# Picoammeters Based on Gradiometric Superconducting Quantum Interference Devices
## 3 Results and Discussion  
Both devices are based on SQUID, including two Josephson junctions having an area of 16 \(\mu\)m\({}^{2}\) each and whose capacitance is \(C_{j}\) = 1.3 pF. The SQUID shunt resistors are \(R_{s}\) = 3 \(\Omega\), and the same value was used for damping one. As expected, the SQUID critical currents are very similar, resulting in I\({}_{\rm c,P}\) = 24.6 \(\mu\)A in parallel configuration, while I\({}_{\rm c,S}\) = 26.4 \(\mu\)A in the series case. In Figure 2, the magnetic flux vs. voltage characteristics of both devices are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Parallel** & **Series** \\ \hline Single washer outer dimension & 786 \(\mu\)m & 512 \(\mu\)m \\ Single washer inner dimension & 100 \(\mu\)m & 35 \(\mu\)m \\ Total slit length & 808 \(\mu\)m & 580 \(\mu\)m \\ Single washer inductance & 278 pH & 142 pH \\ SQUID inductance (L) & 139 pH & 284 pH \\ Input coil turns nr. & 40 & 29 \\ Input coil inductance (L\({}_{\rm s}\)) & 635 nH & 143 nH \\ Mutual inductance (M\({}_{\rm i}\)) & 8.4 nH & 5.7 nH \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main geometrical and electrical parameters of current sensor devices. reported. The bias currents that maximize the curves are 26 \(\upmu\)A and 28 \(\upmu\)A for the parallel and series configuration, respectively. The maximum intrinsic responsivities, as results from the slope of V-\(\Phi\) curves, are V\({}_{\Phi}\) = 350 \(\upmu\)V/\(\Phi_{0}\) and V\({}_{\Phi}\) = 290 \(\upmu\)V/\(\Phi_{0}\), respectively. The smaller value of voltage swings in the series case is due to a larger SQUID inductance parameter \(\beta\)L, since its inductance is significantly higher than the parallel configuration, with \(\beta_{\text{L,S}}\) = 6.75 while \(\beta_{\text{L,P}}\) = 3.3. Note that for the series gradiometer, the washer size has to be reduced to avoid too high an inductance. Therefore, for a minimum patterning pitch of the input coil, this reduced washer size leads to a smaller number of input turns per washer compared to the larger washer of the parallel design. Some evident distortions appear on the V-\(\Phi\) characteristic of the series configuration type (Figure 2b). This is probably caused by the feedback effect due to a parasitic capacitance between the input coil and the ground of the SQUID [19; 20] or even due to the stripline resonance of the input coil whose resonance frequency, inversely proportional to the length of the input coil, could fall in the operative range. However, this condition, despite a slight device instability, produces an increase in intrinsic responsivity that can be exploited, choosing a suitable working point [21]. As mentioned above, the working properties of the SQUID are related to the value of the McCumber parameter, whose value must be maintained below 1. In this case, in parallel configuration, \(\beta_{\text{C,P}}\) = 0.87, and in the series case, \(\beta_{\text{C,S}}\) = 0.94, guaranteeing the absence of any hysteresis occurrence in both devices. As mentioned above, a key factor of a current sensor is the current responsivity. It can be easily obtained by measuring the dc current to feed in the signal coil to couple one flux quantum (\(\Phi_{0}\)) into the SQUID. The measurement scheme is reported in Figure 3. An ac current source is connected to an excitation coil L\({}_{\text{exc}}\) to display the V-\(\Phi\) characteristics and a dc current is generated by a battery via a variable resistor and is fed in the input coil of the SQUID. In such a way, a magnetic flux offset is obtained as observed on an x-axis shift of the magnetic flux-to-voltage characteristic. The current sensitivity is obtained by measuring the current needed to produce one flux quantum shift. For a more accurate evaluation, a large number of \(\Phi_{0}\) shifts is induced.