Table 1. The equations used for modeling the regions of the sensor system.

Si body	oxide	Sensor liquid interface	Liquid
n0  = 1010 cm−3,p0  = 1016 cm−3εSi  = 11.9 ε0	Gate oxide: εSiO2  =  3.9ε0Sensing oxide: εAl2o3  =  9ε0	Na = 8 × 1014 cm−2 (Ka, Kb) = (6, 10)	vi = 2a3ciB,ciB = 50 mM, εw = 80ε0

Where ε_Si, ε_SiO2, ε_w, ε_Al2o3, ε_ware the relative permittivity of silicon, gate oxide, sensing oxide and water respectively, ε₀ is the vacuum permittivity. In column 1, P(x) and n(x) are the silicon hole and electron concentrations with the initial value of p₀ and n₀, q_Si is the total charge in bulk silicon, N_dop is the substrate doping. In column 3, σ₀ is the sensing oxide surface charge density, a_Hs is the activity of hydrogen ion at the sensing oxide surface, K_a and K_b are in order the oxide association and dissociation constant and N_a is the oxide surface charge density. In column 4, q_liq is the solution total charge, c_i is the ion i concentration in solution with the bulk concentration of c_i^B. z_i is the ion i charge number, a_i is the ion i effective hydrated size and v_i is the ion i packing parameter.