Dynamic scaling phenomena in growth processes

Inhomogeneities in a deposition process may lead to formation of rough surfaces. Fluctuations in the height h(x,t), of the surface (at location x and time t) can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest that, quite generally, the height fluctuations have a self-similar character, their average correlations exhibiting a dynamic scaling form, [[h(x,t)-h(x',t')](2)]=\x-x'\(2 alpha)f(\x-x'\(z)/\t-t'\). The roughness and dynamic exponents, x and z, are expected to be universal, depending only on the underlying mechanism that generates self-similar scaling. Despite its ubiquitous occurrence in theory and simulations, experimental confirmation of dynamic scaling has been scarce. In some cases where such scaling has been observed, the exponents are different from those expected on the basis of analysis or numerics. I shall briefly review the theoretical foundations of dynamic scaling, and suggest possible reasons for discrepancies with experimental results.