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Compact Charge Modeling of Double-Gate MOSFETs Considering the Density-Gradient Equation

A compact charge model for double-gate metal–oxide–semiconductor field-effect transistors with the quantum confinement effect is presented. In addition to the Poisson equation, the density-gradient equation with a realistic boundary condition is considered to include the quantum confinement effect. The coupled governing equations are rigorously integrated. Contribution of the density-gradient equation is clearly identified. Based on the resultant integrated equation, a compact charge model is proposed. Expressions for model parameters are found. Numerical examples for various double-gate MOS structures are shown.