Figure 1. Crowding effect of the counter-ions near the charged sensing surface.

(a) Schematic of distribution of non-zero size ions near the surface. (b) Limitation of the classic Boltzmann model due to the saturation of counter-ions at the surface, c_max is the maximum concentration of counter-ion near the surface. (c) The diffusion layer capacitance is reduced as a result of the crowding effect, Ψ_C is the steric potential. At Ψ_C, the counter-ion concentration reaches to c_max.