830 lock-ins to extract derivatives by further demodulating the downconverted signals of the ZI lock-in. **(b)** Comparison of oscillation patterns for derivatives \(d|I|dV_{g}\) and \(d\Theta|dV_{g}\) representing magnitude and phase sensitivity for 40 SEB (blue) and 200 SEB (red) **(c)** Typical fabrication defects found in the devices inspected under SEM. The number of devices in the micrograph by design is 6, but the entire set of bottom source lines to individual SEB is missing. \(C_{IN}\). The results of measurements for the two derivatives, \(dR\)/\(dV_{g}\) and \(d\Theta\)/\(dV_{g}\) at two different values of this capacitor are presented in Figure 14a,b. The results show more than 10 times enhancement of the (phase-gate voltage) sensitivity factor, \(d\Theta\)/\(dV_{g}\). Note that the enhancement of the magnitude response is less pronounced, leading to about a 5-fold boost in the signal in good agreement with simulations in Figure 6. It is also worth noting that according to the simulations the accessible bandwidth is narrower for the network settings close to a match point \(C_{IN}\) = 27 pF (\(\approx\)2.2 MHz) compared to the overcoupled case \(C_{IN}\) = 18 pF (\(\approx\)3.3 MHz). Figure 15 shows a 2D map of derivative \(dRe(T)\)/\(dV_{g}\) versus two gate voltages, \(V_{g\text{ {sens}}}\) and \(V_{g\text{ {tune}}}\), with an apparent moire pattern resulting from multiple line crossings. In comparison with Figure 12, discrimination between individual lines representing individual SEBs is no longer possible. Moreover, multiple line crossings in Figure 15a produced \"bunching\"--an effect that appears to look like a sharp line over a smaller 2D region but visibly fades away on a larger scale--an effect typical for moire patterns. Indeed, crossing lines create that appears as oscillations with a period much shorter than that of a single SEB despite the same gate coupling for each individual box. Most importantly, as discussed for the case of 3 SEBs (Figure 12), the use of a second gate provides means for finding the most sensitive spots for any desired sensing gate region. These most sensitive spots corresponding to extrema in the derivative are delineated by a color change (from red = max, to blue = min) in Figure 15. A plot for the simulated response for 200 SEB array is shown in Figure 15b where it is clearly similar to the experiment. Figure 14: Comparison between the response of the same array of 200 SEB at \(T\) = 4.5 K with two different settings of the \(\Pi\)-network (Figure 4a) is composed of \(L\) = 270 nH Coilctraft 0805 CS inductor, \(C_{\text{{pnd}}}\) = 0.55 pF and \(C_{IN}\): red—\(C_{IN}\) = 27 pF, blue—\(C_{IN}\) = 18 pF.