Continuous Surface Potential versus Voltage Equation of Undoped Surrounding-Gate MOSFETs and Its Solution

A continuous surface potential versus voltage equation is presented and its solution is discussed for long channel undoped (lightly doped) surrounding-gate (SRG) MOSFETs from accumulation to strong inversion region. The equation is derived from the exact solution of a simplified Poisson's equation and then amended from the mathematic condition of continuity, which allows the surface potential and the related derivatives to be accurately and continuously described in the whole operation region. The dependences of surface potential characteristics on device geometry and temperature are analyzed and the results agree with the 3-D simulation, proving the accuracy of the presented equation and its solution for SRG compact modelling development.