  A scanning tunneling microscopy (STM) image of a hydrogen-adsorbed Si(001)
surface is studied using first-principles electron-conduction calculation. The
resultant STM image and scanning tunneling spectroscopy spectra are in
agreement with experimental results. The contributions of the $\pi$ states of
bare dimers to the tunnel current are markedly large, and the $\sigma$ states
of the dimers rarely affect the STM images. The tunnel currents do not pass
through the centers of the dimers but go through the edges of the dimers with
local loop currents. In addition, when the tip exists above the
hydrogen-adsorbed dimer, there are certain contributions from the $\pi$ state
of the adjacing bare dimers to the tunnel current. This leads to the STM image
in which the hydrogen-adsorbed dimers neighboring bare dimers look higher than
those surrounded by hydrogen-adsorbed dimers. These results are consistent with
the experimental images observed by STM.
