Model for Dopant and Impurity Segregation During Vapor Phase Growth
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Model for Dopant and Impurity Segregation During Vapor Phase Growth Craig B. Arnold and Michael J. Aziz Division of Engineering and Applied Sciences, Harvard University, Cambridge MA 02138, USA ABSTRACT We propose a new kinetic model for surface segregation during vapor phase growth that takes into account multiple mechanisms for segregation, including mechanisms for inter-layer exchange and surface diffusion. The resulting behavior of the segregation length shows temperature and velocity dependence, both of which have been observed in experiments. We compare our analytic model to experimental measurements for segregation of Phosphorus in Si(001), and we find an excellent agreement using realistic energies and pre-exponential factors for kinetic rate constants. INTRODUCTION The growth of extremely sharp interfaces in materials has become increasingly important in the devices we build. For example, the device quality for delta doping in semiconductors [1, 2] or certain multi-layered metallic systems [3, 4] is sensitive to the redistribution of atomic species on the monolayer scale. The main physical problem to overcome is the tendency for atoms of one species or another to segregate to the free surface during film growth. Growth of such structures is experimentally challenging, and although there are some exceptions [5], high quality crystal growth with completely suppressed segregation is not generally possible. The physical, chemical, and kinetic principles underlying segregation are not entirely understood in these systems. Several models have been presented in the literature, but none of them have been successful in describing the segregation behavior under a wide variety of conditions. Our objective is to develop a more robust model for surface segregation during vapor phase growth. The approach starts with successful models for liquid phase growth which enables us to include multiple mechanisms for segregation which are missing in earlier models. PREVIOUS MODELS Previous models for segregation can be divided into three major categories based on the type of mechanism used. The first and earliest type of models were phenomenological in nature [6, 7]. Their important conclusion was that at sufficiently low temperatures, there exists a kinetically limited regime in which the impurity atoms cannot move quickly enough to avoid becoming trapped in the bulk. Phenomenological models were followed by a class of models invoking an interlayer exchange pathway for segregation [8, 9]. In these models, an atom is first buried by the incident deposition flux and subsequently may exchange positions with an adjacent atom above or below, provided both are within the first two layers of the free surface. An atom is considered incorporated once it is buried three layers below the surface and unable to make any further exchanges. As did the earlier models, these models display a transition temperature from equilibrium segregation to a kinetically limited segregation regime. However, the main problem P3.11.1
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