We study the electronic structure and the optical properties of germanium c
lusters up to about 10(3) atoms, by using a semi-empirical tight-binding ap
proach. Germanium nanocrystals are related to quantum dots growing, by a se
lf-organization process, in sapphire matrices. The optical properties of su
ch dots are experimentally found to be strongly influenced by quantum confi
nement effects.. We investigate these effects from the theoretical point of
view, calculating the optical spectra in the single-particle approximation
. Inclusion of the electron-hole interaction is found to yield visible effe
cts.