Analytic models of drain, substrate and gate current distributions in the drain section of MOSFETs

A small MOSFET has very strong distribution effects and the description of its characteristics requires distribution models. In this paper, two-dimensional (2-D) analytic distribution models of drain and substrate currents in MOSFET drain section are built by using stream function equations on y cross section. The distribution models of electron and hole gate currents in n-MOSFETs are modeled by using the "lucky-electron" concept and the 2-D distribution models of drain and substrate currents. The distribution model of the hole gate current is based on a new process of hot-hole injection in which the holes are accelerated by the negative vertical electric field. These models are analytic and include sufficient bias and structure parameters of the device, which makes them more accurate and available for all biases and a larger region of the structure size. The drain-source and substrate current models show basically the exact distribution of these current densities. The distribution models of the gate currents can clearly describe injection processes of hot-carriers, which is useful for the modeling of damage distribution, damage growth and damage saturation in MOSFET hot-carrier reliability electronics.