Germanium is one of the promising materials for future CMOS technologies, due to its high carrier mobility and low Schottky barrier height (for PMOS). However, the presence of a small direct gap (in addition to the main indirect gap at the L-point) can result in significant band-to-band tunneling (BTBT), even at low voltages. If not remedied, it is easily the dominant BTBT mechanism. In this letter, the dependence of BTBT on the alloy composition in Ge-rich SiGe is studied using detailed simulation of the bandstructure. It is shown that even a very low stoichiometric fraction of Si in a FinFET results in a dramatic reduction of direct BTBT, much more so than in a corresponding p-i-n diode.