Further ab initio calculations on the C90 explored how adatoms move across the silicon surface, jumping from one inter-atomic space to the next, until they become incorporated in the step edges. To make this calculation feasible, these simulations were done at zero temperature and investigated only certain possible pathways. The results showed the energy barriers that must be overcome for the adatom to "jump" and the binding sites where they end up.
A surprising finding was that the jumps depend to a degree on "dimer buckling." The silicon surface forms bonded pairs of atoms, called "dimers," that tilt, with one atom higher than the other, resulting in an uneven, buckled surface. Bernholc' calculations indicate that it is easier for an adatom to move past a "down" than an "up" atom and that the dimers can shift their tilt in response to the adatom. "This information," notes Bernholc, "would have been difficult or impossible to obtain with experimental methods."
This sideview shows Jerzy Bernholc' CRAY T3D simulations of adatom diffusion at high temperature on a seven-layer silicon slab with a one-atom layer step. Three adatoms (red) are deposited on the surface, two on the lower terrace (violet), one on the upper terrace (aqua). Dimer tilting is somewhat disordered due to the high temperature. Silicon "bulk" atoms (blue) are sandwiched between the stepped surface and a bottom layer (purple). The slab bottom is saturated with hydrogen atoms (white). The slab includes 232 silicon and 72 hydrogen atoms.
With availability of the CRAY T3D, it became feasible to do these calculations at high temperature, which more realistically simulates the silicon growth process as it occurs during MBE. Qiming Zhang, a materials scientist working at PSC as part of Cray Research's Parallel Applications Technology Program, translated Bernholc' QMD code to run on the T3D while also taking advantage of high speed communication between the T3D and C90. A relatively small part of the computing, the atomic movements, runs on the C90 while the electron calculations run on the T3D. The result -- a substantial performance improvement: 6 Gflops using 128 T3D processors, compared to 2.3 Gflops on four C90 processors, one-fourth of the machine in both cases.
Using the T3D code, Bernholc carried out a series of heating up experiments. The results reproduce the high temperature structure observed with STM. More recent simulations focus on diffusion across a heated surface. Further improving on the C90 studies, these calculations allow the adatoms to follow any pathway available to them. So far, despite frequent oscillations in the tilting of the dimers at high temperatures, the jumps correspond to the zero temperature pathways.
"That's the first question," says Bernholc. "Do the atoms follow a different pathway? For the flat surface, the pathway is consistent with low temperature, exactly what we'd expect. We will do the same thing across the step edges. In this high temperature regime, we can see how the jumps occur in real time and probe for new and unforeseen diffusion mechanisms. The T3D has made these simulations possible."
go back to the main page