The authors have combined structural and optical characterizations to investigate the tensilestrained state and the band gap engineering of Ge layers grown on Si(001) using molecular beam epitaxy. The tensile strain is generated in the Ge layers due to a difference of thermal expansion coefficients between Ge and Si. The Ge growth on Si(001) was proceeded using a two-step growth process: a low-temperature step to produce relaxed buffer layers, followed by a:high-temperature step to generate the tensile strain in the Ge layers. For the low-temperature step, the authors have evidenced the existence of a substrate temperature window from 260 to 300°C in which the well-known StranskiKrastanov Ge/Si growth mode transition from two-dimensional to three-dimensional growth can be completely suppressed. The authors show that the value of the tensile strain in the Ge layers lineally increases with increasing the growth temperature and reaches a saturation value of ~0.24 percent in the temperature range of 700-770°C. Post-grown cyclic thermal annealing has allowed to increase the tensile strain up to 0.30 percent, which is the highest value ever reported to date. Finally, photoluminescence measurements reveal both an enhancement of the Ge direct band gap emission and a reduction of its energy due to the presence of tensile strain in the layers.