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Mark E. Law, George H. Gilmer, and Martin Jaraíz Introduction

Ab Initio and MD Methods

Simulation of front-end processing is a critical component of integrated-circuit (IC) technology development. Today’s electronics are so small that characterization of their material parameters is very difficult and expensive. Simulation is often the only effective tool for exploring the lateral and vertical doping profiles of a modern device at the level of detail required for optimization. Additionally, the cost of fabrication and test lots increases with each technology generation; for this reason, simulation becomes especially costeffective, if it can be made accurate. Increasingly, process simulation is being performed by harnessing a hierarchy of tools. Ab initio and molecular-dynamics (MD) codes are used to generate insight into the physics of individual particle reactions in the silicon lattice. This information can be fed to kinetic Monte Carlo (MC) codes to establish the dominant, critical mechanisms. Finally, traditional continuum codes can make use of this information and couple with the other process steps to simulate the entire process flow. Both MC and continuum codes can be compared with experiment in order to validate the calculations. We will introduce the basic concept of the hierarchical modeling of silicon by the illustration of its application to shallow-junction-formation technologies— implantation and diffusion. The article by Cowern and Rafferty in this issue discusses some of the prime experimental evidence; our article will focus on the theoretical framework used to model and understand the data presented in their article.

Simulations of the processing of silicon are being improved dramatically as more of the operative physical mechanisms are implemented and as more accurate values of the configuration energies and event rates are employed. A large amount of detailed information has recently been provided by atomistic modeling techniques. Quantum calculations of electron distributions (ab initio methods) are the most detailed,1 and they have an advantage in that the energies of specific atomic configurations can be calculated directly. Furthermore, the electronic properties are obtained as an inherent part of the calculation, providing values for the electrical activity of the defects, for example. They involve a large computational cost and are limited to systems of several hundred atoms. Energy differences between similar configurations are apparently accurate to several tenths of an electronvolt, although some uncontrolled approximations make a definitive calculation of the uncertainties impossible. Figure 1 shows a density contour for electrons in a crystalline Si lattice containing a substitutional B atom. The thicker bonds are connected to the B atom located near the center, indicating a higher electron density in these bonds. During annealing, interstitials and vacancies annihilate one another, and they coalesce to form {311} defects, vacancy voids, and clusters of dopant atoms mixed with poin