  The vibration of the dimer on Ge(001) surface with the higher vibrational
number excited coherently by STM current is theoretically investigated. The
coherent excitation rate of the dimer vibration is obtained by the Hamiltonian
consisting of the terms of the electron system and the electron-vibration
coupling terms. The transformation of the local structures reported in STM
experiments is shown to be driven by the dimer vibration excited coherently by
the STM current. The sample bias voltage of STM above which the transtormation
to the p(2$\times$2) structure is able to be observed in the experiments, is
semiquantitatively reproduced by the quasi-one-dimensional character of the
$\pi^*$-band. We show that the excitation rate has the term not decaying on the
distance from the STM tip for the one-dimensional band. The contrastive
diffrence of the shapes of the transformed region depending on the sign of the
bias voltage observed by the experiments is explained by the difference between
the quasi-one-dimensional character of the $\pi^*$-band and the two-dimensional
character of the $\pi$-band on Ge(001) surface.
