Kinetic growth with surface relaxation: Continuum versus atomistic models

We introduce a geometrical interpretation to classify possible linear and nonlinear terms in the models for driven growth with surface relaxation. A nonlinear differential equation, distinct from the Kardar-Parisi-Zhang equation, is proposed as a relevant continuum model describing atomistic kinetic growth under conditions of chemical bonding. The scaling relations among growth exponents that we derive from a dynamic renormalization-group analysis are exact for a class of growth models with surface relaxation. The calculated exponents are in excellent agreement with our discrete atomistic growth simulation.