Abstract
A full three-dimensional analytical solution of the Poisson's equation is developed for the first time to predict the threshold voltage of small geometry MOSFETs applicable to any isolation structure. The solution is derived from Fourier analysis of the three-dimensional Poisson's equation using superposition with realistic boundary conditions for the sidewall potential distribution. The present model includes various design and process parameters, which effect the small geometry threshold voltage, such as device length and width, oxide isolation type, ion implantation, and substrate bias. The model requires two fitting parameters chosen for the particular isolation scheme. The sensitivity of the fitting parameters to process and design in investigated. Comparisons of the results obtained for the fully recessed oxide isolation with numerical data and published data show good agreement for small geometry MOSFETs. Potential profiles and electric fields can also be generated from the solutions predicted by this model. The speed, accuracy, and feasibility of this model for different isolation schemes make it extremely useful for CAD applications.
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