Simple generic method for predicting the effect of strain on surface diffusion D. J. Shu, 1 Feng Liu, 2, * and X. G. Gong, 1,3 1 Institute of Solid State Physics, CAS, Hefei 230031, China 2 Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112 3 Department of Physics, Fudan University, Shanghai 200433, China Received 12 September 2001; published 29 November 2001 We show, by first-principles calculations, that the effect of external strain on surface diffusion is inherently correlated with the intrinsic surface stress induced by the adatom along its diffusion pathways. We demonstrate a simple generic method for a priori predicting quantitatively how an external strain will change surface diffusion on any given surface, based on calculations of surface-stress tensors of the unstrained surface. DOI: 10.1103/PhysRevB.64.245410 PACS numbers: 68.35.Fx, 81.05.Tp, 82.20.Kh Surface diffusion is one of the most important kinetic pro- cesses controlling surface growth and thin-film morphology; it has been a subject of extensive experimental and theoreti- cal studies. 1 In heteroepitaxial growth, surface diffusion is inevitably influenced by misfit strain. So far, however, there are only a few studies 2–6 on the effect of strain on surface diffusion. Our understanding of the fundamental physical mechanisms underlying the relationship between strain and diffusion is still very limited. In this paper, we present a comprehensive first-principles investigation of the effect of strain on diffusion on a semiconductor surface. We show that the effect of strain on surface diffusion is inherently corre- lated with the intrinsic surface stress induced by an adatom along its diffusion pathways. We demonstrate a simple ge- neric theoretical method to a priori predict quantitatively how an external strain changes surface diffusion on any given surface. The effect of strain on surface diffusion is not only of general scientific interest but also of technological impor- tance. For example, the strain-affected surface diffusion can alter the transition of growth mode 2,5 from two-dimensional 2D to 3D growth. Surface diffusion directed by a nonuni- form surface strain field is a key ingredient in driving self- organized growth of nanostructures, such as formation of 2D island arrays, 7 coarsening of 2D islands, 8 and growth of 3D island superlattices in multilayer films. 9 Recently, both experiment 5 and theory 6 show that on a metal surface such as Ag111, a biaxial compressive strain increases surface diffusion, while a biaxial tensile strain decreases it. The first- principles calculations 6 further show that the diffusion bar- rier scales linearly with the external strain. A natural question is whether these observations are also true on a semiconduc- tor surface where more complex diffusion processes are gen- erally involved with multiple diffusion pathways and with diffusion anisotropy. And a more fundamental question is what are the underlying physical mechanisms that define the dependence of surface diffusion on strain and whether it is possible to a priori predict the change of surface diffusion under an external strain from the intrinsic surface properties of the unstrained surface. The effects of strain on diffusion on Si001 3,4 and on GaAs001Ref. 2 semiconductor surfaces have been stud- ied before, using empirical potentials. However, the reliabil- ity of these calculations is likely in doubt, because empirical potentials may quantitatively give inaccurate diffusion barri- ers as well as qualitatively produce incorrect diffusion pathways. 10 Therefore, to answer the above questions, we have carried out a series of first-principles calculations of diffusion barries for Si adatoms on Si001, as a model sys- tem for semiconductor surface, under both uniaxial and bi- axial external strains. Our calculations quantitatively confirm the linear dependence of diffusion barrier on external strain, in correlation with the intrinsic surface stress induced by the adatom along its diffusion pathways, as suggested by Dobbs, Zangwill, and Vvedensky. 11 A compressive or tensile exter- nal strain can either increase or decrease surface diffusion, depending on whether the adatom-induced surface stress is under tension or compression. It is thus possible to a priori predict quantitatively the change of surface diffusion under a given external strain, from first-principles calculations of the adatom-induced surface stress on the unstrained surface. The calculations are carried out using the pseudopotential total-energy method within the local-density approximation. The Kohn-Sham orbitals are expanded in plane waves with an energy cutoff of 11 Ry.We use a supercell consisting of a ten-atomic-layer slab with eight atoms per layer and a seven- atomic-layer vaccum  10 Å to model the Si001 surface. The atoms in the surface layer form a p (2 2) reconstruc- tion, as shown in Fig. 1a. A Si adatom is placed on both the top and bottom surfaces of the slab to retain the inversion symmetry of the supercell. The potential-energy surface of the adatom on the unstrained and strained surfaces is mapped out by conjugate gradient minimization, up to a precision of 10 -4 eV in total-energy difference and with forces on the ions converged to 0.01 eV/Å. The unstrained surface corre- sponds to the calculated bulk constant of 5.39 Å. Two special K points are used for the Brillouin-zone sampling. Tests have been done to make sure that all the results are converged with respect to energy cutoff, system size, and k-point sampling. 12 To accurately locate all the minima and saddle points in the complex potential-energy surface and hence accurately determine the diffusion barriers for different diffusion path- ways, we first construct a potential surface on a 0.24 0.24 (Å) 2 fine grid. At each grid point, the z coordinate of the adatom is optimized along with the full coordinates of all other atoms. Next, we determine the exact location and en- ergy of a local minimum site by fully relaxing all the de- PHYSICAL REVIEW B, VOLUME 64, 245410 0163-1829/2001/6424/2454104/$20.00 ©2001 The American Physical Society 64 245410-1