  We theoretically explore the possibility of tuning the topological order of
cubic diamond/zinc-blende semiconductors with external strain. Based on the
tight-binding model, we analyze the evolution of the cubic semiconductor band
structure under hydrostatic or biaxial lattice expansion, by which a generic
guiding principle is established that lattice \emph{expansion} can induce a
topological phase transition of small band-gap cubic semiconductors via a band
inversion, and further breaking of the cubic symmetry leads to a topological
insulating phase. Using density functional theory calculations, we demonstrate
that a prototype topological trivial semiconductor, InSb, is converted to a
nontrivial topological semiconductor with a 2%-3% biaxial lattice expansion.
