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In this paper, we present the unique features exhibited by a proposed structure of coaxially gated carbon nanotube field-effect transistor (CNTFET) with doped source and drain extensions using the self-consistent and atomistic scale simulations, within the nonequilibrium Green's function formalism. In this novel CNTFET structure, three adjacent metal cylindrical gates are used, where two side metal gates with lower workfunction than the main gate as an extension of the source/drain on either side of the main metal gate are biased, independent of the main gate, to create virtual extensions to the source and the drain and also to provide an effective electrical screen for the channel region from the drain voltage variations. We demonstrate that the proposed structure of CNTFET shows improvement in device performance focusing on leakage current, on-off current ratio, and voltage gain. In addition, the investigation of short-channel effects for the proposed structure shows improved drain-induced barrier lowering, hot-carrier effect, and subthreshold swing, all of which can affect the reliability of CMOS devices.