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Random telegraph-signal noise (RTN) is measured in junctionless metal-oxide-silicon field-effect transistors (JL MOSFETs) as a function of gate and drain voltage and temperature. It is shown that the RTN in JL MOSFETs increases significantly when an accumulation layer is formed. The amplitude of RTN is considerably smaller in JL devices than in inversion-mode MOSFET fabricated using similar fabrication parameters. A measurement technique is developed to extract the main parameters of the traps, including the average charge capture and emission time from the traps.