# Application of Single-Electron Transistor to Biomolecule and Ion Sensors
## 2 Mechanism of High Sensitivity in Biomolecule Detection Based on a Single-Electron Transistor
In the fabricated SET sensors, the buffer solution covers not only Coulomb islands but also the nanowire barrier regions. Since the electric field applied by the voltage of the reference electrode changes the barrier height of the nanowire, the tunnel current through the nanowire junction changes with the voltage. The buffer solution also covers a part of the wide source/drain region and the connecting region between the nanowire barrier region and the source/drain region. The width of the connecting region gradually increased from the nanowire barrier region to the source/drain region in the fabricated devices. These regions act as additional resistance to the tunnel junction resistance in the fabricated SET sensors. If there are only these regions with the additional resistance in the channel of an FET, the analytical formula of the current \(I\) can be approximated under the charge-sheet model in the linear region as follows [32]:  
\[I=\mu_{eff}C_{ox}\frac{W}{L}(V_{g}-V_{th})V_{d} \tag{3}\]  
Figure 1:0 Schematic view of \(I_{d}\)–\(V_{g}\) characteristics for the sensor with a single-electron transistor. \(\Delta V_{th}\) is the threshold voltage shift after the attachment of a charged target. \(\Delta V_{th}\) is the threshold voltage shift after the attachment of a charged target. \(\Delta I_{d1}\) and \(\Delta I_{d2}\) are the change in \(I_{d}\) at different \(V_{g}\) values after the attachment. Reproduced with permission from [22], Copyright 2013, AIP publishing LLC. where \(\mu_{eff}\), \(C_{ox}\), \(W\), \(L\), and \(V_{th}\) are the effective mobility, gate oxide capacitance per unit area, effective channel width, effective channel length, and threshold voltage. From the formula, the \(g_{m}\) independent of \(V_{g}\) is obtained as  
Figure 1:1  
Even if only the tunnel junction resistance is taken into account in the FET, the current through it increases with \(V_{g}\) because the increase in \(V_{g}\) decreases the barrier height. In the calculation of Coulomb oscillations, it was assumed that the current in the tunnel junction increases roughly linearly with \(V_{g}\) because the precise shape of the barrier potential was unclear. Therefore, \(V_{g}\) dependence on \(R_{T}\), including the contribution of the additional resistance, was set so that the current through the junction increases linearly with \(V_{g}\) in the calculation. The calculated results (solid curves in Figure 6) did, in fact, show the following points: \(I_{d}\) at the peaks in \(I_{d}\)-\(V_{g}\) characteristics in the SET increases with increasing \(V_{g}\); the maximum \(g_{m}\) values appear at the \(V_{g}\) values near the left-side half maximum of each \(I_{d}\) peak. The maximum \(g_{m}\) increases with increasing \(V_{g}\). At large \(V_{g}\) values, the maximum \(g_{m}\) values are larger in the case of an SET than the \(g_{m}\) in a case where only the nanowire barrier region and the connecting region exist in the channel. In the latter case, the characteristics were calculated for the FET having a nanowire channel with the tunnel junction resistance and the additional resistance (broken curves in Figure 6). It should be noted that the \(V_{g}\) values with the larger \(g_{m}\) in the SET can be made to appear near 0 V by adjusting the dopant concentration in the channel and connecting regions. It is also noted that the larger \(g_{m}\) values still appear in the case of SET, even if the current through the junction increases with \(V_{g}\) more rapidly than linearly. The experimental results of \(I_{d}\)-\(V_{g}\) characteristics for a fabricated SET biosensor in buffer solution at room temperature confirmed the above results and showed clear Coulomb oscillations in which the peak of \(I_{d}\) increases with increasing \(V_{g}\)[22]. Here, \(V_{g}\) was applied by using a reference electrode. This \(I_{d}\) increase is due to the increase in the current of the nanowire barrier region with increasing \(V_{g}\).