A Continuous Heterogeneous Model for the Crystalline to Amorphous Transition in Ion Implanted Semiconductors: Relationsh
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A CONTINUOUS HETEROGENEOUS MODEL FOR THE CRYSTALLINE TO AMORPHOUS TRANSITION IN ION IMPLANTED SEMICONDUCTORS : RELATIONSHIP TO THE "CRITICAL DAMAGE ENERGY DENSITY" MODEL C.
VIEU,
A.
CLAVERIE*'*,
J.
FAURE** AND J.
BEAUVILLAIN**
LMM/CNRS, "Lawrence
196 avenue H. Ravera, 92220 Bagneux, France Berkeley Laboratory, 1 cyclotron road, Berkeley CA 94720, USA **Laboratoire de Microscopie Electronique, 21 rue C. Ader 51100 Reims, France "'*CEMES/CNRS, 29 rue J. Marvig, 31055 Toulouse, France
ABSTRACT A method is presented for calculating amorphization doses of ion implanted semiconductors, based on a continuous heterogeneous description of damage accumulation. This new approach is compared to the classical "critical damage energy density" (CDED) model. For high dose implantations the equivalence of both descriptions is formally established. It is proposed that the main limitation of the CDED model lies in the linear additivity of damage rather than the homogeneous damage build-up.
INTRODUCTION
During the two last decades a large number of papers have been devoted to the crystalline to amorphous (c-a) transition in ion implanted semiconductors, dealing both with the experimental and theoretical point of view. However, the model proposed by Stein et al. [1] in the early stage of ion implantation technology, still remains the most universal approach to the c-a transformation. This approach, often referred to as the "critical damage energy density" (CDED) model, assumes that the damage nucleates homogeneously as a result of Frenkel defect interactions, and that a crystal containing a critical density of defects will spontaneously relax into the amorphous state. By coupling experimental studies on the amorphous phase extension with calculations of damage depth distributions, the critical damage energy density (Edc), which corresponds to the concentration of defects inducing the c-a transformation, has been obtained for several materials. Severe limitations to this description have been recently observed for room temperature implantations of light ions in silicon [2] [3]. These deviations are inherent in the basic assumptions of this model. Indeed, the phenomenological macroscopic threshold EdC does not take into account the microscopic nature of damage deposition through collision cascades, which obviously depends on the incident ion, but also on ion flux and substrate temperature.
Mat. Res. Soc. Symp. Proc. Vol. 230. c 1992 Materials Research Society
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On the other hand, heterogeneous models [4] consider the role of individual ionic impacts in the damage build-up. Although they are expected to give a more realistic description of the c-a transition, they suffer from the lack of available procedures to calculate amorphization doses. The aim of this paper is to show how a continuous heterogeneous description of damage accumulation can be adapted to predict the depth extension of an amorphous layer. This so-called continuous model, which is a generalization of previous discrete heterogeneous descriptions, is applie
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