  We study the influence of a point defect on the profile of a growing surface
in the single-step growth model. We employ the mapping to the asymmetric
exclusion model with blockage, and using Bethe-Ansatz eigenfunctions as a
starting approximation we are able to solve this problem analytically in
two-particle sector. The dip caused by the defect is computed. A simple
renormalization group-like argument enables to study scaling of the dip with
increasing length of the sample L; the RG mapping is calculated approximately
using the analytical results for small samples. For a horizontal surface we
found that the surface is only weakly pinned at the inhomogeneity; the dip
scales as a power law L^\gamma with \gamma= 0.58496. The value of the exponent
agrees with direct numerical simulations of the inhomogeneous single-step
growth model. In the case of tilted surfaces we observe a phase transition
between weak and strong pinning and the exponent in the weak pinning regime
depends on the tilt.

Statistical Mechanics;Disordered Systems and Neural Networks