Kinetic Limitations in Two-and Three-Dimensional Growth
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Kinetic Limitations in Two-and Three-Dimensional Growth K.L. Man1, W.X. Tang1, Hanchen Huang2 and M.S. Altman1 1 Department of Physics, Hong Kong University of Science and Technology, Hong Kong 2 Department of Mechanical Engineering, Rensselaer Polytechnic Institute, Troy, New York ABSTRACT Kinetic limitations related to the Schwoebel-Ehrlich (SE) diffusion barrier are examined in two(2D) and three-dimensional (3D) growth. It is shown that the realization of step instabilities in 2D growth, possibly caused by the SE barrier, may be hindered by other factors such as step permeability and the relative importance of diffusion and step attachment. Growth shapes of Ag crystallites are also determined that reveal the impact of kinetic limitations. Dramatic changes of growth shape caused by In codeposition suggest that surfactants can modify the 3D SE barrier.
INTRODUCTION Advances in the fabrication of nanostructures and devices depend largely upon the degree to which one can understand and control the growth process. Growth shape and morphology will be affected, or even dictated, by kinetic limitations that may be present during growth. One such limitation, which has received a great deal of attention, occurs in growth at surfaces when there is an additional Schwoebel-Ehrlich (SE) diffusion energy barrier to atomic motion descending a monolayer height step, EB in Fig.1. Interest in the SE barrier arises partly because it may induce asymmetry of the step attachment kinetic coefficients, K, with respect to the direction that an atom approaches a step (leading vs. trailing terrace). Step attachment asymmetry is recognized to be an important and possibly common cause of growth instabilities, particularly in step flow [1,3-8]. It was also proposed recently that an analogous 'three-dimensional' (3D) SE energy barrier can exist to atomic diffusion across the ridge that separates two facets on a three-dimensional crystal (Fig.1) [9,10]. The 3D SE barrier stems from the reduced coordination at the ridge. Differences of the adatom formation energies on adjacent facets will cause the 3D SE barrier to be asymmetric, EB1 ≠ EB2 in Fig. 1 . This asymmetry is expected have an impact on growth shapes of three-dimensional crystals beyond the earlier concept that the growth rates of crystal faces is simply proportional to their surface energies [11]. The relationship between this barrier, the SE barrier in two dimensions and a kink or corner-crossing barrier in quasi one-dimension has been pointed out [12]. In this paper, we examine how kinetic limitations originating in the SE barrier may be manifested in growth in two- and three-dimensions. Strictly speaking, asymmetric step attachment caused by the SE barrier in two-dimensional growth is important in the context of growth instabilities only if it causes the current densities of adatoms that attach to a step from the adjacent terraces to be unequal. We show in the next section that the realization of asymmetric current density may be hindered in real systems by other factors su
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