Analytic yet continuous surface potential versus voltage equation of intrinsic nanoscale surrounding-gate MOSFETs and solution from accumulation to strong inversion region

摘要

A continuous surface potential versus voltage equation is proposed and then its solution is further discussed in this paper for a long channel intrinsic surrounding-gate (SRG) MOSFET from the accumulation to strong inversion region. The original equation is derived out from the exact solution of a simplified Poisson equation and then the empirical correction is performed from the mathematic condition required by the continuity of 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 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.