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SIMULATIONS OF SOLID PHASE EPITAXIAL GROWTH IN SILICON

Noam Bernstein, Michael J. Aziz, Div. of Engineering and Applied Sciences, Harvard University, Cambridge, MA; Efthimios Kaxiras, Physics Dept and Div. of Engineering and Applied Sciences, Harvard University, Cambridge, MA.

We simulate solid phase epitaxial growth (SPEG) in silicon, the process by which the amorphous phase transforms into the crystal phase at an amorphous-crystal interface, using empirical potential molecular dynamics (MD). We use the environment dependent interatomic potential (EDIP) [1] which was optimized for defective crystalline and amorphous silicon structures. We create an interface sample by placing a bulk crystal sample and a bulk amorphous sample together and annealing the resulting slab. When the interface sample is evolved at a constant temperature between 700 K and 1150 K, the crystal phase grows epitaxially at the interface. By simulating growth at different temperatures we measure an activation energy for growth of 0.4 eV below 950 K and 1.7 eV above 950 K, compared with 2.7 eV at all temperatures in experiment. We speculate that the low temperature behavior is dominated by existing defects that are much more plentiful in our simulation than in experiment, and that the high temperature regime is more relevant for comparison to experiment. By varying components of the applied nonhydrostatic stress in MD simulations at 1000 K we measure an activation strain in the high temperature regime. In qualitative agreement with experiment hydrostatic pressure speeds up growth, but in plane compression speeds up growth substantially less than compression perpendicular to the interface.

To understand the microscopic mechanism for cystallization we need to distill, from the atomic positions as a function of time that we obtain from MD, a description of the underlying network rearrangements. To conform to our picture of a ``mechanism'' this description should comprise a series of localized connectivity changes that lead to the crystallization of some atoms. To that end we calculate time averaged positions from an MD run (to smooth out thermal vibration), and find clusters of adjacent atoms that change network connectivity at the same time. We do this for each time step, and define ``mechanisms'' composed of a time series of clusters that overlap in some of their participating atoms.

By inspecting sequences of configurations from an MD run we pick out groups of atoms that crystallize and approximately when they move into crystal lattice positions. This information allows us to select the network connectivity change ``mechanisms'' that lead to crystallization. By playing back the configurations captured from the MD run with all motion outside of the crystallizing ``mechanism'' frozen out we generate a sequence of atomic positions. These are completely relaxed, and then used as an input to a program that finds low energy paths connecting the stable configurations. This program creates chains in configuration space coupled by harmonic springs and minimizes the total energy of the path by conjugate gradient relaxation. Using this procedure we have found seven events that led to the crystallization of a total of 16 atoms. These include some simple mechanisms with high activation energies, some complex ones with lower activation energies, and one very complex mechanism with a high activation energy.

References:

  1. M. Z. Bazant, E. Kaxiras, and J. F. Justo, Phys. Rev. B 56, 8542 (1997).

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