Concept Of Critical Thickness Research Articles

A Model Describing the Process of the Electrodeposition of Zinc Loose Deposits in Pulsed Current Modes

A phenomenological model describing the change in the structural characteristics of loose zinc deposits obtained in pulsed current modes is presented. Comparison of experimental data on the structural properties of deposits with the results of model calculations indicates the adequacy of the model. To describe the features of the dendritic deposit growth and to determine the duration of the homogeneous structure formation in pulsed modes, the concept of critical thickness is introduced, at which a sharp change in the loose deposit density occurs. The dependence of the zinc deposit critical thickness on the pulse duty ratio under pulsed current modes is determined. The increasing of the pulse duty ratio leads to denser deposits with rounded dendrite shapes and fewer growth points, as compared with the deposit obtained in galvanostatic mode.

Anticorrosion Performance of Sol–Gel Driven SIO2-Al2O3 Coatings on Low Carbon Steel

Anticorrosion performance of the sol–gel coatings was investigated for their applications to carbon steels. Cracking seemed to be a major problem in achieving the corrosion protection of the sol–gel coatings. It was found that some modifications from the original coating material such as the reduced particle size and structural change of the coating layer exerts a significant effect on the crack formation, which can be understood by the concept of critical thickness. Once corrosion occurred at the steel/coating interface, the cracking of the coating became accelerated as a result of oxide formation at the interface as it generates tensile stress on the sol–gel coating for the crack propagation. From the EIS analysis, it is demonstrated that the sol–gel coating would be not an ideal barrier for corrosion protection. Even though there was no crack on the coating, the charge transfer occurred through the film (frequency shift of time constant) with time, resulting in the corrosion at the steel/sol–gel coating interface with the crack propagation of the coating.

Critical Depth of Buried Isothermal Circular Pipes

ABSTRACTWe address the two-dimensional heat conduction problem due to a periodic array of isothermal pipes buried in a conductive medium. The upper surface of the medium is subjected to convection with a uniform heat transfer coefficient, and the lower surface is insulated. Similar to the concept of critical thickness associated with a slab embedded with isothermal strips, we show that there exists a critical depth such that the heat transfer rate is maximized. As the Biot number tends to infinity, the critical depth approaches zero for a single pipe buried in a semi-infinite medium. For a periodic array of isothermal pipes, there is also a critical Biot number beyond which the critical depth is zero. Furthermore, insulating the pipes reduces the critical depth, and the heat transfer rate does not vary significantly with respect to the depth.

Critical Thickness of a Low Permeable Coal Bed for Horizontal Well Production in China

This article presents a concept of critical thickness in low permeable coalbed methane reservoirs with a simulation study when a horizontal well is used. The equations proposed to finish the simulation study are based on the Langmuir equation, Fick pseudo-steady state law, and Darcy equation, in which equivalent radius model and function of pseudo pressure are combined to consider the effect of diffusivity and compressibility. The method of finite difference is presented to solve the equations. Then we established the partial differential equations and the definite conditions that describe the mechanism of coal gas and water flow. As the low permeable property of a coal bed in China, we discussed the applicability of a horizontal well according to the reservoir thickness. The significant results from our study include: (1) There is critical reservoir thickness in developing low permeable coalbed methane reservoir with horizontal well. (2) When the thickness is less than the critical value, the cumulative gas production will be lower and the commercial efficiency is unsatisfactory. When the value is more than the critical one, the productivity will not increase as quickly as the reservoir thickness. On the contrary, it will be almost stable along with the reservoir thickness increase. (3) The production effect of the horizontal well on a low permeable coalbed methane reservoir will be decreased when the reservoir thickness is too high. (4) The peak gas rate will go down first and move upward later as the reservoir thickness increases. Consequently, the adaptability of the horizontal well to a low permeable coalbed methane reservoir should be analyzed first according to the reservoir thickness.

Flows through energy dissipaters with sudden reduction and sudden enlargement forms

The energy dissipation of flood discharges has been one of important problems that affect directly the safety of hydropower projects. The energy dissipater with sudden reduction and sudden enlargement forms, used widely in large-scale projects, has been a kind of effective structure for energy dissipation. The concept of critical thickness was defined, which is related to both the geometric parameters and the hydraulic parameters of the energy dissipater, and the factors affecting the critical thickness, were analzsed by means of dimensional analysis. The empirical expression about the critical thickness was obtained and could be used as the criterion to distinguish the flows through the energy dissipater, i.e., the plug flow and the orifice plate flow. The error analysis showed that the critical thickness calculated by the expression has the errors of smaller than 10% in the estimation of the flows for the energy dissipater mentioned above.

The effect of surface steps on the critical thickness for spreading of threading dislocations in thin epitaxial films

Experimentally, there is a critical thickness of an epitaxial thin film, below which misfit dislocations are not observed and above which threading dislocations are found to glide. There are several theoretical critical thicknesses that may or may not coincide with the observed value. We show that the presence of a properly aligned surface step can strongly influence the motion of a threading dislocation, enhancing or retarding its motion. Anisotropic elastic and elastic inhomogeneity effects are considered. The results are discussed in terms of the critical thickness concept. The anisotropic elastic prediction of the critical thickness for spreading agrees well with the experimental results for a Ni film on Cu.

Dislocations and Internal Stresses in Thin Films: A Discrete-Continuum Simulation

The plasticity of thin films and layers is of considerable technological interest. For instance, the relaxation of internal stresses in semiconducting epitaxial layers has been the object of many studies [1, 2]. This relaxation is usually treated via the concept of critical thickness, the latter being defined as the maximum layer thickness below which dislocations cannot spontaneously move and relax the internal stresses. The various internal stresses present in epitaxial layers (e.g. the misfit and elastic incompatibility stresses at the film/substrate interface and the image force in a free-standing film) can be computed within a continuum frame. However, the way they influence the motion of a dislocation has not yet been computed, even in a approximate manner. An useful approximation that allows treating the boundary condition at the surface of a free-standing film consists of making use of the concept of image dislocation. Then, the critical stress for moving a dislocation in a free-standing film is the same as that of a capped layer of thickness twice that of the film. To date, models and dislocation dynamics (DD) simulations are available that involve several levels of approximation for the treatment of the dislocation/interface and dislocation/surface interactions [3–7]. For reasons that are not clearly understood, however, these models predict critical thicknesses that are systematically larger than the expected ones. The comparison with experiment is, in addition, made difficult because stresses have to be artificially introduced to replace the internal stresses and approximations have to be done to treat the image stresses. In the present work it is shown that it is now possible to fully account for the contribution of the various sources of internal stresses to the critical stress for the motion of a threading dislocation. This is performed numerically with the help of a hybrid code that combines a DD code for the treatment of the dislocation dynamics and a Finite Element (FE) code for the treatment of the boundary conditions. In what follows, several applications of this discrete-continuum model (DCM) to the study of dislocation motion in epitaxial layers are presented. The motion of a dislocation in a thin film is considered, including the image force and successively adding a misfit stress and an elastic incompatibility stress at the film/substrate interface.

Analysis of the strained-layer critical thickness concept based on a Peierls—Nabarro model of a threading dislocation

Abstract The Peierls–Nabarro theory of crystal dislocations is applied to estimate the critical thickness of a strained layer bonded to a substrate for a given mismatch strain. Strained epitaxial layers are common in microelectronic structures. The electronic properties of a film depend in most cases on the misfit strain (and hence the misfit stress). Unfortunately, an excessive strain may lead to the nucleation and propagation of defects, such as misfit dislocations. One such defect that has received wide attention in recent years is the so-called threading dislocation, which runs from the free surface of the strained layer to the interface, where it continues as an interfacial misfit dislocation. The critical thickness is achieved when the net driving force necessary to extend the misfit dislocation becomes positive. Previous analyses were based on the continuum theory of elastic dislocations, and hence depended on the artificial core cut-off parameter r0. The Peierls–Nabarro theory makes use of an inte...

The driving force for glide of a threading dislocation in a strained epitaxial layer on a substrate

T he process of epitaxial growth of a very thin layer onto a substrate crystal is considered for the particular situation in which the layer and substrate materials have the same crystal structure and orientation but different lattice parameters. Under these conditions, the layer grows with an intrinsic elastic strain determined by the mismatch in lattice parameters. The associated stress in the crystalline layer provides a driving force for the nucleation and motion of defects, primarily dislocations. The focus here is on the glide of a dislocation extending from the free surface of the layer to the layer-substrate interface, the so-called threading dislocation. A general definition of driving force for glide of a threading dislocation is introduced on the basis of work arguments. The definition is then applied to calculate the driving force for steady motion of an isolated threading dislocation in a strained layer, and the result includes Matthews' critical thickness concept as one of its features. Next, a kinetic equation for glide of a dislocation in semiconductor materials is proposed to estimate the glide rate of a threading dislocation in these low mobility materials. Finally, for the case of cubic materials, the general definition of driving force is applied to estimate the additional driving force on a threading dislocation due to an encounter with a dislocation on an intersecting glide plane. The results indicate that this effect is significant in blocking the glide of a threading dislocation for large mismatch strains and for layer thicknesses near the critical thickness.

The Use of Superlattices to Block the Propagation of Dislocations in Semiconductors

ABSTRACTSince the discovery in 1973 that GaAs/GaAsP superlattices can be grown with low dislocation densities, considerable interest has developed in utilizing superlattices as dislocation filters in multilayer semiconductor device structures. Many attempts to implement this process have been described, with varying degrees of success being achieved. Some investigators have reported favorable results; some have observed no effect; and in some cases the situation was actually made worse. This paper analyzes these reports and attempts to clarify the confusion that has arisen. Suggestions are made for improved effectiveness. Factors considered include the strain between layers, the layer thickness, the concept of critical thickness, the dislocation geometry, and the influence of buffer layers and growth conditions.

Mechanics of Elastic Dislocations in Strained Layer Structures

AbstractApplication of the elastic continuum theory of dislocations to modeling of phenomena associated with elastic strain relaxation in strained layer epitaxial heterostructures is discussed. The concept of critical thickness for onset of strain relaxation in a strained epitaxial layer is first reviewed, and some extensions to periodic arrays of dislocations and to multiple layers are described. Then, two issues are addressed that arise when the assumptions underlying the critical thickness concept are not met. One issue concerns the nucleation of dislocations at the growth surface of an epitaxial film, particularly the influence of surface irregularities on the activation energy for surface nucleation. A second issue concerns the kinetics of glide of a threading dislocation as it lays down an interface misfit dislocation when the layer thickness exceeds the critical thickness. A generalized driving force for the glide process is defined, and a relationship between this force and the glide speed is proposed.