5.8.3 Examples for ISFETs as pH Sensor

An ISFET device as depicted in Fig. 2.9 has been simulated for different pH values. The studied device exhibits a channel length of $15\,\mu\mathrm{m}$ and thus fits well into the drift-diffusion regime of transport. Therefore, the Poisson equation in conjunction with the drift-diffusion model for current transport has been exploited within the semiconductor, while the Poisson-Boltzmann model was used in the solute. The experimentally determined voltage shifts per pH decade, are well reproduced by the site-binding model by Yates [198] without any special adjustments to the model parameters.

Fig. 5.7 shows the potential profile for a cut perpendicular to the gate dielectric. The predicted voltage shift per pH step for $Si_{3}N_{4}$has been reported in the range $52-58\,\frac{\mathrm{mV}}{\mathrm{pH}}$ (Table 5.2). As can be seen in Fig. 5.7 the voltage shifts fit quite well the experimental data. Furthermore, the influence of the incorporated Phospate Buffered Saline (PBS) depends strongly on its concentration. A decreasing PBS concentration correlates to reduced screening within the solute and thus results in a longer decay of the potential in combination with saturation at higher pH levels. PBS is a buffer solution commonly used in biological research. This salty solution consists of sodium chloride and sodium phosphate and in some formulations additionally of potassium chloride and potassium phosphate. The buffer is normally applied to maintain constant pH and the osmolarity and ion concentrations of the solution match those of the human body. It is valuable due to its isotonicity and non-toxicity to cells and therefore is regularly employed for diluting substances or rinsing container holding cells. In the simulations carried out only potassium chloride was accounted for, because it represents $\approx90\%$ of the ingredients. Incorporating the whole buffer would have increased the computational effort without changing the results significantly.

Figure 5.7: Potential profile for a cut perpendicular to the surface of the ISFET (beginning at the left border: semiconductor, dielectric, and solute). The simulations were carried out for a.) $100\,\mathrm{mMol}$, b.) $10\,\mathrm{mMol}$, and c.) $1\,\mathrm{mMol}$ phosphate buffered saline (PBS). $Si_{3}N_{4}$was utilized as gate dielectric at different pH values. Simulation results with the parameter set by Harame et al.[1], fit excellent the experimental values. With decreasing buffer concentration the screening is reduced and the saturation starts at higher pH values. The reduced screening is also reflected in the prolonged decay of the potential in the liquid.

a.)

b.)

c.)