Misfit Strain Relaxation Research Articles

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.

Strain Relief in Cu-Pd Heteroepitaxy

We present experimental and theoretical studies of Pd/Cu(100) and Cu/Pd(100) heterostructures in order to explore their structure and misfit strain relaxation. Ultrathin Pd and Cu films are grown by pulsed laser deposition at room temperature. For Pd/Cu, compressive strain is released by networks of misfit dislocations running in the [100] and [010] directions, which appear after a few monolayers (ML) already. In striking contrast, for Cu/Pd the tensile overlayer remains coherent up to about 9 ML, after which multilayer growth occurs. The strong asymmetry between tensile and compressive cases is in contradiction with continuum elasticity theory and is also evident in the structural parameters of the strained films. Molecular dynamics calculations based on classical many-body potentials confirm the pronounced tensile-compressive asymmetry and are in good agreement with the experimental data.

The evolution of the structure of quantum size effect Pb nanocrystals on Si(1 1 1) 7×7

We have carried out diffuse X-ray scattering measurements of the growth of Pb nanocrystalline islands on Si(1 1 1). Analysis of our data shows that islands growing on an initially rough wetting layer transforms the portion of the wetting layer below them into ordered fcc sites. Therefore, the islands grow directly on top of the Si surface with a disordered wetting layer occupying the region between the islands and, consequently, the island height responsible for the quantum well depth is one layer thicker than reported by LEED and STM. These islands have an extremely good vertical order until the islands coalesce into a closed film. At that point the disorder of the film increases consistent with misfit strain relaxation.

Influence of Ge concentration and compressive biaxial stress on interdiffusion in Si-rich SiGe alloy heterostructures

The Si–Ge interdiffusivity in SiGe alloys grown epitaxially on Si (100) substrates was systematically measured for Ge concentrations between 0.075 and 0.192 over a temperature range of 770–870°C. For several alloy compositions, interdiffusion kinetics were compared between films with nominally identical Ge concentration profiles, but different degrees of misfit strain relaxation. X-ray diffraction measurements of the decay rate of small, periodic, modulations in composition superimposed onto the average background alloy fraction were used to determine interdiffusivity values. The interdiffusion rate was found to increase by about a factor of 2 over the concentration range studied. The measured activation enthalpy for interdiffusion decreased linearly with Ge concentration by 4.05±0.25eV∕unit Ge atomic fraction. The prefactor for interdiffusion was proportional to exp(−35XGe). Extrapolating these trends to a Ge fraction of zero yielded a prefactor and activation enthalpy consistent with accepted values for Si and Ge tracer diffusion in pure Si. Furthermore, it was found that changes in the compressive biaxial misfit strain during postgrowth annealing of these heterostructures yielded no detectable change in measured interdiffusion rates. These results were incorporated into an interdiffusion model that successfully predicted experimental results derived from a large composition-amplitude Si∕Si0.78Ge0.22 superlattice and from intermixing at the interfaces between Si capping layers and both Si0.9Ge0.1 and Si0.78Ge0.22 blanket films.

Wetting-layer transformation for Pb nanocrystals grown on Si(111)

We present the results of in situ x-ray scattering experiments that investigate the growth of Pb nanocrystalline islands on Si(111). It is conclusively shown that the Pb nanocrystals do not reside on top of a Pb wetting layer. The nucleating Pb nanocrystals transform the highly disordered Pb wetting layer beneath the islands into well-ordered fcc Pb. The surface then consists of fcc Pb islands directly on top of the Si surface with the disordered wetting layer occupying the region between the islands. As the Pb nanocrystals coalesce at higher coverage we observe increasing disorder that is consistent with misfit strain relaxation. These results have important implications for predicting stable Pb island heights.

Effect of lattice-misfit strain on the process-induced imprint behavior in epitaxial Pb(Zr0.52Ti0.48)O3 thin films

The effect of lattice-misfit strain on the process-induced imprint behavior in Pb(Zr0.52Ti0.48)O3 (PZT) capacitors with Pt (top), and SrRuO3, La0.7Sr0.3MnO3 or LaNiO3 (bottom) electrodes has been studied. With the different oxide electrodes and by changing the deposition oxygen pressure, various lattice-misfit strains in the epitaxial PZT films have been produced. It was found that after in situ annealing at reduced oxygen pressures, the capacitors showed an increased voltage offset in the polarization-electric field hysteresis loops with increasing the misfit strain, irrelevant to the oxide electrodes employed, while lattice disorder at the bottom interface can effectively eliminate the voltage shift. Our results suggest that the imprint behavior is caused by oxygen loss via dislocations generated by the misfit strain relaxation at the growth temperature.

Integration of MgO on Si(001) Using SrO and SrTiO3 Buffer Layers by Molecular Beam Epitaxy

Epitaxial MgO was deposited onto Si(001) substrates by molecular beam epitaxy using elemental metallic sources and molecular oxygen at temperatures from 150 to 400∘C. To facilitate epitaxy through misfit strain relaxation, epitaxial MgO layers were grown on SrO and SrTiO3 buffer layers deposited on Si(001) substrates. The structure of the epitaxial layers was determined by X-ray diffraction, reflection high-energy electron diffraction and transmission electron microscopy. The observed orientation for the MgO/SrO/Si multilayer is cube-on-cube. The X-ray rocking curve full width half maximum of the MgO on SrO buffer layers was 2.2∘. SrTiO3 buffer layers grown by recrystallization were epitaxial and exhibited improved morphology relative to those grown at a fixed growth temperature. X-ray analysis of a 5.2 nm recrystallized SrTiO3 film indicates a fully relaxed and phase pure film. The observed orientation of MgO using SrTiO3 buffer layers is MgO[100]‖SrTiO3[100]‖Si[110].

Misfit strain relaxation by dislocations in SrRuO3/SrTiO3 (001) heteroepitaxy

Misfit relaxation by dislocations in perovskite SrRuO3/SrTiO3 (001) heterostructure with low lattice mismatch (f=0.64%) was studied. Pure edge misfit dislocations (MDs) with a Burgers vector of the a〈011〉 type were found to be the major interfacial defects responsible for the misfit relief. They were introduced by half-loops expansion from the film surface as well as by extension of pre-existing dislocations in the substrate. These 45°-MDs formed along the 〈100〉 directions in a rectangular grid pattern, preferentially at surface steps of the TiO2-terminated SrTiO3 (STO) substrate. At film thicknesses much higher than the critical film thickness (hc), however, the MD spacing was not reduced but saturated in a nearly constant value far above the equilibrium prediction (∼61.4 nm). The saturated spacing of MDs corresponds to roughly the ledge distances on the STO surface (120–150 nm). It is suggested that difficulties in the multiplication of MDs by the already-formed ones lead to the abnormally high residual strain. Further accumulation of residual strain results in microstructural modifications such as surface undulations and the two-layered structure along the growth direction.

Oxygen-dosage effect on the structure and composition of ultrathin NiO layers reactively grown on Ag(001)

NiO ultrathin films have been prepared under UHV conditions on Ag(001) substrate by metal deposition in ${\mathrm{O}}_{2}$ atmosphere. The films were prepared by deposition of the amount of metal correspondent to 1 ML (monolayer) of NiO in the presence of different oxygen-to-metal flux ratios, to investigate the oxygen dosage effect on the structure and composition of the growing layer and on the stoichiometry of Ni oxide. Thicker films (up to 20 ML) were also prepared. The structure has been monitored both in reciprocal and direct space by low-energy electron diffraction and primary-beam diffraction-modulated electron emission. Core-level x-ray photoemission spectroscopy has been used to study film chemistry and composition. At low coverage (below 2 ML) a dramatic dependence of structure and composition on the oxygen-to-nickel flux ratio has been observed. Low oxygen dosage induces a $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstruction in the 1-ML films that evolves to a $(1\ifmmode\times\else\texttimes\fi{}1)$ phase as the dosage and/or the film thickness increases. In the layers prepared at low oxygen dosage a large fraction of metallic Ni coexists with the Ni oxide, but the oxidized fraction largely prevails for high oxygen dosage. The oxygen dosage during the growth also affects thicker films. The mosaic formation, which has been ascribed to misfit strain relaxation, is related to a low oxygen-to-nickel flux ratio.

Revealing of threading and misfit dislocations in partially relaxed InGaAs/GaAs heterostructures

Both threading and misfit dislocations in partially relaxed InGaAs/GaAs heterostructures with a small lattice-mismatch have been investigated by means of chemical etching and atomic force microscopy (AFM). An anisotropic etching in HF–H2SO4–H2O2 based aqueous solution was successfully used to determine the polarity of the crystallographic surfaces and an ultrasonic-vibration aided etching in CrO3–HF–H2O based solution was employed to reveal threading dislocations on the heterostructure surfaces. AFM measurements of surface morphology of the structures revealed a well-resolved cross-hatch pattern, which reproduced the network of underlying misfit dislocations, and, in addition, the outcrops of threading dislocations on the surface in a form of characteristic craters. Analysis of the results allowed drawing a conclusion on the mechanism of misfit strain relaxation in the investigated heterostructures. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

Microstructure and electronic properties of InGaN alloys

AbstractThe InxGa1−xN system has electronic band gaps extending from under 1eV to 3.4 eV, and as such they are used as the active layer in commercially available visible‐light emitting devices. There are many interesting features that make these nitride semiconductor alloys especially useful for efficient light emitters. It has been conjectured that the combination of piezoelectric fields and local composition inhomogeneities may be responsible for the observed high emission efficiencies, in spite of their characteristic high dislocation densities. But it is very difficult to grow InxGa1−xN layers with high indium composition. This paper presents an overview of the properties of InxGa1−xN epilayers based on a systematic study of thick layers and of quantum well structures. We find that the microstructure of thick films varies significantly with indium composition. For x < 0.08, the composition is uniform and unperturbed by dislocations. For 0.10 < x < 0.20, secondary phases nucleate at threading dislocations. For x > 0.20, spontaneous phase separation occurs resulting in a polycrystalline, inhomogeneous layer. A correlation between optical properties and microstructure is presented. It is observed that the misfit strain is affected by threading dislocations. Mechanisms of misfit strain relaxation are presented for InxGa1−xN layers grown on standard GaN on sapphire and on epitaxial‐lateral‐overgrowth GaN layers. In addition, we have studied the properties of quantum well structures using several novel techniques. The electrostatic fields across the wells have been profiled using electron holography in the TEM. The effect of well thickness on the strength of the fields is reported. The effects of localization by compositional fluctuations and of internal field screening have been studied using time‐resolved cathodoluminescence spectroscopy. In spite of significant progress that has been made in the last ten years, much work remains ahead in order to master the science and technology of these alloys. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Structural and Compositional Evolution of Self-Assembled Germanium Islands on Silicon (001) During High Growth Rate LPCVD

AbstractUnderstanding the process of self-organization of Ge nanostructures on Si with controlled size distribution is a key requirement for their application to devices. In this study, we investigate the temporal evolution of self-assembled islands during the low pressure chemical vapour deposition (LPCVD) of Ge on Si at 650°C using high growth rates (6–9 nm/min). The islands were characterized by atomic force microscopy, transmission electron microscopy, Rutherford backscattering spectrometry and micro-Raman spectroscopy. We found that the first nanostructures to assemble were small islands, with a narrow size distribution, typical of the ‘lens-shaped’ structures reported in previous studies. Next to form were a population of larger ‘lens-shaped’ islands with a similar surface density to that of the small islands, but with broad height and width distributions. These islands differ from the pyramid-shaped islands previously reported for a similar size range. On further Ge deposition, the population evolves into one of large square-based truncated pyramids with a very narrow size distribution. Such pyramidal structures were previously reported at smaller sizes. Furthermore, we see no evidence of the multifaceted domes previously reported in this size range. The small ‘lens-shaped’ islands appear to be strained, whilst some of the intermediate-sized islands and all the large truncated pyramids contain misfit strain relaxation induced defects. Additionally, in the both the intermediate size ‘lens-shaped’ islands and in the large size truncated pyramidal islands, there is evidence of Si-Ge strain-induced alloying, more significant in the first than in the latter. Our observation of ‘lens shaped’ islands and truncated pyramids at larger sizes than are normally observed, suggests a kinetically driven process that delays the evolution of energetically favourable island structures until larger island sizes are reached.

Mechanisms of misfit strain relaxation in epitaxially grown BLT (Bi4-xLaxTi3O12, x = 0.75) thin films

AbstractMechanisms of misfit strain relaxation in epitaxially grown Bi4-xLaxTi3O12 (BLT) thin films deposited on SrTiO3 (STO) and LaAlO3 (LAO) substrates have been investigated by means of transmission electron microscopy (TEM). The misfit strain of 20 nm thick BLT films grown on STO substrate was relaxed by forming misfit dislocations at the interface. However, cracks were observed in 100 nm thick BLT films grown on the same STO. It was confirmed that cracks were formed because of high misfit strain accumulated with increasing the thickness of BLT, that was not sufficiently relaxed by misfit dislocations. In the case of the BLT film grown on LAO substrate, the magnitude of lattice misfit between BLT and LAO was very small (~1/10) in comparison with the case of the BLT grown on STO. The relatively small misfit strain formed in layered structure of the BLT films on LAO, therefore, was easily relaxed by distorting the film, rather than forming misfit dislocations or cracks, resulting in misorientation regions in the BLT film.

Structural characterization and 90° domain contribution to ferroelectricity of epitaxial Pb(Zr0.35,Ti0.65)O3 thin films

Remanent polarizations (Pr) of 200-nm-thick epitaxial Pb(Zr0.35,Ti0.65)O3 (PZT) thin films deposited on (001), (110), and (111) SrTiO3 (STO) substrates coated with SrRuO3 (SRO) were compared to the domain configurations that were precisely and quantitatively characterized by high-resolution x-ray diffraction reciprocal space mapping (HRXRD-RSM). (001)/(100), (101)/(110), and (111) oriented domains were obtained for films grown on (001), (110), and (111) STO substrates coated with SRO, respectively. HRXRD-RSM showed that the films grown on (001) and (110) STO substrates mainly consisted of (001) and (101) domains, although they also included about 32% and 25% of (100) and (110) domain, respectively. Tilt growths in the domains were found except for the (001) domain. The tilt growths in the (100), (101), and (110) domains were attributed to the geometrically induced tilt by the 90° domain that had {101} domain walls. On the other hand, the tilt in the (111) domain was attributed to the misfit strain relaxation by introducing tilt growth in the domain but not due to the 90° domain. The Pr ratios of films having different domain configurations were well explained by the estimated Pr ratios from the volume fractions of the domains, based on the assumption that the 90° domain was not reoriented by the externally applied electrical field and did not contribute to the measured Pr values. This indicates that the 90° domain is strongly pinned in epitaxial 200-nm-thick PZT films and the 180° domain switching is the dominant contribution to the total remanent polarization.

Migration of Dislocations in Strained GaN Heteroepitaxial Layers

Transmission electron microscopy has been used to study the relaxation of misfit strains in GaN/Al0.28Ga0.72N layers grown on (0001) sapphire. It has been observed that threading edge-type dislocations migrate laterally in the top GaN layer to form misfit dislocations. This leads to reactions with other threading dislocations, to generate either closed loops or more complex nodes, which reduce the total threading dislocation density. The proportion of edge-type dislocations compared to screw-type and mixed dislocations is reduced with increasing GaN thickness. It is proposed that the lateral migration of the dislocations is predominantly by a climb rather than a glide mechanism.

Microstructure of duplex-phase NbSi 2(C40)/MoSi 2(C11 b) crystals containing a single set of lamellae

Microstructures of duplex-phase C40/C11 b silicides from combinations of NbSi 2, VSi 2 or TiSi 2 with MoSi 2 were investigated focusing on formation and alignment of lamellae. The lamellar structure was formed by zone melting and subsequent appropriate heat treatment for all combinations, but oriented lamellae were obtained only in NbSi 2/MoSi 2 duplex crystals. The oriented lamellar structure satisfied the crystallographic relationship of (0001) C40//(110) C11b, < 1 ̄ 2 1 ̄ 0 ] C40//[1 1 ̄ 0] C11b and <10 1 ̄ 0] C40//[001] C11b, resulting in formation of three variants of the C11 b phase and two kinds of boundary: a type of C11 b/C11 b grain boundary and a type of C11 b/C40 phase boundary. Further annealing induced coarsening of both phases and changed the crystallographic relation due to relaxation of misfit strain at boundaries.

Voltage shift phenomena in a heteroepitaxial BaTiO3 thin film capacitor

Voltage shift phenomena of the hysteresis loop were characterized for a c-axis oriented heteroepitaxial BaTiO3 film by means of switching current measurements using various types of pulse sequences. During application of voltage, the hysteresis loop gradually shifted along the voltage axis according to the polarity of the voltage. Even after the application of voltage, while the top and bottom electrodes were short-circuited, the hysteresis loop continued to move. Under certain conditions, a part of the hysteresis loop shifted back, whereas the rest shifted forward. These results were explained, assuming that there is a nonswitching layer between the ferroelectric layer and the bottom electrode, and that the discontinuity of polarization can be compensated by injection of negative charges from the electrode. It was suggested that the nonswitching layer is possibly formed by relaxation of lattice misfit strain in the heteroepitaxial ferroelectric thin film.

Atomistic simulation study of misfit strain relaxation mechanisms in heteroepitaxial islands

ABSTRACTThe mechanisms of the misfit strain relaxation in heteroepitaxial islands are investigated in two-dimensional molecular dynamics simulations. Stress distributions are analyzed for coherent and dislocated islands. Thermally-activated nucleation of misfit dislocations upon annealing at an elevated temperature and their motion from the edges of the islands towards the positions corresponding to the maximum strain relief is observed and related to the corresponding decrease of the total strain energy of the system. Differences between the predictions of the energy balance and force balance criteria for the appearance of misfit dislocations is discussed. Simulations of an island located at different distances form the edge of a mesa indicate that the energy of the system decreases sharply as the island position shifts toward the edge. These results suggest that there may be a region near the edge of a mesa where nucleation and growth of ordered arrays of islands is favored.

Ferroelectric Domain Structures in Epitaxial PZT Thin Films: A Review

Heteroepitaxial growth of thin films of non-cubic ferroelectric materials on cubic single crystal substrates inevitably accompanies twin domain formation. Since the presence of twin domains strongly affects on the ferroelectric properties, studies on the twinning phenomena are crucial for controlling their properties. Ferroelectric twin-domain formation in epitaxial Pb(Zr,Ti)O 3 thin films has been investigated by changing several processing parameters such as film composition, substrate selection, and film thickness in order to determine the crucial stain factors controlling final domain structures. In order to investigate the effect of transformation strains involved in the phase transition at and below the Curie temperature, epitaxial (Pb 1 m x La x )(Zr y Ti 1 m y )O 3 thin films grown on MgO(001) have been examined as a function of composition, x and y, and temperature. The effect of misfit strain and its relaxation during film fabrication on the final domain structures of epitaxial PbTiO 3 was studied by changing cubic substrates including MgO(001), SrTiO 3 (001), and KTaO 3 (001). In particular, considering thermodynamic equilibrium relief of coherency strain at the initial growth stage based on the Mattews-Blakeslee criteria, effect of film thickness on domain formation was analyzed for the epitaxial PbTiO 3 thin films grown on MgO(001) substrates, and the correlation of final domain structures with the degree of misfit strain relaxation by dislocation generation was established. Finally, evolution of equilibrium domain structures in epitaxial PZT thin films was simulated successfully by the finite element method employing a commercial package, ABAQUS, and the strains un-relaxed during film fabrication could be reasonably estimated.