Molecular Dynamics Simulation of Epitaxial Growth
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MRS BULLETIN/NOVEMBER 1988
the problem. 4 In these calculations, given an interatomic potential and a procedure for controlling temperature, the classical equations of motion of the whole system are solved simultaneously without further approximations. The weakness of the method resides in the availability of "correct" interatomic potentials. This is especially true for epitaxial growth where an atom approaches a free surface. Although a technique developed quite recently allows recalculating the interatomic potentials at every MD step,5 the computational capabilities required prohibit applying this method to epitaxial growth. Moreover, as I will show, a number of important and interesting properties can be studied without such sophisticated methods.
have only varied the sizes (cr,) and kept constant the depth of the potential. Semiconductors, on the other hand, require more complex potentials such as the fourfold coordinated Stillinger-Weber potential,7 which consists of two body parts of LJ type: Mrq) = A(Bf - 1) exp[(r> - a)"'] (2) and three body parts hir^r^.e^K
exp[y(r,y - a)"1 +
y(rtt - a) 1 ] [cos 6jik + 1/3]"2 (3) with A = 7.049556, B = 0.6022246, p = 4, a = 1.80, X = 21.0, and y = 1.20. It is important to stress that the conclusions drawn at present from such simulations are only qualitative and should not be applied to specific systems (e.g., a particular element).
Spherically Symmetric Potentials: Metals Spherically symmetric potentials are expected to give a reasonable, qualitative idea for the physics of metal epitaxy. A more precise description of the physics of metals would require the use of volumedependent potentials 8 or of the new combined density-functional-moleculardynamics technique developed by Car and Parinello.5 With the present understanding of epitaxial growth, a number of interesting conclusions can be drawn without the addition of such complications. Moreover, many interesting phenomena (e.g., "columnar growth") Potentials and Epitaxy To simulate metals it is customary to require studying large numbers of partiuse spherically symmetric potentials such cles, making the use of more complicated schemes prohibitive. as the Lennard-Jones (LJ) or Morse potentials.6 In some cases the potential Homoepitaxy ("like on like" growth) parameters are determined by a detailed reveals a number of interesting phefit to a bulk property such as the elastic nomena in qualitative agreement with constants. Since many other MD studies experimental observations. 9 Figure 1 have been performed using LJ potenshows the particle density along the tials, most studies of epitaxial growth z axis (perpendicular to the substrate) have also been done using this same after the deposition of 2,052 atoms potential. Moreover, the general concluat a substrate temperature Ts = 0. The sions drawn from these studies rely only arrangement of atoms in the layers is on the fact that the LJ potential consists shown in Figure 2. Even at very low temof a hard-core repulsive core, an attracperatures, the growth is into defected t
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