Thermal Spike Related Nonlinear Effects in Ion Beam Mixing at Low Temperatures
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THERMAL SPIKE RELATED NONLINEAR EFFECTS IN ION BEAM MIXING AT LOW TEMPERATURES G-S. Chen%, D. Farkas and M. Rangaswamy Department of Materials Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA ABSTRACT A semi-empirical model for ion mixing at low temperatures was developed taking into account collisional mixing and thermal spike effects, as well as the thermal spike shape. The collisional mixing part was accounted for by the Kinchin-Pease model, or, alternatively dynamic Monte Carlo simulation. For the thermal spike, the ion beam mixing parameter Dt/(1) is derived as being proportional to X2+,, where the damage parameter is defined as, X= - FDIAHC.,, F0 is the damage energy deposited per unit path length, and Asis a constant dependent on the thermal spike shape and point defect density in the thermal spike regions. The shape of the thermal spike that best fit the experimental results depends on the magnitude of the cascade density. For relatively high density collisional cascades, where thermal spikes start to be important, it was found that a spherical thermal spike model was more consistent with experimental measurements at low temperatures. However, for extremely high density collisional cascade regions, a cylindrical thermal spike gave better results. Finally, three different regions of ion beam induced mixing were recognized according to different density levels of damage energy scaled by the damage parameter X. INTRODUCTION Ion beam induced atomic transport at low temperatures is composed of three different mechanisms which are (i) cascade collisional mixing, (ii) Thermal spike induced short-range diffusion, and (iii) Radiation enhanced diffusion. Extensive theoretical studies have been carried out by Winterbon [1], Andersen [2], and Sigmund [3]. Computer simulation of the process has been developed [4], based on the computer code TRIM [5]. Experimental work has been carried out in different temperature ranges, such as Nb/Si [6] and Cr/Si [7] bilayer systems. It was found that the mixing efficiency is weakly dependent on temperature below certain critical temperature points. Thus, cascade collision mixing was suggested for some time to be the dominating mechanism in the ion beam mixing process. However, most experimental results showed much greater mixing than that predicted by cascade collisional mixing even after using adjusted values of the displacement energy [8,9]. The additional mixing observed can be understood as produced by thermal spike effects. High density collisional cascades generate displaced atoms in a very localized volume. While these atoms cannot displace other atoms further, they can impart some of their energy to neighboring atoms through a many-body interaction. Thus most of their neighbor atoms are thermalized or energetically equalized in accordance to the Maxwell-Boltzmann distribution, and this results in a liquid-like thermal spike region in which the average characteristic energy of each atom is around 1 eV. This corresponds to an equ
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