It is demonstrated that the annealing process for Ti in-diffusion to z-cut $LiNbO_3$ at temperature lower than the curie temperature in a platinum (Pt) box can cause a ferroelectric micro-domain inversion at the +z surface and Li out-diffusion, therefore which should be avoided or suppressed for waveguide type periodically poled lithium niobate (PPLN) devices. The depth of the inversion layer depends on the Ti-diffusion conditions such as temperature, atmosphere, the sealing method of $LiNbO_3$ in the Pt box and crystal orientation is experimentally examined. The result shows that the polarization-inverted domain boundary appears at the only +z surface and its thickness is about $1.6{mu}m$. Also, for the etched $LiNbO_3$, surface the domain shape was observed by the optical microscope and atomic force microscopy (AEM), and distribution of the cation concentrations in the $LiNbO_3$ crystal by the secondary ion mass spectrometry (SIMS).