The effect of stress on the dielectric properties of barium strontium titanate thin films

Abstract

Barium strontium titanate thin films are being developed as capacitors in dynamic random access memories. These films, grown on silicon substrates, are under tensile residual stress. By a converse electrostrictive effect, the in-plane tensile stress reduces the capacitance in the thickness direction of the film. We measured the substrate curvature change upon the removal of the film, and found the magnitude of the residual stress to be 610 MPa. In a separate experiment, we applied a force to vary the stress in a film on a substrate, and simultaneously recorded the capacitance change of the film. The measurements quantify the effect of stress on thin film capacitance. The stress free capacitance was found to be 23% higher than the capacitance under residual stress.

Metal-organic chemical-vapor deposition of (Ba,Sr)TiO3: Nucleation and growth on Pt-(111)

“…From the average strain of = ͑−0.85± 0.25͒% we obtain a stress of = 800± 200 MPa using E = 135 GPa and = 0.32. 22 This value is in reasonable agreement with direct stress measurements of ϳ610 MPa from the wafer bending. 22 Larger values for the stress, ϳ1200 MPa, might be obtained by using elastic constants derived from single-crystal data for BaTiO 3 , 23 which are, however, still lower than earlier values of 2200 MPa as deduced from strain measurements.…”

Curie–Weiss-type law for the strain and stress effects on the dielectric response of ferroelectric thin films

“…7 Although the measurements in Ref. 7 were made on polycrystalline films, our approach can be used in this case as well because the straining of a thin film on a thick substrate is a macroscopic phenomenon similar in epitaxial and polycrystalline films. 8 We first extract the actual permittivity of BST films from the data presented in Ref.…”

“…Such a bending test was recently performed by Shaw et al for Ba 0.7 Sr 0.3 TiO 3 films grown on platinum coated silicon substrates. 7 They evaluated the associated change of the in-plane biaxial stress in the film and attributed the observed variation of the capacitance to the stress effect. During the dielectric measurements, however, the film grown on a thick substrate is under a fixed strain, but not at constant stress.…”

“…When the film is in a paraelectric state, the reciprocal dielectric susceptibility 33 in the film thickness direction is a linear function of the misfit strain: 3,4 33 ϭ2a 1 Ϫ4S m Q 12 /(s 11 ϩs 12 ), where a 1 is the dielectric stiffness of a bulk crystal, which linearly depends on temperature T, Q 12 is the electrostrictive constant of paraelectric phase, and s i j are the film elastic compliances at constant polarization. Therefore, to describe the misfit-strain dependence of the dielectric susceptibility 33 7 However, as follows from the misfit strain-temperature phase diagrams of ferroelectric thin films, 3,4 Eqs. ͑1͒ and ͑2͒ are valid only at misfit strains not exceeding the second critical value S m **ϭa 1 (s 11 ϩs 12 )/(Q 11 ϩQ 12 ), at which the paraelectric state loses its stability against the appearance of the in-plane polarization.…”

Thin fim barium strontium titanate capacitors for tunable RF frond-end applications

“…3) a more pronounced influence of the low relative permittivity interface layer on the measured ε r of thin films [87,90]. The ferroelectric layer can in some cases be partly interfaced with an interface layer with a low relative permittivity, e.g., due to material diffusion through the electrodes.…”