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Low-frequency noise in an electrolyte-insulator-semiconductor (EIS) structure functionalized with multilayers of polyamidoamine (PAMAM) dendrimer and single-walled carbon nanotubes (SWNT) is studied. The noise spectral density exhibits dependence with the power factor of and for the bare and functionalized EIS sensor, respectively. The gate-voltage noise spectral density is practically independent of the pH value of the solution and increases with increasing gate voltage or gate-leakage current. It has been revealed that functionalization of an EIS structure with a PAMAM/SWNTs multilayer leads to an essential reduction of the noise. To interpret the noise behavior in bare and functionalized EIS devices, a gate-current noise model for capacitive EIS structures based on an equivalent flatband-voltage fluctuation concept has been developed.