Multilayer He-3 film growth on weak-binding alkali substrates is inves
tigated with a nonlocal density functional theory. Although He-3 wets
all substrates down to zero temperature, prewetting transitions are pr
edicted to occur on Cs, Rb, and K. Continuous wetting is recovered wit
h increasing strength of substrate potential. Emphasis is put on the r
ole played by the Fermi statistics. The heat capacity and the magnetiz
ation of the films exhibits steps associated with the occupation of tw
o-dimensional Fermi disks.