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    Ion Implantation and Activation: Volume 3
    Ion Implantation and Activation: Volume 3
    Ion Implantation and Activation: Volume 3
    Ebook284 pages1 hour

    Ion Implantation and Activation: Volume 3

    By Kunihiro Suzuki

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    About this ebook

    Ion Implantation and Activation – Volume 3 presents the derivation process of related models in a comprehensive step by step manner starting from the fundamental processes and moving up into the more advanced theories.
    Ion implantation can be expressed theoretically as a binary collision, and, experimentally using various mathematical functions. Readers can understand how to establish an ion implantation database by combining theory and experimental data. The third volume of the series describes the diffusion phenomenon under the thermal equilibrium on point defect concentration and the features of transient enhanced diffusion (TED). The volume also presents methods for the oxidation and redistribution of impurities in polycrystalline silicon for extraction as well as some analytical models related to the VLSI process.
    This book provides advanced engineering and physics students and researchers with complete and coherent coverage of modern semiconductor process modeling. Readers can also benefit from this volume by acquiring the necessary information to improve contemporary process models by themselves.

    LanguageEnglish
    PublisherBentham Science Publishers
    Release dateMay 11, 2013
    ISBN9781608057924
    Ion Implantation and Activation: Volume 3

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      Book preview

      Ion Implantation and Activation - Kunihiro Suzuki

      Diffusion Under Thermal Equilibrium

      Abstract

      We derive a diffusion flux and diffusion equation step by step, starting with a rough sketch one to a practical one. The flux is described with the paring with point defects, and the dependence of diffusion coefficients on doping concentration is emerged. We can predict diffusion profiles by solving the equation.

      Keywords:: Ion implantation, diffusion, diffusion flux, diffusion equation, diffusion coefficient, point defects, doping concentration, lattice sites, jumping frequency, electric field, mobility, Einstein’s relationship, interstitial Si, intrinsic carrier concentration, statistic mechanism.

      Introduction

      Ion implanted impurities are introduced to Si substrates physically, and they are not set at the lattice sites in general. Further, the impurities introduce many defects, and they do not play a role of donors or acceptors as they are. Thermal processes, that are, annealing processes are indispensable to activate the impurities. The impurities redistribute during these annealing processes, and the final redistributed profiles determine the device characteristics. Therefore, it is important to predict the diffusion profiles.

      Figure 1)

      Schematic diffusion flux.

      Diffusion flux

      The flux f of any species is defined as the number of particles passing through unit area in unit time. Let us consider two boxes of length a as shown in Fig. 1. The location of the left side box is x, and the corresponding concentration is N(x). The location of the right side box is x+a, and the corresponding concentration is N(x+a). Therefore, the amount of impurities in the boxes are N(x)a and N(x+a)a, respectively. We assume that impurities in the boxes randomly jump to the left or right box in the next step. Therefore, half of the impurities go to the right box, and the others to the left one. The flux from the x-location box to the x+a-location box f1 is then expressed by

      On the other hand, the flux from x+a-location box to the x-location box f2 is given by

      Consequently, the net flux that crosses the boundary of the both boxes f is given by

      Note that the flux is proportional to the gradient of the concentration. This is attributed to the random motion of the impurities.

      Some points are oversimplified in the above discussion.

      We assumed that all impurities move to the left or the right box. However, the crystal substrate atoms form a series of potentials hills which impede the impurities to move to other boxes as shown in Fig. 2. The impurities are not in the box, but in the valley of potential with a barrier height of ΔE. The impurities should overcome the potential barrier ΔE, and most of the impurities stay at their original location. According to the statistic mechanism, the probability of the impurities that overcome the potential hill, and move to the neighbor location is proportional

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