# Self-consistent modeling of accumulation layers and tunneling currents through very thin oxides

## Abstract

Poisson and Schrödinger equations are solved self-consistently for accumulated layers in metal-oxide-semiconductor devices and applied to the calculation of tunneling currents at 300 K and 77 K and extraction of parameters for very thin oxides. Calculations at 300 K show strong agreement with measured tunneling currents and also point out the sources of inaccuracies in extracting thicknesses of oxides by electrical methods such as through measurement of capacitance. Direct tunneling current in thin oxides (1.5-2.0 nm) are shown to achieve larger than 1 A/cm2 current density for applied voltages smaller than 3 V, pointing to possibilities of achieving high endurance injection across thin oxides. Comparison of calculations using a classical approach and self-consistent approach shows fortuitous agreements in tunneling currents despite large differences in the physical models. Appropriate methods for calculating tunneling currents from bound and extended quantum states are also described. © 1996 American Institute of Physics.