Ephraim Suhir

New approach to the high quality epitaxial growth of lattice‐mismatched materials

We have reconsidered the problem of the critical layer thickness hc for growth of strained heterolayers on lattice‐mismatched substrates, using a new approach which allows us to determine the spatial distribution of stresses in a bi‐material assembly and include the effects of a finite size of the sample. The possibility of dislocation‐free growth of lattice‐mismatched materials on porous silicon substrates is discussed as an example of a more general problem of heteroepitaxial growth on small seed pads of lateral dimension l, having a uniform crystal orientation over the entire substrate wafer. It turns out that for a given mismatch f, the critical film thickness hlc strongly depends on l, rising sharply when the latter is sufficiently small, l≲lmin. The characteristic size lmin( f ) below which, effectively, hlc( f )→∞, is determined in terms of the experimentally known (or calculated for growth on a monolithic substrate) function h∞c( f )≡hc( f ). When l≲lmin, then the entire elastic stress in the epit...

Applied Probability for Engineers and Scientists

Random events discrete random variables continuous random variables systems of random variables functions of random variables entropy and information random processes - correlation theory random processes - spectral theory extreme value distributions reliability Markovian processes random fatigue geometric tolerance random loads and responses in some engineering systems processing of experimental data.

Thermal properties of carbon nanotube array used for integrated circuit cooling

Carbon nanotubes (CNTs), owing to their exceptionally high thermal conductivity, have a potential to be employed in micro- and optoelectronic devices for integrated circuit (IC) cooling. In this study we describe a photothermal metrology intended to evaluate the thermal conductivity of a vertically aligned CNT array (VCNTA) grown on a silicon (Si) substrate. Plasma-enhanced chemical vapor deposition, with nickel (Ni) as a catalyst, was used to grow CNT. The experimentally evaluated thermal conductivity of the VCNTA and the thermal contact resistance at the interface between the VCNTA and the “hot” surface was found to be in a satisfactory agreement with theoretical predictions. The measured effective thermal resistance is measured to be 0.12∼0.16cm2∙K∕W. This resistance was compared to the measured resistance of commercially available thermal grease. Based on this comparison, we conclude that, although the thermal resistance of CNTs might not be as low as it might be desirable, there exists a definite inc...

Mechanical approach to the evaluation of the low temperature threshold of added transmission losses in single-coated optical fibers

An easy-to-use calculation procedure for the evaluation of thermally induced forces in single-coated optical fibers is discussed. The calculations show that the increase in the lateral pressure at the cladding-coating interface adequately reflects the experimentally observed increase in the added transmission losses at low temperatures. The measurements were carried out on loose fibers in a test chamber, where mechanical effects other than the thermally induced shrinkage of the coating were excluded. It is suggested that the thermally induced lateral pressure be used as a tentative criterion of the low temperature threshold of the expected added optical losses in single-coated fibers. The increase in this pressure reflects the increase in the axial thermal loading as well. Single-coated optical fibers can be successfully used in transmission media operated at moderately low temperatures (for instance, in undersea systems) which do not cause large thermally induced forces; otherwise, a dual-coated fiber design should be considered. The final selection of the most feasible coating design must be based on all the material, optical, chemical, technological, mechanical, environmental, and cost considerations. >

Analysis of interfacial thermal stresses in a trimaterial assembly

The interfacial stresses in, and the curvature of, an elongated trimaterial assembly, subjected to the change in temperature, are predicted based on an approximate structural analysis (strength-of-materials) model. The obtained results can be helpful in stress–strain evaluations and physical design of trimaterial assemblies in microelectronic and photonic packaging.

Is the maximum acceleration an adequate criterion of the dynamic strength of a structural element in an electronic product

The dynamic strength of structural elements of micro- and portable electronic products is often evaluated on the basis of the measured maximum acceleration which these elements experience during shock or drop tests. It is well known, however, that it is the dynamic stress, not the acceleration, which is a true criterion of the dynamic strength. Using examples of structural elements that can be idealized as a simply supported beam or a cantilever beam with a concentrated mass at the end, we show that for elements of the given geometry and weight, the level of the maximum stress can be indeed judged upon on the basis of the measured acceleration. However, the application of the measured acceleration as a criterion of the dynamic strength can be misleading if applied to elements of different dimensions, weight and materials. We conclude that although the maximum acceleration is substantially easier to measure, it is the maximum dynamic stress that should be evaluated experimentally or theoretically when there is a need to establish the level of the dynamic strength of a structural element of an electronic product and the role of different factors affecting this strength. The obtained information can be helpful when evaluating the results of, or designing drop tests for electronic products.

Effect of initial curvature on low temperature microbending in optical fibers

An analytical evaluation of the thermally induced microbending in dual-coated optical fibers is presented, with an emphasis on the effect of the initial local curvatures. The analysis has shown that these curvatures could cause appreciable additional deflections of the glass fiber even at moderately low temperatures, thereby resulting in added transmission losses. The developed formulas are considered simple, easy-to-use, and to indicate clearly the role of various factors affecting the prebuckling behavior of fiber. They also indicate what could be done to bring down, if necessary, the temperature-induced curvatures and the resulting added transmission losses. Some recommendations for the selection of the thicknesses and material characteristics are presented. The numerical examples are executed for silicone/nylon coated systems, which were studied experimentally by Y. Katsuyama et al. (1983). The theoretical prediction agrees well with the experimental observations. >

Thermally induced stresses in an optical glass fiber soldered into a ferrule

An analytical model is developed for the evaluation of the thermally induced stresses in the midportion of an optical glass fiber soldered into a ferrule. The purpose of the analysis is to select the appropriate solder material and the geometry of the solder joint. We show that the ferrule has the major effect on the stresses in the glass and the solder, and that, for conventional solders, low expansion ferrules (Invar) result in high-tensile radial and tangential stresses in both the glass and the solder. On the other hand, high-expansion ferrules (aluminum, nickel) result in excessive compressive stresses and therefore should also be avoided. However, ferrule materials of moderate expansion (Kovar) lead to low stresses and are recommended, We show also that high-modulus solders, such as gold-tin, result in substantially higher stresses than low modulus solders, such as silver-tin, and that thinner solder layers lead to lower stresses in the glass, but to higher tangential and axial stresses in the solder. We conclude that the appropriate solder material and the thickness of the solder ring can be established, based on the developed stress model, depending on the material and thickness of the ferrule, and the characteristics of the solder itself. >

Predicted thermal stresses in a bimaterial assembly adhesively bonded at the ends

The interfacial shearing and “peeling” stresses in an elongated bimaterial assembly, adhesively bonded at the ends and subjected to the change in temperature, are predicted, based on an approximate structural analysis (strength-of-materials) model. The stresses in the bonded joints due to the thermal expansion (contraction) mismatch of the adherend materials within the bonded areas (“local” mismatch), as well as the stresses, caused by the thermal mismatch of the adherend materials within the unbonded midportion of the assembly (“global” mismatch), are considered. The interaction of the “local” and the “global” stresses is evaluated and analyzed. It is shown that if the bonded joints are made long enough, the maximum stresses in the assembly will not be different from the stresses in an assembly with a continuous adhesive layer, no matter how long the unbonded midportion of the assembly might be. The obtained results can be helpful in the stress–strain evaluations and physical (mechanical) design of bimat...

Stresses in Adhesively Bonded Bi-Material Assemblies Used in Electronic Packaging

The magnitude and the distribution of stresses in elongated adhesively bonded bi-material assemblies subjected to uniform heating or cooling are determined and discussed. The suggested approach enables one to evaluate the stresses in the assembly components themselves, as well as the shearing and normal (peeling) stresses in the interface, with consideration of the attachment compliance. The case of an epoxy bonded assembly is used to illustrate the developed theory.