Investigation of moisture diffusion in electronic packages by molecular dynamics simulation

Moisture-related failure is one of the main concerns in the integrated circuit (IC) package design. To minimize such failure in multi-layered electronic assemblies and packages, it is important to develop a better understanding of the reliability at a molecular level. In this paper, molecular dynamics (MD) simulations were conducted to investigate the respective moisture diffusion into the epoxy molding compound (EMC) and at the EMC/Cu interface. Moisture diffusion coefficients into the bulk EMC material and at the EMC/Cu interface can be derived from the mean-squared displacements calculated from MD simulations. The MD results showed that the seepage along the EMC/Cu interface is more prevalent when compared to moisture diffusion into the bulk EMC and, thus, rendering it a dominant mechanism causing moisture induced interfacial delamination in plastic packages.     

Material properties of the cross-linked epoxy resin compound predicted by molecular dynamics simulation

Molecular dynamics (MD) simulations were conducted to estimate the material properties of the cross-linked epoxy resin compound. A periodic amorphous structure of the cross-linked epoxy resin compound was constructed and it was simulated by continuous accumulation of structure configurations at various temperatures. Based on the simulation results, glass transition temperature (T_g), linear thermal expansion coefficients and Young's modulus of the cross-linked epoxy resin compound were predicted. The predicted values of these material properties are in good agreement with the experimental values in the literature.     

Roles of cyclic units in copolyethylene crystallization: a molecular dynamics simulation

Molecular dynamics (MD) simulations of several polyethylene copolymer chains containing 1,2-, 1,3- or 1,4-disubstituted cyclopentane or hexamethylene structures in the main chain (with 500 CH₂) are performed to investigate the influence of cyclic units on the crystallization properties of polyethylene (PE). From the isothermal relaxation process it is found that they generally collapse to a globule via a local collapse process. The copolymer chains containing 1,2-disubstituted cycloparaffin structures form more kinks and take shorter time to totally collapse into a single globule than the others. Moreover, from the morphology of the crystal structures after annealing it is found that the copolymer chains containing 1,2-disubstituted cycloparaffin structures can yield more ordered structures with cyclic units rejected to the fold surface. For the copolymer chains containing 1,3- or 1,4-disubstituted cycloparaffin, the lamellar structures are not perfect and some cyclic units are always incorporated in the crystalline phase.     

Ab initio molecular dynamics simulation of the structural and electronic properties of aluminoborosilicate glass

In this study, the structural and electronic properties of aluminoborosilicate glass, which has a wide range of applications in fields such as microelectronics and displays, were examined using ab initio molecular dynamic simulations. Computing models containing 220 atoms correctly described the local structure of the glass. The reliability of the computing models was verified by the consistency between the experimental results, obtained using high-energy X-ray diffraction and solid-state nuclear magnetic resonance, and the simulation results pertaining to structural factors, pair distribution functions, Qⁿ distribution, and elastic properties. The presence of B and Al increased the flexibility and asymmetry of the system, as shown by the bond angle and ring size distributions. Based on the electronic properties, we observed that the introduction of Al and B atoms into the network could also cause covalent interactions with the O atoms, similar to that with Si atoms. However, the Na and Mg atoms still interacted with all kinds of atoms in the network via charge transfer and exhibited highly non-localized effects on the charge of the network formers. These results extend our understanding of the structure of aluminoborosilicate glass and have guiding significance for improving and designing new types of this glass.     

The crystallization of low-density polyethylene: a molecular dynamics simulation

Three models (star-shaped, H-shaped, and comb-shaped polyethylenes) are used to study the crystallization behavior of low-density polyethylene at the molecular level by means of molecular dynamics simulation. It is shown that, for the three types of polyethylene corresponding to the models, the neighboring sequences of trans bonds firstly aggregate together to form local ordered domains, and then they coalesce to a lamellar structure. In the process, the branching sites are rejected to the fold surface gradually. The driving force for the relaxation process is the attractive van der Waals interaction between the chain segments. Furthermore, it is found that the number of the branch sites and the length of the branch play an important role in determining the formation of the lamellar structure. The longer the length of the branch and the fewer the number of the branch sites, the more perfect lamellar structure can be formed.     

Diffusion of single alkane molecule in carbon nanotube studied by molecular dynamics simulation

Full atomistic molecular dynamics simulations have been used to study the diffusion of alkane molecule in single wall carbon nanotube (SWCNT), with different alkane chain lengths and nanotube diameters. In this paper, we calculated the self-diffusion coefficient, mean-square gyration and bond-orientation order parameter of alkane molecule and the average intermolecular interaction energy per segment between SWCNT and alkane. Furthermore, structure of alkane in SWCNT was characterized through the radial distribution function, with results showing that the self-diffusion coefficient is related to the nanotube diameter. The component of mean-square gyration in z-direction scales with alkane chain length in SWCNT(9,9) like N1.07±0.04, which is in good agreement with the prediction from scaling theory for polymers. The obtained results show that nanotube diameter and alkane chain length are important factors affecting the behavior of one-dimensional confined alkanes.     

Structural and mechanical properties of advanced polymer gels with rigid side-chains using coarse-grained molecular dynamics

Computational modeling was utilized to design complex polymer networks and gels which display enhanced and tunable mechanical properties. Our approach focuses on overcoming traditional design limitations often encountered in the formulation of simple, single polymer networks. Here, we use a coarse-grained model to study an end-linked flexible polymer network diluted with branched polymer solvent chains, where the latter chains are composed of rigid side-chains or “spikes” attached to a flexible backbone. In order to reduce the entropy penalty of the flexible polymer chains these rigid “spikes” will aggregate into clusters, but the extent of aggregation was shown to depend on the size and distribution of the rigid side-chains. When the “spikes” are short, we observe a lower degree of aggregation, while long “spikes” will aggregate to form an additional secondary network. As a result, the tensile relaxation modulus of the latter system is considerably greater than the modulus of conventional gels and is approximately constant, forming an equilibrium zone for a broad range of time. In this system, the attached long “spikes” create a continuous phase that contributes to a simultaneous increase in tensile stress, relaxation modulus and fracture resistance. Elastic properties and deformation mechanisms of these branched polymers were also studied under tensile deformation at various strain rates. Through this study we show that the architecture of this branched polymer can be optimized and thus the elastic properties of these advanced polymer networks can be tuned for specific applications.     

A molecular dynamics simulation study on the crystallization of 22,8-polyurethane

By means of the molecular dynamics (MD) simulation, the crystallization mechanism of 22,8-polyurethane which contains hydrogen-bond units is investigated and the results show that the crystallization process at a fixed temperature can be characterized by three stages: (1) The extended chain collapses to a globular random coil; (2) The random coil reorganizes into an ordered lamellar structure; (3) Accompanied with the segments clustering due to the hydrogen-bond formation, the lamellar develops with local defects. Two kinds of hydrogen-bond, which are formed between NH group and CO group (N-H?OC), and between NH group and urethane alkoxy oxygen (N-H?O), respectively, are found to play an important role in the crystallization process of 22,8-polyurethane. Furthermore, the effect of temperature on the crystallization is also studied by selecting three temperatures 200, 300 and 400 K. The lower the crystal temperature is, the slower the crystallization rate is and the stronger the hydrogen-bonding interactions are presented. This is in harmony with the experimental results.     

Composition-structure-properties relationship of lithium-calcium borosilicate glasses studied by molecular dynamics simulation

The composition-structure-properties relationship of the lithium-calcium borosilicate (LCBS) glasses, which have a composition of 0.4[(1-x)Li₂O-xCaO]-0.6[(1-y)B₂O₃-ySiO₂] with x in the range of 0–1 and y in the range of 0.33–0.83, is investigated by the molecular dynamics (MD) simulation with the Buckingham potential. The structure of the silicon-oxygen tetrahedron is relatively independent of the glass compositions; however, the structure of the boron-oxygen polyhedron and the local environment around the modifier cations change significantly with increasing [SiO₂]/[B₂O₃] ratio (K) and CaO content. The relationships between glass composition and simulated linear thermal expansion coefficient (α_L), glass transition temperature (T_g), self-diffusivity (D), activation energy of electrical conductivity (Ea^σ) and fragility (m) are strongly affected by the change of glass network structure, and consistent with those of experimental results.     

Mechanical properties of SWNT X-Junctions through molecular dynamics simulation

The mechanical behavior of seven different carbon nanotube (CNT) X-junctions with a varying number of bonds was investigated through molecular dynamics simulations. The X-junctions are composed of two (6,0) single-walled carbon nanotubes (SWNTs) created via vibration-assisted heat welding. The junctions, containing anywhere between one and seven bonds, are subject to uniaxial tensile, shear and torsional strain, and then the stiffness values are determined for each case. When subjected to tensile and shear strain, both the arrangement and orientation of bonds are found to affect the stiffness of junctions more substantially than the number of bonds, bond length or bond order. Surprisingly, anisotropic shear behavior is observed in the X-junctions, which can be attributed to the junction's bond orientation. Also, the stiffness of X-junctions tested under an applied torque (torsion) differs from the stiffness under tensile and shear strain, however, in that it is more substantially affected by the number of bonds present in the junction than by any other property.     

Study on nanometric cutting of germanium by molecular dynamics simulation

Three-dimensional molecular dynamics simulations are conducted to study the nanometric cutting of germanium. The phenomena of extrusion, ploughing, and stagnation region are observed from the material flow. The uncut thickness which is defined as the depth from bottom of the tool to the stagnation region is in proportion to the undeformed chip thickness on the scale of our simulation and is almost independent of the machined crystal plane. The cutting resistance on (111) face is greater than that on (010) face due to anisotropy of germanium. During nanometric cutting, both phase transformation from diamond cubic structure to β-Sn phase and direct amorphization of germanium occur. The machined surface presents amorphous structure.     

Time evolution of dynamic heterogeneity in a polymeric glass: a molecular dynamics simulation study

Dynamic heterogeneity, where it is noticed in molecular dynamics (MD) simulations that, for example, conformational transition rates vary greatly from bond to bond, is characteristic of polymeric glasses. The phenomenon can be attributed to the fact that certain local bond sequences are more capable of conformational rearrangement than others. These local sequences become fixed sites when the overall chain trajectory is frozen-in in the glass. Although this is no doubt the case, because of the relatively short times of MD trajectories and the relatively small numbers of transitions it is important to establish that the heterogeneity does evolve in time in the manner expected from the local site picture and is not an artifact of short simulations or small numbers. This is undertaken here using a polyethylene system that has been much studied previously. Long trajectories are generated where the time evolution of heterogeneity can be studied. It is found that both the standard deviation and the mean value of the transitions over the bonds evolve linearly in time. This is consistent with the local fixed site picture and not with a random process involving relatively small numbers of transitions.     

Microstructure dependent diffusion of water-ethanol in swollen poly(vinyl alcohol): A molecular dynamics simulation study

Molecular dynamics (MD) simulation was used to study the swelling properties of poly(vinyl alcohol) (PVA) in ethanol solutions containing 15, 30 and 45 wt% water. The characteristics of the swollen PVA, intrinsic relation between the microstructure of the swollen PVA and the diffusion of water and ethanol in the PVA matrix were analyzed. It was found that the free volume of the swollen PVA reduced with reductions in the degree of crystallinity was accompanied by an increase in the mobility of PVA chains. Water located mostly in the hydrophilic region of the hydroxyl groups of PVA chains; and hydrogen bonding formed between water and PVA. It was also noted water clusters form in the swollen PVA, whose size increased with increasing degree of swelling, whereas ethanol molecules disperse almost individually in the PVA matrix. The diffusion coefficients of water and ethanol in the swollen PVA are predicted to increase linearly with increasing swelling.     

Non-equilibrium molecular dynamics simulation of gas separation in a microporous carbon membrane

We have carried out non-equilibrium molecular dynamics simulations of gas separation in a “selective surface flow” membrane. The gas mixture studied is hydrogen/methane, which is relevant to hydrogen purification in refineries. The simulations give insight into the separation mechanism, which is based on the transport of the more strongly adsorbing species (methane) in a dense layer near the pore wall, with the less strongly adsorbed species (hydrogen) diffusing through a less dense region close to the centre of the pore. Good agreement is obtained with experimental selectivity data. This work is also relevant to the study of the combined effects of adsorption and diffusion in microporous carbon adsorbents.     

A molecular dynamics simulation study of the influence of free surfaces on the morphology of self-associating polymers

Molecular dynamics simulations of thin films and bulk melts of model self-associating polymers have been performed in order to gain understanding of the influence of free surfaces on the morphology of these polymers. The self-associating polymers were represented by a simple bead-necklace model with attractive groups (stickers) at the chain ends (end-functionalized polymer) and in the chain interior (interior-functionalized polymer). The functionalized groups were found to form clusters in the melt whose size is representative of that found experimentally in many ionomer melts. While the size distribution and shape of the clusters in the thin films were found to be relatively unperturbed compared to their corresponding bulk melts, the morphology of the self-associating melts was found to be significantly perturbed by the free surfaces. Specifically, a strong depletion of stickers near the interface and the emergence of clearly defined layers of stickers parallel to the surface was observed. Increased bridging of clusters by the functionalized polymers was also observed near the free surface. We conclude that these effects can be associated with a high free energy for stickers in the low-density interfacial regime: stickers prefer to be in the higher-density interior of the film where relatively unperturbed sticker clusters can form.     

Study of surface conditions and shear flow of LCP melts in nanochannels through molecular dynamics simulation

The rheological properties and phase orientation of liquid crystalline polymer (LCP) melts flowing in a nanochannel with different surface roughness are investigated by molecular dynamics (MD) simulations. The molecular chains of LCPs are depicted by a newly developed molecular model named GB-spring-bead model, which has proved to be efficient and accurate in studying the phase transition behaviors of semi-flexible main chain LCPs [Yung KL, He L, Xu Y, Shen YW. Polymer 2005;46:11881 [1]]. The surfaces are modeled as rough atomic serrated walls whereby the roughness is characterized by the period and amplitude of serrations. Simulation results have shown that the surface roughness affects greatly the rheological properties and phase orientations of LCP melts in a nanochannel (the distance between the upper wall and the lower wall is 12.8 nm). As the amplitude of serration increases, the shear viscosity of LCP increases nonlinearly while its orientational order parameter decreases. When the serration amplitude reaches a certain magnitude, a phase transition (from nematic to isotropic phase) happens, which increases the viscosity of the nano LCP flow drastically. On the other hand, the influence of serration period on the shear viscosity and orientational order parameter is not so obvious relatively. Findings in this study provide very useful information in the injection molding of plastic products with nanofeatures.     

Investigation of packaging adhesive properties by molecular dynamics and experiments

Adhesive polymer is a common and important material used for packaging of microelectronics and microsystem by attaching dies onto packaging shell, and its mechanical property plays a vital role in isolating dies from the thermal stress of substrate. Therefore, it is extremely significant to evaluate the polymer property in a specific packaging process. The molecular dynamics (MD) simulation is conducted in this article to investigate the material properties of the cross-linked epoxy resin formed by epoxy resin component diglycidyl ether bisphenol A (DGEBA) and curing agent 1,6-Diaminohexane. The polymer network with conversion up to 87.5% is successfully generated and simulated by constant pressure-constant temperature ensemble (NPT) and canonical ensemble (NVT) at different temperatures of curing process. Glass transition temperature (T_g) and Young's modulus are extracted and the predicted material properties are in great agreement with the experimental data. The conclusion provides a guideline to design the special curing process for different adhesive requirements.     

Molecular dynamics simulation of miscibility in several polymer blends

The miscibility in several polymer blend mixtures (polymethylmethacrylate/polystyrene, (1,4-cis) polyisoprene/polystyrene, and polymethylmethacrylate/polyoxyethylene) has been investigated by using Molecular Dynamics simulations performed for fully atomistic representations of short chains. The trajectories obtained from simulation boxes representing the mixtures have been analyzed in terms of the collective scattering structure function. The Flory-Huggins parameter is determined from fits of the simulation results for this function to the random phase approximation expression. The numerical values of this parameter and its variation with temperature obtained with this procedure show a general qualitative and semi-quantitative agreement with existing experimental data for the different systems, though with significant error bars. These results together with those previously obtained for the polyvinylmethylether/polystyrene blends with the same method are compared with data yielded by other computational simpler approaches, which are considerably more sensitive to different parameter choices.     

Investigation of the polyurethane chain length influence on the molecular dynamics in networks crosslinked by hyperbranched polyester

Several non-conventional polyurethane (PU) networks crosslinked with hyperbranched polyester (Boltorn^®H40) were synthesised with an aim to determine an influence of the PU chain length on molecular relaxations in such systems. The PU chain length was regulated by changing the macrodiol length or by changing the number of the repeating macrodiol/diisocyanate units n. Molecular dynamics were investigated by broadband dielectric spectroscopy and by dynamic mechanical analysis. It was found that the macrodiol length has a strong influence on the glass transition and the α-relaxation, and also on the crystallization. By contrast, the changes of n practically do not affect the molecular relaxations. This effect was explained by the formation of a physical network by hydrogen bonds between urethane groups, controlling the molecular mobility. The rheological measurements have shown, that at temperatures above 150 °C, when hydrogen bonds were thermally destroyed, not only macrodiol length but also n had strong influence on the flowing point.