substrate as and can be written as, s s 0 f f ep a a a 1 E − −ν σ = (7) where a0 is the lattice parameters of the PZT(0.58/0.42) thin film in the cubic phase before phase transition at the deposition temperature Ts=650 oC. a f and as are the lattice parameters of the film and the substrate in the cubic phase. Ef and vf are, respectively, Young’s modulus and Poisson’s ratio of the thin film and they are, respectively, 85GPa and 0.28. Since the substrate thickness is much greater than that of the film, the resulting epitaxial stress during growth in the film is tensile for as>a0 and compressive for as<a0 if we assume the absence of structural relaxation. However, since epitaxial strain develops at the growth temperature, it is reasonable that structural relaxation mechanisms (i.e., the formation of misfit dislocations at film/substrate interfaces) should be active to relieve this stress. Therefore, epitaxial stress has not contribute to residual stress[4]. The intrinsic stress can be relaxed by the orientation change. The difference of the c-axis lattice parameter before and after the annealing process was used to calculate the stored intrinsic stress as follows, [ ] f f f f f in A(c) A(c) B(c) 2 E − ν σ = − (8) where A(c)f and B(c)f are c-axis lattice parameters of PZT thin film in tetragonal phase at room temperature before and after annealing, respectively. The lattice parameters were calculated with the (002) peak position in the XRD patterns. In the investigation the c-axis lattice parameters A(c)f are, respectively, 4.0958 A0,4.0861 A0 and 4.0817 A0 for the thickness of 0.05µm,0.5µm and 1.0µm PZT thin film. The c-axis lattice parameters B(c)f are, respectively, 4.0958 A0,4.0861 A0 and 4.0817 A0 for the thickness of 0.05µm,0.5µm and 1.0µm. The intrinsic stresses for different film thickness are shown in figure 4. One finds that the intrinsic stress has the same profile as the total stress. Therefore, it is obvious the intrinsic stress greatly contributes to the total stress. 0.0 0.2 0.4 0.6 0.8 1.0 -250 -200 -150 -100 -50 0 Residual stress: Experimental results Residual stress: Theoretical results Intrinsic stress Transition stress Stress (MPa) Thin film thickness (µm) Figure 4: The contributions of intrinsic stress and transition stress to residual stress in PZT thin film The thermal stress develops from thermal expansion mismatch between the film and substrate during cooling from the processing temperature to room temperature. The thermal stress can be written as, [ ] [ ] { } ) (T T ) ) (T T ) ( (T) ( (c) ) (1 E 0 tr s f tr s s f f f th α −α − + α −α − −ν σ = (9) where α(c)f and α(T)f are the thermal expansion coefficients of PZT (0.58/0.42) thin film in the basal plane for the cubic and tetragonal phases, respectively and they are assumed to be same and are taken as 7.0×10-6/K. αs is the thermal expansion coefficients of the substrate is taken as 3.5×10-6/K. The thermal stress is about 0.26GPa and it is not dependent on film thickness. Since it is difficult for structural relaxation to occur at low temperature, thermal stresses are stored in the film. For many materials, the resultant residual stress often result in microcracking of the film.
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