Optimization of graphene transistor sensors based on quantum capacitance and charge carrier mobility analysis

Charge density of molecules $(N{\mathrm{m}})$ in hybrid nanostructures that is formed at the interface of graphene and liquid in solution gated graphene field effect transistors (SGFETs) determines the selective response of chemical and biological sensors based on these SGFETs. For optimization of this response it is important to determine how it depends on characteristics of SGFETs such as quantum capacitance $(C_{\mathrm{q}})$ and charge mobility $(\mu)$ which are functionally linked to $N_{\mathrm{m}}$. The proposed model shows that when the gate voltage $(V_{\mathrm{gate}})$ is near the minimum point of graphene conductivity (Dirac point) the sensor response is low and increases with gate voltage until $C_{\mathrm{q}}$ is approximately equal to the capacitance of the formed double layer $(C{\mathrm{dl}})$ in SGFETs. A decrease in sensor response is predicted upon further increase of $V_{\mathrm{gate}}$ in cases where there is a stronger dependence of $\mu$ on $N_{\mathrm{m}}$ than $\mu\propto 1/N_{\mathrm{m}}$. A comparison of the predicted results of the model and literature data obtained in SGFET sensors for lysine in an aqueous solution are in agreement with the assumption that the optimal condition of $C{\mathrm{q}}\approx C{\mathrm{dl}}$ is reached approximately in the $V_{\mathrm{gate}}$ region of (0.5–1.4) V from the Dirac Point.