In 2+1 dimensions, KMC simulations tend to facet easily. This makes sense as more bonds nearest and next-nearest neighbor bonds occur in 2+1 dimensions. Indeed, on the diamond lattice used throughout our 3D simulations, an atom posses 4 nearest neighbor and 12 next-nearest neighbor bonds. If we wish to model nanowire growth by the VLS method, it is desirable for our liquid (which resides on the lattice) to not be faceted. In this note, we describe preliminary results in our search for the correct energy and temperature parameters that allow this to occur.
Our first set of simulations involve annealing a spherical droplet composed of some material at different temperatures and bonding energies. We denote the nearest neighbor bond strengths as and next-nearest neighbor bond strengths as . The energy was varied between 0.10 and 0.20 eV, and for simplicity we set . All simulations start of with a spherical droplet of radius 32 atoms which is annealed at some temperature ranging between 400 and 650 K for 300 seconds. We expect that at lower temperatures and higher bond strengths, faceting will occur.
Here are simulation results for fixed eV and variable temperature:
As temperature is increased, we see increased faceting. This is readily explained. At low temperatures, surface diffusion is extremely slow, and hence the system does not have a chance to come to equilibrium even after 300 seconds. Indeed, we can count the number of actual MC steps performed for the simulations:
# MC STEPS | |
400 | 26349 |
450 | 491111 |
500 | 14541653 |
550 | 259746357 |
600 | 1000000002 (terminated early) |
650 | 1000000002 (terminated early) |
Hence, we could conclude that given enough time, very significant faceting will occur for and . Therefore the results presented in previous meetings depicting a spherical droplet at and eV are misleading and incorrect. We expect faceting to occur there, although at an exaggerated time scale due to the slowness of surface diffusion.
The same phenomena is observed if we vary bond strengths, fixing :
eV | |
eV | |
eV | |
eV | |
eV | |
eV | |
eV | |
eV | |
eV |
As bond strength increases, the droplet becomes (or rather stays) more spherical only because diffusion becomes slower and hence it takes longer to come to equilibrium.
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