  The pyramid-to-dome transition in Ge$_{x}$Si$_{1-x}$ on Si(100) initiated by
step bunching on pyramidal quantum dots is atomistically simulated using a
novel multi-state lattice model incorporating effective surface
reconstructions. Results are explained by a simple theory based on a shallow
island approximation. Under given deposition conditions in $d$ dimensions, the
shape transition is shown to occur at island size $n_c$ following $n_c^{1/d}
\propto x^{-\zeta}$ independent of temperature and deposition rate, where
$\zeta\alt 2$ and $x$ is the actual Ge concentration in the island. The
transition has an energy barrier dominated by the facet interface energy. Fast
deposition however can out-run and delay the transition to larger island sizes.
