Relaxation Of Layers Research Articles

Surface energy and stress release by layer relaxation

The surface energy $(\ensuremath{\gamma})$ and surface stress $(\ensuremath{\tau})$ for semi-infinite close-packed surfaces of $4d$ transition metals have been calculated using ab initio total-energy methods. The moderate agreement between the present and former theoretical data for $\ensuremath{\tau}$ indicates the high level of numerical difficulty associated with such calculations. For the most close-packed surfaces, the present unrelaxed $\ensuremath{\tau}$ values follow the typical trend characteristic for the cohesive energy in nonmagnetic transition-metal series, whereas the relaxed $\ensuremath{\tau}$ values group around $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{mJ}∕{\mathrm{m}}^{2}$, obtained for Y, Zr, and Ag, and $\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\mathrm{mJ}∕{\mathrm{m}}^{2}$, calculated for Nb, Mo, Tc, Ru, Rh, and Pd. We have found that the average surface energy reduction upon layer relaxation is around 4%. At the same time, a large part of the surface stress is released during the surface relaxation process. To explain the observed behaviors, we have established a simple relationship, which connects the variations of $\ensuremath{\gamma}$ and $\ensuremath{\tau}$ to the layer relaxation. This relation reveals the principal factors determining the difference between the surface energy and stress release rates at $4d$ transition-metal surfaces.

Strained Silicon on Ultrathin Silicon-Germanium Virtual Substrates

Molecular beam epitaxy is employed for the growth of strained-Si layers on top of virtual substrates with highly-relaxed ultrathin SiGe buffers in a continuous procedure. An initial growth stage at a temperature-ramp down to below 200°C causes misfit-dislocation generation by nucleation from point defects and provides an early relaxation in the SiGe buffers. In situ monitoring is used for the growth control. Layer thicknesses and composition are proved by ex situ spectroscopic ellipsometry. %Raman investigations on the layer stacks reveal high degrees of relaxation (70-100%) in sub-100nm SiGe buffer layers containing from 12 to 42 % Ge. Stress in strained Si layers estimated by means of Raman-spectra shift is adjustable from 0.92 to 6.84 GPa by the Ge-content in virtual substrates. Surface morphology of strained Si and of relaxed SiGe buffers is smooth and crosshatch-free. Device test structures show substantial increase of carrier mobilities in nMOSFETs fabricated on these strained-Si layers.

Surface relaxation and surface stress of 4d transition metals

Using the density functional theory formulated within the framework of the exact muffin–tin orbitals method, we present a systematic study of the top layer relaxation and surface stress of 4d transition metals. Our calculations predict layer contractions for most surfaces. We also find that the relaxations of the close packed surfaces decrease with increasing atomic number through the 4d series. We propose that the relaxation is mainly due to the reduction of the number of sp electrons in the surface layer relative to bulk. The surface stress is found to be very sensitive to the relaxation and, therefore, an accurate determination of the layer relaxation is necessary for obtaining reliable values for the surface stress. Comparing the top layer relaxations for the close packed surfaces, we see essential deviations between data derived in different ab initio calculations. At the same time, the overall trend for the present surface stress of 4d metals is in reasonable agreement with recent full-potential data.

Application of 19F NMR relaxometry to the determination of porosity and pore size distribution in hydrated cements and other porous materials

The potential to determine the porosity of cements and other porous materials by employing 19F NMR relaxometry was explored for samples of hydrated Portland cement, white cement and calcium aluminate, filled with Freon 11. The dependence of 19F signal amplitudes on the content of Freon in samples with completely filled pores was linear with a small (< 6%) intercept thus allowing a direct determination of total porosity. Additionally it was found that magnetic susceptibility (hence the content of paramagnetic compounds) of the solid can be evaluated from 19F NMR spectra of samples containing exterior liquid. Information concerning pore size distribution can be obtained from the analysis of multiexponential relaxation of 19F nuclei in samples with completely filled pores. Mathematical models employing sets of distributions of relaxation rates have been developed for this purpose. Distributions were assumed to be of a (fixed) square/triangular type allowing for the calculation of moments of any order from the estimated initial value, width of distribution and asymmetry factor. Longitudinal and transverse relaxation were characterised by either single or several continuous distributions of relaxation rates. One of the relaxating phases (assigned to fluid occupying throats connecting the pores) was found to selectively disappear when Freon was evaporated from samples. Another approach is to analyse the dependencies of means and variances of relaxation rates on Freon content. This has been done by employing the two-site relaxation model with a permanent adsorption layer and pore-dependent relaxation enhancement. Simultaneous fitting of dependencies of means and variances of relaxation rates on Freon content yields parameters of pore size distribution and of the dependence of relaxation enhancement on the pore radius. Analysis of experimental data shows agreement between these two approaches.

Lattice relaxation and dislocation generation/annihilation in SiGe-on-insulator layers during Ge condensation process

Dislocation behaviors in SiGe-on-insulator (SGOI) layers during the Ge condensation process are systematically studied by employing transmission electron microscopy, X-ray diffraction, Raman spectroscopy and secondary ion mass spectroscopy, in order to obtain insights into sufficient relaxation of SGOI layers with good crystal quality. It is found that misfit dislocations (MDs) are generated in the ramping up process in Ge condensation, whereas they disappear and threading dislocations (TDs) are generated after the oxidation process. This TD generation is attributable to the fact that the MDs were fragmented into dislocation half-loops and then rose to the SiGe surface. Thus, suppression of the rising motion is a key to fabricating high-quality SGOI substrates by the Ge-condensation technique.

Formation of misfit dislocations at the thin strained Si∕strain-relaxed buffer interface

Misfit dislocations at the strained Si∕SiGe strain-relaxed buffer interface are known to enhance leakage currents of strained Si metal oxide semiconductor devices. As we show in this letter, misfit dislocations at this interface might be generated even for Si thicknesses below the critical thickness for layer relaxation. The important parameter is the degree of relaxation of the strain-relaxed buffer. If the strain-relaxed buffer is not fully relaxed, threading dislocations can glide during thermal treatments. This results in misfit dislocations at the strained Si∕SiGe interface, because the threading dislocation segments within the strained Si are blocked by its tensile stress.

Limits of strain relaxation in InGaAs∕GaAs probed in real time by in situ wafer curvature measurement

In situ stress measurements during molecular-beam epitaxy growth of InxGa1−xAs∕GaAs provide insight into the relaxation behavior of thin films grown on mismatched substrates. Strain relaxation in the materials studied occurs due to the formation and glide of dislocations. Measurements of additional relaxation during growth interruptions show that relaxation is kinetically limited during the early stages of growth. In thicker films, the residual strain is not significantly affected by growth conditions. We find that relaxation in thick layers does not proceed as far as predicted by models which consider the formation of dislocation arrays or dislocation blocking, and we discuss this discrepancy between theory and experiment. We discuss the effect of a nonuniform dislocation array configuration on the overall relaxation behavior. Results from dislocation dynamics simulations are presented which provide evidence that nonuniform dislocation array distributions limit the extent of plastic relaxation.

Dielectric relaxation in thin liquid crystal layers formed on cylindrical pore walls

Dielectric spectroscopy was used to study the influence of layer thickness of confined liquid crystal (with different orientation of molecules at pore walls) on relaxations due to surface induced polarization and due to molecular reorientations. Low frequency measurements provided information on the relaxation of surface polarization that arose at the liquid crystal–pore wall interface. The dynamics of molecular reorientations were investigated in high frequency experiments. The relaxation of surface induced polarization was slower for confined liquid crystal with axial boundary conditions than for that with a radial orientation, suggesting that the mobility of molecules in surface layers was strongly affected by boundary conditions. The radial alignment of molecules facilitated the investigation of the librational mode. Temperature dependence of relaxation time of this mode was different from that of reorientations of molecules around their short axes.

Relaxation issues in nanoindentation experiments

This contribution reports on a systematic investigation of mechanical properties of coarse grained, polycrystalline titanium samples and antimony doped SnO2 thin films (ATO) by depth sensing indentation (nanoindentation) experiment. The combination of nanoindentation and atomic force microscopy provides a straightforward method to follow the indentation and relaxation process of the material, revealing not only the hardness and Young’s modulus of the sample, but also gaining information on the deformation process taking place during the indentation. A method was worked out based on computer evaluation of AFM images of nanoindentation impressions to resolve spatially the shape differences between the relaxed hardness indents and the ideal indenter pyramid. It provides a quantitative method to investigate the relaxation characteristic of different materials. Single grains in coarse-grained titanium and the ATO layers were investigated by this combined method, anisotropy and relaxation effects were studied. The hardness and Young’s modulus of the ATO layers have been found to be dependent on the preparation method, but the relaxation of various layers are largely uniform. Different Ti grains, however, have uniform hardness and Young’s modulus, but the relaxation effects in these samples show orientation dependence.

Interface relaxation and electronic corrugation in thePb∕Si(111)−Pb−α−√3×√3

The corrugation observed on top of Pb islands grown on $\mathrm{Si}(111)\text{\ensuremath{-}}\mathrm{Pb}\text{\ensuremath{-}}\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\surd}3\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}3$ (as a result of the Moire pattern formation at the $\mathrm{Si}∕\mathrm{Pb}$ interface) offers a different way to obtain information about the interface. Results from several probes (high resolution LEED, STM, STS, model image calculations) are compared. The origin of the corrugation is predominantly geometric (because of layer relaxation in the island) and to a lesser degree electronic (related to the confined electrons within the island). This is deduced from the hexagonal ringlike features in LEED and the quantitative comparison of the corrugation contrast in calculated vs measured STM and STS images.

Proton Transfer of Excited 7-Azaindole in Reverse-Micellar Methanol Nanopools: Even Faster than in Bulk Methanol

The methanol-catalyzed double-proton transfer of photoexcited 7-azaindole in the free cores of solvation-restricted reverse micelles takes place on the time scale of 90 ps, even shorter than in bulk methanol. This anomalous rate increase with a large kinetic isotope effect of 5 experimentally proves the widely discussed two-step model for the overall reaction of solvent-mediated proton transfer. On the other hand, the molecules in the bound layers and in the headgroup layers relax in 900 and 6000 ps, respectively, without going through proton transfer. The tautomerization and the relaxation of excited 7-azaindole can be exploited to probe the nanopools of methanol reverse micelles.

Electron-phonon interaction via the Pekar mechanism in nanostructures

We consider an electron-acoustic phonon coupling mechanism associated with the dependence of crystal dielectric permittivity on the strain (the so-called Pekar mechanism) in nanostructures characterized by strong confining electric fields. The efficiency of Pekar coupling is a function of both the absolute value and the spatial distribution of the electric field. It is demonstrated that this mechanism exhibits a phonon wavevector dependence similar to that of piezoelectricity and must be taken into account for electron transport calculations in an extended field distribution. In particular, we analyze the role of Pekar coupling in energy relaxation in silicon inversion layers. Comparison with the recent experimental results is provided to illustrate its potential significance.

Structural and optical properties of GaN/AlN multiple quantum wells for intersubband applications

GaN/AlN multiple quantum well structures of 1, 5 and 20 periods were grown by molecular beam epitaxy (MBE). To investigate structural parameters, symmetrical scan (0 0 0 2) and reciprocal space mapping in the vicinity of the GaN ( 1 0 1 ¯ 5 ) plane were made by X-ray diffraction (XRD). The layer thickness, composition and relaxation were determined and gave good agreement with simulated results. The 20 period multiple quantum well (MQW) sample exhibited an intersubband resonance at 360 meV, which corresponds well to the structure data determined by XRD.

Hplacement inCr(Mo,Fe)∕Vsupercells: The origin of the dead layers

Transport properties within the Boltzmann transport equation for metallic multi-layer structures as well as bulk materials, were the prime topic of this work. Ab initio total energy calculations for Hydrogen loaded metallic multi-layers were performed in order to shed some light onto problem of H depleted layers at the interfaces that have been experimentally observed. It was explained in connection with structural relaxation of the interface layers. Further on conductivity behavior of Fe/V vs. Mo/V during Hydrogen load was discussed. The difference in, on first sight, rather similar multi-layer structures was explained by the magnitude of Hydrogen induced Vanadium expansion. Problem of variation of conductivity with changed c/a ratio of metals and semiconductors in general was addressed as well. The variations due to change of the Fermi surface of the corresponding materials were observed as well as some intriguing general patterns. The phenomenon could be regarded as piezoresistivity on electronic structure level. For the 3d transition metals variation of conductivity/resistivity through the period was studied.A possible explanation for anomalous behavior of Manganese resistivity due to its much greater lattice constant in comparison to its neighbors in the period is presented. Field of disordered alloys and low dimensional magnetism was touched by discussing Mo/Ru formation energy as well as magnetic nano-wires grown on surfaces.All total energy calculations as well as band structure calculations were performed by using Density Functional Theory based numerical computations. A short but comprehensive review of most common linear-response electron transport techniques is given.

Evolution of the defect structure in helium implanted SiGe∕Si heterostructures investigated by in situ annealing in a transmission electron microscope

The evolution of the He-implantation induced defect structure in SiGe∕Si heterostructures is observed during in situ annealing at 650 and 800°C within a transmission electron microscope. The He implantation and annealing results in the formation of He precipitates below the SiGe∕Si interface, which at first show a platelike shape and subsequently decay into spherical bubbles. The coarsening mechanism of the He bubbles is revealed as coalescence via movement of entire bubbles. The nucleation of dislocation loops at overpressurized He platelets and their propagation into the heterostructure could be observed as well. We found distinctly different velocities of the dislocations which we attribute to glide and climb processes. The in situ experiments clearly show that the He platelets act as internal dislocation sources and play a key role in the relaxation of SiGe layers.

Biaxial strain effect in exciton resonance energies of epitaxial ZnO layers grown on 6H–SiC substrates

Thickness-dependent biaxial strain relaxation of epitaxial ZnO layers grown on 6H–SiC substrates has been addressed. The strain ratio under the biaxial stress was estimated to be 0.38, while the c/a ratio changed from 1.593 to 1.608. The biaxial strain was accounted maximum for the ZnO layer thickness of ⩾6–⩾200 nm. Free (FX A ), donor-bound (D 0X), and neutral acceptor-bound (A 0X) excitons energies were blue shifted with the increase of layer thickness to be 2.5, 4.8, and 5.8 meV, respectively. The strain-induced band shift for the FX A , FX B , and D 0X bands was estimated with the corresponding energies of 13.1, 16.4, and 14.6 eV.The strain-induced optical band structure was analyzed using the Hamiltonian for the valence bands under the out-of-plane biaxial strain.

Layer relaxation and intermixing inFe∕Cu(001)studied by surface x-ray diffraction

The structure of Fe films thermally deposited on Cu(001) was analyzed using surface x-ray diffraction in the coverage range between 6 and 8 monolayers. Based on the analysis of crystal truncation rod data measured at 120 and $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, i.e., below and above transition temperatures reported for ferro- and antiferromagnetic ordering, no changes of the interlayer spacings larger than about $\ifmmode\pm\else\textpm\fi{}0.015\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ are found. Within the Fe film these correspond to fcc Fe $(1.78\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$, while the top-layer spacing is expanded by 3--5 % in agreement with previous low-energy electron diffraction studies. Lateral disorder of surface atoms as described by the Debye parameter indicates displacements of the top-layer positions up to $0.23\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ corresponding to zigzag displacements observed in the $p2mg$ $(2\ifmmode\times\else\texttimes\fi{}1)$ superstructure. The inherent large penetration depth of the x rays also allowed the study of the structure and composition of the buried $\mathrm{Fe}∕\mathrm{Cu}$ interface. The data indicate $\mathrm{Fe}\ensuremath{-}\mathrm{Cu}$ intermixing, where nearly 50% of a Fe (Cu) monolayer are exchanged. Four layers across the interface are significantly affected. About 30% of the first Fe (Cu) and up to 15% of the second Fe (Cu) layer is alloyed by Cu (Fe).

An All-electron FLAPW Study of the Relaxation and Electronic Structure for (001) Surface of α-U

The full potential linear augmented plane wave method is used to study the relaxation and electronic structure of (001) surface for αU. The current work predicts a contraction of the topmost layer by 2.9% accompanied by an outward expansion of the second and third layers by 1.1% and 0.2%, respectively. The relaxation of topmost and second layers makes up the largest contribution of relaxation energy. Due to the shortrange screening effect, the atomic interaction is mainly limited to adjacent layers. For the surface atoms, due to the reduced nearest neighbors, the contribution to the bonding from 5f electrons is reduced and 5f electrons appear to be more localized.

Enhanced relaxation of SiGe layers by He implantation supported by in situ ultrasonic treatments

Helium implantation-enhanced strain relaxation of SiGe layers grown pseudomorphically on Si substrates is an interesting alternative for the creation of strained Si CMOS structures. Here we demonstrate the application of additional in situ ultrasonic treatment (UST) during He ion implantation for the formation of relaxed Si 0.8Ge 0.2 buffer layers. By Raman spectroscopy and X-ray diffraction we show increased relaxation of the SiGe layers under the influence of UST. A rectangular dislocation network with a high dislocation density of about 10 9–10 10 cm −2 concentrated near the interface between the SiGe layer and the Si substrate is shown by TEM for 100 nm SiGe/Si heterostructures after heat treatment at 750 °C, 60 s. Application of ultrasonic waves during He implantation keeps a low surface roughness of about 0.5 nm.

Surface Relaxation Influenced by Surface States

A detailed theoretical investigation of the relaxation of the simple metal surface Al(100) is presented. We show the influence of electronic surface states in this context. The sign and magnitude of the relaxation of the topmost atomic layers is mainly determined by the rearrangements of the surface state charge. The degree of surface relaxation convergence, with respect to the number of slab layers, is determined by the location of the surface state band relative to bulk bands.