A crystal facet is metastable under stress, but the process of growth or su
blimation roughens the facet and is expected to render it unstable. This po
ses a fundamental limit for heteroepitaxial growth of planar layers, e.g..
in semiconductor devices. An analysis shows that this facet-growth instabil
ity can be suppressed to an arbitrary degree by growing slowly. Moreover, t
he local stress ("force dipole") inherent in atomic steps introduces a new,
purely kinetic effect that dominates at low strain and can render planar g
rowth dynamically stable.