Effects of strain gradient on charge offsets and pyroelectric properties of ferroelectric thin films

Abstract

The Landau-Ginzburg-Devonshire theory is used to study the effects of the strain gradient due to the epitaxial stresses in ferroelectric thin films sandwiched between two different substrates. The polarization in the film is found to be nonuniform, resulting in charge offsets and an asymmetric hysteresis response with characteristics similar to those in compositionally graded ferroelectric materials. The authors' results suggest that the charge offset and pyroelectric effects can also be produced with effect of the strain gradient in film. In addition, such effects are found to be sensitive to an applied load. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2335369͔Functionally graded ferroelectrics in the form of either bulk or thin films possess properties 1-8 different from those of homogeneous ferroelectrics. The distribution of the polarization in graded ferroelectric devices is asymmetric and graded, and there is a translation of the hysteresis loop along the polarization axis with an attendant charge offset. As a result of this asymmetry, other properties such as the effective pyroelectric response, temperature dependence of the dielectric behavior, etc., 1,3 are also affected.At the same time, a strain gradient in a uniform ferroelectric thin film may also produce similar effects. [9][10][11][12][13][14] In this letter, we report on our investigation of the effects of the strain gradient caused by the epitaxial stresses in ferroelectric thin films ͑FTFs͒ sandwiched between two different substrates. Following the Landau-Ginzburg-Devonshire ͑LGD͒ theory, a general model that includes effects of flexoelectricity and stress gradient is formulated and applied.The thickness of the FTF is L, and the thicknesses of the rigid substrates are assumed to be much larger than L, so that the system can be considered to remain flat. The polarization P due to the eigenstrain of the ferroelectric transformation ͑simply called self-polarization͒ is assumed to be perpendicular to the film surface and is homogeneous on the x-y plane. Using the LGD theory and the Legendre transformation, the total free energy per unit area of the film can be written as: 4,9,10,15where A, B, and C are the expansion coefficients of the Landau free energy and D can be approximated as 2 · ͉A͑T − T c0 ͉͒, where T c0 is the Curie-Weiss temperature of the bulk material and is the characteristic length along which the polarization varies. 1 ␥ and are the direct and converse flexoelectric coefficients, respectively. 9,10 Q 12 is the electrostrictive coefficient describing the coupling between the mechanical deformation and the self-polarization. P 0 and P L are the polarizations, and ␦ 0 and ␦ L are the extrapolation lengths at the upper and lower surfaces, respectively. s ij is the elastic compliance tensor. E d ͑z͒ is the depolarization field and E ext ͑z͒ is the external field, which have been defined in Refs. 1, 3, and 4. u is the total biaxial in-plane residual strain in the thin film. x 1 = x 2 = x 0 is the transformation strain given by x...

Effects of interface dislocations on properties of ferroelectric thin films

“…In this work, the critical thickness of the interface dislocation generation is about 4 nm when ferroelectric is in paraelectric state, the calculated dislocation separations for the 10, 20 and 50 nm-thick films are, respectively, $18, $15 and $13 nm. We must note that the interface dislocation density and critical thickness of the interface dislocations generation should also be determined by the polarization in ferroelectric thin film (Wang et al, 2003;Zheng et al, 2006c). In this work, we only assume that no additional dislocations form during ferroelectric phase transition.…”

“…When surface effects are negligible, qP=qz ¼ 0 at z ¼ 0 and h, corresponding to extrapolation lengths of d 0 ¼ d L ! 1 (Zheng et al, 2006c). The mechanical boundary conditions for the ferroelectric thin film are taken as: the ''upper'' surface is traction-free and the interface is determined by the interface dislocation.…”

Pyroelectric response of lead zirconate titanate thin films on silicon: Effect of thermal stresses

“…7,8,[20][21][22][23][24] Prior work also shows that the pyroelectric properties of FE thin films can be optimized through engineering misfit and thermal strains. 14,19,25,26 For example, theoretical studies of barium strontium titanate (Ba x Sr 1-x TiO 3 , BST) films on Si and sapphire substrates indicate that the pyroelectric response of these films may vary with film composition, the substrate material, and the processing temperature. 6,14 Lead zirconate titanate [Pb(Zr x Ti 1-x O) 3 , (PZT x:1-x)] thin films with x 0.5 are of particular interest for IR devices due to their relatively large bulk pyroelectric properties at room temperature (RT ¼ 25 C).…”

Controlling dielectric and pyroelectric properties of compositionally graded ferroelectric rods by an applied pressure

“…In the absence of an applied electric field ͑E ext =0͒, optimizing the total free energy with respect to the polarization field yields the Euler-Lagrange equation ␦F / ␦P = 0, through which the stationary values of P can be solved. [10][11][12][13][14] In the present analysis, the rod is assumed to be sufficiently thick so that effects of lattice relaxation on all surfaces of the rod can be neglected. The boundary conditions are assumed to satisfy ‫ץ‬P / ‫ץ‬z =0 at z = 0 and z = h, corresponding to a complete charge compensation 1 on the interface between the ferroelectric and the substrates.…”