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The low-frequency noise has been studied in nMOSFETs with an HfO2--SiO2 gate stack, for different thickness of the SiO2 interfacial layer (IL). It is observed that the 1/f-like noise in linear operation, is about 50 times higher in the HfO2 devices with a 0.8-nm chemical oxide IL, compared with the 4.5-nm thermal oxide reference n-channel transistors. This is shown to relate to the correspondingly higher trap density in the dielectric material. In addition, it is demonstrated that the noise rapidly reduces with increasing thickness of the IL. From the results for a 2.1-nm SiO2 IL, it is derived that at a certain gate voltage range, electron tunneling to a defect band in the HfO2 layer may contribute to a pronounced increase in the flicker noise.