Improved analytic models and efficient parameter extraction for computationally efficient 1D and 2D ion implantation modeling

Computationally efficient ion implantation modeling is highly essential for efficient silicon device technology development and improved process control. Indeed, analytic models are particularly desirable for two-dimensional simulations, which are very expensive in terms of computation time. This paper describes analytic models for both the impurity and the damage profiles in one and two dimensions. Legendre polynomials are used as model functions and their orthogonality property is exploited to simplify and allow the automation of parameter extraction. Using 14 Legendre polynomials (16 model parameters), a wide variety of impurity and damage profiles can be modeled accurately. In addition, the shortcomings of the conventional superposition approach to 2-D modeling are explained, and a modified approach based on dose-splitting is proposed. The 2-D impurity and damage profiles generated by this modified superposition approach are shown to have very good agreement with the physically based and experimentally verified Monte-Carlo simulator, UT-MARLOWE. Computation times can be reduced by approximately a factor of 50 without sacrificing accuracy when the analytic approach is used instead of a Monte-Carlo simulation.