MedeA®: Atomistic Simulations for Designing and Testing Materials for Micro/Nano Electronics Systems

A. France-Lanord, D. Rigby, A. Mavromaras, V. Eyert*, P. Saxe, C. Freeman, and E. Wimmer

Materials Design SARL, Montrouge, France Materials Design, Inc., Angel Fire, NM, USA

*Corresponding author: veyert@materialsdesign.com

Abstract Results of atomic-scale simulations are presented

including thermal conductivity, elastic moduli, diffusion, and adhesion. This type of simulations is most conveniently performed with the MedeA® computational environment, which comprises experimental structure databases together with building tools to construct models of complex solids, surfaces, and interfaces for both crystalline and amorphous systems. Central to MedeA® are state-of-the-art modules for the automated calculation of thermodynamic, structural, electronic, mechanical, vibrational, and transport properties combined with the corresponding graphical analysis and visualization tools. These capabilities are illustrated for both inorganic and organic materials. For Si-Ge alloys and amorphous-crystalline silicon superlattices we find a drastic reduction of the thermal conductivity compared with bulk crystalline Si. In addition, the Si-Ge alloys reveal a considerable sensitivity of their thermal conductivity to disorder. The second part of this study addresses properties of epoxy resin based thermosets, including their mechanical stiffness, thermal conductivity, and adhesion on alumina. In addition, we present calculated results for oxygen and water diffusivities in cross-linked epoxy systems and discuss factors influencing such diffusivities as, e.g., mass effects or the concentration of residual hydroxyl groups in the polymer.

1. Introduction The last decades have seen unprecedented progress

of atomistic simulations in materials science and engineering. Nowadays, atomic-scale methods have evolved as an indispensable part of research both in industry and academia. In industrial research laboratories, the corresponding computational tools have found widespread application in solving complex engineering problems. At the same time, they are routinely used at universities and national laboratories to address fundamental questions of condensed matter research and to explore so far unknown materials with exciting properties.

The MedeA® computational environment of Materials Design has become a well-appreciated tool in this community. The MedeA® software offers a unique, comprehensive, and innovative software environment, which combines experimental structures and phase-diagrams with state-of-the-art computational procedures for property predictions for systems

including alloys, semiconductors, ceramics, glasses, polymers, and fluids. Building on quantum mechanics, MedeA® facilitates the simulation of electronic structures and mechanical properties, as well as the thermal behavior for complex structures such as interfaces, heterostructures, grain boundaries, defect structures, and random alloys. Using high-performance molecular dynamics, MedeA® calculates transport properties such as diffusion coefficients and heat conductivity in amorphous oxides. Besides predicting fundamental properties of nanoelectric devices, the functionality of MedeA® addresses topics related to packaging, device assembly and component mounting. These include the prediction of thermal conductivity for semiconductors, metals, and oxidized metal heat sinks and epoxy thermoset encapsulation materials, as well as tools to investigate mechanical, adhesive and diffusive properties relevant to device performance and reliability.

In this paper, we demonstrate the capabilities of MedeA® with selected examples. In doing so, we focus especially on the thermal conductivity using forcefield methods as implemented in the software environment. The thermal conductivity is of high interest in different fields. In thermoelectrics, materials are sought with a high electrical conductivity combined with a low thermal conductivity as can be found in doped semiconductors with a high density of states near the band edges. In the present paper, we investigate the thermal conductivity of Si-Ge alloys and a-Si/c-Si superlattices and discuss the influence of defects, disorder, and amorphous structures. We find that in Si-Ge alloys the thermal conductivity can be reduced to 2 W/m/K for about 12% Ge as compared to 128 W/m/K of bulk crystalline silicon. However, layered systems are much more efficient than disordered materials in this respect.

The second part of the paper deals with epoxy resin based thermosets, which are widely used in semiconductor devices. In this context, a high thermal conductivity is desired in order to facilitate fast heat dissipation. Specifically, for the epoxy system consisting of a stoichiometric mixture of diglycidyl ether of bisphenol A (DGEBA) and meta phenylene diamine (m-PDA) cross-linked with degrees of cure up to ~80% we find good agreement with experimental data. Calculations of the elastic properties for the same thermoset reveal the sensitivity of the tensile modulus on the level of curing. Additionally, we address the adhesion of DGEBA-Jeffamine® on alumina. The

simulations for the present model show that without direct chemical bonding between the organic and inorganic phases the work of separation is 0.15 Jm-2. Finally, we study the diffusivities of oxygen and water, respectively, in the DGEBA-Jeffamine® epoxy systems. The calculations involve NVE molecular dynamics, which give access to mean-square displacements of the molecules. For DGEBA-Jeffamine® our results point to similar activation energies for oxygen and water and an increased diffusivity of oxygen as compared to water at ambient conditions.

2. Lattice Thermal Conductivity in Semiconductors Lattice thermal conductivity is one of the

fundamental transport properties of materials. Its knowledge is necessary, for instance, in evaluating semiconductor efficiency for thermoelectric device applications. As heat dissipation in microelectronics and nanoelectronics becomes more and more important, the ability to predict thermal conductivity is of crucial importance for modern science and technology.

There are currently two standard approaches for obtaining the lattice thermal conductivity, namely: (i) calculation of the phonon properties of the system, which are connected to the thermal conductivity through the Boltzmann transport equation (BTE) [1] and (ii) molecular dynamics (MD) simulations [2, 3] at both equilibrium (EMD) and non-equilibrium (NEMD).

Despite their inherent approximations, classical molecular dynamics simulations give very good results for thermal conductivity in agreement with experiments for various semiconductors around room temperature or higher [4, 5]. In particular, they allow computations for very large models of more than a million atoms representing complex geometries.

Quantum effects on the thermal transport are accounted for by using Boltzmann transport calculations, but this method suffers from several flaws. First, these calculations are much more expensive than MD: large or aperiodic systems cannot be simulated. Second, the relaxation time approximation used to solve the BTE drastically reduces the predictive power of the method since empirical parameters are needed. This is clearly opposed to the MD formalism, which is "classically exact", and does not rely on approximate theoretical expressions. 2.1 Thermal conductivity prediction using MedeA®

In the following we will sketch the basic principles of equilibrium molecular dynamics (EMD) and reverse non-equilibrium molecular dynamics (RNEMD) simulations for the calculation of the thermal conductivity. This methodology is implemented in Materials Design’s computational environment MedeA®, which takes advantages of the LAMMPS

[6, 7] molecular dynamics package, for both EMD and NEMD procedures. The capabilities of this approach are illustrated in the subsequent section. 2.1.1 Equilibrium Molecular Dynamics

At the equilibrium state, one can determine the thermal conductivity of a system using the Green-Kubo relation [8]:

( ) ( ) dttVTkB

∫∞

=0

2 031 JJκ (1)

where κ is the thermal conductivity tensor, kB is the Boltzmann constant, V is the volume of the system, T its average temperature, and J(t) the heat flux vector. Relatively long simulations - depending on the system size, and the species involved - in the NVE (constant number of atoms, volume, and energy) microcanonical ensemble are needed to obtain a well converged value of the heat flux, and therefore of its autocorrelation function. It is also necessary to model a sufficiently large domain, in order to avoid artificial size effects, due to the cutoff of the long wavelength phonons.

The major advantage of EMD simulations is that one can obtain the full thermal conductivity tensor in only one simulation. This is very important for systems showing important thermal anisotropy, like for instance Si-Ge superlattices. Equilibrium molecular dynamics have been used to determine the thermal properties of a wide range of semiconductors, including core-shell silicon nanowires [9], Si-Ge nanocomposites[10], and Bi2Te3 nano-wires [11]. 2.1.2 Reverse Non-Equilibrium Molecular Dynamics

Transport phenomena intrinsically derive from the non-equilibrium state: for instance, when a temperature gradient is imposed on a system, the energy will flow until equilibration is achieved. This is the basis of non-equilibrium molecular dynamics simulations for thermal properties evaluation: in a way similar to experiments, one applies a temperature gradient, generally with the use of heat reservoirs, and evaluates the resulting heat flux. The thermal conductivity is then obtained using Fourier's law: T∇⋅−= κJ (2)

where κ is the thermal conductivity tensor, J is the heat flux vector, and ∇T is the temperature gradient.

The need of external thermostating can be suppressed by swapping the cause and the effect [12]. In reverse-NEMD (RNEMD) simulations, a heat flux is imposed by regularly exchanging the kinetic energies of hot and cold particles resulting in a temperature profile that can be determined once the steady state is reached. In this way, the total energy and total linear momentum are conserved; hence no external thermostating is needed. The RNEMD method is implemented in practice by dividing the system in slabs following, by default, the z direction. The z=0 slab is defined as the cold slab, and

the z = Lz/2 as the hot slab, Lz being the length of the simulation box. After every n time steps, the hottest atom in the cold slab and the coldest atom in the hot slab are identified and swapped: each of the components of their velocities are exchanged. Once the steady state is reached, the temperature profile is obtained by evaluating the mean temperature of each slab. The gradient in the z direction ∂T/∂z is then post-processed, by identifying the slope of the temperature profile. The corresponding diagonal component of the thermal conductivity tensor can then be calculated.

Generally speaking, NEMD procedures are well adapted for nanomaterials, and all kind of semiconductors. Simulations are usually less time-consuming than EMD ones, but one should pay attention to size effects, that are of greater importance. Moreover, only the diagonal component of the thermal conductivity tensor perpendicular to the slabs can be determined in this approach. Still, NEMD simulations are very well adapted to semiconductors, e.g., in the form of superlattices [13–15]. 2.2 Tailoring thermal properties using MedeA®: An

example In order to maximize the efficiency of

thermoelectric devices, one aims at lowering the thermal conductivity of semiconductors without deteriorating their electronic transport properties. Molecular dynamics simulations allow predicting and quantifying the thermal conductivity and its changes on introducing structural distortions as, e.g., defects and local disorder.

Here we will compare two ways to alter the thermal conductivity of bulk Si: by adjoining amorphous regions in between crystalline Si regions (a-Si/c-Si superlattices), and by replacing a certain number of Si atoms by Ge atoms. Both types of changes modify the phonon properties of the system, and it is possible to predict their impact using simple NEMD simulations.

With the help of MedeA® the following calculations can be very efficiently performed. To begin with, structural models are built using the corresponding tools implemented in MedeA®. Once these structural models are created, EMD or NEMD (depending on the structure – size, geometry, species) simulations using MedeA®-LAMMPS are carried out leading to the results shown in the figures below.

As a reference, the thermal conductivity of bulk silicon as computed using MedeA®'s Thermal Conductivity module amounts to 128 W/m/K, which compares excellently to the measured lattice thermal conductivity of 130 W/m/K (Ioffe Institute).

In this study, different systems were compared. First, the Random Substitution module of MedeA® was used to create Si43Ge by randomly replacing a Si atom by a Ge atom, this leading to a defect concentration of 2.27%. Second, superlattice models with the same Ge concentration were created by arranging the Ge atoms in layers, which are separated by 43 Si slabs. Finally,

for the latter arrangement Si43Ge5 superlattices were also considered.

RNEMD simulations were undertaken using MedeA® on these samples, leading to highly accurate results of the thermal conductivity. Finally, these results are compared to the ones of a recent study [16] on the thermal conductivity of a-Si/c-Si superlattices that was computed using NEMD with LAMMPS. Figure 1 shows three different samples, using MedeA®’s visualization tools.

Figure 1: Three systems as generated from MedeA®’s visualization tools. Top: a layered Si43Ge5 sample. Middle: an amorphous/crystalline superlattice. Bottom: a Si system, with few random replacements of Ge atoms (Si43Ge). Light color: Si, dark color: Ge.

Of course, these systems have different qualities and fields of application: The Si-Ge superlattice is one of the best material for high temperature thermoelectric applications, while a-Si/c-Si structures present a very high thermal conductivity anisotropy (the in-plane one is up to six times higher than the cross-plane one), very useful for heat spreading in optoelectronics [17] or heat shields, for instance.

Calculated temperature profiles of the Si43Ge random and layered structures as directly resulting from MedeA® are shown in Figure 2.

The results of the calculations are summarized in Figure 3, which shows the thermal conductivity of different systems as a function of the Ge concentration in Si-Ge and the fraction of amorphous Si in a-Si/c-Si, respectively. Given the thermal conductivity of crystalline Si of 128 W/m/K it is clear that the depression in a-Si/c-Si samples is due to the amorphous layers. Even with very thin layers, the thermal conductivity is reduced by a factor of 20 relative to the bulk value. Yet, according to Figure 3 the decrease of the thermal conductivity seems to saturate at about 25% of amorphous Si.

A similar drastic reduction of the thermal conductivity is observed for Si-Ge. On replacing only one out of 44 Si atoms by Ge the thermal conductivity drops by about a factor of 20 relative to bulk Si. Furthermore, the drop is even more drastic for the

layered structure, which brings about further reduction to less than 4 W/m/K. Finally, for the layered systems it is found that the decrease in thermal conductivity is enhanced with increasing Ge concentration.

Figure 2: Temperature profiles of layered (top) and random (bottom) Si43Ge structures. Circles and the dots making the horizontal line give the mean temperature and the number of atoms, respectively, in each slab. Thin lines are automatic fits to the mean temperature points, which are used to determine the temperature gradient.

Figure 3: Thermal conductivity as a function of the proportion of amorphous Si and Ge, respectively. Note that the two sets of calculations used different computation protocols. A quantitative comparison between the two series may thus contain systematic deviations.

3. Thermo-mechanical Property Simulation of Epoxy-Based Thermosets Epoxy resin based thermosets, in the form of epoxy

molding compounds (EMCs) are widely used in a variety of electrical and electronic devices, ranging from use as insulating materials in high voltage transformers, cable terminations and associated equipment, to use as encapsulation materials in electronic components. At either extreme of the device scale, the essential requirement is that the epoxy acts as an insulator, while retaining the ability to dissipate excess heat generated within the device.

Epoxy thermosets themselves however suffer from the limitation that they typically possess relatively low thermal conductivity. Consequently filler consisting of electrically insulating but thermally conductive particulate material is often added to the EMCs used to fabricate the components. Often, this material consists of relatively high loadings of 50-80% silica micro- or nanoparticles bonded to the resin matrix using a silane-based coupling agent. However, the modest thermal conductivity of silica, coupled with a desire to exploit more effectively the properties of the cross-linked resin matrix has led to interest in using much lower loadings - up to 5% - of other fillers such as aluminum oxide, aluminum nitride, boron nitride, or even carbon nanotubes and nanoplatelets [18, 19].

From a device fabrication and durability perspective, the combination of cross-linked base resins, fillers, active electrical or electronic components and other parts such as connector leads presents interesting challenges, many of which are amenable to study at the atomistic level using quantum or classical mechanics simulation methods. Topics of interest include: 1. Effectiveness of the filler-coupling agent-epoxy

interaction in enhancing, for example, mechanical properties of the device.

2. Absorption and aggregation of water after exposure to humid environments and the resulting effect on properties, including delamination and catastrophic failure (e.g. the 'popcorn' effect [20]).

3. Wetting and adhesion of resin and other device materials (e.g. Al2O3, semiconductor material, Au leads, etc.).

4. Thermal conductivity and thermal expansion of the cross-linked base resin and resin-filler systems. In recent work, we have developed building,

simulation and analysis tools within the MedeA® modeling environment suitable for conducting a variety of studies relevant to electrical and electronic devices and device packaging. Thus, for example, we have recently developed the MedeA® Thermoset Builder for construction of realistic models of epoxy and other thermosets. In the following sections we accordingly provide illustrations of applications of atomistic modeling to probe the behavior of specific regions within EMC encapsulated devices.

1 10 100

1

2

3

4

5

6

7

8

Ge or a-Si proportion (%)

Therm

al

conductivity

(W/m

K)

Si-Ge (layered)

Si-Ge (random)

a-Si/c-Si (SLs)

3.1 Interaction Between Cross-linked Epoxy and Alumina Surfaces Initial studies of adhesion between epoxy and

alumina interfaces have focused on the fully hydroxylated Al2O3 surface, viewed as representative of the extreme of the most common physical presentation of such surfaces. Separate layers of hydroxylated alumina, consisting of a 28.76Å × 33.21Å × 23.10Å slab of Al2O3, with initial structure of a hydroxylated unit cell first optimized using the MOPAC 2012 semiempirical quantum mechanics program, and cross-linked epoxy layer containing 40 diglycidyl ether of bisphenol A and 20 Jeffamine® D-230 cross-linker molecules (Figure 4) and commensurate a and b cell dimensions and thickness 30.30Å, were combined to form the composite interfacial system (Figure 5). The resulting structure was then subjected to constant volume, constant temperature (NVT) molecular dynamics simulation using the LAMMPS simulation program [7] combined with the PCFF+ forcefield, which has been developed since 2009 at Materials Design, based on the original PCFF class II forcefield [21] distributed with the LAMMPS software. Thorough NVT equilibration of the interface was followed by a lengthy production stage to sample configurations suitable for determining the ensemble average of the interfacial energy, which resulted in an interfacial energy of 0.15 J/m2. Figure 4: Diglycidyl ether of bisphenol A resin and polyoxypropylene diamine curing agent.

Figure 5: Assembled alumina-cross-linked epoxy interfacial model prior to equilibration. 3.2 Thermal Conductivity of Cross-linked Epoxy Base

Resin Thermal conductivity has been examined using a

base epoxy system consisting of a stoichiometric

mixture of diglycidyl ether of bisphenol A (DGEBA) and meta phenylene diamine (mPDA) cross-linked with degrees of cure up to ~80%, as studied experimentally by Kline [22], Krealing and Kline [23] and Cherkasova [24]. The simulations have employed the Müller-Plathe reverse non-equilibrium MD method outlined previously, using a periodic cell measuring 29.32Å × 29.32Å × 87.97Å. For systems of this size, simulations of duration 5-10 ns are normally required to achieve a precision better than ± 10%.

An example of a typical temperature profile is illustrated in Figure 6 for a system cured to slightly below 80%. The resulting thermal conductivity is calculated as 0.211 ± 0.024 W/m/K, which is slightly above the values in the range 0.176-0.188 W/m/K reported by Kline, but within the range 0.180-0.243 W/m/K measured between 298K and 363K by Cherkasova [24]. Further studies, probing the degree of cure in more detail and investigating the breadth of the distribution obtained with multiple cross-linked configurations, which our previous work has shown to be necessary when performing mechanical property studies [25], are accordingly desirable.

Figure 6: RNEMD temperature profile obtained for a sample of m-phenylene diamine cured DGEBA simulated at 298K. 3.3 Small Strain Elastic Constants of Cross-linked

Epoxy Small strain elastic constants for the DGEBA-

mPDA system have been computed using multiple configurations of models prepared using 40 DGEBA molecules and 20 cross-linker molecules, for which the simulation cell sizes are slightly below 30 Å, containing ~2300 atoms. In almost all cases studied the degree of cure is close to 100%, as illustrated in Figure 7, which depicts the maximum bond strain of any bond during the 'curing' process applied by the MedeA® Thermoset Builder.

The tensile moduli for the batches of configurations analyzed – typically in groups of ~20 to permit optimal

use of available computational resource – have been analyzed according to the Hill-Walpole method, which permits precise bounds definition when the moduli have been obtained for multiple small domains, as is the case whenever many independent atomistic realizations of a system have been simulated, as discussed at length for amorphous polymers by Suter and Eichinger [26], and applied in our previous work in this area [25].

Figure 8: Comparison of calculated tensile moduli at 298K with experimental values obtained using different curing protocols and measured over a range of temperatures [23]. 3.4 Oxygen and Water Transport in Cross-linked

Epoxy Barrier properties of cross-linked epoxies are of

particular interest in coatings and adhesive applications, in which penetration of small molecules such as oxygen and water, followed by subsequent chemical reaction with metal substrates, can have significant effects on performance and integrity of the epoxy-substrate interface. Since the associated diffusion coefficients of even the smallest molecules – typically in the range 10-7 – 10-11 cm2/s – are difficult to determine using atomistic molecular dynamics simulations with typical durations of perhaps a few nanoseconds, it is accordingly common to adopt an indirect method to study penetrant mobility. One preferred method involves computing diffusivities at elevated temperatures up to a few hundred degrees above the temperature of interest, followed by extrapolation to lower temperature with the assumption of Arrhenius behavior, which can be demonstrated experimentally in many systems. Thus one first performs a series of constant pressure (NPT) molecular dynamics simulations at a series of decreasing temperatures to estimate the system density, followed by a second, or accompanying, series of simulations in the microcanonical (NVE) ensemble at the calculated densities to monitor the mean square displacement, <r2> or MSD, of penetrant species as a function of time, from which the diffusivity D is obtained using the

standard Einstein relation <r2> = 6Dt (for diffusion in three dimensions).

A mean square displacement (MSD) plot is illustrated in Figure 9 for diffusion of oxygen in the DGEBA-Jeffamine® system discussed in section 3.1, at a temperature of 423K. Here it is observed that while the overall MSD often shows clear linear behavior, individual X, Y and Z components sometimes show evidence of the stepwise hopping that frequently dominate the diffusion mechanism.

Figure 9: Mean square displacement plots for oxygen in cross-linked DGEBA-Jeffamine® epoxy system at 423K.

Figure 10: Arrhenius plot of oxygen and water diffusivities in cross-linked DGEBA-Jeffamine® epoxy systems. Densities at each temperature were determined from NPT molecular dynamics simulations.

The corresponding Arrhenius plots for oxygen and water diffusion in this epoxy system are illustrated in Figure 10, together with the least squares fits (inset). The slopes of the plots are observed to be similar for the two penetrants, suggesting similar activation energies for the diffusive process. Moreover, the results suggest that for this system the diffusivity of oxygen is higher than that of water by a factor of 4.5-5 under ambient conditions.

Experimentally, the relative diffusivities of oxygen and water in polymers can vary somewhat [27], with oxygen mobility sometimes exceeding that of water while in other systems the reverse applies. The situation in cross-linked epoxy systems has been discussed by Yarovsky and Evans [28], who applied

molecular simulations to relatively small water-soluble epoxy models containing one of two phosphated epoxy components cross-linked using one of two different curing agents. These authors observed relative oxygen and water diffusivities in which either the oxygen or water was more mobile depending on the system, and argued that the slower oxygen diffusivities observed in two systems were mostly attributable to the higher mass of the oxygen, while the slower water diffusivity in a third system was attributable to the much higher concentration of residual hydroxyl groups remaining in the polymer after the cross-linking, with the hydrogen bonded interactions between bound hydroxyl and water reducing the overall water mobility. Such a situation is likely to apply to the DGEBA-Jeffamine® thermosets studied in this work, in which the cured systems contain two hydroxyl groups for each DGEBA moiety. Such interactions are also likely to lead to a higher solubility of water in the cross-linked epoxy, which is expected to increase the water permeability of the material in spite of the reduced water mobility. Consequently, small molecule solubility and its effect on permeability of the material as a whole is an ongoing topic of study.

4. Summary and Conclusions As part of integrated computational materials

engineering (ICME), atomistic simulations play an increasingly important role in the development of electronic systems to meet the challenges of higher performance, predictable reliability, lower cost, and environmental responsibility. Atomistic simulations provide understanding of key mechanisms governing the behavior of materials and they deliver quantitative materials property data, which can be used as input into finite element methods. In this context, the present work has demonstrated the application of MedeA®, a comprehensive state-of-the-art software environment for atomistic materials simulations, to the areas of thermal conductivity, elastic properties, adhesion, and diffusion.

As an example of an inorganic material, the effect of alloying and amorphization on the thermal conductivity of silicon has been demonstrated. Simulations revealed that only a few percent of Ge atoms reduce the thermal conductivity of crystalline silicon by a factor of about 20. The effect is even more dramatic if Ge atoms are ordered in the form of layers, where the thermal conductivity is reduced by a factor of 33 at 2% Ge and by about 60 at 12% Ge reaching values below 2 W/m/K. Also the introduction of amorphous Si into crystalline Si has a very pronounced effect on the thermal conductivity. Simulations showed that the thermal conductivity of pure silicon can be reduced from 128 W/m/K for a perfectly crystalline material to values as low as 4 W/m/K if 25% of silicon is amorphous. However, a further increase of the amorphous fraction does not lower the thermal conductivity below this value.

Calculations of the thermal conductivity of an epoxy thermoset were performed to show the capability of MedeA® to treat organic polymeric systems. Specifically, the epoxy system consisting of a stoichiometric mixture of diglycidyl ether of bisphenol A (DGEBA) and meta phenylene diamine (mPDA) cross-linked with degrees of cure up to ~80% has been investigated. The computed value of 0.211 ± 0.024 W/m/K is consistent with experimental data, thus showing the remarkable quantitative performance of current simulation technology.

For the same thermoset, namely DGEBA-mPDA calculations of the elastic properties have been performed, which show the sensitivity of the tensile modulus on the level of curing. An important aspect of reliable simulations of the materials properties for polymers is the ability to perform calculations on a series of different structural models in order to achieve statistically meaningful results. The MedeA® computational environment makes such large-scale computations readily doable with a minimum of human intervention, thus enabling the systematic screening of different materials under a range of various temperatures, pressures, and strains.

The adhesion of an epoxy on an inorganic surface has been demonstrated for the system of DGEBA-Jeffamine® on alumina. In this model, the surface is assumed to be covered by a layer of aluminum oxide with the dangling bonds on the surface saturated by hydroxyl group as they may occur in an ambient environment with moisture in the air. The simulations for the present model show that without direct chemical bonding between the organic and inorganic phases the work of separation is 0.15 J/m2.

Finally, diffusivities of oxygen and water, respectively, in the DGEBA-Jeffamine® epoxy system were investigated. Molecular dynamics simulations of these molecules in the epoxy allow calculating their mean-square displacements, from which the corresponding diffusivities can be deduced. For DGEBA-Jeffamine® the simulations reveal similar activation energies for oxygen and water. Furthermore, the oxygen diffusivity is higher than that of water by a factor of 4.5-5 under ambient conditions.

In summary, the present work demonstrated the capabilities of state-of-the-art atomistic simulations as implemented in the MedeA® software environment in the computation of materials properties including thermal conductivity, elastic moduli, adhesion, and diffusion, thus providing insight at the atomistic level as well as quantitative materials property data. The examples discussed in this work represent only a fraction of the capabilities of MedeA®, which include the calculation of chemical reactions on surfaces as they occur in the processing and also corrosion of materials, predictions of electronic, optical, and magnetic properties for nanoscale structures, as well as the behavior of liquids and gases.

Driven by the need to solve the tremendous challenges faced by the electronics industry and fuelled by the ever growing computing power, atomistic simulations are becoming increasingly valuable. In fact, leading electronics companies around the globe have made this type of approaches already an integral part of their R&D efforts. Leveraging the power and convenience of integrated software systems as implemented in MedeA®, the stage is set for exciting and rewarding applications of atomistic simulations as part of integrated computational materials engineering.

Acknowledgments The authors would like to express their gratitude to

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