Modeling of Quasi-Static Floating-Gate Transistor Biosensors

Abstract

Floating-gate transistors (FGTs) are a promising class of electronic sensing architectures that separate the transduction elements from molecular sensing components, but the factors leading to optimum device design are unknown. We developed a model, generalizable to many different semiconductor/dielectric materials and channel dimensions, to predict the sensor response to changes in capacitance and/or charge at the sensing surface upon target binding or other changes in surface chemistry. The model predictions were compared to experimental data obtained using a floating-gate (extended gate) electrochemical transistor, a variant of the generic FGT architecture that facilitates low-voltage operation and rapid, simple fabrication using printing. Self-assembled monolayer (SAM) chemistry and quasi-statically measured resistor-loaded inverters were utilized to obtain experimentally either the capacitance signals (with alkylthiol SAMs) or charge signals (with acid-terminated SAMs) of the FGT. Experiments reveal that the model captures the inverter gain and charge signals over 3 orders of magnitude variation in the size of the sensing area and the capacitance signals over 2 orders of magnitude but deviates from experiments at lower capacitances of the sensing surface (<1 nF). To guide future device design, model predictions for a large range of sensing area capacitances and characteristic voltages are provided, enabling the calculation of the optimum sensing area size for maximum charge and capacitance sensitivity.

Keywords: biosensing; electronic detection; extended gate; field-effect transistor; floating gate; modeling.

Figure 1.

Device layouts for EGTs and FGTs. (a) Side-gated EGT device and inverter measurement circuit. The gate voltage (V_G) is applied at the gate pad, the supply voltage (V_DD) is applied across both EGT and the load resistor, and the output voltage (V_OUT) is measured between the channel and the load resistor (R_L). The semiconductor channel (red) consists of the organic semiconductor poly(3-hexylthiophene) (P3HT) gated by an ion-gel in contact with the floating gate (FG1). (b) Corresponding FGT device with the inverter circuit, where the CG is connected to the right arm of the floating gate (FG2) through the aqueous electrolyte (blue). (c) Top-view scheme of the FGT device in (b). To show all relevant details, the figure is not to scale. (d) Equivalent circuit diagram. The lumped capacitance C₂ includes the FG2/aqueous interface and the CG/aqueous interface.

Figure 2.

EGT and FGT responses. (a) Inverter curve for the reference EGT (black, from ref 21) and model fit (red). The best-fit parameters are κ_EGT = 0.6, V_T = 0.08 V, and V₀ = 28 mV, with a root-mean-square error (RMSE) of 21 mV computed using all of the data. (b) FGT inverter output (black, from ref 21) and the prediction for the FGT device (red) based on the parameters from (a). The RMSE is 22 mV.

Figure 3.

Sensor gain vs the aqueous electrolyte capacitance, C₂. Error bars are the standard deviation measured for three separate FGT devices.

Figure 4.

Example signals from FGT experimental data. (a) Capacitance sensing using a small FG1 area. (b) Charge sensing using a small FG1 area. (c) Capacitance sensing using a large FG1 area. (d) Charge sensing using a large FG1 area. The quantity $V_{\text{G}}^{*}$ is the shifted gate voltage to correct for device-to-device variability for capacitance sensing. The difference curve (the signal) is calculated by subtracting the black curve from the gray curve.

Figure 5.

Capacitance and charge sensitivity to the choice of C₂ and C₁. (a) Capacitance sensing. Error bars are the standard deviation of three signal peaks obtained from the pairs of FGT devices coated with C16 and C8 SAMs. (b) Charge sensing. Error bars are the standard deviation of the three signal peaks obtained by exposing an MUA monolayer at pH 4 and 10.

Figure 6.

Predicted capacitance and charge signals as a function of the C₂/C₀ ratio for (a) small and (b) large values of C₁. The region at small C₂/C₀ where the predicted capacitance signals deviate from the experimental values is dashed.