Anisotropic In-plane Strain Research Articles

Domain stability of PbTiO3 thin films under anisotropic misfit strains: Phase-field simulations

The domain stability and domain structures of (001)-oriented PbTiO3 ferroelectric thin films subject to anisotropic in-plane strains were studied using phase-field method. Based on the simulation results, a room temperature domain/phase stability diagram was constructed for PbTiO3 thin films with the in-plane strains ranging from −5% to 5%. The predicted diagram is both quantitatively and qualitatively different from those obtained using thermodynamic calculations based on a single-domain assumption.

Optical polarization properties of interband transitions in strained group-III-nitride alloy films on GaN substrates with nonpolar orientation

The authors present results of a perturbation theory study of the combined effects of composition and anisotropic in-plane strain on the optical polarization properties of the three interband transitions in the vicinity of the fundamental energy gap of wurtzite group-III-nitride alloy films, pseudomorphically grown on GaN substrates with nonpolar orientation such as M-plane GaN(11¯00). Valence band mixing induced by the anisotropic in-plane strain is shown to have a dramatic influence on the optical polarization properties. The results indicate that an increased efficiency of light emission in the visible spectral range can be achieved with compressively strained InxGa1−xN active layers. While AlxGa1−xN layers under tensile strain will exhibit a very poor light emission efficiency in the ultraviolet (UV) spectral range, efficient emission in the UV range can instead be achieved with InxAl1−xN films. These results also hold for alloy films on A-plane GaN(112¯0) substrates.

In-plane anisotropic strain in a-ZnO films grown on r-sapphire substrates

We deposited (112¯0) nonpolar a-plane ZnO (a-ZnO) films on (011¯2) r-sapphire substrates using metalorganic chemical vapor deposition. Unit cell deformation due to interfacial strain in films was determined by triple-axis x-ray diffraction. Due to low symmetry of a-plane, anisotropic strain is observed along the [0001] (c-axis) and [11¯00] (m-axis) in-plane axes. Out-of-plane strain along [112¯0] (a-axis) is tensile and relaxes for film thickness ⩾2μm. The in-plane m-axis is under tensile strain and c-axis is under compressive strain. Increase in film thickness increases in-plane strain anisotropy due to faster relaxation along the m-axis. Thermal and lattice mismatch strains are separated by curve fitting.

Polarization rotation transitions in anisotropically strained SrTiO3 thin films

Commensurately strained epitaxial SrTiO3 thin films on a GdScO3 substrate with anisotropic in-plane tensile strains of 1.46% and 1.59% were grown. By using optical second harmonic generation and polarization measurements, a ferroelectric transition from a tetragonal 4∕mmm phase to a ferroelectric mm2 phase at ∼400K and an antiferrodistortive transition to a multiferroic phase at 150–175K are observed, which are in agreement with thermodynamic calculations. In addition, a series of polarization rotation transitions between ⟨100⟩p to ⟨l00⟩p (0<l<1) is observed in the 4–400K temperature range.

Tuning in-plane magnetic anisotropy in (110) La2∕3Ca1∕3MnO3 films by anisotropic strain relaxation

We have investigated structural and functional properties of (110) La2∕3Ca1∕3MnO3 films grown on (110) SrTiO3 substrates. We have observed that there is an anisotropic in-plane lattice strain relaxation with faster relaxation along the [1−10] direction than along the [001] one, which leads to an anisotropic in-plane stress that evolves gradually with film thickness. The resultant anisotropy of the magnetoelastic energy imposes the [001] direction to be the in-plane magnetic easy axis and the strength of the in-plane magnetic anisotropy can be tuned by varying film thickness.

Polarization-Controlled Surface Grating VCSELs Under Externally Induced Anisotropic Strain

The polarization control of surface grating vertical-cavity surface-emitting lasers (VCSELs) is tested under externally applied anisotropic stress and is compared to that of a nominally identical standard VCSEL without a surface grating. This is done by bending the VCSEL chip in a well-defined way. The anisotropic in-plane strain thus induced in the VCSELs leads to a polarization switch of the standard VCSEL for rather moderate strain. In contrast, the polarization of the surface grating VCSELs is fixed by the grating and remains unchanged despite a high strain which causes a wavelength splitting of the two polarization modes of about 130 pm. Such a result is of high practical relevance, since strain is unavoidably induced during VCSEL fabrication and mounting and counteracts any method applied for polarization control.

Valence-band mixing in neutral, charged, and Mn-doped self-assembled quantum dots

We analyze the optical emission of single II-VI quantum dots containing 0 or 1 magnetic atom (manganese) and a controlled number of carriers (0, $\ifmmode\pm\else\textpm\fi{}1$ electron). The emission of these quantum dots presents a large degree of linear polarization. This linear polarization is attributed to a valence-band mixing and we show that in nonmagnetic quantum dots combining both a shape anisotropy and an anisotropic in-plane strain distribution, the linear polarization direction of the exciton are controlled by an interplay between valence-band mixing and electron-hole (e-h) exchange interaction. Similarly, under strong transverse magnetic field, the direction of the linearly polarized emission of the charged excitons is simultaneously controlled by the valence-band mixing and the direction of the magnetic field. In quantum dots containing a Mn atom, the valence-band mixing allows simultaneous hole-Mn spin flips coupling bright and dark excitons. These spin flips are responsible for linearly polarized transitions in the emission of the charged excitons at zero magnetic field.

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.

Material and optical properties of Trenched Epitaxial Lateral Overgrowth of a ‐plane GaN

The crystal quality of a-plane GaN film was successfully improved by using trenched epitaxial lateral overgrowth (TELOG) of a-plane GaN. Not only the threading dislocation density but also the difference of anisotropic in-plane strain between orthogonal crystal axes can be mitigated by using TELOG. The low threading dislocation density investigated by transmission electron microscopy was estimated to be 3×107 cm–2 on the N-face GaN wing. According the results of μ-PL and CL, the threading dislocations are the strongly non-radiative center in a-plane GaN film. Finally, we concluded that a narrower stripped GaN seeds and deeper stripped trenches etched into the surface of sapphire could derive a better quality a-plane GaN film. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Optical Anisotropic Properties of m-Plane GaN Film Grown by Metalorganic Chemical Vapor Deposition

Spontaneous and piezoelectric polarization could lower the efficiency of GaN-based light-emitting diodes. In order to eliminate or reduce this undesirable effect, m-plane GaN film was prepared by metalorganic chemical vapor deposition (MOCVD) on LiAlO 2(100) substrate with a GaN buffer layer. Since the c axis of the m-plane GaN lays in the grown plane, the breakage of in-plane symmetry gave rise to an optical anisotropy, which was revealed by a difference in refractive indexes of E-field parallel and perpendicular to the c axis of the m-plane GaN measured by polarized reflection measurement. In addition, in-plane strain anisotropy due to the lattice mismatch between the GaN film and the LiAlO 2 substrate changed the Electronic Band Structure (EBS). The change of EBS also led to an in-plane optical anisotropy. Polarized absorption and Photoluminescence (PL) measurements showed a split in energy of 32 meV for optical absorption edge and 37 meV for PL peak energy respectively.

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.

Intrinsic photoluminescence of M-plane GaN films on LiAlO2 substrates

Polarized photoluminescence spectra of M-plane GaN films grown on LiAlO2 substrates demonstrate the existence of a large polarization anisotropy in the near-band-gap excitonic transitions, which is consistent with the reduction of the in-plane crystal symmetry and the anisotropic strain generated by the lattice mismatch between GaN and LiAlO2. Band structure calculations based on the k∙p formalism support the observed experimental results and allow us to explain the temperature dependence of the photoluminescence energy. From the results of these calculations and the measured excitonic transition energies, we accurately determined the in-plane strain. The strain relaxation as a function of temperature and the role of the film thickness in the in-plane strain anisotropy are also discussed.

Very narrow-band ultraviolet photodetection based on strained M-plane GaN films

The authors demonstrate a photodetection configuration where the responsivity in the ultraviolet spectral region is limited to a few nanometers, representing high-quality-factor, narrow-band detection together with polarization sensitivity. Both features are obtained by utilizing a polarization-sensitive photodectector in combination with a polarization filter made from two identical M-plane GaN films on γ-LiAlO2 (100) substrate. The optical band gap of these films depends on the direction of the in-plane polarization vector of the incident light beam with respect to the c axis. Electronic-band-structure calculations show that the naturally present anisotropic in-plane strain in these films is the crucial parameter to achieve both a high responsivity and a high polarization contrast.

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.

Impact of in-plane anisotropic strains on the dielectric and pyroelectric properties of Ba0.7Sr0.3TiO3 thin films

A modified Landau-Devonshire phenomenological thermodynamic theory is used to describe the influence of in-plane anisotropic strains on the dielectric and pyroelectric properties of epitaxial Ba0.7Sr0.3TiO3 thin films grown on dissimilar tetragonal substrates. The in-plane anisotropic strain factor-temperature phase diagram is developed. The in-plane anisotropic strains play a crucial role in the dielectric and pyroelectric properties of BST thin films. The theoretical maximum dielectric tunability approaching 100% can be attained at the critical anisotropic strain factor corresponding to the structural phase transformation from ca1 to a1 phase. Moreover, the anisotropic strain factor has an opposite effect on the figure of merit and pyroelectric coefficient, respectively. Furthermore, in the case of isotropic strains, our theoretical results are well consistent with the experimental results.

Fast time behavior of the polarization filtering in anisotropically strained M ‐plane GaN films

The dynamic behavior of the polarization filtering in M -plane GaN films is investigated by time-resolved pump-and-probe spectroscopy. The reduced in-plane crystal symmetry and the anisotropic in-plane strain in M -plane GaN films lead to different absorption coefficients along the two principle in-plane axes. The absorption can be selectively bleached by additional pumping with polarized light along one of these two axes. On an ultra-fast timescale, the resulting pump-and-probe transients are governed by two different processes, namely the relaxation dynamics of holes in the two uppermost valence bands and the coherent coupling artifact. The recovery of the absorption is analyzed using the time symmetry of the coherent artifact and a rate-equation model for carrier relaxation and redistribution in the valence bands. The analysis yields redistribution times below 1 ps and carrier recombination times of about 15 ps. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Trenched epitaxial lateral overgrowth of fast coalesced a-plane GaN with low dislocation density

The crystal quality of a-plane GaN films was improved by using epitaxial lateral overgrowth on trenched a-plane GaN buffer layers. Not only the threading dislocation density but also the difference of anisotropic in-plane strain between orthogonal crystal axes can be mitigated by using trenched epitaxial lateral overgrowth (TELOG). The low threading dislocation density investigated by the cross-sectional transmission electron microscopy was estimated to be 3×107cm−2 on the N-face GaN wing. On the other hand, the Ga-face GaN wing with a faster lateral overgrowth rate could be influenced by the thin GaN layer grown on the bottom of the trenches, resulting in higher dislocation density generated. As a result, the authors concluded that a narrower stripped GaN seeds and deeper stripped trenches etched into the surface of sapphire could derive a better quality a-plane GaN film. Finally, they demonstrated the fast coalescence process of TELOG GaN films below 10μm thick.

Depth-resolved X-ray determination of surface strain in free-standing films of HVPE-grown GaN and 71Ga NMR characterization

Free-standing GaN films grown by hydride vapor phase epitaxy (HVPE) on c-plane sapphire have been studied for in-plane anisotropic strain. Lattice parameters are obtained from high-resolution X-ray diffraction data and the film quality is determined by measuring the rocking curves and by 71Ga nuclear magnetic resonance (NMR). The in-plane strain was determined using grazing incidence X-ray diffraction and conventional X-ray measurements. It is found that the in-plane lattice parameter varies with depth and has estimated surface strain anisotropy of 4.0791×10-3 up to a thickness of 0.3 μm. The 71Ga NMR experiments reveal different degrees of inhomogeneity amongst the three samples. This is shown by the appearance of an additional broad central-transition peak shifted to higher frequency by a Knight shift from conduction electrons in sample regions having high carrier concentrations.