Metal-ceramic constraints for multilayer electronic packages

A comprehensive analysis of cermet design and thermal cyclic stability via elasto-viscoplastic crystal plasticity modeling

The corrugated layer structure bismuth has been successfully tailored into negative thermal expansion along c axis by size effect. Pair distribution function and extended X-ray absorption fine structure are combined to reveal the local structural distortion for nanosized bismuth. The comprehensive method to identify the local structure of nanomaterials can benefit the regulating and controlling of thermal expansion in nanodivices.

Light-polymerized compomers: Coefficient of thermal expansion and microhardness

Flip chip ball grid array (FCBGA) is one of the most broadly used package types in different types of electronic packages. In a FCBGA package, the die/ silicon is flipped and attached to substrate with help of copper pillars. The material property coefficient of thermal expansion (CTE) mismatch between die/ silicon and substrate materials like core, dielectric material results in package thermal warpage and may lead to thermo-mechanical related failures in electronic packages. CTE can be defined as the rate at which a material expands with change in the temperature. Material expansion increases with a higher CTE. The CTE of die/ silicon is lower than the overall CTE of organic substrate. During reflow, as an electronic package cools down it warps in a convex or crying shape which indicates positive package warpage, and as the electronic package heats up it warps in a concave or smiling shape which indicates negative package warpage. Induced thermal warpage during the electronic package reflow assembly process is an important factor affecting the package assembly and thermo-mechanical reliability of FCBGA packages; therefore, precise package thermal warpage prediction is one of the most significant parameters for the electronic package design processes. In this study, the effect of different electronic package parameters (core material CTE, core thickness, package type) of the FCBGA package on its warpage are assessed by using finite element analysis (FEA) mechanical simulation methodology. A bare die FCBGA package having substrate core material with lower coefficient of thermal expansion (CTE) shows lower package warpage as the mismatch between die/ silicon and substrate core material CTE becomes dominant factor to drive the package warpage. To understand the package warpage trend, warpage is evaluated at room temperature & high/ reflow temperature. The package warpage trend is reversed for larger FCBGA packages with stiffener ring. Substrate core material with higher CTE shows lower package warpage as CTE mismatch between substrate core material and stiffener ring material (steel/copper) CTE becomes the dominant factor to drive the package warpage. The counter intuitive package warpage data from mechanical simulation is compared with shadow-moire test data and it shows good correlation and validates the simulations findings. Based on this work, it is recommended that a thorough investigation for large size packages be conducted before choosing packaging materials. This work shall provide new insights for package designers to optimize thermal warpage and stress during package initial design phase.

Mechanics of discontinuous ceramic tile core sandwich structure: Influence of thermal and interlaminar stresses

Thermal expansion is an important design parameter of materials, which should be taken into account when developing, producing and using products. To control this significant characteristic of new materials, it is necessary to develop equipment, methods and measurement procedures that take into account the novelty of the specific behavior of these materials. The production of specially shaped samples is the main limitation in thermal expansion measurements. This primarily applies to new materials (heterogeneous, composite, poorly processed) developed for special tasks. These factors necessitated the development of a method for measuring the temperature coefficient of linear expansion of products and materials with arbitrary sample shapes, which was not available in previous implementations of interferometric methods. An interference speckle dilatometer SD was developed for measuring samples with irregular shape in the temperature range from 200 to 400 K. When creating the speckle dilatometer SD, the speckle interferometry method was implemented to measure the elongation of samples with an irregular surface with nanometer sensitivity. Since this device has no analogues, a study was conducted on the uncertainty components arising when measuring the thermal coefficient of linear expansion of materials on this device. The analysis of the uncertainty components of the measurement of the thermal coefficient of linear expansion of materials on the speckle dilatometer SD was carried out. An experimental determination of the measurement uncertainty of the thermal coefficient of linear expansion of TCLE measures of arbitrary shaped samples was obtained using the SD speckle dilatometer. After research and initial certification, the developed measurement instrument was approved and included in the State Secondary Standard of the unit of thermal coefficient of linear expansion of solids in the range of values from 0.05 · 10–6 to 100.0 · 10–6 K–1 in the range of temperature values from 90 to 1,900 K.

The coefficient of thermal expansion (CTE) of concrete is one of the important properties that are responsible for the thermal cracking of concrete structures. To reveal the essence of thermal expansion and predict the CTE accurately, this paper establishes a multiscale model for predicting the drained and undrained CTEs of concrete according to the microstructure based on the theory of continuum micromechanics. The microstructure of concrete is quantitatively analyzed according to the raw materials and degree of hydration. The CTEs are homogenized level by level from calcium silicate hydrate to cement paste, cement mortar, and concrete. Given the initial information of concrete, the CTEs can be predicted by the model. The experimental data of concrete from the literature validated the applicability of the proposed model. The influence mechanism of factors on CTEs can be explained by the influence on the microstructure of concrete. The model has good potential in optimizing the material design of concrete to obtain a lower CTE to minimize the risk of thermal cracking.

The coefficient of thermal expansion (CTE) is one of the most critical parameters for concrete pavement design. Concrete paving mixtures with high CTEs are generally subjected to temperature-related stresses and deterioration. In this study, a 2k design of experiment was applied to evaluate the effects of concrete mix design variables on the CTE of resultant concrete mixtures. Laboratory experiments were conducted by controlling six mix design variables, each at two levels, including aggregate type (granite or dolomite), fine sand type (manufactured or natural), fly ash type (Class C or Class F), cement content (314 or 273 kg/m 3), coarse aggregate content (1246 or 682 kg/m 3), and air content (3% or 6%). The respective and collective effects of these factors on the CTE were analysed. It showed that the type of coarse aggregate, fine sand, fly ash, and their respective contents are significant in explaining the variance of the lab-measured CTEs. The minimum CTE is a result of the concrete mixture consisting of low content of granite and cement in combination with high content of manufactured sand and Class F fly ash. To generalise the results, a parsimonious model was formulated and is capable of explaining over 92% of the total variance of the CTE and predicting it in a reasonably accurate manner.

Three-dimensional microstructure based model for evaluating the coefficient of thermal expansion and contraction of asphalt concrete

In-situ investigation of anisotropic crystalline and bulk negative thermal expansion in titanium alloys

High density polyethylene (HDPE) is a thermoplastic polymer which is classified as one of the highly consumed types of plastics. One major advantage of thermoplastic materials is their ability of recycling and reprocessing which will bring considerable economic and environmental benefits. The present paper, therefore, endeavors to explore the practical possibility of using recycled HDPE hollow section as a replacement of virgin HDPE made by the extrusion process. The main focus of the study was to evaluate the mechanical performance of the recycled HDPE and compare the results with virgin or non-recycled HDPE. The modulus of elasticity, tensile yield and ultimate strength, compressive yield and ultimate strength, flexural yield and ultimate strength and the coefficient of thermal expansion were the main parameters to be checked against the respective mechanical properties. Thus, pursuant to the results, it was found out that the modulus of elasticity and the tensile yield strength are lower in recycled HDPE compared to the non-recycled HDPE. However, there is no significant difference between the recycled and non-recycled HDPE for the tensile ultimate strength, compressive yield strength and compressive ultimate strength. The flexural yield strength and flexural ultimate strength properties of the recycled HDPE proved to be superior to those of the non-recycled HDPE. The coefficient of linear thermal expansion of the recycled HDPE sample was 130 μm/(m.°C) and that for the non-recycled HDPE was 142 μm/(m.°C).

The effect of cracks on the thermal expansion of rocks

Copper–matrix composites reinforced with Al2O3, SiO2, SiC and MgO nanoparticles were fabricated using powder metallurgy. The effects of the different nanoparticles on the thermal expansion behaviour of the composites were examined. The thermal expansion properties of the composites were evaluated using the coefficient of thermal expansion from 50 to 500°C. The relationship between interface stress and coefficient of thermal expansion of the copper–matrix composites with various reinforced phases was determined using theoretical models and experimental data. The results show that introducing dispersed nanoparticles into the copper matrix can significantly reduce the coefficient of thermal expansion. By contrast, increasing the temperature increases the thermal expansion coefficient of the copper–matrix composites and the interfacial pressure between the reinforcements and the copper matrix. The calculated pressure values at the nanoparticle–copper matrix interface suggest that plastic deformation occurred in the temperature range from 200 to 250°C for the SiO2/Cu and SiC/Cu composites and at 350°C for the MgO/Cu and Al2O3/Cu composites. These values are consistent with the variations observed in the measured coefficient of thermal expansion.

Modelling and verification of a novel bi-material mechanical metamaterial cellular structure with tunable coefficient of thermal expansion

The nonequilibrium Green's function method is applied to investigate the coefficient of thermal expansion (CTE) in single-walled carbon nanotubes (SWCNT) and graphene. It is found that atoms deviate about 1% from equilibrium positions at T=0 K, resulting from the interplay between quantum zero-point motion and nonlinear interaction. The CTE in SWCNT of different sizes is studied and analyzed in terms of the competition between various vibration modes. As a result of this competition, the axial CTE is positive in the whole temperature range, while the radial CTE is negative at low temperatures. In graphene, the CTE is very sensitive to the substrate. Without substrate, CTE has large negative region at low temperature and very small value at high temperature limit, and the value of CTE at T=300 K is $-6\times 10^{-6}$ K$^{-1}$ which is very close to recent experimental result, $-7\times 10^{-6}$ K$^{-1}$ (Nat. Nanotechnol. \textbf{10}, 1038 (2009)). A very weak substrate interaction (about 0.06% of the in-plane interaction) can largely reduce the negative CTE region and greatly enhance the value of CTE. If the substrate interaction is strong enough, the CTE will be positive in whole temperature range and the saturate value at high temperature reaches $2.0\times 10^{-5}$ K$^{-1}$.