# Advances in Graphene Field Effect Transistors (FETs) for Annine Neurotransmitter Sensing
## 2 Problem Outline
### GFET Characterisation
#### 2.5.2 Electrical Characterisation  
Estimating sheet resistance in graphene is critical in NT detection since it is an important component of sensor performance. Graphene-based GFETs are dependent on changes in graphene's electrical characteristics produced by interactions with biomolecules. The ongoing monitoring of sheet resistance helps to determine the sensor's signal-to-noise ratio. The four-point probe approach is one of the most-used methodologies to measure graphene sheet resistance (or conductivity). The method involves measuring electrical sheet resistance in thin films using various pairs of electrodes for current injection and voltage detection (Figure 3a). The approach is spatially localised, with the characteristic length scale determined by the distance between the probes. FET-based sensors are fundamentally based on electrical measurements, precisely electrical current measurements in the device channel, in this case, the graphene layer [109]. Transistor transfer curves are obtained by sweeping the gate voltage \(\mathrm{V_{G}}\) while maintaining a fixed bias \(\mathrm{V_{DS}}\) between the source and drain electrodes (Figure 1a). The resulting current \(\mathrm{I_{DS}}\) is displayed as a function of gate bias. In GFETs, this plot usually produces a V-shaped curve, as shown in Figure 3b. When the gate voltage is swept, the polarity of the majority of charge carriers in the graphene layer changes: the left branch (or p-branch) represents an increasing density of positive charge carriers (holes), while the right branch (or n-branch) represents negative charge carriers (electrons). Between the two branches, the density of charge carriers, and hence current, reaches a minimum with equal populations of positive and negative carriers, known as the Dirac point. The most commonly used electrical metric in GFET sensing is a change in the Dirac point voltage, which is determined by the graphene's doping level: for intrinsic graphene at low drain/source bias, it is expected to be close to 0 V, but in practice, it can be positive if the graphene is p-doped (indicating a higher density of holes) or negative if the graphene is n-doped (a higher density of electrons). The doping level depends on numerous aspects, including the nature of the contact between graphene and other materials (substrate, electrodes, and media) and the distribution of charged species and impurities [142]. A second metric is a change in transconductance, which is the slope of the linear portion of the transfer curve's p- or n-branch. Transconductance is an essential indication of transistor performance, namely its capacity to convert a small voltage change into a large current change [143]. The third metric is a shift in the current's amplitude, which can occur in the p/n branches, at the Dirac point, or in both. Current is determined by the product of carrier charge density and velocity; therefore, a change in current implies a change in charge carrier density, scattering processes, or a combination of the two. Aside from transfer curves, GFETs can be used to measure output curves, in which the drain/source current \(\mathrm{I_{DS}}\) is plotted against the drain/source voltage \(\mathrm{V_{DS}}\) for a fixed gate voltage \(\mathrm{V_{G}}\). As the applied bias increases from zero, so does the current's amplitude,  
Figure 3: **(a)** A schematic of the four-point probe setup for measuring the sheet resistance of the graphene layer. **(b)** The transfer curve of a GFET shows the difference in the Dirac points in forward and reverse sweeps (as indicated by arrows). which has the same polarity. The curvature of the output curve is typically regarded as a good indicator of the quality of the connections between graphene and the source/drain electrodes and charge transport along the graphene. A linear ohmic regime at low bias is typically assumed when graphene and electrical contacts are suitable [144; 145].