  We report the 1/f noise characteristics at low-frequency in graphene
field-effect transistors that utilized a high-k dielectric tantalum oxide
encapsulated layer (a few nanometers thick) placed by atomic layer deposition
on Si3N4. A low-noise level of ~ 2.2 x 10^(-10) Hz-1 has been obtained at f =
10 Hz. The origin and physical mechanism of the noise can be interpreted by the
McWhorter context, where fluctuations in the carrier number contribute
dominantly to the low-frequency noise. Optimizing fabrication processes reduced
the number of charged impurities in the graphene field-effect transistors. The
study has provided insights into the underlying physical mechanisms of the
noise at low-frequency for reducing the noise in graphene-based devices.
