  The fusion process of $^{48}$Ca induced reactions is studied with the
two-step model. In this model, the fusion process is devided into two stages:
first, the sticking stage where projectile and target come to the touching
point over the Coulomb barrier from infinite distance, and second, the
formation stage where the di-nucleus formed with projectile and target evolve
to form the spherical compound nucleus from the touching point. By the use of
the statistical evaporation model, the residue cross sections for different
neutron evaporation channels are analyzed. From the results, optimum reactions
are given to synthesize $Z$ = 117 element with $^{48}$Ca induced reactions.
