A nonlinear differential equation is derived for the surface shape evolution in epitaxial growth, from a transport equation for the adatoms. A negative Ehrlich-Schwobel barrier is assumed to be present at atomic steps, favoring downhill migration of adatoms. Expressions for the coefficients in the growth equation are obtained in terms of the deposition rate, step density, step edge potential barrier, and adatom release rate from step edges. The analytical model is tested by comparison with a kinetic Monte Carlo simulation of a solid-on-solid model, which includes the same physical phenomena.
