Computer Simulation of Surface Diffusion of Silicon and Carbon Adatoms on SiC(001)
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439 Mat. Res. Soc. Symp. Proc. Vol. 423 0 1996 Materials Research Society
Figure 1: Area scanned on the (2 x 1) reconstructed SiC(001) surface to create the energy contour map. The light and dark shaded atoms are Si and C atoms respectively. The MD method requires a knowledge of the forces on each atom. Although it is now possible to perform ab initio calculations to extract these forces, such calculations are rather computer intensive. Semi-empirical interatomic potentials have been shown to give a good description of the surface reconstructions found in semiconductor structures. We have therefore chosen to use the coordination dependent potential of Tersoff [5] in performing the calculations described below. The dynamic surface diffusion properties (activation energies, diffusion paths and diffusion constants) of the adatoms were also obtained by the application of the MD method. In this case, an adatom was initially placed at or near a minimum energy site and the whole system (or just the adatom) given some kinetic energy (temperature). The system was then allowed to evolve according to the equations of motion. The diffusion path is obtained by simply charting the path taken by the adatom on the substrate surface. The activation energy for diffusion can be obtained using the method of Matthai [6] or from a knowledge of the temperature dependence of the diffusion coefficient. The diffusion coefficient, D, can be calculated from the mean square displacement which is valid at long time (t) scales and is given by [7]
D = -1j(r(t) - r(0)112
(1)
Information on the dynamics of the diffusing atom can be also be obtained from the velocity autocorrelation funciton (VACF). One of the advantages of using the MD method is that the VACF is relatively easy to calculate from a knowledge of the velocities of the diffusing atom. The diffusion coefficient is given by 440
--
ABOVE 0.9 0.4- 0.9 -0.5- -0.0 -0.9 - -0.5
n
-
S
M
M Ml
-1.4- -0.9 -1.8- -1.4 -2.3- -1.8 -2.3 -2.7 -3.2-- -2.7 -3.6 - -3.2
-4.1 - -3.6 -4.5- -4.1 S-5.0- -4.5 -5.4 - -5.0 .9 - -5.4 S-5 BELOW -5.9
S
Figure 2: Contour energy map for a carbon adatom on a C-terminated surface over the area scanned in Figure 1. The energy scale in eV is shown on the left. Note that the energy minimum is atop a dimer.
D
,,(,,-),(,- + t))dt
(2)
It has been shown that the value of D given by these two methods differ by 10-15% for between 1000 and 2000 time steps, but reduces to less than 2% for 10i time steps. RESULTS Once the relaxed reconstructed surfaces were determined, Si and C adatoms were placed onto the surface and energy contour maps produced. On the C-terminated surface, Si adatoms were found to be in a minimum energy site when it was a bulk continued site (ie, atop a carbon dimer). The C-dimers were found to open up to 2.53Aas compared to their original separation of 1.46A. Interestingly, this was also the favoured site for the C-adatom (see Figure 2), as the three carbon atoms form a trimer structure. From an analysis of the energy contours, there are two
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