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By D. Kinderlehrer, et al.,

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Extra resources for An Introduction to Variational Inequals and Their Applns

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The validity of the linear cascade approximation holds for cascade Regime 11, when the number of moving atoms is small with respect to the total number of atoms contained within the collision volume. As mentioned above, the nature of the collision cascade depends on M1/M2,and the incident ion energy. For a typical FIB application using a 550 keV Ga+ ion beam, E, is moderate, MI = MZ,and thus the conditions to produce a cascade characterized by linear collision dynamics are satisfied. Therefore, elastic energy losses can be assumed to be the result of a series of uncorrelated binary collisions and, the resulting phenomena can be readily modeled with MC computer simulation methods.

Dose) corresponds to an increase in concentration, since steady state implantation conditions are not met. Ion implantation however, is a non-equilibrium process with the capability of producing materials with compositions unattainable by other conventional means. Thus, in FIB milling, an increase in dose does not alter the steady state equilibrium process of ion implantation, but rather, just increases the time in which the FIB milled surface will recede. , the depth of a FIB milled box cut.

In equation (4), O(R) is the universal screening function, R = rla the reduced interatomic separation, Z l and Z2 are the atomic numbers of the each of the two interacting species, and V(r) is the functional form of the interaction potential between the two atoms. The stopping power, S(E), is the average energy transferred when summed over all impact parameters as given in equation (5): 4 M, M, where y = (MI +~ 2 ) :' Thus, both the conservation of momentum and the interatomic potential are taken into account when the nuclear stopping power of an incident ion in a target material is considered.

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