Anisotropic Misfit Strains Research Articles

Microstructure of gallium nitride films grown on silicon (110)

The microstructure of GaN layers grown on Si(110) is studied by transmission electron microscopy. The GaN layers were grown by metal-organic vapor phase epitaxy using low-temperature AlN interlayers and a high-temperature AlN seed layer. Anisotropic misfit strain originating at the AlN/Si(110) interface is notably reflected in the microstructure of the GaN layers. The stress produced in GaN/Si(110) films is relieved by bending of edge type threading dislocations over the basal plane, generating horizontal segments aligned all along the closely lattice matched direction [11¯00]. It is proposed that the horizontal defects are generated by a driven force with glide- and climb-components manifested on some of the prismatic slip planes of GaN. The general mechanism of the change in the propagation direction of dislocations is discussed.

Phenomenological analysis of phase transitions in epitaxial perovskite ferroelectric thin films

A phenomenological Landau–Ginzburg–Devonshire theory is employed to investigate the effect of biaxial misfit strains and in-plane shear strain on thermodynamic equilibrium states and dielectric properties of single domain KNbO 3, BaTiO 3, and PbTiO 3 thin films. For KNbO 3 thin films grown on cubic substrates, the constructed isotropic misfit strain–temperature phase diagram is in qualitative agreement with the result from first-principle calculations. For BaTiO 3 and PbTiO 3, misfit strain–temperature phase diagrams at constant in-plane shear strains are constructed. In-plane shear strain is shown to restrain formation of a phase (polarization along [1 0 0]). The anisotropic misfit strain–temperature and misfit strain–misfit strain phase diagrams are also developed for KNbO 3 thin films grown on orthorhombic substrates. The anisotropic biaxial misfit strains lead to appearance of orthorhombic phases (a 1, a 2) and monoclinic phases (a 1c, a 2c).

PHASE TRANSFORMATION CHARACTERISTICS OF BARIUM STRONTIUM TITANATE FILMS ON ANISOTROPIC SUBSTRATES WITH (001)//(001) EPITAXY

ABSTRACT The role of anisotropic misfit strains on the spontaneous polarization of (100) oriented Ba0.6Sr0.4TiO3 thin films on (100) orthorhombic substrates is theoretically analyzed. A modified thermodynamic model is utilized to evaluate the equilibrium polarization values as a function of the anisotropic misfit strains. Results show that ferroelectric phases that cannot be observed in single-crystal Ba0.6Sr0.4TiO3 can be stabilized due to the reduction in the symmetry induced by the anisotropic strain state.

Misfit strain–misfit strain diagram of epitaxial BaTiO3 thin films: Thermodynamic calculations and phase-field simulations

The effect of anisotropic strains on the phase transitions and domains structures of BaTiO3 thin films was studied using both thermodynamic calculations and phase-field simulations. The misfit strain–misfit strain domain stability diagrams were predicted. The similarity and significant differences between the diagrams from thermodynamic calculations assuming single domains and from phase-field simulations were analyzed. Typical domain structures as a result of anisotropic misfit strains are presented.

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered β phase from a disordered α matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of β phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = ϵ yy / ϵ xx , where ϵ xx and ϵ yy are the principal components of the misfit strain tensor. Our phase field simulations show that the morphology of β phase particles is significantly influenced by t, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit ( t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when −1 ⩽ t ⩽ 0. In the special case of a pure shear misfit strain ( t = −1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti–Al–Nb alloys.

A model for evolution of shape changing precipitates in multicomponent systems

Recently the authors introduced a concept of shape factors to extend an already established model for the growth and coarsening kinetics of spherical precipitates in multicomponent multiphase environments to needle- and disc-shaped geometries. The geometry of the precipitates is kept in the original version of the concept to be self-similar with a given fixed aspect ratio. In the present treatment, the aspect ratios of individual precipitates are treated as independent evolving parameters. The evolution equations of each precipitate, described by its effective radius, mean chemical composition and the aspect ratio, are derived by application of the thermodynamic extremal principle. The driving force for the evolution of the aspect ratio of the precipitate stems from the anisotropic misfit strain of the precipitate and from the orientation dependence of the interface energy. The model is used for the simulation of the precipitation of Ti 3AlN and Ti 2AlN in Ti–Al–0.5 at.% N matrix.

Anisotropic, non-uniform misfit strain in a thin film bonded on a plate substrate

Current methodologies used for the inference of thin film stresses through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to non-uniform stress and curvature states for the thin film subject to non-uniform, isotropic misfit strains. In this paper we study the same thin film/substrate system but subject to non-uniform, anisotropic misfit strains. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.

Anisotropic misfit strain relaxation in lattice mismatched InGaAs/GaAs heterostructures grown by MOVPE

The relaxation process in InGaAs/GaAs heterostructures with a small lattice mismatch (less than 1%), grown by metalorganic vapour-phase epitaxy (MOVPE), has been investigated by means of high-resolution X-ray diffraction (HR-XRD). Transmission electron microscopy (TEM) revealed a two-dimensional (2D) network of 60° misfit dislocations formed at the (0 0 1) interface in the two orthogonal 〈1 1 0〉 crystallographic directions. The structural analysis by X-ray diffractometry was performed with the samples oriented either in the [1¯ 1 0] or the [1 1 0] perpendicular directions, using reciprocal lattice mapping. The observed anisotropic-strain relaxation, related to the asymmetry in the formation of α and β misfit dislocations along [1¯ 1 0] and [1 1 0] directions, respectively, causes distortion of the epilayer unit cell and lowers its symmetry to orthorhombic.

Anisotropic, non-uniform misfit strain in a thin film bonded on a plate substrate

Current methodologies used for the inference of thin film stresses through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to non-uniform stress and curvature states for the thin film subject to non-uniform, isotropic misfit strains. In this paper we study the same thin film/substrate system but subject to non-uniform, anisotropic misfit strains. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.

Phase diagram and dielectric behavior of Ba0.6Sr0.4TiO3 thin films grown on orthorhombic substrates

Abstract Using Landau–Devonshire (LD)-type phenomenological model, we investigate the phase diagrams and dielectric behaviors of single-domain single-crystal Ba 0.6 Sr 0.4 TiO 3 films deposited on orthorhombic substrates. An anisotropic strain factor is introduced to quantitatively calculate the effects of anisotropic in-plane misfit strains. Investigation indicates that anisotropic strains play a crucial role on formation of stable ferroelectric phases and dielectric properties. The anisotropic strains induce tetragonal phases which only contain one in-plane spontaneous polarization component. These phases do not exist in BST films of the same composition under isotropic strains. Moreover, permittivity and tunability of films can reach to maximum when the corresponding spontaneous polarization component disappears at the boundaries of structural phase transition.

Dielectric and pyroelectric properties of barium strontium titanate films on orthorhombic substrates with (110)//(100) epitaxy

The role of anisotropic misfit strains on the spontaneous polarization, dielectric properties, and pyroelectric response of (110) oriented Ba0.6Sr0.4TiO3 (BST 60/40) thin films on (100) orthorhombic substrates is analyzed theoretically. The anisotropic in-plane strain state and the rotation of the elastic and the electrostrictive constants of the BST 60/40 films result in strongly directional and unique properties, different from BST 60/40 films on cubic substrates with (100)BST//(100)substrate epitaxy. The thermodynamic formalism also incorporates the thickness dependence of the internal stress state due to the anisotropic relaxation of epitaxial stresses through the formation of misfit dislocations along the two in-plane directions. In particular, the model is applied to (110) BST 60/40 ferroelectric films on (100) NdGaO3 orthorhombic substrates. A more generalized analysis treating the in-plane misfit strains as parameters shows that ferroelectric phases that cannot be observed in single-crystal perovskite ferroelectrics can be stabilized due to the reduction in the symmetry induced by the anisotropic strain state.

Anisotropic in-plane misfit strains dependence of phase diagrams and dielectric behavior in epitaxial Pb(Zr1−xTix)O3 thin films

Abstract A phenomenological Landau–Devonshire thermodynamic theory is used to describe the effects of anisotropic in-plane misfit strains on equilibrium polarization states and dielectric properties of single domain epitaxial Pb(Zr1−xTix)O3 thin films grown on dissimilar orthorhombic substrates. Compared with the “isotropic in-plane misfit strains-temperature” phase diagrams, the characteristic features of “misfit strain-misfit strain” and “misfit strain-temperature” phase diagrams under the circumstance of strain anisotropy are the presence of four different phases ( a ′ , a ″ , a ′ c , and a ″ c ) and the direct 90° polarization switching between c phase and a ′ phase (or a ″ phase), between a ′ phase and a ″ phase. The misfit strain dependence of polarization components, the small-signal dielectric responses and the tunabilities at room temperature are also calculated. We find that the phase diagrams and dielectric properties largely depend on anisotropic in-plane misfit strains as well. Moreover, the strain anisotropy will lead to the polarization and dielectric anisotropy.

Effects of external mechanical loading on phase diagrams and dielectric properties in epitaxial ferroelectric thin films with anisotropic in-plane misfit strains

A phenomenological Landau-Devonshine theory is used to describe the effects of external mechanical loading on equilibrium polarization states and dielectric properties in epitaxial ferroelectric thin films grown on dissimilar orthorhombic substrates which induce anisotropic misfit strains in the film plane. The calculation focuses on single-domain perovskite BaTiO3 and PbTiO3 thin films on the assumption that um1=−um2. Compared with the phase diagrams without external loading, the characteristic features of “misfit strain-misfit strain” phase diagrams at room temperature are the presence of paraelectric phase and the strain-induced ferroelectric to paraelectric phase transition. Due to the external loading, the “misfit strain-stress” and “stress-temperature” phase diagrams also have drastic changes, especially for the vanishing of paraelectric phase in “misfit strain-stress” phase map and the appearance of possible ferroelectric phases. We also investigate the dielectric properties and the tunability of both BaTiO3 and PbTiO3 thin films. We find that the external stress dependence of phase diagrams and dielectric properties largely depends on strain anisotropy as well.

Effects of anisotropic in-plane strains on the phase diagram of BaxSr1−xTiO3 thin film

Based on the Landau-Devonshire phenomenological theory, phase diagram of epitaxial BST50∕50 thin films on anisotropic in-plane strains is investigated. Different from BaTiO3 thin films, the paraelectric phase appears under the anisotropic misfit strains on barium strontium titanate (BST)50∕50 thin films at room temperature. The pyroelectric property of the BST films is also calculated. We find that the position of pyroelectric peak greatly depends on anisotropic misfit strains.

Effect of external stress on phase diagrams and dielectric properties of epitaxial ferroelectric thin films grown on orthorhombic substrates

A Landau-Ginsburg-Devonshire(LD)-type thermodynamic theory was used to describe the effect of external stress on phase diagrams and dielectric properties of epitaxial ferroelectric thin films grown on orthorhombic substrates which induce nonequally biaxial misfit strains in the films plane. The “misfit strain-external stress” and “external stress-temperature” phase diagrams were constructed for single-domain BaTiO 3(BT) and PbTiO 3(PT) thin films. It is shown that the external stress may lead to the rotation of the spontaneous polarization and a gradual change of its magnitude, which may result in phase transition. Nonequally biaxial misfit strains dependence of the stability of polarization states may be governed by external stress. At room temperature, stress-induced ferroelectric/paraelectric phase transition which occurs in film on cubic substrate does not take place in the ferroelectric thin film grown on orthorhombic substrate. It is also shown that the nonequally misfit strains in the film plane may lead to the appearance of new phases which do not form in films grown on cubic substrates under external stress. The dependence of the dielectric response on the external stress is also studied. It is shown that the dielectric constants of single-domain PT and BT films are very sensitive to the external stress under the given anisotropic misfit strains-temperature conditions. It presents theoretical evidence that the external stress and anisotropic misfit strains can be employed for improving the thin films physical properties.

Equilibrium shapes of strained islands with non-zero contact angles

The equilibrium morphology of a strained island on an elastic substrate is determined. The island is assumed to partially wet the substrate (Volmer–Weber growth) and thus makes a non-zero contact angle with the surface. Both isotropic and anisotropic misfit strain are allowed. Two- and three-dimensional equilibrium island shapes are determined by using expressions for the elastic strain energy in the small-slope approximation. In this limit, the problem can be reduced to a singular integral-differential equation for the island thickness. We find that when there is a non-zero contact angle, all island shapes, for a given ratio of the elastic stress to surface energy, attain a form that is independent of the specific contact angle under an appropriate scaling. We show that for islands with non-zero contact angles, as the island volume increases, the shape approaches the geometry of a completely wetting island. But when the volume decreases, these islands approach a point while islands with a zero contact angle, approach a finite length line segment of zero volume. Multiple-hump equilibrium shapes are found. Single-humped islands are shown to have a lower chemical potential than multiple-humped islands, implying that they are the most stable. This conclusion is shown to be consistent with a stability analysis of the two-dimensional case. The effects of a tetragonal misfit strain on the three-dimensional island shape is investigated.

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&amp;gt;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&amp;lt;200. The films with 10&amp;lt;h&amp;lt;25nm are of monoclinic symmetry due to a finite principal shear stress along [110] of the initial orthorhombic cell.

Dielectric behavior of ferroelectric thin films grown on orthorhombic substrates

Using Landau–Devonshire (LD)-type phenomenological model, we investigate the dielectric behaviors of single-domain PT thin films grown on orthorhombic substrates. Effects of in-plane misfit strains and external electric fields are combined on dielectric properties. In our calculation of permittivities, we take account of the susceptibility matrix. Basing on the assumption that in-plane misfit strains u m 1 = − u m 2 , we find that in-plane permittivities ε 11 and ε 22 are symmetrical about the line where in-plane misfit strains are zero. Same is out-plane permittivity ε 33 . Anisotropic in-plane misfit strains result in anomalies of permittivities at boundaries of phase transitions. Further calculation reveals that dielectric tunability reach to maximums at boundaries of phase transitions where the same direction polarization component appears or disappears. So the permittivities and tunabilities can be chosen to satisfy different demands by controlling applied fields and changing in-plane misfit strains.

Misfit strain anisotropy in partially relaxed lattice-mismatched InGaAs/GaAsheterostructures

Partially relaxed InGaAs/GaAs heterostructures with a small lattice mismatch have beenstudied by means of atomic force microscopy and high-resolution x-ray diffractometry.Additionally, electron-beam induced current in a scanning electron microscopeand transmission electron microscopy have been employed to investigate misfitdislocations formed at the (001) heterostructure interface. The measurementsrevealed a direct correlation between the surface cross-hatched morphology and thearrangement of interfacial misfit dislocations. The reciprocal lattice mapping and therocking curve techniques employed for the samples aligned with either the or the [110] crystallographic direction perpendicular to the diffractionplane revealed anisotropic misfit strain relaxation of the InGaAs layers.This anisotropy results from an asymmetry in the formation of theα and β types of misfit dislocations oriented along the and [110] directions, respectively, which differ in their core structures. The misfit strainanisotropy causes a distortion of the unit cell of the layer and lowers its symmetry toorthorhombic.

D(A) steps and 2D islands of double layer height in the SiGe(001) system

The surfaces of step graded, partially relaxed Si(1-x)Ge(x)/Si(001) buffers were studied by scanning tunneling microscopy. The surface slips along <110> forming the crosshatch pattern, consisting of bunches of D(A) steps of double layer height. The D(A) steps are present in regions of large surface gradients close to the slips, as well as in planar regions between the slips. These regions are also characterized by the appearance of 2D islands of double layer height. The observations can be explained by assuming the strain due to the misfit dislocations to be locally anisotropic. Anisotropic misfit strain and efficient strain relaxation by the ( 2x8) Ge reconstruction were identified as the main factors causing the unusual step structure.