Boron segregation from submonolayer interfacial B deposition during molecular beam epitaxy (MBE) growth of Si1-xGex and Si layers in the temperature range 350-800 degrees C has been investigated by high resolution secondary ion mass spectroscopy and modeled by an atomistic description as a function of growth temperature and alloy composition. In the case of Si-MBE, beginning at 550 degrees C segregation-induced profile broadening occurs and at 600 degrees C kinks appear in the boron profiles developing into shoulders for higher growth temperatures. At temperatures above 700 degrees C at the shoulder a concentration of(1-2) x 10(19) cm(-3) was found. For Si1-xGex growth the segregation is significantly reduced and a decay length of 0.6-0.8 nm can be obtained in the range 350-450 degrees C. From a fit of the B-profile between 450 degrees C and 600 degrees C we obtained a kinetic barrier for a jump to the surface state of approximately 2.1 eV and a Gibbsian heat of segregation of 0.44 eV in the case of Si-MBE. The transition temperature from strong surface segregation to kinetically limited segregation yields 640 degrees C. In the case of Si1-xGex growth the activation energy for segregation increases up to 4.5 eV for germanium, comparable with that of bulk diffusion.