A three-scale analysis of crystal growth process is newly proposed based on the first-principles calculation and on the finite element analysis in order to generate a new biocompatible piezoelectric thin film. Crystal growth process of lead-free BaTiO 3 thin films was designed and experimentally generated on SrTiO 3 (100), (110), (111), and MgO(100) substrates using the radio-frequency magnetron sputtering method. Crystal structures of BaTiO 3 were measured by X-ray diffraction (XRD) h/2h scan. We used Pt for the electrode and measured piezoelectric strain constants d 33 using the ferroelectric measurement system. As a result, analytical crystal orientation fractions on SrTiO 3 (110) and (111) substrates had good quantitative agreement with experimental ones, and ones on SrTiO 3 (100) and MgO(100) substrates corresponded with these experimental crystal structures. Furthermore, analytically determined piezoelectric strain constants d 33 qualitatively showed a good agreement with experimental ones. Especially, for SrTiO 3 (100) and MgO(100) substrates, the differences of d 33 depending on orientation fractions were analyzed by the three-scale simulation accurately. Consequently, it is confirmed that the three-scale analysis is a useful simulation tool to design new biocompatible piezoelectric thin films.

A numerical prediction scheme of crystal growth on various substrates by using the first-principles calculation was proposed to analyze the epitaxial processes of the piezoelectric thin films, such as the sputtering, the chemical vapor deposition and the molecular beam epitaxy processes. At first, we analyze the epitaxial strain of crystal cluster in piezoelectric thin film, which is caused by the lattice mismatch with the substrate. When the epitaxial strain is introduced in the unit cell of the crystal cluster, the total energy can be calculated by employing the pseudo-potential method based on the density functional theory. Then, a preferred orientation of crystal cluster is selected from the crystal conformations on the substrate which satisfy the structural stability condition. This numerical scheme was applied to BaTiO 3 thin films processes fabricated on various substrates, such as SrTiO 3 (110), SrTiO 3 (001), MgO(100) and LaTiO 3 (001). Numerical results show that our process crystallographic design scheme, which employs the total energy increment of cluster, is efficient tool to evaluate the possibility of thin film crystal growth. Finally, it was confirmed that numerical results of preferred orientations have good correspondence with experimental ones.

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