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An analytic model for the nanowire MOSFETs (NWFETs) with Ge/Si core/shell structure is developed in this paper. The analytical expressions of electrostatic potential and charges of this device are derived from classical device physics under the gradual channel approximation. Then, a drift-diffusion (DD) mechanism-based drain current model is obtained and verified by comparisons with the numerical simulation results. By modifying the intrinsic carrier concentration under 2-D confinement, quantum-mechanical effect is also taken into account approximately, and then, a ballistic current model is developed to study the impact of quantum-mechanical effect on the device characteristics. The performances of Ge/Si core/shell NWFETs are analyzed, and significant characteristics are demonstrated, in detail, by the proposed model. The presented analytic model may provide a base for device scientists and circuit engineers to understand the device physics and further develop a compact model of the NWFETs with Ge/Si core/shell heterostructure for circuit design and simulation.