Monte Carlo Simulation of Ion Implantation for Three-Dimensional Structures Using an Octree

Hannes STIPPEL  Siegfried SELBERHERR  

IEICE TRANSACTIONS on Electronics   Vol.E77-C   No.2   pp.118-123
Publication Date: 1994/02/25
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on 1993 VLSI Process and Device Modeling Workshop (VPAD 93))
Category: Process Simulation
ion implantation,  Monte Carlo method,  point location,  octree,  

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A fully three-dimensional simulation tool for modeling the ion implantation in arbitrarily complex three-dimensional structures is described. The calculation is based on the Monte Carlo (MC) method. For MC simulations of realistic three-dimensional structures the key problem is the CPU-time consumption which is primarily caused by two facts. (1) A large number of ion trajectories (about 107) has to be simulated to get results with reasonable low statistical noise. (2) The point location problem is very complex in the three-dimensional space. Solutions for these problems are given in this paper. To reduce the CPU-time for calculating the numerous ion trajectories a superposition method is applied. For the point location (geometry checks) different possibilities are presented. Advantages and disadvantages of the conventional intersection method and a newly introduced octree method are discussed. The octree method was found to be suited best for three-dimensional simulation. Using the octree the CPU-time required for the simulation of one ion trajectory could be reduced so that it only needs approximately the same time as the intersection method in the two-dimensional case. Additionally, the data structure of the octree simplifies the coupling of this simulation tool with topography simulators based on a cellular method. Simulation results for a three-dimensional trench structure are presented.