## 5 Experimental Results and Discussion
### Characterization of SEB Arrays
#### 5.2.1 Characterization of a Small (\(N=3\)) SEBA
While accurate quantitative comparison between experimentally obtained and simulated response of arrays can only be performed for a properly calibrated (i.e., error-corrected) system, an accurate qualitative comparison between arrays of a different size, \(N\), can be performed for arrays of a different size simultaneously connected to the same MN. In this setup, each array is biased with its own gate like it is shown in Figure 4c (for simplicity each array is represented as a single SEB). To reduce cross-coupling the values of capacitances \(C_{21}\) and \(C_{12}\) need to be much smaller than sensing gate capacitances \(C_{11}\) and \(C_{22}\) in Figure 4c. In the experiment, this is achieved by picking two arrays separated by about 5 mm on a chip. A block-diagram of the experiment where two important parameters characterizing sensitivity, \(d|\Gamma|dV_{g}\) and \(d\Theta dV_{g}\) are acquired simultaneously for two arrays with a nominal size \(N=40\) and \(N=200\) SEB is presented in Figure 13. Note that since the SEB is a two-terminal device, its admittance can be probed either way (see Section 5.2.3 for further discussion); in this experiment both arrays had their sensing gates tied together. In addition to the ramp voltage, \(V_{g}\), small modulation signals with a magnitude of 0.5 mV and frequency of \(f_{1}=1.45\) kHz and \(f_{2}=2.48\) kHz are applied to the common sources of 40 SEB and 200 SEB arrays, respectively. The reflectometry setup utilized the MN tuned at 305.7 MHz and homodyne reflectometer (labeled \"R\" in Figure 12a, see Figure 4a for details) followed by two synchronous demodulators operating at frequencies \(f_{1}\) and \(f_{2}\). For this purpose, the bandwidth of ZI UHF demodulator is set to pass the signals at frequencies \(f_{1}\) and \(f_{2}\) without attenuation. The signals \(d|\Gamma|dV_{g}\) and \(d\Theta dV_{g}\) are obtained for both 40 SEB and 200 SEB arrays by performing a second demodulation using two low-frequency lock-ins operating at \(f_{1}\) and \(f_{2}\). The results  
Figure 12: (**a**) Experimentally obtained two dimensional maps of derivatives \(d|\Gamma|dV_{g}\) (top) and \(d\Theta|dV_{g}\) (bottom) for the 3 SEB array from Figure 9a. The maps are acquired without curve averaging using an equivalent noise bandwidth of 53 Hz. \(T=0.305\) K and RF carrier excitation \(\approx 50\) uV measured at the input of the MN. (**b**) Simulations of respective derivatives using MN parameters obtained from fitting to the experimentally obtained resonant curve. Junction capacitances for simulations parameters are obtained from Figure 10a: \(C_{ij}=\) [32 34 28] af C\({}^{(i)}_{S}=\) [2.59, 2.7, 3.16] af; C\({}^{(i)}_{t}=\) [0.057 0.129, 0.248] and \(R_{ji}=\) [70, 400, 500] k\(\Omega\), where \(i=\) 1,2,3. The calculation is performed for \(T=0.5\) K. MN parameters are obtained by a procedure similar to that for Figure 10c, adjusted for lower temperature. of the experiment are presented in Figure 13b where \(d|I|dV_{g}\) and \(d\Theta|dV_{g}\) are shown for both the 40 SEB array (blue) and 200 SEB array (red). Curve averaging (58 ramps, about 25 s each) is used to boost SNR by a factor \(\approx\)7.6; the equivalent BW of the signals presented in Figure 13b is 26 Hz. The results, however, indicate that the ratios of magnitudes of peaks in both derivative signals deviate from the expected value of \((200/40)^{1/2}\approx 2.23\) as the 200 SEB array signal appeared to be \(>\)4 times stronger than that from the 40 SEB array. The likely cause for this discrepancy is the presence of fabrication defects, which might result in a reduction of the number of functional devices. An SEM micrograph Figure 13c shows several examples of such defects (observed in a different device). It is clear that only half of the inspected devices on that sample, namely the SEBs above the gate line, are functional. Simulations indicate that the observed ratio of 4 in signal strength suggests that the actual ratio of functional devices in the 200 SEB vs. 40 SEB array is close to 16, rather than 5.