$PbTiO_3$ thin films were deposited on MgO(100) substrates and $SrTiO_3(100)$ substrates by reactive D.C. magnetron sputtering of Pb metal and Ti metal in oxygen and argon gas mixture. Film orientation was examined by X-ray diffraction methods. The stress state was examined by observing the variation of the c-axis orientation ratio with the film thickness, and calculated by finite element method. In the $PbTiO_3$ thin films deposited on the MgO(001) substrate, the c-axis orientation ratio was increasing with the film thickness. The a-axis orientation near the interface was observed, and the c-axis orientation ratio was increased from 80% to 90% when the film thickness was more than 1000Å. The phenomenon was explained by the lattice mismatch stress generated at the interface between the $PbTiO_3$ thin film and $MgO$ substrate.
To investigate the effect of the intrinsic stress on the orientation ratio, the annealing method was used. The intrinsic stress was uniform regardless of the film thickness. But the difference of the c-axis orientation ratio between before and after annealing was varied with the film thickness. and it was increased with increasing the film thickness in the range of 0~1000Å, but was uniform value of the 15% when the thickness was more than 1000 Å. This phenomenon was explained by the distribution of the total stress of the film. The total stress was the sum of lattice mismatch stress, thermal stress, tranformation stress, and intrinsic stress. To observe the stress distribution with the film thickness, the author analyzed the stresses by using the finite element method(FEM). The stress distributions of the lattice mismatch stress, the thermal stress, and intrinsic stress were analysed. The total stress at the thickness less than 1000 Å was tensile stress state, but was changed from tensile stress to compressive stress with incresing the film thickness.
