# Sharp Switching Characteristics of Single Electron Transistor with Discretized Charge Input
## 4 Results and Discussion
Several experimental studies reported that semiconductor-based SETs with tunable tunnel barriers to close to the quantum resistance enhanced the switching performance [24; 25]. Applying our approach is also preferable to boost the switching characteristics of the semiconductor-based SETs. Figure 4a,b shows CB diagrams extracted from stability diagrams of numerical calculations of the SETs without and with the ID, using the condition of Table 1 and symmetrically voltage biased condition at \(T=0\) K. The numbers in Figure 4a,b indicate the excessive charge state in \(n_{2}\) for the SET without the ID; in \(n_{1}\) and \(n_{2}\) for the SET with the ID. We set the charge numbers to zero across \(V_{\text{g}}=0\) V. Horizontal dotted lines, which correspond to Figure 3, indicate bias voltages of \(V=78\,\mathrm{\SIUnitSymbolMicro\SIUnitSymbolMicro V}\) for the SET without the ID and \(V=74\,\mathrm{\SIUnitSymbolMicro V}\) for the SET with the ID. Whereas conventional Coulomb  
Figure 4: \(I\)-\(V\) characteristics as a function of \(V_{\text{g}}\) from numerical simulations at \(T=0\) K. Solid red lines denote thresholds of the Coulomb blockade region. (**a**) the SET without the ID; (**b**) the SET with the ID. The numbers indicate the charge state in \(n_{2}\) for the SET without the ID; \(n_{1}\) and \(n_{2}\) for the SET with the ID. An area “A” indicates the steep current switching region, and an area “B” indicates bi-stability region. Horizontal dotted lines denote bias points of \(V=78\,\mathrm{\SIUnitSymbolMicro V}\) and \(V=74\,\mathrm{\SIUnitSymbolMicro V}\) corresponding to Figure 3.  
diamonds of an SET appear in the device of SET without the ID in Figure 4a, abrupt \(V\) changes of the CB thresholds are clearly seen in the SET with the ID in Figure 4b. Slopes of CB of the SET without the ID in the asymmetrical biased condition, which is maximum voltage gain in metal-based SET referred in Reference [12], was estimated \(C_{\text{C}}/C_{\text{J}_{2}}\approx 5.5\) in our design. In Figure 4b, vertical and inclined threshold lines to \(V_{\text{g}}\) stem from the ID and the SET, respectively [12]. Since the \(C_{\text{C}}\
eq C_{\text{B}}\) condition bears the shapes not only minimal and maximal regions but also intermediate regions of Coulomb diamonds of an SET, large and small steps of \(\Delta V\) (typical region marked \"A\" in Figure 4b) appear against the \(V_{\text{g}}\) alternately, which correspond to the input-output characteristics of the SET with the ID in Figure 3. Partially overlapped regions (typical region marked \"B\" in Figure 4b) can be seen. When two electrons sequentially tunnel through \(J_{1}\) and either \(J_{2}\) or \(J_{3}\), bi-stability regions appear inside the threshold of CB (\((n_{1},\,n_{2})\rightarrow(n_{1}-1,\,n_{2}+1)\) or \((n_{1}+1,\,n_{2}-1)\)). According to the simulation result, \(I\) flows through the SET during an unstable condition of \((n_{1}-1,\,n_{2})\) or \((n_{1}+1,\,n_{2})\). Moreover, we evaluated the differential conductance of the SETs with and without the ID via the absolute value of \(\text{d}I/\text{d}V_{\text{g}}\). In Figure 5, simulated results of differential conductance of each samples were plotted as a function of temperature. From the measurement, \(|\text{d}I/\text{d}V_{\text{g}}|\) of SET without the ID were also plotted as a blue crossed mark. In the SET with the ID, we picked six points on both sides of the slopes extracted from the top to third peaks of maximal \(I\) in Figure 3 and plotted a median value as a red open square. Note that both measurement results plotted at \(T=65\) mK were estimated from the fitting curve of the simulation. For comparison, values of \(|\text{d}I/\text{d}V_{\text{g}}|\) are normalized by respective \(R_{j_{2}}+R_{j_{3}}\). Under the low temperature, series junction resistances \(R_{j_{2}}+R_{j_{3}}\) of the SETs with the ID and without the ID were 122 k\(\Omega\) and 124 k\(\Omega\), respectively.