W. K. Simon

Anisotropic strain relaxation in (Ba0.6Sr0.4)TiO3 epitaxial thin films

We have studied the evolution of anisotropic epitaxial strains in ⟨110⟩-oriented (Ba0.60Sr0.40)TiO3 paraelectric (m3m) thin films grown on orthorhombic (mm2) ⟨100⟩-oriented NdGaO3 by high-resolution x-ray diffractometry. All the six independent components of the three-dimensional strain tensor were measured in films with 25–1200-nm thickness, from which the principal stresses and strains were obtained. Pole figure analysis indicated that the epitaxial relations are [001]m3m‖[001]mm2 and [1¯10]m3m‖[010]mm2 in the plane of the film, and [110]m3m‖[100]mm2 along the growth direction. The dislocation system responsible for strain relief along [001] has been determined to be ∣b∣(001)=3∕4∣b∣. Strain relief along the [1¯10] direction, on the other hand, has been determined to be due to a coupled mechanism given by ∣b∣(1¯10)=∣b∣ and ∣b∣(1¯10)=3∕4∣b∣. Critical thicknesses, as determined from nonlinear regression using the Matthews–Blakeslee equation, for misfit dislocation formation along [001] and [1¯10] direction...

In-plane microwave dielectric properties of paraelectric barium strontium titanate thin films with anisotropic epitaxy

In-plane dielectric properties of ⟨110⟩ oriented epitaxial (Ba0.60Sr0.40)TiO3 thin films in the thickness range from 25–1200nm have been investigated under the influence of anisotropic epitaxial strains from ⟨100⟩ NdGaO3 substrates. The measured dielectric properties show strong residual strain and in-plane directional dependence. Below 150nm film thickness, there appears to be a phase transition due to the anisotropic nature of the misfit strain relaxation. In-plane relative permittivity is found to vary from as much as 500–150 along [11¯0] and [001] respectively, in 600nm thick films, and from 75 to 500 overall. Tunability was found to vary from as much as 54% to 20% in all films and directions, and in a given film the best tunability is observed along the compressed axis in a mixed strain state, 54% along [11¯0] in the 600nm film for example.

Effect of misfit strains on fourth and sixth order permittivity in (Ba0.60,Sr0.40)TiO3 films on orthorhombic substrates

The in-plane dielectric response of [110] oriented Ba0.60Sr0.40TiO3 epitaxial films grown on [100] NdGaO3 is used to determine the field induced polarization at 10GHz. The nonlinear polarization curve is used to determine the linear and nonlinear permittivity terms for the in-plane principal directions, [001] and [1¯10]. Studied films are in the thickness range of 75–1200nm, and clearly show the influences that drive tunability down with increasing residual strain. The variation of the tunability, along the [001] direction, proves to be less sensitive to residual strain then the [1¯10] direction, although [1¯10] is capable of greater tunability at low residual strains.

Misfit strain relaxation in (Ba0.60Sr0.40)TiO3 epitaxial thin films on orthorhombic NdGaO3 substrates

Strain relaxation in (Ba0.60Sr0.40)TiO3 (BST) thin films on ⟨110⟩ orthorhombic NdGaO3 substrates is investigated by x-ray diffractometry. Pole figure analysis indicates a [010]BST∥[1¯10]NGO and [001]BST∥[001]NGO in-plane and [100]BST∥[100]NGO out-of-plane epitaxial relationship. The residual strains are relaxed at h∼200nm, and for h>600nm, films are essentially strain free. Two independent dislocations mechanisms operate to relieve the anisotropic misfit strains along the principal directions. The critical thickness for misfit dislocation formation along [001] and [010] are 11 and 15nm, respectively. Stress analysis indicates deviation from linear elasticity for h<200. The films with 10<h<25nm are of monoclinic symmetry due to a finite principal shear stress along [110] of the initial orthorhombic cell.

Polycrystalline Ba0.6Sr0.4TiO3 thin films on r-plane sapphire : Effect of film thickness on strain and dielectric properties

Polycrystalline Ba0.6Sr0.4TiO3 (BST) films grown on r-plane sapphire exhibit strong variation of in-plane strain over the thickness range of 25–400nm. At a critical thickness of ∼200nm, the films are strain relieved; in thinner films, the strain is tensile, while compressive strain was observed in the 400nm film. Microwave properties of the films were measured from 1to20GHz by the interdigital capacitor method. A capacitance tunability of 64% was observed in the 200nm film, while thinner films showed improved Q factor. These results demonstrate the possibility of incorporating frequency agile BST-based devices into the silicon on sapphire process.

Nonlinear dielectric properties and tunability of 0.9Pb(Mg1∕3,Nb2∕3)O3–0.1PbTiO3 and Ba(Ti0.85,Sn0.15)O3 paraelectrics

We investigate the nonlinear dielectric properties of 0.9Pb(Mg1∕3,Nb2∕3)O3∙0.1PbTiO3 (PMN-PT) and Ba[Ti0.85,Sn0.15]O3 (BTS) paraelectrics experimentally and theoretically. We measure the nonlinear dielectric response in the parallel plate capacitor configuration, whereby we obtain the low frequency linear permittivity (e33), and the higher order permittivities (e3333,e333333) at 298K as e33PMN-PT=2.1×10−7 and e33BTS=4.1×10−8F∕m, e3333PMN-PT=−4.9×10−20 and e3333BTS=−7.3×10−21F3m∕C2, and e333333PMN-PT=7.6×10−33 and e333333BTS=9.85×10−34F5m3∕C4. By using a self-consistent thermodynamic theory in conjunction with the experimental data, we compute the E3 dependence of electrostatic free energy ΔG, the field-induced polarization P3, and the thermodynamic tunability ∂2P3∕∂E32, and prove that electrostatic free energy has to be expanded at least up to the sixth order in the electric field to define the critical field ∣E3*∣ at which maximum tunability is attained. We also show that ∣E3*∣ is a function on ∣e3333∣∕e...

Paraelectric thin films by nanoscale engineering of epitaxy and planar anisotropy for microwave phase shifter applications

Epitaxial and lang110rang oriented paraelectric thin films of Ba0.60Sr0.40TiO3 were grown on lang100rang oriented NdGaO3 orthorhombic substrates, and the nonlinear dielectric properties were studied at 10 GHz along selected in-plane crystallographic directions in the film thickness range of 25-1200 nm. The measured dielectric properties show strong residual strain and in-plane directional dependence. For instance, the in-plane relative permittivity is found to vary from as much as 500 to 150 along [1macr10] and [001], respectively, in the 600 nm film. Tunability was found to vary from as much as 54% to 20% in all films and directions. In a given film, the best tunability is observed along the compressed axis in a mixed strain state, 54% along [1macr10] in the 600 nm film. It is shown that, by nanoscale manipulation of epitaxy and planar anisotropy, the return loss and phase shift in a paraelectric can be tuned over a rather wide range. The approach presented herein opens avenues for obtaining various degrees of phase shift on the same film, enabling one with an additional degree of freedom in device design and fabrication as well as multifunctionality

Barium strontium titanate thin film varactors on r-plane sapphire

This paper presents the microwave properties of barium strontium titanate (BST) thin films on r-plane sapphire substrates. A series of films with thickness 25-400 nm was prepared by pulsed laser deposition (PLD). Microwave properties of the films, including capacitance tunability and loss tangent, were extracted by patterning interdigitated capacitors (IDCs) on the film surface. The highest tunability of 64% was observed in the 200 nm film. These results demonstrate the possibility of integrating BST into the silicon on sapphire process.

Effect of Misfit Strain Relaxation on Nonlinear Dielectric Properties of Epitaxial (Ba 0.60 Sr 0.40 ) Thin Films on NdGaO 3

Strain relaxation in (Ba0.60 Sr0.40)TiO3 epitaxial films on <110>-oriented NdGaO3 substrates is investigated in the thickness range, h= 25-1200 nm. The BST films prepared by PLD show that residual strains mostly relax by h~200 nm, and for h>600 nm films are essentially strain free. Two independent dislocation mechanisms operate to relax anisotropic strains along the principal directions. The critical thickness for misfit dislocation formation along [001] and [010] were found to be 11 and 15 nm, respectively. Deviation from linear elasticity for h<200 was observed, and increased as thickness decreased. Films with h<25 nm are monoclinic due to a finite principal shear stress along [110] of the BST cell. The effects of misfit strain relaxation on the nonlinear dielectric response and tunability will be discussed as well. The in plane dielectric response demonstrates a directional dependence that increases with the magnitude of the residual strain.

Nonlinear Dielectric Properties of (Ba 0.60 , Sr 0.40 )TiO 3 Thin Films with Anisotropic Epitaxy

Nonlinear dielectric response of (Ba0.60 Sr0.40)TiO3 epitaxial films on <100> and <110>-oriented NdGaO3 substrates were investigated as a function of film thickness. The second, fourth and sixth order permittivities were determined at 10 GHz and at room temperature from which the so-called critical field for maximum tunability was computed using a thermodynamic formalism recently developed by the authors along the principal residual misfit strain directions. It is shown that the critical field is anisotropic in the plane of the film and its magnitudes are governed by the film thickness.