Kinetics of Surface Growth: Phenomenology, Scaling, and Mechanisms of Smoothening and Roughening

The growth of solid surfaces via vapor phase processes can be viewed as proceeding in either of two directions: outward by physical or chemical deposition or inward by physical or chemical etching. Figure I is a sche­ matic illustration of the evolution of a surface, S(r, t), where S is the z­ coordinate of the growing surface at the position r = (x,y) and time t, and the initial condition S(r) = 0 at t = 0 corresponds to initiating the growth on a perfectly fiat surface. The average value of the new surface height at any particular time <S(r) corresponds to the amount of material added to or removed from the original surface. As illustrated in Figure I, surfaces typically roughen during growth. Many technological applications in optics and electronics require extremely smooth surfaces, and at present, both areas are hampered by inherent roughness resulting from growth processes. A qualitative understanding of how growth mechanisms affect surface morphology is very useful, but to be able to optimize grown structures, a method to predict surface topology quantitatively will be required. Because rough surfaces are inherently very complex and do not appear to have underlying symmetry constraints to simplify mathematical