Accurate and computationally efficient analytical 1-D and 2-D ion implantation models based on Legendre polynomials

Computationally efficient ion implantation modeling has become the essential tool for efficient and accurate CMOS design as aggressive scaling of devices continues. Specifically, computationally efficient two-dimensional (2-D) analytical models are often more attractive than physically-based Monte Carlo simulations since the latter are expensive in terms of computational time. Here we present new computational-efficient analytical models to simulate one-dimensional (1-D) and 2-D impurity and damage profiles. Legendre polynomials are used as basis functions in view of their orthogonality and good interpolation property. Conventional superposition approaches for 2-D implant modeling are explained and the shortcomings are analyzed. A dose splitting approach is incorporated in the new 2-D model to account for the nonlinear dc-channeling effect as implantation-induced damage accumulates. Good agreement with a physically-based and experimentally verified Monte Carlo simulator (UT-MAR-LOWE with TOMCAT) has been obtained for both impurity and damage profiles with a 50× reduction of computational time for medium-energy implants