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A non-charge-sheet surface-potential-based compact drain-current model for long-channel undoped gate-all-around (GAA) silicon-nanowire (SiNW) MOSFETs is developed. The surface-potential equation is derived from cylindrical Poisson equation for undoped silicon and solved iteratively with a very good initial guess to reach equation residue below 10-16 V within a few iterations. The single-piece current equation is derived and validated with numerical simulations for all operation regions without any fitting parameters. The results show that the proposed model can be used for bench-marking long-channel SiNW models, and demonstrate a first step towards a practical SiNW model for inclusion of various short-channel and quantum-mechanical effects.