Multiscale modeling of ion implantation damage in silicon

Abstract

Although ion implantation is a well-established doping technique, it inevitably leads to damage generation, which affects dopant profiles during the ion implantation process as well as during the post-implant annealing step. Upon annealing, the damage contributes to dopant clustering and results in transient enhanced diffusion, which can only be predicted with an accurate damage accumulation model. Beside undoubted success achieved in the field of damage modeling, many processes are not quantitatively modeled up to date. A variety of standard simulation models is widely used for the simulation of the ion implantation process, from quantum mechanical ab-initio, molecular dynamics (MD), binary collision (BC), kinetic Monte Carlo (kMC) to continuum models. But, no single simulation approach can simulate the whole process alone. In order to solve this problem it is important to improve and combine existing methods in a hierarchical scheme at different stages of process evolution. The aim of this thesis is to extend the range of problems which can be modeled quantitatively, combining the available and proposing new simulation methods. In order to explain the amorphization process upon heavy ion implants an amorphous pocket model is proposed. The model uses binary collision simulations to generate the spatial distribution of deposited energy and the numerical solution of the heat transport equation to describe the quenching process. The heat equation is modified to consider the heat of melting when the melting temperature is crossed at any point in space. Space is discretized with the finite volume method on grid points that coincide with the crystallographic lattice sites, what allows us to resolve the initial conditions and the resulting amorphous zones at the atomic level. Atoms are assumed to be molten if the atom as well as its four nearest neighbors cross the melting temperature. In addition the local collapse of the crystal lattice once the damage level exceeds a threshold is taken into account. From the obtained results it can be concluded that considering the local lattice collapse when a damage level exceeds a threshold plays a crucial role for the amorphization process. The results obtained with this model are in very good agreement with published experimental data on P, As, Te and Tl implantations in Si and with data on the polyatomic effect at cryogenic temperature. Compared to the molecular dynamics approach the proposed model has the advantage of being capable to cover a much wider implant energy range with much lower computational cost. Within the framework of the thesis a Rutherford backscattering spectrometry channeling (RBS/C) simulation code has been written. The code uses the principle of the close encounter probability and the Rutherford scattering cross section. In order to improve the damage models used for the interpretation of simulated RBS/C spectra a new atomistic model of damage is proposed. Using classical molecular dynamics simulations and ab-initio calculations we determine the coordinates of the split-<110> interstitial, of the di-, tri-, and four-interstitial cluster, and of the tetrahedral interstitial as well as the strain on neighboring atoms induced by the presence of these defects. Introducing these coordinates in binary collision simulations of RBS/C spectra we investigate the influence of the calculation method, of the channeling direction, and of the defect type on RBS/C yield. We show that the RBS/C yield calculated from empirical potentials may significantly deviate from that obtained using atomic coordinates from ab-initio calculations. The variation of the backscattering yield with the assumed defect type is larger with the defect coordinates obtained by the empirical potential than by the ab-initio calculations.<br />The simulation results illustrate the influence of the strained regions around the defects, as well as the importance of the correct defect model in multiaxial analysis of Si. In addition the effects of mutual defect interaction versus damage concentration for all available defect types are investigated.<br />The conclusion is that the model based on isolated point defects and their strained fields can be used up to a concentration of 6-7% of the Si atomic density. The proposed model improves the physical description of damage of Si containing low levels of disorder and could be used for modeling of light ion implant damage.