MD-Simulations Wafer Bonding


Elastic boundary conditions

K. Scheerschmdit and A. Belov


Coupling of length and time scales in empirical MD means bridging to the first principle particle interaction and bridging to the box environment. It can be done either using embedding and handshaking or by a separate treatment and a parameter transfer between the subsystems. The coupling between MD and an elastic continuum is a handshaking method based on an extended Lagrangian (for details cf. reference 2006). The elastic continua may be coupled to MD when the potential energy of an infinite crystal with a defect as shown in the Fig. is approximated in the outer region II only by generalized coordinates. In the defect region I, characterized by large strains, the positions of atoms are treated by empirical MD. The atomic positions in the outer regions II and III result from the linear theory of elasticity. The Lagrangian results in equations of motion


                           m.d2ri/dt2=F in I and

                           µd2ak/dt2=Fk  in II,


thus extending the Newtonian equations of the particle positions ri by equivalent ones for the generalized coordinates ak.




The Figure shows the dislocation geometry (a, I= MD-region, II=elastic, III=overlap) to apply elastic boundary conditions for an dipole of 60o dislocations, and snapshots during MD annealing: 500 K (b), 600 K (c), 0 K (d).



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