# Application of Single-Electron Transistor to Biomolecule and Ion Sensors
## 2 Mechanism of High Sensitivity in Biomolecule Detection Based on a Single-Electron Transistor  
After the attachment of charged biomolecule, drain current (\(I_{d}\)) changes from an on-current state (\(I_{d0}\)) to an off-current state at the same gate voltage (\(V_{g0}\)) due to the threshold voltage shift (\(\Delta V_{th}\)) of \(I_{d}\)-\(V_{g}\) curve (Figure 1). Therefore, sensitivity is closely related to both magnitudes of \(\Delta V_{th}\) and the change amount of \(I_{d}\) (\(\Delta I_{d}\)) after the attachment. The larger the magnitudes of \(\Delta V_{th}\) and \(\Delta I_{d}\), the higher the detection sensitivity of the biosensor. Based on the above consideration, there are two main mechanisms of increase for the detection sensitivity of an FET sensor. One is the increase in transconductance (\(g_{m}\)). Since \(g_{m}\) is defined as \(g_{m}=\partial I_{d}/\partial V_{g}\), the FET sensor with a larger \(g_{m}\) has a larger magnitude of \(\Delta I_{d}\) (\(1\,\Delta I_{d}\,1\)) after the attachment of charged target molecule, as shown in Figure 2. Namely, owing to the larger \(g_{m}\) for the FET1 in Figure 2, the magnitude of \(I_{d}\) change (\(1\,\Delta I_{d1}\,1\)) for the FET1 is larger than that (\(1\,\Delta I_{d2}\,1\)) for the FET2. The other mechanism of the increase in detection sensitivity is the suppression of the effect of percolation for carriers to transfer through the channel in the case of the same polarity of charges between the target molecule and carrier. If the channel width is larger than the size of charged target biomolecule, carriers in the channel can avoid passing through the close region of the target biomolecule and can transfer through the channel; because of this, the percolation path and \(I_{d}\) do not change very much from that prior to the attachment. On the other hand, if the channel width is small enough compared with the size of the target biomolecule, carriers cannot avoid passing through the close region of the molecule, leading to the disappearance of the percolation path and large changes to the \(I_{d}\). From the viewpoint of this mechanism, it is effective to decrease the channel width of FET to  
Figure 1: Drain current (\(I_{d}\)) _versus_ gate voltage (\(V_{g}\)) characteristics of a field effect transistor before and after the attachment of charged biomolecule. \(I_{d}\) changes from an on-current state (\(I_{d0}\)) to an off-current state at the same \(V_{g}\) (\(V_{g0}\)) by the threshold voltage shift (\(\Delta V_{th}\)). Figure 2: Schematic view to explain that the sensor that has a field effect transistor (FET) with a larger transconductance (\(g_{m}\)) has a larger magnitude of the change in drain current \(I_{d}\) (\(\Delta I_{d}\)) after the attachment of charged target molecule. Owing to the larger \(g_{m}\) for the FET1, the magnitude of \(\Delta I_{d}\) for the FET1 (\(1\,\Delta I_{d1}\,1\)) is larger than that for the FET2 (\(1\,\Delta I_{d2}\,1\)). \(\Delta V_{th}\) is the threshold voltage shift after the attachment of charged target. increase the detection sensitivity. With regard to this percolation effect, the sensitivity enhancement due to the decrease in the channel width of ISFET was confirmed by Monte Carlo simulation [23]. Here, the site percolation property of a finite-size two-dimensional square-lattice system was analyzed to investigate the effect of charged substances on the properties of ISFETs. It should be noticed that the operation principle of biosensors with an FET is basically the same as that of floating dot memories, because the attachment of a charged biomolecule on the gate insulator in the biosensors plays the same role as the charge injection of a floating dot in the dot memories. For example, the detection of a biomolecule with an extremely small charge in solution using an FET sensor with a nanowire channel resembles the detection of a single electron injection to a floating dot of the single-electron memory [24; 25; 26].