# Sharp Switching Characteristics of Single Electron Transistor with Discretized Charge Input
## 4 Results and Discussion  
Initially we set \(V_{\mathrm{bg}}\) to ground, and measured \(I\) versus \(V\) characteristics as a function of \(V_{\mathrm{g}}\) for the SET with the ID. Colour plot of \(I\) versus \(V\) and \(V_{\mathrm{g}}\) in steps of 0.2 mV were depicted in Figure 2. Contour lines of \(I\) except 0 A were drawn from \(-0.4\) to \(0.4\) by 0.1 nA step. In this measurement, although thresholds are unclear to determine the the shape of the CB owing to insufficient numbers of step of \(V_{\mathrm{g}}\) to the period of the Coulomb oscillation, several steep modulations of \(I\) to \(V_{\mathrm{g}}\) shown by yellow arrows can be seen. Subsequently, on applying fixed \(V\), we tuned \(V_{\mathrm{bg}}\) of the SET with the ID in order to obtain the maximal modulation of \(I\) at \(V_{\mathrm{g}}\) near to 0 V. Figure 3 shows \(I\) versus \(V_{\mathrm{g}}\) as the input-output characteristics for the SETs without and with the ID at \(T<80\) mK. Crossed marks and open squares indicate the SET without the ID at \(V=78\,\mathrm{\SIUnitSymbolMicro V}\), the SET with the ID at \(V=74\,\mathrm{\SIUnitSymbolMicro V}\); and two solid lines indicate the best fits of both SETs without and with the ID using the numerical simulation  
Figure 2: Current \(I\) characteristics of the SET with the ID as a function of \(V\) and \(V_{\mathrm{g}}\) for \(V_{\mathrm{bg}}=0\) V at \(T<80\) mK. Borders of contour lines are plotted of 0.1, 0.2, 0.3, 0.4, \(-0.1\), \(-0.2\), \(-0.3\) and \(-0.4\) nA. Abrupt modulation of \(I\) against \(V_{\mathrm{g}}\) are indicated by yellow arrows. at \(T=65\) mK, respectively. In the simulation, the offset charge of the island was zero and \(V_{\rm{bg}}\) was 780 mV for the SET without the ID, \(n_{2}\) was 0.015 \(e\) and \(V_{\rm{bg}}\) was 140 mV for the SET with the ID. The SET without the ID responded to a typical Coulomb oscillation. In contrast, sharp switching \(I\) clearly came against the \(V_{\rm{g}}\) almost periodically in the SET with the ID. This result exhibited that the ID provides the quantized charge input, which was partially corresponded with the switching periodicity of the SET. Carrying out the simulation and examining the input-output characteristics, we listed the extracted capacitive and resistive parameters in Table 1. Both the values of \(C_{\rm{C}}\) of SETs without and with the ID were identical of 872 aF. The value of \(C_{\rm{B}}\) of the SET with the ID was estimated 1100 aF, that is 26 percent larger than the value of \(C_{\rm{C}}\) yielding a shifted charge period from \(e/2\). In this measurement, current spikes like random telegraph noise in the SET with the ID can be seen (for instance, at \(V_{\rm{g}}=-0.68\) mV, \(-0.62\) mV, \(-0.16\) mV). These current noise were prominent even compared to its the SET without the ID. We presume that the island \(n_{1}\) enlarged with the metallic plate corresponding \(C_{\rm{B}}\) is more sensitive to the dielectric charge traps in the substrate, or the natural oxidized layer of Al on the surface of the sample [23]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Device**} & \(C_{\rm{C}}\) & \(C_{\rm{B}}\) & \(C_{I_{1}}\) & \(C_{I_{2}}=C_{I_{3}}\) & \(C_{\rm{T}}\) & \(C_{\rm{BG}}\) & \(R_{I_{3}}=R_{I_{3}}\) \\  & **(aF)** & **(aF)** & **(aF)** & **(aF)** & **(aF)** & **(aF)** & **(aF)** & **(aF)** \\ \hline SET without ID & 872 & - & 120 & 160 & 900 & 96 & 60 \\ SET with ID & 872 & 1100 & 120 & 160 & 900 & 96 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Typical parameter values for the SETs (single-electron transistors) with and without the ID (input discretizer). Figure 3: \(I\)-\(V_{\rm{g}}\) for input-output characteristics. Crossed marks, open squares and two solid lines correspond the SET without the ID at \(V=78\) mV, the SET with the ID at \(V=74\) mV and the best fits using a numerical simulation, respectively. Curves are vertically shifted by 250 pA for clarity.