Polarization dependent Pd deposition structure on LiNbO$_{3}$ \{0001\} surface*

We investigate effects of polarization orientation on atomic structure of palladium deposited on lithium niobate (LiNbO$_{3}$) \{0001\} surface, using density functional theory (DFT) and kinetic Monte Carlo (kMC) simulations. Adsorption, diffusion, aggregation and clustering process -- include geometries, paths and energies -- of Pd clusters were calculated from DFT simulations. It has been observed that energy barriers of Pd motions on the negatively poled ($c^{-}$) surface are much larger than those on the positively poled surface ($c^{+}$), which indicates the Pd motions on the $c^{-}$ surface are much slower than that of $c^{+}$ surface. We demonstrate, using kMC with kinetic parameters from DFT, very slow motion of Pd on $c^-$ surface leads dispersed small clusters or atoms while fast motion on $c^+$ surface leads large clusters, indicating larger Pd-covered area on $c^-$ surface than $c^+$ after Pd deposition.