Relief Of Misfit Strain Research Articles

Origin of residual strain in heteroepitaxial films

Heterogeneous integration of diverse materials structures is critical to the scaling of electronic and photonic integrated circuits. For a model system of Ge-on-Si, we experimentally examine the roles of lattice misfit and thermal expansion misfit in determining the residual strain in as-grown and annealed heteroepitaxial films. We present data for Ge-on-Si growth from 400 to 730 °C followed by heat treatment from 500–900 °C. We show that strain fluctuations of 5.02% enable misfit dislocation formation, and we propose a comprehensive model for the conversion of compressive misfit strain to tensile elastic strain. The model is expressed in terms of three regimes: (1) misfit control for the low temperature growth regime at 400 °C; (2) point defect control via annealing in the point defect recovery regime at 500–650 °C; and (3) thermal expansion control for growth or anneal at T > 650 °C in the dislocation recovery regime. Growth from 400 to 730 °C exhibits near complete misfit strain relief by misfit dislocations leaving a consistent residual compressive strain of 0.09%. Growth at 400 °C followed by post growth heat treatment at 600 °C results in vertical threading dislocation density reduction via a point defect-mediated climb mechanism that gives minimal strain relief. Anneal above 650 °C promotes strain relief by dislocation glide. Temperature excursions at T > 730 °C followed by cooling to room temperature yield plastic strain in the Ge film that cannot be further relieved by thermal expansion misfit accommodation. Growth at 400–730 °C retains a residual compressive strain that represents the nucleation threshold for misfit dislocations.

Strain Relaxation of Self-nanostructured Solution Derived La0.7Sr0.3MnO3 Films

AbstractThe morphological and microstructural evolution associated with an exsolution driven self-nanostructuration process of La0.7Sr0.3MnO3 films, is investigated using scanning force microscopy, reciprocal space mapping and transmission electron microscopy. The focus is placed on the misfit strain relaxation mechanism. Surfaces with atomically flat terraces are already developed after 1hour at 1000 °C while first fingerprints of phase exsolution do not appear until 9-10 hours. X-ray diffraction reciprocal-space mapping reveals that 24 nm thick films remain strained during the whole microstructural evolution, while 12 hour annealed films undergo almost total plastic relaxation of the misfit strain at a thickness of 60 nm. Overall, these results point to a kinetic limitation of dislocation mechanisms. It is argued that chemical relaxation provides a significant contribution to misfit strain relief.

Interplay between misfit strain relief and Stranski–Krastanov growth in fcc (111)/bcc (110) ultrathin film epitaxy: Part 2. Quantification using embedded atom method potentials

The main objective of this investigation has been to study the influence of misfit strain (MS) relief on the transition from monolayer-by-monolayer (ML-by-ML) Frank–van der Merwe (FM) to Stranski–Krastanov (SK) growth. The investigation involves (a) selection of appropriate materials [Cu, Pd, Pt on Fe(110)] to hopefully meet the appropriate stability criteria for misfit accommodation and bond strength, and of atomic interaction potentials [embedded atom method (EAM)] needed for quantification, and (b) development of appropriate analytical procedures to facilitate the description and quantification of the relevant parameters. The computations revealed that MS relief by misfit dislocations (MDs), for the selected materials, falls outside the SK transition thickness regime. The investigation has thus been limited to MS relief by a misfit vernier. The main objective of assessing the influence of MS relief on the transition to SK growth has been accomplished by showing that the growth mode discriminants, needed to predict quasi-equilibrium growth mode development, change with MS relief. The computation that culminated in the quantification of growth mode discriminants also yielded as by-product several interesting results of wider application in the field of epitaxy — the dependence on substrate proximity and bond strengths of: interlayer and intralayer relaxation, equilibrium misfit, critical misfit and thickness, substrate coverage change, optimum Fourier coefficients of periodic epilayer–substrate interaction potentials and stability of misfit accommodation and growth modes.

Interplay between misfit strain relief and Stranski–Krastanov growth in fcc (111)/bcc (110) ultrathin film epitaxy: Part 1. Analytical approach

The main objective of this investigation is to study the impact of misfit (homogeneous) strain (MS) relief by misfit dislocations (MDs) — or a misfit vernier where the relaxation into oscillatory strains characteristic of MDs becomes insignificant — on the Stranski–Krastanov (SK) growth mode, the perception being that the driving force for the transition is dominated by short range proximity effects of the vacuum and a strongly bonding substrate. The influence of misfit strain relief with increasing thickness on the transition from two-dimensional (2D) to three-dimensional (3D) growth, characteristic for SK growth, is investigated. Here, the dominating parameters are identified and the mathematical formulae for the governing relations, needed for quantification in Part 2, using embedded atom methods (EAM) potentials, are derived: (i) the dependence of substrate coverage on epilayer misfit ( f) and deformation ( ē); (ii) the structure of Fourier series to model fcc (111) epilayer–bcc (110) substrate interaction potentials V( x, y) for a Kurdjumov–Sachs (KS) orientation, including optimum Fourier coefficients V hk for low order truncations; (iii) the harmonic intra-epilayer interaction suitable to describe MDs and to model misfit vernier accommodation of mismatch related to homogeneous Poisson strain; (iv) the average in-plane strain energy suitable (a) to handle the large repeat periods involved in homogenous epilayer deformation within the short wavelength periodic epilayer–substrate interaction potentials and (b) to define stiffness constants for epilayer deformation within such a field; (v) stability criteria for MS relief of 2D coherent and one-dimensional (1D) KS coherent — registry of two opposing sets of parallel closest packed atom rows on either side of the interface — epilayers in Nishiyama–Wassermann and KS orientations, respectively, applying continuum and discrete approaches; and (vi) criteria for growth mode realization, emphasizing transitions to the SK mode and its dependence on proximity effects. The analytical considerations reveal (a) that the transition from a 2D coherent misfit accommodation mode to a 1D KS mode is favored by a large excess strain energy ε 2D− ε 1D and large substrate surface free energy, but opposed by strong epilayer–substrate bonding and (b) the MS energy ε makes no contribution to the growth mode discriminant if proximity effects of the interface and free surface are absent.

Stress and relief of misfit strain of Ge/Si(111)

The intrinsic stress and morphology of the Stranski–Krastanow system Ge/Si(111) have been investigated at deposition temperatures of 700–950 K. In a broad range of intermediate temperatures, only one distinct decline of stress is observed at the onset of three-dimensional islanding. Supported by a recent transmission electron microscopy study, the results demonstrate that the strain of Ge/Si(111), where the substrate surface in contrast to Ge/Si(001) is the glide plane for dislocations, is relieved by incorporation and continuous rearrangement of dislocations during the island stage.

Stress and Relief of Misfit Strain of Ge/Si(001)

The intrinsic stress of the Stranski-Krastanov system Ge/Si(001) was investigated in the range 700--1050 K. Characteristic stress features indicate that the relief of the misfit strain proceeds mainly in two steps: (i) by the formation of 3D islands on top of the Ge wetting layer and (ii) via misfit dislocations in larger 3D islands and upon their percolation. The temperature dependence of strain relief by 3D islands as well as their nucleation and growth behavior support a kinetic pathway for 3D islanding.

The energetics of the relief of misfit strain in InAS yP 1−y films grown on 〈100〉 InP substrates by means of three sets of dislocations

The energetics of the relief of misfit strain in InAS yP 1−y films grown on 〈100〉 InP substrates by means of three sets of dislocations

Theory of strained-layer epitaxial growth near step flow.

A reaction-diffusion theory of homoepitaxial growth on a stepped surface introduced by Myers-Beaghton and Vvedensky [Phys. Rev. A 44, 2457 (1991)] and Fuenzalida [Phys. Rev. B 44, 10 835 (1991)] is generalized to the case of heteroepitaxy by taking account of misfit strain relief in the growing epilayer. For deposition conditions where two-dimensional (2D) islands nucleate on the terraces before individual adatoms can migrate to vicinal step edges, analysis of the distribution of island sizes resolved in both space and time reveals a strain-driven transition from the familiar layer growth mode dominated by 2D island coalescence to a form of step flow where moving steps engulf very many very small 2D islands. The latter mode of growth is predicted to persist until three-dimensional island formation disrupts layer growth altogether. Both with and without strain, it is found that the island size distribution averaged over a terrace very rapidly approaches a steady-state form, even when kinematic theory predicts oscillations in the signal from diffraction measurements.

An assessment of the roles of climb and glide in misfit strain relief

In order to assess the relative contributions of glide and climb processes in the relaxation of misfit strain in heteroepitaxial layers, the glide and climb velocities of dislocations are compared at several temperatures. It is shown that the glide velocity is much greater than the climb velocity under normal conditions. For copper and silicon, about four orders of magnitude can exist at 3/4 of the melting temperature with lower temperatures leading to larger differences. One therefore expects relaxation of misfit strain to proceed primarily by glide mechanisms. Two cases are addressed here in which climb processes can be important: (i) by-passing of an obstacle and (ii) redistribution of an irregular array of interfacial misfit dislocations into a regular array of lower energy.

Elastic and structural properties of f.c.c. {111} thin films part 2. A monolayer on a {110} b.c.c. substrate

Simple qualitative considerations suggest that the inherent mechanical properties—equilibrium structure and elastic constants—of thin epilayers are influenced by proximity effects. The computational effort to calculate these properties, using any form of atomic interaction, becomes enormous when epilayer and substrate are discommensurate and the repeat period is large—an important feature of misfit strain relief in epilayers. A procedure is proposed by which this problem can be overcome for an epimonolayer, and can be extended to multilayers. The procedure involves the following assumptions: (i) the mechanical behavior of the monolayer (ML) is governed by the principle of minimum energy, the average energy per ML atom being minimized in this case, (ii) the field of interaction emanating from the substrate is periodic (with the periodicity of the substrate surface) within the plane of the ML, (iii) the substrate field can be mapped by calculation involving the translation of the ML—as if “rigid”, having registry dimensions and allowing for height equilibration—on the substrate surface, (iv) the ML may be constrained to its average (constant) equilibrium height with negligible discrepancies in the energy. The procedure is demonstrated, and numerically justified, by its application to {111} MLs of Ni and Cu in Nishiyama-Wassermann orientation on W {110}, using embedded-atom-method potentials. The calculations produce convincing evidence to substantiate the validity of the procedure, showing that the contribution of the substrate to the embedding energy of ML atoms can be fairly accurately described in terms of its average electron density in the ML plane, the effect of the periodic oscillations in the electron density being negligible. A similar procedure is valid for the embedding of substrate atoms. The application to Ni and Cu on W shows that proximity effects are drastic: the in-plane elastic constants of a supported ML, an ML in the crystal interior and a free standing ML are respectively and crudely in the ratio 1:1.5:2.5. Proximity effects are likewise important in anharmonicity.

Evidence for strain relaxation via composition fluctuations in strained quaternary / quaternary and quaternary / ternary multiple quantum well structures

The occurence of large-scale contrast modulations is discussed, which have been observed in the transmission electron microscope in cross-sectional samples containing Ga x In 1− x As y P 1− y with a number of different x and y values. 90°-wedge samples were used because of their known geometry, in which thin-foil contrast effects can be excluded. The samples exhibiting large-scale modulations of a period greater than 100 nm all contained quaternary / quaternary or quaternary / ternary multiple quantum well stacks. Indications for a correlation between the onset, strength and frequency of the modulations with the well/barrier composition and its proximity to the centre of the miscibility gap are presented. The contrast is also found to be influenced by the stack thickness and strain. In large stacks, the modulations are related to waviness in epi-layer growth. The contrast is discussed in terms of composition modulation patterns connected with strain fluctuations, which are set up in interfacial regions and which evolve into wavy layer growth as means of misfit strain relief.

The crystallization kinetics, growth mechanism, and stability of co-evaporated NiSi 2±0.2 thin alloy films

The crystallization kinetics and morphology, growth mechanisms and stability of the phases of NiSi 2±0.2 alloy films were studied. The alloys were co-evaporated on two substrates namely: (1) silicon single-crystal (Si(100)), (2) thermally oxidized silicon single-crystal (Si(100)). Crystallization, throughout the whole thickness of the film, was observed to occur at temperatures lower than 200°C. The activation energy depends upon the Si content in the thin alloy film as well as on the type of substrate. The activation energy of the alloys deposited on the Si substrate was found to be higher than that obtained for the inert one. After the crystallization is completed, for the films deposited on the silicon oxide, oriented {111} grain growth takes place. On the Si(100) substrate, epitaxial growth of NiSi 2 was observed to occur (∼ 400°C) at the polycrystalline NiSi 2/Si interface. This was accompanied by the appearance of twins as a misfit strain relief mechanism. Simultaneously, at the free surface, {111}-oriented grain growth occurs, which lowers the surface energy.

Strain relaxation in epitaxial overlayers

The misfit between an epilayer and a substrate may be accommodated by misfit dislocations (MDs) or misfit strain (MS) or both. In a small misfit system the misfit is accommodated by MS alone up to a critical thickness whereafter the residual MS decreases as the thickness increases. The main objective of this paper is to review theoretical work aimed at understanding MS relief in a growing epilayer by the introduction of MDs, with the view of resolving the discrepancies between predicted and observed critical thickness and residual MS after onset of MS relief. Since the predictions are based on equilibrium principles, equilibrium theories for monolayers (MLs) in the Frenkel-Kontorowa model, and for thickening epilayers (growing ML-by-ML) in the Volterra model, are briefly summarized, including some consideration of the conditions for ML-by-ML growth. Since equilibration can be drastically retarded by barriers to nucleation and motion of dislocations the observed quantities are most often non-equilibrium values. Calculations show (i) that MD sources are normally needed to the onset of MS relief, (ii) that threading dislocations are the “softest” sources, (iii) that even with threading dislocation sources MS relief may lag behind equilibrium predictions and (iv) that Peierls friction may lead to an infinitely large critical thickness.

Interdiffusion phenomena in Au/Cu and Cu/Au bilayers

The microstructures of epitaxial deposits of (111) Cu/(111) Au and (111) Au/(111) Cu at various stages of interdiffusion are described. The most prominent microstructural features of Au/Cu films (where gold deposition occurred at temperatures less than 400 °C) were (Matthews) coincidence lattice misfit dislocations lying along < 1 1 0 > directions in the film plane with |b| = a 2 < 110 > directed out of the film plane. Their spacings, transmission electron microscopy (TEM) hot stage behavior and generation mechanisms are discussed. For more severe diffusion anneals, the coincidence dislocation density decreased and hexagonal networks identified as ( van der Merwe) natural lattice misfit dislocations became resolvable. They are edge type (lying along <11 2 > directions in the film plane) with |b| = a 2 < 1 10 > . For the case of Cu/(111) Au bilayers, copper deposited at and below 315 °C with a 20 min anneal again showed coincidence misfit networks. Higher temperature deposition of copper (or hot stage annealing) resulted in natural lattice misfit dislocations in the microstructure. The densities of both types of dislocations were determined and their TEM hot stage behavior was investigated. The method by which the two networks contribute to the relief of misfit strain in both bilayers is discussed.