## 5 Experimental Results and Discussion
### Characterization of SEB Arrays
#### 5.2.1 Characterization of a Small (\(N=3\)) SEBA  
As shown theoretically in Section 2 and confirmed experimentally in Section 5.1, the SNR for the reflectometry response of a single SEB is low due to very small magnitude of admittance oscillations caused by single electron charging even if an optimized MN described in Section 3 is used. Recently, we have demonstrated that for small SEBA SNR scaling by a factor \(N\) is achievable [33]. To study the sensitivity trends in SEBA with resolvable individual characteristics, we performed a detailed study of a small array nominally composed of four SEBs and controlled by two gates in the range of temperatures from 0.3 to 30 K. Post-experimental SEM image of the array is presented in Figure 10a. Figure 10b shows the equivalent circuit of MN used in an experiment tuned close to a matching point  
Figure 9: (**a**) High resolution SEM image of an array composed of 8 SEBs. Probing gate is located in close proximity to the array and has nominally equal coupling to each SEB. Tuning gate is located farther away and is unequally coupled to each SEB element. (**b**) example of an array composed of a large number of SEBs (\(>1000\)). Small dots below the lines are secondary islands resulting from the Dolan bridge process, and the two horizontal lines leading to the left are the gate. (**c**) An example of a self-aligned 9 SEB array with a footprint less than \(1\times 1\)um\({}^{2}\). by a capacitor \(C_{IN}\) = 28.2 pF, and Figure 10c presents the results of MN characterization vs. carrier frequency at \(T\) = 11.5 K, which shows a nearly perfect match. The results of the SEBA response measurements at temperature 11.5 K are presented in Figure 11a as the two respective magnitude \(d|\Gamma|dV_{S}\) and phase \(d\Theta/dV_{S}\), derivatives (solid lines in two subplots). The beating pattern, expected for the addition of asynchronous periodic signals with similar periods is clearly visible. The FFT spectrum of the beating pattern of oscillations acquired over the 16 V \(V_{S}\) span (Figure 11b) unveiled the presence of three primary \"frequencies\" in 1/V units (\(A1\), \(B1\) and C1) corresponding to the three distinct periods of Coulomb blockade oscillations (respective gate capacitances): \(A1\): 1/53.3 mV (3.0 aF), \(B1\): 1/57.2 mV (2.8 aF) and C1: 1/56.7 mV (2.7 aF). Indeed, post-experimental inspection of this array under SEM revealed a fabrication defect for one SEB (delineated by a dashed white line in Figure 10a) reducing the number of functional devices to three. The FFT spectrum also indicates that at \(T\) = 11.5 K signals generated by SEBs are almost sinusoidal, i.e., with clear dominance of the 1 st harmonic. The magnitudes of the 2 nd harmonics are hardly visible and signals from higher harmonics fell below the noise floor. Superimposed with experimental data are oscillations of \(d|\Gamma|dV_{S}\) and phase \(d\Theta/dV_{S}\) (red in Figure 11a) simulated for 3 SEB using Formula (2), which are then passed through the MN depicted in Figure 10b. For simulations, the values of the three gate capacitances are extracted from the FFT plot acquired over the 16 V \(V_{S}\) span. The values of junction capacitances 32, 34 and 28 aF and respective junction resistances, 80, 70 and 100 k\(\Omega\) for the three respective SEBs are obtained by generating oscillations of SEBA admittance using (2), passing it through the MN shown in Figure 10b and then fitting the magnitude of oscillations in the reflected  
Figure 10: (**a**) High resolution SEM image of the 3 SEBA (only 3 out of 4 SEBs are operational). The three lines leading to the right are drains that are bonded in parallel to the MN. The vertical line situated about 0.5 \(\upmu\)m away from the islands is the probing gate. The tuning gate is situated much farther (about 10 \(\upmu\)m) below the entire array (not shown). A fabrication defect for one SEB is delineated by a dashed white line. The data for the 3 SEBA presented below are obtained from this very device. (**b**) Model of the MN used in simulations.