Elucidation of Adhesive Interaction between the Epoxy Molding Compound and Cu Lead Frames.

Clarification of adhesive interactions in semiconductor packages can improve reliability of power electronics. In this study, the adhesion interfaces between the epoxy molding compound and Cu-based lead frames were analyzed using the density functional theory. A resin fragment was prepared based on the polymer framework formed in the curing reaction of epoxy cresol novolac (ECN) and phenol novolac (PN), which are typical molding materials. The resin fragment was optimized on the surfaces of Cu and Cu2O. We calculated the charge density differences for adhesion structures and discussed the origin of adhesive interactions. The ECN-PN fragment's adhesion to the Cu surface relied mainly on dispersion forces, whereas in the case of Cu2O, the resin bonded chemically to the surface via (1) σ-bonds formed between the ECN-PN's OH group oxygen and coordinatively unsaturated copper (CuCUS) and (2) hydrogen bonds between resin's OH groups and coordinatively unsaturated oxygen (OCUS) located close to to CuCUS, resulting in a stable adhesive structure. The energy required to detach the resin fragment from the optimized structure was determined using the nudged elastic band method in each model of the adhesive interface. Morse potential curve was used to approximate the obtained energy, and the energy differentiation by detachment distance yielded the theoretical adhesive force. The maximum adhesive stress was 1.6 and 2.2 GPa for the Cu and Cu2O surfaces, respectively. The extent to which the ECN-PN fragment bonded to the Cu2O surface stabilized was 0.5 eV higher than in the case of the Cu surface.

Introduction

Adhesive and bonding technologies play an important role in the assembly of semiconductor packages. Die bonding technology is used to connect semiconductor chips to the lead frame; wire bonding or Cu-clip methods are applied in the building of electrical connections.[1] The long-term protection of the device from vibration, mechanical shock, and corrosive chemical species is then achieved by encapsulation of its electrical connections in a resin, called the epoxy molding compound (EMC). The EMC consists of ceramic fillers (e.g., silica and alumina), epoxy resins, curing agents, and additives, such as curing accelerators and adhesion promoters.[2] Because EMCs affect a number of semiconductor properties, such as insulation, stability, and flame retardancy, several methods have been proposed and developed to improve the performance of the compounds.[3,4] Regarding adhesives, we would like to add that bioinspired adhesive materials have attracted much attention in recent years. Polydopamine-based adhesives have been reported with excellent properties like self-adhesivity and bioadhesive applications.[5,6]

A robust adhesive interface between the EMC and lead frame in power packages is extremely important for ensuring the reliability of the device. Semiconductor packages are expected to withstand long-term moisture and thermal strain. However, in actual devices, the adhesive interface delaminates easily, which is a serious problem. Adhesion cannot be maintained under significant thermal stresses, such as solder reflow processes and temperature cycling tests.[7,8] Delamination of the adhesive interface accelerates crack generation and propagation in the die bonding area and results in rapid deterioration of the device’s heat dissipation. Such fatal flaws can then cause a loss of functionality in the power device. Therefore, it is necessary to ensure a high quality, long-lasting adhesion when designing new semiconductor packages.

Several studies, which have explored the adhesive structure and location of the fractures to address the delamination issue, found that the thickness of the copper oxide film on the surface of lead frames correlates with the adhesion strength, and fractures are most likely to occur at either Cu2O/CuO or Cu/Cu2O interfaces.[9−11] Another study analyzed fracture traces resulting from a button shear test, which measured the shear strength of button-shaped EMCs on a lead frame using X-ray photoelectron spectroscopy (XPS).[12] The adhesive layer fractured between the EMC and Cu2O and the interfacial adhesion strength increased linearly with the thickness of the Cu2O layer.[13] It was also reported that reduction of the CuO/Cu2O ratio on the lead frame surface increases the adhesion strength.[13] Despite a large amount of experimental data, a unified view of the essential adhesion mechanism between the EMC and the lead frame is yet to be reached.

First-principles calculations were recently employed in the theoretical exploration of the adhesive interface structure between metals and epoxy resins.[14−16] Density functional theory (DFT) simulations of the adhesive interface used the energy change during the detaching process to calculate the adhesive force.[17−19] Adhesion interactions in electronics were also investigated to gain an insight into the die bonding technique using conductive adhesives.[20−22] Thus, DFT calculations could clarify molecular interactions at the adhesion interface, which are difficult to observe experimentally. This calculation method is effective in elucidating the adhesive interface of resin on metals or ceramics.

The purpose of this study is to theoretically elucidate the adhesive interactions between the Cu-based lead frame and EMC using first-principles calculations. Because copper is a typical lead frame material, we used DFT calculations to model an ideal adhesive interface between the epoxy resin and metallic or oxidized Cu. The adhesion strength was calculated using a detaching process simulation. Lastly, the probability of fracturing at the adhesive interface between the EMC and the lead frame was investigated from the theoretical chemistry viewpoint.

Methodology

Selection of Materials for Modeling of Adhesive Interface

Whereas the inorganic fillers controlling the mechanical properties of the EMC (e.g., the Young’s modulus and linear expansion coefficient)[23] account for 70–90 wt % of the EMC,[24] the resin, which causes the adhesion between the EMC and the semiconductor chip or lead frame, represents ∼14 wt % of the EMC. Because this study focuses on the adhesion interface between the epoxy resin component and the surface of the lead frame, fillers that do not contribute directly to adhesion were excluded from the modeling.

EMC resins are required to exhibit high stability, insulation, and adhesion. The first widely used epoxy resin in semiconductor packaging applications was ortho-cresol novolac (OCN),[25,26] which is electrically, mechanically, and thermally suitable for the encapsulation process.[27] Many new types of epoxy resins (e.g., biphenyl and multiaromatic resins) with improved performance were developed in recent years.[28−30] Here, we selected the OCN epoxy resin polymer cured with phenol novolac (PN) resin as the most basic example of an adhesive component.

The molecular structures of epoxy resins modeled in this study are illustrated in Figure . The monomers of OCN resin, which are synthesized by condensation of ortho-cresol and formaldehyde, are connected by methylene groups either in the ortho- or para-position.[31] Further glycidyl etherification of the OCN’s phenolic hydroxy groups lead to the formation of the epoxy cresol novolac (ECN), as shown in Figure a.[32] The ECN resin is then hardened by cross-linking with PN resin (Figure b). Epoxy ring opening can yield two different products, depending on which of the two C–O bonds is cleaved.[33] The preferred cleavage site is determined by the type of curing agent and the catalyst. In this study, we assumed β-cleavage, which dominates the epoxide ring opening in phenols.[34]

Figure 1

(a) Reaction schemes for the synthesis and epoxidation of OCN resin. (b) Cross-linking reaction between epoxidized OCN (ECN) resin and PN resin (curing agent). The chemical structure in the area enclosed by the dashed line is later used as a model fragment.

In real-life applications, further complexity of the interface arises from (1) three-dimensional cross-linking reaction occurring both in the bulk and vicinity of the adherend, (2) curing- and shrinkage-related change in polymer volume resulting in additional stress, and (3) interfacial segregation caused by the enrichment of specific resin constituents.[35,36] Although it would be intriguing to calculate the adhesive interface using a realistic polymer model, our aim in this study was to clarify the essential aspects of resin interaction with the adherend surface.

A molecular fragment representing the characteristic part of the ECN–PN cross-linked structure (Figure b) was selected for quantum chemical calculations. The selected fragment includes hydroxy, ether, methylene, methylphenyl, and phenyl moieties. The epoxy ring opens during the curing reaction and, thus, is not included within the analyzed fragment. Notably, the ortho- and para-positions of the aromatic rings in the ECN–PN fragment remain unsubstituted, whereas they would be linked by methylene groups to form a polymer in the actual cured material. We could have substituted the ortho- and para-positions in the fragment with methyl groups to simulate the methylene linkers; however, we decided to use fragments with more reaction points instead, to account for possible interactions between polymer ends and the substrate surface. An example of such an interaction was reported with a different type of polymer and was found to affect the wettability of the substrate surface.[37]

Lead frames in power electronics electrically connect semiconductor chips to their external circuit and release heat generated by the devices. Therefore, power packages require lead frames with low electrical resistance and high thermal conductivity to withstand a higher allowable current. Copper represents an effective lead frame material that meets the required criteria at a low cost. Consequently, we selected elemental copper as the lead frame surface for our study.

Model of the Adhesive Interface between the ECN–PN Fragment and the Cu Surface

Because Cu has a face-centered cubic lattice (Figure a), the most densely packed plane (111), which is also the lowest in energy, was selected for our study.[38] To create a slab model of the Cu surface, we first optimized the Cu unit cell using the Vienna ab initio simulation package (VASP), a plane-wave basis DFT calculation program,[39−41] and the generalized gradient approximation of Perdew–Burke–Ernzerhof (GGA-PBE), as the exchange–correlation functional.[42] The cut-off energy was set to 500 eV and the k-point mesh = 2π × 0.05 Å–1. The self-consistent field (SCF) convergence threshold was set to 1.0 × 10–5 eV and the relaxation atomic force threshold = 0.05 eV Å–1. Pseudopotential generated using the projector augmented wave method was used;[43,44] the dispersion force correction methodology developed by Tkatchenko and Scheffler was applied.[45] The optimized Cu unit cell was then cleaved along the (111) plane and expanded into a 5 × 5 supercell containing three atomic layers. The Cu(111) slab model was completed by the addition of a vacuum layer (30 Å) above the Cu surface (Figure b); the model contained 75 Cu atoms, with the bottom two layers being fixed during the optimization. The atomic-scale structures were drawn using VESTA.[46]

Figure 2

Optimized structures of (a) conventional Cu unit cell and (b) Cu(111) surface slab model. The Cu atoms in the bottom two layers are fixed in the simulation.

The adsorption of ECN–PN fragments onto the Cu surface was calculated using molecular dynamics (MD) in Forcite Plus program,[47] implemented in Materials Studio 2016.[48] First, the ECN–PN fragment was placed randomly within the Cu slab model’s vacuum layer. Then, the MD calculation was performed using the COMPASS force field[49] with the ensemble set to NVT and the Nose–Hoover–Langevin thermostat[50] set to 350 K. The calculation length was 300 ps with a time step of 1 fs.

The adsorbed structure, obtained from the previously described MD calculation with an NVE, was then evaluated by quench dynamics (initial temperature = 350 K, duration of MD calculation = 5 ps, time step = 1 fs, quench: every 250 steps). Twenty-one structures were obtained, and the lowest energy structure was further optimized using DFT under the same conditions as those used for the Cu cell optimization. The adhesion interface between ECN–PN and Cu obtained by this procedure was named ECN–PN/Cu(111).

Modeling of Adhesive Structure on the ECN–PN Fragment and the Copper Oxide Surface

Copper is readily oxidized by atmospheric oxygen to form a reddish-brown surface layer of the Cu2O film. For our study, we decided to model the surface of Cu2O(111) as the most energetically stable Cu oxide structure.[51] The VASP-optimized Cu2O unit cell is shown in Figure a. The cut-off energy for this calculation was increased to 520 eV,[52] and the 5 × 5 supercell of the Cu2O(111) surface slab model consisted of nine O–Cu–O trilayers (Figure b). There are two types of Cu2O(111) surface structures: an oxygen (O)-terminated nonpolar surface and a copper (Cu)-terminated polar surface. According to a previous study,[53] the energy of the O-terminated surface is lower than that of the Cu-terminated one. Therefore, we selected the O-terminated surface for our calculation. The bottom three trilayers of the Cu2O slab model were fixed during the simulation, and a vacuum layer (30 Å) was added above the Cu2O surface (Figure b,c). The surface layer of Cu2O(111) contains both coordinatively unsaturated Cu (CuCUS) and O atoms (OCUS).[52,53]

Figure 3

Surface models of copper oxide: (a) optimized copper oxide unit cell, (b) Cu2O(111) slab model, and (c) detailed view of the Cu2O(111) surface. Colors of atoms are assigned as follows: Cu, pink and O, red. Only the atoms of the topmost trilayer are shown in color in (c); the rest are represented by small gray dots.

The surface relaxation of the Cu2O(111) slab model was performed using VASP, ab initio MD calculations.[54,55] First, we optimized the structure of the Cu2O(111) slab model under the same conditions as the Cu2O unit cell described earlier. Surface relaxation of the Cu2O(111) slab model was then achieved by annealing in the 0–300 K temperature range with a step number of 5000 and a time step of 1 fs.

To model adhesion between the ECN–PN fragment and relaxed Cu2O surface, the ECN–PN fragment was first placed randomly within the vacuum layer of the Cu2O(111) slab model and then adsorbed to the Cu2O surface using the previously described MD method. To prevent any unnecessary structural changes to the relaxed Cu2O surface, all substrate atoms were fixed during this calculation.

The MD calculation was performed using the Forcite Plus program with the NVT ensemble, analogously to the Cu surface calculation presented earlier. We used the COMPASS III force field,[56] implemented in Materials Studio 2020,[57] to conduct a quench dynamics simulation using the NVE ensemble. The structure of the adhesive interface obtained from the quench dynamics was then further optimized using DFT, where only the atoms of the bottom three O–Cu–O trilayers were fixed. The VASP optimization was performed under the same conditions as the Cu2O unit cell optimization.

Numerical Analysis

The energy change of the resin fragment, which was vertically pulled away from the optimized adhesion structure’s surface, can be calculated according to previously published procedures,[17,58] and the adhesive force can be obtained by differentiation of the energy with respect to the detachment distance. In this study, we used the nudged elastic band (NEB) method,[59] which can identify the minimum-energy path between two local minima. The first local minimum was the adhesion structure optimized with quench dynamics followed by the DFT calculation, and the second was the structure optimized after vertical removal of the resin fragment from the surface.

The NEB method was implemented using VASP. The energy curve associated with resin detachment was obtained by plotting the energy of the intermediate NEB images as a function of detachment distance (Δr) and can be approximated by the Morse potential curve, as shown in eq where De corresponds to the binding energy between the resin fragment and the surface and a is a constant that determines the width of the potential well (calculated using the least-squares method). Differentiation of the obtained potential energy curve with respect to Δr then gave the adhesive force. The adhesive stress was calculated by dividing the adhesive force by the cross-sectional area of the unit cell.

To see the electron density changes resulting from the interaction between the surface and resin, the electron density difference, or charge density difference, was calculated using the following equationwhere ρtotal is the electron density of the optimized adhesion structure, ρsurface is the electron density of the surface slab model, and ρfragment is the electron density of the resin fragment.

Results and Discussion

Adhesion Interface between ECN–PN Fragment and Metallic Copper

The OH groups generated by the curing reaction are not directed toward the Cu surface, as can be seen in the DFT-optimized structure of the ECN–PN/Cu(111) adhesion interface depicted in Figure , suggesting that the OH groups neither interact with the Cu surface nor contribute to the adhesive interface stabilization. We assumed that the probability of coordination bonding between metallic Cu on the surface and the OH groups in the resin fragment is minimal owing to copper’s high d-band occupancy.[60] Conversely, the benzene ring of the ECN–PN fragment might interact with metallic Cu, as it is oriented parallel to the substrate’s surface.[61] A previous study demonstrated that the Cu(111) surface can adsorb benzene at either on top or hollow sites.[62] The expected top site adsorption distance between a single benzene molecule and the surface is 3.17 Å. Our model shows that both the phenyl and methylphenyl groups stabilized slightly off the on-top site positions (Ph–Cu distances = 3.41 and 3.20–4.15 Å, respectively), as depicted in Figure a. The methylphenyl group is stabilized further away from the copper surface likely owing to steric hindrance caused by the methyl group and the molecular arrangement restrictions of the polymer fragment.

Figure 4

Top (a) and side (b) views of the DFT-optimized ECN–PN/Cu(111) adhesive structure. Typical adsorption sites are shown in view (a). The measured distance between highlighted atoms of the phenyl group and the Cu surface is depicted in view (b). The distance was calculated based on the atomic coordinates of the optimized structure. Atoms are color-coded as follows: Cu, pink; H, white; C, gray; and O, red.

The NEB-calculated potential energy change of ECN–PN/Cu(111) is plotted as a function of Δr (Figure a). The structure optimized at Δr = 3 Å was chosen as the endpoint of the NEB calculation. At Δr < 3 Å, the resin fragment readsorbed onto the Cu surface, returning to the Δr = 0 Å structure as the optimization progressed. The energy curve obtained from the NEB calculation was approximated by the Morse potential (dashed line in Figure a). The determination coefficient confirmed a good fit of the Morse approximation (R2 = 0.988) using system parameters: a = 1.14 Å–1 and De = 2.29 eV. The adhesive stress curve was plotted by differentiation of the obtained potential energy curve with respect to Δr and dividing the result by the cross-sectional area of the unit cell (135.59 Å2), and the maximum adhesion stress was found to be 1.55 GPa.

Figure 5

(a) Potential energy curve of the ECN–PN fragment detaching from the Cu(111) surface and the fitting parameters of De [eV] and a [Å–1] of the Morse potential approximation. (b) Theoretical adhesion stress between the ECN–PN fragment and the Cu(111) surface, calculated by differentiating the energy potential curve with respect to the detachment distance (Δr) and dividing it by the cross-sectional area of the unit cell.

To understand why the calculation predicted a very high maximum adhesion stress (1.55 GPa) at the ECN–PN/Cu(111) interface, we visualized the differences in electron density upon adsorption to evaluate the effects of electron transfer (Figure ). The regions with accumulated and depleted charge, depicted in Figure , are colored in cyan and purple, respectively. We did not observe a significant change in the electron density and, thus, concurred that electron transfer probably does not affect the ECN–PN/Cu(111) adhesion interface.

Figure 6

Calculated difference in electron density for the adhesive interface between the ECN–PN fragment and the Cu(111) surface viewed from the top (a) and the side (b). The isovalue level = 0.002 Bohr–3. The areas of charge accumulation and depletion are shown in cyan and purple, respectively.

The predicted large adhesion force at the ECN–PN/Cu(111) interface was thus expected to originate from dispersion force contribution. To verify this hypothesis, we separated the effects of electronic interactions and dispersion forces. The initial structure obtained from the quench dynamics simulation was further optimized using DFT without the dispersion force correction. The comparison of structures optimized with and without dispersion force correction is shown in Figure . Even though the dispersion correction does not significantly affect the structure of the resin fragment, the optimized distance between the resin and Cu surface was 0.44 Å longer in the structure optimized without the dispersion correction.

Figure 7

Structural comparison of the ECN–PN/Cu(111) adhesive interfaces optimized (a) with and (b) without the dispersion force correction.

The potential energy curve and adhesion stress were calculated according to the procedure that was used to obtain data shown in Figure . The energy change following the resin detachment from the surface shows how the process was affected by dispersion (Figure a): the energy required to move the fragment 3 Å from the surface was 0.08 eV without dispersion (∼26-fold lower than with the dispersion).

Figure 8

Comparison of (a) potential energy curves and (b) adhesive stresses calculated with and without the dispersion force correction for the detachment of the ECN–PN fragment from the Cu(111) surface. The filled circles represent dispersion-corrected results, whereas the empty squares correspond to results lacking the dispersion correction. The fitting parameters De [eV] and a [Å–1] of the Morse potential approximation and determination coefficients (R2) are shown near each potential energy curve.

The relationship between the resin detachment distance Δr and adhesive stress is depicted in Figure b. The theoretical adhesion strength of the dispersion-disabled model was significantly weaker than that of the dispersion-enabled. Note that the determination coefficient of the results obtained from calculation without dispersion correction is small (R2 = 0.546), suggesting an error that is discussed in depth in the Supporting Information. Based on the performed analyses, we concluded that the adhesion between the ECN–PN epoxy resin and the metallic Cu surface relies predominantly on dispersion forces, which are the main components of the van der Waals interactions.

Adhesive Interactions between the ECN–PN Fragment and the Oxidized Copper Surface

The lead frames in semiconductor packages are commonly heated during assembly, which increases the likelihood of surface oxidation prior to encapsulation with mold resin. The relaxed slab model structure of the Cu2O(111) surface generated using ab initio MD, containing nine O–Cu–O trilayers, is shown in Figure . These trilayers slightly rearranged their respective positions during relaxation by annealing (Figure a). The surface copper and oxygen atoms adopt hexagonal configuration with CuCUS, which remains unsaturated even upon relaxation, at the center of each hexagon (Figure b).[52]

Figure 9

Cu2O(111) slab model structure relaxed by annealing from 0 to 300 K using ab initio MD. The side view (a) shows a slight variation of the atomic positions, whereas the top view (b) depicts the change of CuCUS position even as it remains unsaturated. As in Figure , only the atoms in the top surface of the trilayer are shown in color.

To identify the stable adsorption structure, the ECN–PN fragment was placed randomly within the vacuum layer of the relaxed Cu2O(111) slab model and subjected to the MD simulation, followed by structural optimization using DFT. The optimized adhesive interface structure shows the formation of three new bond types at the ECN–PN/Cu2O(111) interface (Figure ): (1) a dative bond between oxygen in the ECN–PN OH group and a surface CuCUS atom, (2) hydrogen bonding between H in the ECN–PN OH group and OCUS in the surface, and (3) coordination bond between the ECN–PN phenyl group and CuCUS atom. These bonds are discussed in detail later using an electron density difference analysis. Based on these results, we concluded that when the same ECN–PN fragment is used, the appearance of the adhesive interface depends predominantly on the surface state of copper (Cu(111) versus Cu2O(111)).

Figure 10

DFT-optimized adhesion interface between the ECN–PN fragment and the Cu2O(111) surface. The oblique view shows interactions between (1) OH group in the fragment and CuCUS, (2) H in the ECN–PN OH group and OCUS in the surface, and (3) ECN–PN fragment’s phenyl group and a CuCUS atom. See the Supporting Information for the top view.

The theoretical adhesion force was calculated using the NEB method, starting from the optimized ECN–PN/Cu2O(111) adhesive structure, analogously to the Cu surface adhesion calculation. Because the model shown in Figure contains 253 atoms, excessive computational resources would be required to perform the NEB calculation. Hence, we removed atoms in the bottom five O–Cu–O trilayers of the Cu2O slab, which would not affect the adhesive interface. Among the four remaining trilayers, the bottom one was fixed and the structure was optimized using DFT. The optimized model consisting of 133 atoms is referred to as the small model throughout the further text. The adhesive interface structure of the small model did not show any significant variation from the initial model.

The potential energy curve of the ECN–PN fragment’s detachment from the Cu2O surface was calculated based on the optimized small model interface (Figure a). A detachment distance >4 Å was required to completely separate the fragment molecule from the Cu2O surface with the adhesion energy of detachment 2.79, which is ∼0.5 eV higher than the energy required to detach the ECN–PN fragment from the metallic Cu surface. Thus, the adhesion to Cu2O(111) is more stable. The potential energy curve calculated without correction for dispersion forces (Figure a) shows that ∼0.9 eV is required to detach the ECN–PN fragment from the Cu2O(111) surface. In other words, there are bonds with an energy of ∼0.9 eV in addition to the dispersion forces. The relationship between Δr and adhesive stress is depicted in Figure b. The maximum adhesive stress caused by detachment of the ECN–PN fragment from the Cu2O surface was calculated to be ∼2.2 and 1 GPa for dispersion-enabled and dispersion-disabled models, respectively, which are higher than that for the metallic Cu surface.

Figure 11

(a) Potential energy curves for the detachment of the ECN–PN fragment from the Cu2O(111) surface and (b) plots of the calculated adhesive stress vs detachment distance Δr. Two calculations, with (filled circles) and without (empty squares) dispersion correction, are presented. The fitting parameters De [eV] and a [Å–1] of the Morse potential approximation and determination coefficients (R2) are shown near each potential energy curve.

The small model’s adhesion structures optimized with and without dispersion are compared in Figure , confirming that the ECN–PN OH groups chemically bond with CuCUS regardless of the dispersion correction status. The lengths of newly formed bonds were almost identical between the structures optimized with and without the dispersion correction, indicating that dispersion forces affect the molecular structure at the adhesion interface between the ECN–PN fragment and the Cu2O(111) surface only minimally. This is in direct contrast with the observations made for the adhesion to metallic Cu.

Figure 12

Structural comparison of the adhesive interfaces between the ECN–PN fragment and the Cu2O(111) surface optimized (a) with and (b) without dispersion correction.

To clarify the effect of electronic interaction on the interfacial bonding, we calculated the electron density difference upon fragment adsorption (Figure ) and found significant electron density changes in the proximity of bonds formed between the surface CuCUS and OH and Ph groups of the ECN–PN fragment (Figure b). The oxygen atom in the OH group forms a σ-bond with the CuCUS atom on the surface via p–d orbital interaction and the lone electron pair of OCUS concurrently shifts closer to the hydrogen atom, resulting in hydrogen bonding.[63]

Figure 13

(a) Plot of electron density difference calculated for the adhesion interface of ECN–PN/Cu2O(111). The isovalue level is set to 0.002 Bohr–3. The areas of charge accumulation and depletion are shown in cyan and purple, respectively. (b) Corresponding contour plots for the interaction near the CuCUS–OH (left) and the CuCUS–phenyl (right) interfaces.

Comparison of Calculated Adhesion Interactions with Experimental Data

The calculated results (Table ) were compared with actual experimental data. The maximum adhesion force between the EMC and Cu lead frame reported in the literature, based on the button shear test, was ∼114 N.[64] The adhesion stress was calculated to be 28.4 MPa for button dimensions of 2 × 2 × 2 mm. Conversely, the adhesion stress calculated in our study was as high as 1.55 GPa for Cu(111) and 2.18 GPa for Cu2O(111) surfaces. Although the theoretical adhesion stress seems to be too high, it is consistent with the experimental data, where the failure is typically considered to originate in the weakest part. The present study suggests strong chemical bonding between the epoxy resin and Cu2O surface, redirecting the origin of adhesion failure to the lead frame’s oxide film or internal portion of the EMC, rather than the interface. Therefore, the experimentally observed adhesive forces may be smaller than the theoretical values. To support our claim, we compared our results with previously reported experimental bond strength measurements between EMCs and lead frame obtained using mechanical methods and fracture mark evaluation performed using XPS.[10,13] The experimental reports assume the cohesive failure of EMCs and crack propagation within the surface copper oxide layer to be the cause of delamination.

Table 1

Summary of the Calculation Results for Adhesive Interactions between the ECN–PN Fragment and Cu or Cu2O Surfaces

adherend	Cu(111)	Cu2O(111)
detachment distance	3 Å	4 Å
adhesion energy	2.29 eV	2.79 eV
adhesion energy calculated without dispersion correction	0.08 eV	0.91 eV
maximum adhesive stress	1.55 GPa	2.18 GPa

The DFT calculations presented in this article revealed that the adhesion mechanisms and energies differ significantly depending on the structure of the adherend surface at the atomic level (i.e., Cu vs Cu2O). The actual adhesive interface may not be represented by only one specific molecular fragment model but by a variety of structures. In this study, the structure with the lowest energy obtained from the MD calculation was optimized by using DFT. In the MD calculation, various other structures with different energies were also observed (see Figure S4 in the Supporting Information). However, it is assumed that there would be no significant change in the nature of the adhesive interaction because the atomic configuration is only slightly different from each other.

As the next step, modeling of a lead frame surface with a more realistic structure should be attempted. Because CuCUS atoms are highly reactive, water adsorption could have a significant effect on the adhesion interface. Also, it is presumed that the degree of oxidation of the Cu surface affects the adhesion mechanism. Therefore, investigation into the influence of such a change in the adherend’s surface structure on the adhesive interaction with the epoxy resin will be valuable and is a subject for future work.

Conclusions

In this study, the adhesion interface between EMCs and Cu-based lead frames in semiconductor packages was analyzed using DFT calculations. Assuming the curing reaction of ECN and PN resins, which are typical molding materials, a resin fragment molecule was proposed based on the polymer framework. The resin fragment was optimized on Cu and Cu2O surfaces, and the ideal adhesive structures were calculated. We found that dispersion forces were the source of adhesion between the ECN–PN fragment and Cu surface, whereas in the case of Cu2O, OH groups in the resin chemically bonded to the atoms on the oxide surface (HO–CuCUS σ-bond and OH–OCUS hydrogen bonding) to produce a stable adhesive structure. The energy required to detach the resin fragment from the optimized structure was determined using the NEB method. The theoretical adhesive force was calculated by differentiating the energy curve, obtained from the NEB calculation, with respect to the detachment distance Δr. The maximum adhesive stress was calculated to be 1.6 and 2.2 GPa for the Cu and Cu2O surfaces, respectively. The Cu2O-bonded ECN–PN fragment was found to be more stabilized (by 0.5 eV) than that bonded to the Cu surface. Lastly, the surface structure of the adherends significantly impacts the adhesion mechanism at the interface between the mold resin and lead frame in semiconductor packages.