Continuous surface potential versus voltage equation of intrinsic surrounding-gate MOSFETs and analytic solution from accumulation to strong inversion region

A continuous surface potential versus voltage equation is proposed and then its solution is further discussed for a long channel intrinsic surrounding-gate (SRG) MOSFET from the accumulation to strong inversion region. The original equation is derived from the exact solution of a simplified Poisson equation and then the empirical correction is performed from the mathematical condition required by the continuity of the solution, which results in a continuous surface potential versus voltage equation, allowing the surface potential and the related derivatives to be described by an analytic solution from the accumulation to strong inversion region and from linear to the saturation region accurately and continuously. From these results, the dependences of surface potential and centric potential characteristics on device geometry are analyzed and the results are also verified with the 3-D numerical simulation from the aspect of accuracy and continuity tests.