Calculation Of Critical Thickness Research Articles

Fracture behavior of metal oxide/silver nanowire composite electrodes under cyclic bending

The mechanical responses under cyclic bending of Ag nanowire composite electrodes coated with various metal oxide films of different thicknesses were explored, in an attempt to evaluate their applicability to flexible transparent electrodes. Al2O3, HfO2, and TiO2 films were deposited onto Ag nanowire electrodes by atomic layer deposition at a low temperature of 100 °C, and cyclic bending tests with in situ resistance measurements were conducted for up to 300,000 cycles. Thicker metal oxide films resulted in greater increases in the resistances of the composite electrodes under cyclic bending due to the reduced fracture strength of the films. Regardless of the type of metal oxide, however, similar tendencies were observed in the resistance changes in response to cyclic bending. It was found that the critical thickness calculation based on the Griffith theory for the evaluation of the brittle-to-ductile transition was not applicable to the metal oxide/Ag nanowire composite electrodes. By correlating the mechanical, ambient, and thermal reliability test results with those of optoelectrical property evaluations, the optimal thickness of Al2O3 film, as a representative metal oxide film, was determined to be 3–5 nm for Ag nanowire composite flexible transparent electrodes.

Onset of plastic relaxation in semipolar ([formula omitted]) InxGa1−xN/GaN heterostructures

The onset of plastic relaxation via misfit dislocation (MD) formation in InxGa1−xN layers grown by metal-organic chemical vapor deposition on the (112¯2) semipolar plane of GaN substrates is investigated using high-resolution X-ray diffraction, transmission electron microscopy and cathodoluminescence. The results of critical thickness calculations for MD formation as a function of InxGa1−xN alloy composition x are compared with experimental observations. MD generation is observed initially as a result of slip on the (0001) slip plane, and subsequently as a result of additional slip on inclined {11¯00}-typem-planes, which eventually leads to an increase in threading dislocation density.

Misfit dislocation formation via pre-existing threading dislocation glide in (112¯2) semipolar heteroepitaxy

Cathodoluminescence (CL) was used to study the onset of mechanical stress relaxation in low indium composition semipolar (112¯2) InxGa1−xN lattice-mismatched layers grown on bulk GaN substrates. Monochromatic CL of short interfacial misfit dislocation (MD) segments showed a single threading dislocation (TD) associated with each MD segment—demonstrating that the initial stage of MD formation in semipolar III-nitride heterostructures proceeded by the bending and glide of pre-existing TDs on the (0001) slip plane. The state of coherency as determined by panchromatic CL is also compared to that determined by x-ray diffraction analysis based on crystallographic epilayer tilt and Matthew-Blakeslee’s critical thickness calculations.

An engineering method of calculating the critical thickness of the discs of the windings of transformers for resistance-welding machines

It is established that resistance welding machine's transformer winding discs thicknesses growth higher than certain critical value causes loss increase and excessive consumption of the winding copper. An analytical calculation of this value is given. Relative units' application in analytic expressions considerably simplifies disc critical thickness calculation.

Equilibrium critical thickness for misfit dislocations in III-nitrides

The critical thickness gives the transition point between fully strained and relaxed heteroepitaxial films and determines the onset of defect generation, including misfit dislocations, cracks, and V-pits. An important variable in critical thickness calculations concerning misfit dislocations is the dislocation energy. It consists of two contributions: the elastic energy of the bulk material around a dislocation and the energy of the dislocation core. The latter part is often neglected. Recent atomistic calculations have estimated this quantity together with the radius of dislocation cores in wurtzite III-nitrides. The effect of the dislocation core energy on equilibrium critical thickness values for III-nitrides is investigated theoretically and is shown to be significant. The calculated values of the critical thickness are compared with experimentally determined values of the critical thickness for misfit dislocations in the InGaN/GaN system using transmission electron microscopy and x-ray diffraction techniques. A comparison of the present model with experimental observations, together with a wide range of data from the literature for both AlGaN/GaN and InGaN/GaN systems, shows reasonable agreement. Finally, we speculate on a possible reason for differences between theory and experiment.

Buffer influence on AlSb/InAs/AlSb quantum wells

Buffer influence on AlSb/InAs/AlSb quantum wells (QWs) was investigated by using Hall measurement, atomic force microscopy (AFM) and X-ray diffraction (XRD). We found that the electron mobility of AlSb/InAs/AlSb QW with GaSb buffer is higher than that with AlSb buffer though the surface and crystal qualities of AlSb buffer are better than GaSb buffer. Relaxation measurement indicated that the 150 Å InAs grown on AlSb buffer is partially relaxed, while it is fully strained when grown on GaSb buffer, which is also supported by critical thickness calculation. Because of InAs relaxation on AlSb buffer, mismatch dislocations will appear in the InAs layer and the interfaces of InAs QW will get rough, which is suggested as the reason leading to the lower mobility of InAs QW grown on AlSb buffer than on GaSb buffer.

Impact of Heavy Boron Doping and Nickel Germanosilicide Contacts on Biaxial Compressive Strain in Pseudomorphic Silicon-Germanium Alloys on Silicon

AbstractIn recent years, the semiconductor industry has increasingly relied on strain as a performance enhancer for both n and p-MOSFETs. For p-MOSFETs, selectively grown SiGe alloys in recessed source/ drain regions are used to induce uniaxial compressive strain in the channel. In order to induce compressive strain effectively using this technology, a number of parameters including recess depth, SiGe thickness (junction thickness), sidewall thickness, dopant density, dislocation density, and contact materials have to be optimized. In this work, we have studied the effects of heavy boron doping and self-aligned germanosilicide formation on local strain. Raman spectroscopy has been used to study the impact of heavy boron doping on compressive stress in SiGe films. Strain energy calculations have been performed based on Vegard's law for ternary alloys and the effect of boron on strain in SiGeB alloys modeled quantitatively. It will be shown that, owing to the smaller size of a boron atom, one substitutional boron atom compensates the strain due to 6.9 germanium atoms in the SiGeB film grown pseudomorphically on silicon. The critical thickness of SiGeB has been calculated for the first time based on kinetically limited critical thickness calculations for metastable SiGe films. It will be shown that the critical thickness of the alloy increases as the boron content in the alloy is increased, making boron concentration an additional parameter for optimizing strain in the MOSFET. Based on these conclusions, boron concentration can be used to preserve the strain for thicker SiGeB films (compared to SiGe films) while keeping the dislocation density low. Furthermore, we show that NiSiGe contacts can have a profound impact on the SiGe strain. Our results indicate that NiSiGe introduces additional stress in the underlying SiGe, which further affects the strain induced in the channel

Stillinger-Weber potentials for III–V compound semiconductors and their application to the critical thickness calculation for InAs/GaAs

Parameters in the Stillinger-Weber interatomic potentials are obtained for III–V compounds from the cohesive energy, the lattice constant, and the elastic properties. The obtained potentials coincide with the Keating potentials for small distortion (<1%) but are more accurate for larger distortion. Using the SW potentials, the critical thickness of misfit dislocation nucleation is calculated for InAs/(001)GaAs. The critical thickness is 5 ML for a 60° dislocation and 2 ML for an edge dislocation. These thicknesses are smaller than those calculated using the Keating potentials. Results obtained by the classical elastic theory do not agree with the present results.

The stresses due to arrays of inclusions and dislocations of infinite length in an anisotropic half space: Application to strained semiconductor structures

Abstract Exact closed-form solutions are derived for the stresses due to periodic arrays of dislocations and arbitrarily polygonal inclusions of infinite length in a generally anisotropic half space. These solutions allow the analysis of the stability of a range of strained semiconductor structures. Critical thickness calculations are performed for unburied strained layers and for buried strained layers and quantum wire arrays in the GeSi/Si system. For strained layers (buried and unburied) these are in agreement with experiment. The results for quantum wires suggest that, once buried, they may be able to support, without loss of coherency, up to seven times the lattice mismatch that may be accommodated by a strained layer of comparable thickness. Comparison of these results with those obtained in the isotropic approximation show that for the GeSi system the effect of anisotropy is to increase the predicted critical thickness by more than 30%. Dislocation formation above the critical thickness is studied ...

Strain relief in compositionally graded Si1-xGex formed by high dose Ion implantation

Strain relief mechanisms have been investigated in alloys of Si and Ge formed by high dose ion implantation followed by solid phase epitaxy. Both compressive and tensile strain states were studied by implanting: (i) 200 keV Ge into (001) Si to form Si-rich alloys and (ii) 150 keV29Si into (001) Ge to form Ge-rich alloys. We report that Si-rich compressively strained alloys above a critical implant dose relax via the introduction of a/6(112) partials (bounding stacking faults) when regrown by solid phase epitaxy below ≈600° C. Alloys formed by implanting Si into (001) Ge and regrown at 450° C also undergo strain relaxation above a critical dose but, in this case, relaxation proceeds via the introduction of planar defects + partials, Lomers, and 60° dislocations. The high dose ion implantation technique produces alloys in which the concentration, and hence lattice mismatch, is a Gaussian function of depth from the surface. In this work we present a modification of the conventional critical thickness calculation which includes: (i) balancing forces acting on defects in a strain gradient to define an interface above which strain relief occurs and (ii) integration of the strain energy in the portion of the compositionally graded film above this interface. Critical dose implant plots based on these calculations are presented. The model provides a good fit to cross-sectional and TEM observations of regrown alloys with implant doses above and below the predicted critical dose. A TEM characterization of the strain relieving defects for both compressive and tensile films is presented.

The effect of frictional stress on the calculation of critical thickness in epitaxy

A critical-thickness model is proposed for lattice-mismatched epitaxial layers which incorporates for the first time both the equilibrium and kinetic components of misfit accommodation. The model is an attempt to provide a physical basis for the discrepancy between the observed and calculated critical thickness in zinc-blende semiconductors. The equilibrium components of the model use a force balance and a Volterra description of the dislocation line tension with frictional forces includiing Peierls barriers and dislocation atmospheres. The effect of the frictional forces is to shift the critical thickness to a larger value and to produce a residual elastic strain which persists for large thicknesses. The frictional barriers are low in face-centered-cubic metals and produce minor changes from the previous theories; however, for semiconductors the frictional forces may be high and produce a substantial increase in the predicted critical thickness. The kinetic component of misfit accommodation has been addressed through a dynamic frictional force. The explicit form of the kinetic component of misfit accommodation depends on the operative mechanism of misfit-dislocation generation. A simple criterion is proposed to estimate whether the generation of misfit dislocations will be controlled by equilibrium or kinetic factors.

Mbe Growth of Strained-Layer InSb/InAlSb Structures

ABSTRACTThe MBE growth and related materials characterisation of InSb/InAlSb strained-layer structures is described. Band-gap considerations and critical thickness calculations are presented and indicate that this material system should offer considerable device potential. Detailed structural studies, performed using both transmission electron microscopy and X-ray diffraction, confirm the growth of high quality multiple quantum-wells, and 2K photoluminescence has shown corresponding energy upshifted transitions.