Cubic sp-line collocation enhancement for modeling of MOS transient

Abstract

A symmetrical telescopic modification of the cubic sp-line collocation method with an application in modeling the transient response of MOS transistors is proposed. The novel methodology represents an extremely accurate spatial piecewise solution of the continuity equation in such a way that it transiently models the MOS device in terms of the normalized channel charge density. Based on this treatment, this paper discusses the full detailed derivation of optimum inversion channel segmentation in order to solve the partial differential form of continuity equation which is convenient to model the transient mode of MOS transistors. Additionally, the boundary as well as the initial conditions of the MOS transient equation are determined by means of the compact charge based of EKV model. The ability of such model to represent a unique formula of the continuity equation for all regions of operation of the MOS transistor is the reason of choosing it in our processing. Moreover, our proposal makes use of the physical reality of the commonness of spatial natural conditions along the inversion channel that distinguishes the transient propagation of the surface channel charges from the source to the drain and vice versa. Due to the symmetry of such physical meaning, the symmetrical telescopic framing of the cubic sp-line collocation method is declared. The suggested approach proves an accurate modeling up to 97% of the channel length. This approach is tested with transient ramp slope of 1010 V/sec. It has been applied to the standard CMOS 0.18μm technology for NMOS transistors. The PMOS transistors are modeled in the standard CMOS 0.15μm technology. The novel model is validated using MATLAB R2014a. The obtained results demonstrate that the introduced procedure has an astonishing impact on different electronic components that expert transient events such as low dropout regulators and switched capacitor circuits.