## 3 Results
### Biosensor Modelling by AVS Model  
In this section, the general sensing system operation pattern is explained and applied to biological samples. Specifically, the physical properties of GFET are influenced by the charge magnitude and/or dipole moment of DNA molecules attached to the surface of graphene. Figure 10 shows the GFET transfer characteristic with its related physical phenomena. When DNA molecules are bound by receptors attached to the graphene surface, positive or negative charges transfer between them depending on the energy dispersion, and the neutral point shifts, as shown in Figure 10a. Additionally, the hole and electron mobility is influenced by the Coulomb potential to produce a slope change in the hole and electron branch of the \(I_{d}/V_{gs}\) profile, respectively, as shown in Figure 10b,c. Additionally, the minimum conductivity changes at the near of NP due to modulation of residual carriers and/or charged impurities by DNA molecules, as shown in Figure 10d. Therefore, it is possible to model these four effects by similarity parameters of the AVS model as the electron branch resistance \(R_{elc}\), the hole branch resistance \(R_{hole}\), injection velocity carrier \(v_{x0}\), and Dirac-point voltage \(v_{min0}\). The DNA-specific information and its effects on GFET can be characterized within a feature space, as shown in Figure 11. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Meaning** & **Lg = 140 nm** & **Lg = 3000 nm** & **Lg = 650 nm** \\ \hline \(R_{elc}\) & Resistance due to electron concentrations (\(\Omega\)-\(\mu\)m) & 373.8705 & 450.2130 & 486.7588 \\ \hline \(R_{hole}\) & Resistance due to hole concentrations (\(\Omega\)-\(\mu\)m) & 586.6873 & 760.9854 & 1092.3329 \\ \hline \(\beta\) & Saturation parameter (unit-less) & 1.8000 & 1.8000 & 1.8000 \\ \hline \(Q_{min}\) & Minimum background doping (unit-less) & 3.0000 & 3.0000 & 1.0000 \\ \hline \(\mu\) & Carrier mobility (\(\frac{m^{2}}{18}\)) & 1130.7361 & 1721.3129 & 2220.9262 \\ \hline \(v_{x0}\) & Injection velocity of carriers (m/s) & 5.4084 & 4.5471 & 3.0554 \\ \hline \(\Delta\)V & Shift in threshold (v) & 0.0000 & 0.2363 & 0.2564 \\ \hline \(V_{min0}\) & Dirac-point voltage (v) & \(-0.6401\) & \(-0.8731\) & \(-1.0608\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters in the AVS v1.0.0 model that are extracted upon calibration with NEGF data. Figure 9: (**a**) Output characteristics of 140-300-650 nm device. (**b**) Output characteristics of 40 nm device. NEGF data are shown in symbols, while solid lines show the GFET model fits by AVS. To optimize the proposed AVS parameters according to experimental data, the results in [35] are considered. Probe DNAs (5\({}^{\prime}\)-AGG-TCG-CCG-CCC-SH-3\({}^{\prime}\)) with a high concentration (1 mM in 40 mL PBS buffer), complementary (3\({}^{\prime}\) TCC-AGC-GGC-GGG-5\({}^{\prime}\)), and one-base mismatched (3\({}^{\prime}\) TCC-AGC-GGC-GTG-5\({}^{\prime}\)) DNAs were used in [35]. In [35], the transfer profile, Id/Vgs, has been measured before and after the addition of probe DNA molecules, and after the addition of complementary and one-base mismatched DNAs, with different concentrations. The transfer curve, Id/Vgs, shows ambipolar behavior of GFET, as shown in Figure 12. The results show that the Vmin0 is left-shifted to the immobilization of probe DNAs and significantly left-shifted with the addition of complementary DNA molecules, proposing an n-doped GFET. Additionally, the minimum current at Vmin0  
Figure 11: Schematic illustration of different parameter effects of AVS model. (**a**) \(R_{elec}\), (**b**) \(R_{hole}\), (**c**) \(V_{min0}\). (**d**) and \(v_{x0}\). Figure 10: DNA molecule effects on Ids/Vgs profile of GFET. (**a**) Charge-neutral point movement; (**b**) the hole branch slope changing due to the DNA molecule; (**c**) the electron branch slope changing due to the DNA molecule; (**d**) the height changing of the charge-neutral point due to DNA molecules. decreased by adding complementary DNAs concentration.