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We have introduced a continuous, explicit, surface potential model for symmetric undoped and lightly doped double gate metal-oxide-semiconductor field-effect transistor devices. The surface potential model considered both hole and electron quasi-Fermi potential effects. An explicit current model has been introduced in terms of both source and drain charge densities at which hole and electron quasi-Fermi level or IMREFs are defined. The introduced models are directly related to the device biasing and device structure without the need for fitting parameters. Both of the surface potential and current models are continuous from below to above threshold and from linear to saturation of operation regimes. Good agreement has been obtained when our analytical models are compared to numerical results. The effects of hole IMREF on the small-signal (or ac) parameters are also reported. We predicted that the presence of holes has raised the saturation voltage. Also, we have observed from the gate capacitance curve that the hole IMREF should be taken into our account for low frequency applications.