The incorporation of dilute Sn concentrations CSn during Ge(001) low-temperature molecular-beam epitaxy significantly increases the critical thickness h1(Ts) for the onset of epitaxial breakdown. With CSn = 6×1019 cm−3, h1 increases by an order of magnitude at Ts = 95 °C, while gains in h1(Ts) by factors ranging from 3.2 at 95 °C to 2.0 at 135 °C are obtained with CSn = 1×1018 cm−3 (20 parts per million!). Nevertheless, the ratio of the surface width at breakdown to the in-plane correlation length remains constant, independent of Ts and CSn, showing that epitaxial breakdown for both Ge(001) and Sn-doped Ge(001) is directly related to surface roughening. We attribute the dramatic Sn-induced increases in h1(Ts) to enhancements in both the Ge surface diffusivity and the probability of interlayer mass transport. This, in turn, results in more efficient filling of interisland trenches, and thus delays epitaxial breakdown during low-temperature growth. © 2003 American Institute of Physics.