MOSFET analytical substrate current model for circuit simulation

The MOSFET (metal-oxide-silicon field-effect transistor) substrate current has been expected to increase dramatically due to the transistor size shrinkage in a deep-submicron process (transistor channel length below or equal to 0.25 mu m. This is a major concern for the accuracy of the existing models in predicting the transistor channel current and degradation of the device life-time, [1]. The main source for this substrate current increase is the hot-carrier effect, impact ionization. Most of the existing impact ionization rate models are accurate; however they require numerical analysis to determine the final solutions, [2-4]. The numerical methods applications in semiconductor device modeling are mostly limited at the device simulation level. For circuit analysis application, analytical solutions are preferred because of their simplicity and computational speed. In [5, 6], the Gauss-Laguerre integration method is shown to be effective in determining an accurate compact analytical model for the impact ionization rate. In this paper we apply same method, Gauss-Laguerre, on the substrate current model equation of [7], and the accuracy of our final analytical model is determined by comparing it with a well known compact analytical substrate model equation, [1] in the fitting of data from a 90nm device [11].