Circuit simulators like SPICE and timing simulators like MOTIS are used extensively for critical path verification of integrated circuits. MOSFET model evaluation dominates the run time of these simulators. Changes in technology results in costly updates, since modifications require reprogramming of the functions and their derivatives.

The computational cost of MOSFET models can be reduced by using multidimensional ploynomial splines. Since simulators based on the Newtow Raphson algorithm require the function and first derivative, quadratic splines are sufficient for this purpose. Quadratic splines are inexpensive and derivatives are guaranteed to be correct. The cost of updating the MOSFET model due to technology changes is greatly reduced since splines are derived from a set of points. These points can come from measured data, a device simulator, equation evaluation, etc.

Crucial for convergence speed of simulators is the fact that MOSFET characteristic equations are monotonic. This must be maintained by any simulation model. The splines which the author has designed do maintain monotonicity. This is achieved by using constrained numerical optimization techniques without increasing the number of spline segments. A new tableau style formulation for calculating the spline coefficients has been developed for multidimensional functions.

Multidimensional splines have a large storage requirement for the coefficients. A new data compression technique has been developed to greatly reduce this storage requirement.

The above coefficients are calculated off-line and stored in a model library. During simulation, model evaluation is reduced to evaluation of a (multidimensional) quadratic polynomial.