Multivariate Cubic Spline: A Versatile DC Modeling Technique Suitable for Different Deep Submicron Transistors

This work presents multivariate cubic spline polynomial as a versatile and efficient method for DC modeling of modern transistors with very different underlying physics including MOSFET (metal-oxide-semiconductor field-effect transistor), MESFET (Metal-Semiconductor-Field-Effect-Transistor), HBT (heterojunction bipolar transistor), HEMT (High-electron-mobility transistor) and a novel silicon-on-insulator four-gate transistor (G4FET). A set of available training data from TCAD simulation, analytical expression and experimental measurements is used to determine the coefficients of the spline model and then the model is validated using another set of test data. The developed model expresses the drain current as a multivariate cubic spline and it is shown to be valid across a wide range of bias conditions provided the independent variables are inside the range of data set used for training. The formulation of the cubic spline ensures its continuity along with the continuity of its first and second order derivatives which is highly desirable for implementation in a SPICE simulator. The model shows excellent predictive capability for different kinds of devices. This can be very useful for modeling deep-submicron emerging devices for which any closed-form analytical solution is not yet available.