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Comparative characterization of chip to epoxy interfaces by molecular modeling and contact angle determination
Microelectronics Reliability 52 (2012) 1285–1290
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Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Comparative characterization of chip to epoxy interfaces by molecular modeling and contact angle determination O. Hölck a,b,⇑, J. Bauer a, O. Wittler a, B. Michel c, B. Wunderle a,b,c a
Fraunhofer Institute for Reliability and Microintegration (IZM), Gustav Meyer Allee 25, 13355 Berlin, Germany Chemnitz University of Technology, Materials and Reliability of Microsystems, Germany c Fraunhofer Institute for Electronic Nano Systems (ENAS), Germany b
a r t i c l e
i n f o
Article history: Received 15 November 2011 Received in revised form 15 February 2012 Accepted 6 March 2012 Available online 10 May 2012
a b s t r a c t An investigation of interfacial interaction has been performed between three epoxy molding compound materials and a native silicon dioxide layer (SiO2) usually found at chip surfaces. The epoxy materials were an industry oriented epoxy molding compound Epoxy Phenol Novolac (EPN), its filled variety EPNF (with silica particles) and a model aromatic epoxy1 (2 1 2). All systems are described in full in [1] and [2]. The free surfaces of the solid materials were experimentally analyzed by contact angle measurements of three different liquids (water, methylene-iodide (MI) and glycerol). Results are compared to interfacial energies obtained by analysis of the interfaces in bimaterial molecular models, yielding reasonable agreement. A qualitative prediction regarding the influence of water on the interfacial strength between chip and molding compound is attempted. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
2. Interface delamination
The investigation of the mechanisms of delamination or fracture between the interfaces of different materials is a challenging yet necessary task in microelectronic packaging. A lot of the failure modes that are detected in highly integrated System in Package (SiP) devices originate directly or indirectly in the failure of adhesive strength and thus causing loss of performance or function [3]. For a comprehensive reliability assessment of microelectronic components, the development of a physical understanding of the failure mechanisms is necessary (‘‘physics of failure’’ approach). The involved processes are complex in nature and therefore all scales involved need to be taken into account, that is, phenomena at system level and the level of surface finish (macro- and microscale), as well as phenomena on molecular and even atomic level (meso- and nanoscale) need to be investigated [4]. We present in this work delamination as a process consisting of several contributions. These are roughly estimated as to their magnitude and experimental or numerical possibilities of a more thorough treatment is given. The center of our attention lies on the investigation of the thermodynamic work of adhesion and a comparative analysis of molecular modeling and experimental contact angle results.
The critical energy release rate Gc, is a measure of interfacial strength between two materials. It may be obtained from fracture experiments like 3- or 4-point bending tests or mixed-mode bending tests, using fracture mechanics and beam theory [5–7]. This procedure is well established and of great practical value, however, it must be understood, that a macroscopical quantity for the interfacial toughness is obtained that consists of several mechanisms of different physical origin. In a first approximation, the contributions can be identified as follows:
⇑ Corresponding author at: Fraunhofer Institute for Reliability and Microintegration (IZM), Gustav Meyer Allee 25, 13355 Berlin, Germany. E-mail address: [email protected] (O. Hölck). 1 1,3-Bis(2,3-epoxypropoxy)-benzene and a 1,2 diamino(ethane)2 hardener in a 2:1 mixing ratio. 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.03.019
i. ii. iii. iv.
physical interaction: w12 chemical bonds: wchem mechanical interaction: u heat dissipation: Dh
By physical interaction (i) the interatomic or intermolecular forces across an interface are meant, which give the thermodynamic work of adhesion w12 between two materials 1 and 2. According to the theory of van Oss et al. [8,9], van der Waals forces and polar forces are mainly responsible for this interaction. In general, the thermodynamic work of adhesion is discussed in terms of this interaction energy per unit area of interface and can be related to the difference in system energy and the sum of free surface energy of each material (see discussion below), i.e. the energy needed to create ideal free surfaces. This contribution w12 to delamination will be discussed more thoroughly in a later paragraph.
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Fig. 1. Rough surface of a silicon chip measured by AFM and transfered to ANSYS for area calculation, leading to a correction factor u > 0. The z-axis is scaled by a factor of 10 compared to x and y.
If chemical bonds are formed across the interface (ii), these will need to be broken for delamination to occur and contribute as chemical interactions. Chemical bonds may be formed during or after the curing process of the molding compound, if the surfaces of the respective materials contain relevant groups. As a quick estimate we assume the formation of a carbon–oxygen bond between an epoxy group of the molding compound and an oxygen of a SiO2surface. C–O-bonds typically exhibit an energy of ECO = 350 kJ/mol [10]. If we further assume a density of one such bond per 400 Å2 (interface-area of our molecular models, see below). Equating these assumptions leads to a contribution to interfacial strength of the order of wchem 150 mJ/m2. Regardless of the accuracy of these assumptions, this estimation shows that if chemical bonds are likely to occur, their contribution to interfacial toughness are not to be neglected and it can be stated that chemical interaction wchem would contribute to the energy per unit area needed to separate the interface. We would like to note, that at room temperature TR, the thermal contribution to dissociation of covalent bonds Eth is negligible (Eth NAkBTR 2.5 kJ/mol with NA Avogadro and kB Boltzmann constants). Physical (i) and chemical (ii) interaction refer to a contribution per unit area of an ideal interface, meaning two materials in full contact with each other at ideally flat surfaces. However, real materials always exhibit a surface roughness, which leads to non-ideal contact, enlargement of the surface area A⁄ with respect to the apparent surface area A or mechanical interlocking of the interfaces (iii). In turn, this real interfacial area A⁄ = A(1 + u) will lead to change in the contribution of (i) and (ii) per unit apparent interface area, that is, the macroscopically measured interface area. Experimental values for the interface roughness may be obtained by atomic force microscopy (AFM). An example of such a measurement can be seen in Fig. 1. The AFM-scan of the area of 1 lm2 with resolution of 128 points on x and y-axis results in depth-profile with maximum height of about 20 nm. The values can be read into ANSYS and the resulting surface can easily be analyzed (note the scaled z-axis by a factor of 10 in Fig. 1). For our samples, a surface factor of (1 + u) = 1.002 results, revealing for this case negligible influence of the surface roughness. In the zone of fracture and especially at the crack-tip, where elastic theory would result in a singularity of the stress field, plastic deformation occurs in the materials (iv). In the process of irreversible material deformation energy is dissipated as heat Dh and thus adds to the sum of macroscopically observed fracture energy. In an attempt to quantify this energy, the mechanisms of irreversible plastic deformation (besides rupture of covalent bonds) need to be identified that possibly contribute to heat dissipation in the fracture zone. Let us assume that for an epoxy delaminating from a chip surface (native SiO2), no deformation in the SiO2 will take place. Furthermore it can be assumed that at room temperature, long-range cooperative motions as they appear in the glass
Fig. 2. Sessile drop of methylene-iodide (MI, see inlet) on a solid surface of EPNF for determination of the contact angle h.
transition exhibit too large relaxation times to play a major role at room temperature (order of days or weeks, depending on activation energy). However, short range cooperative motions as they appear in the b-relaxation [11–13] like a crankshaft-motion down to flips of aromatic rings seem possible candidates. If we roughly assume for the epoxy to contain one relaxable motion group in between two crosslinks, that is, the number-density of b-groups equals that of the crosslinks (qb qxl 4 kmol/m3), using up the average b-relaxation activation energy of Eb 50 kJ/mol, and further assuming the relaxation to take place up to d = 10 nm from the crack-tip (volume of the process zone dAd), the dissipating energy during the fracture process can be estimated as Dh = bb Eb d = 2 J/m2 (again neglecting the thermal contribution). In summary, the contributions i.–iv. can be expressed as
Gc ¼ ðw12 þ wchem Þð1 þ uÞ þ Dh
ð1Þ
we are aware that Eq. (1) and the above estimates present only a first approximation to assess the magnitude of the individual contributions. All of the contributions will need further consideration as they contain rather complex effects and phenomena. In this work, we will focus on the first contribution w12 and in the following we present results of evaluating the physical interactions at interfaces by way of molecular dynamics simulations validated by experimental contact angle measurements. 3. Contact angle measurement The thermodynamic work of adhesion per unit area w12 is a measure of the attraction between two surfaces of the materials 1 and 2. The well known Dupré equation [5] relates the work of adhesion to the specific surface energy of the materials ci:
w12 ¼ c1 þ c2 c12 ¼ wad
ð2Þ
where c12 denotes the specific interfacial energy. The surface energy of a solid may be obtained experimentally by contact angle measurements. Following the theory of van Oss and coworkers [8,9], interfacial interaction consists of a combination of the Lifshitz-van
Table 1 Surface-energy components of different materials and liquids. Material or liquid a
Water MI(CH2I2)a Glycerola SiO2b SiO2 EPN EPNF 212 a b
cL or cS (m J/m2) cd (m J/m2) c+ (m J/m2) c (m J/m2) 72.8 50.8 64.0 44.6 47.3 36.4 38.6 62.8
Literature values: Ref. [14]. Literature values: Ref. [15].
21.8 50.8 34.0 40.6 33.1 34.9 37.5 36.7
25.5 0.0 3.92 0.1 1.8 0.6 5.4 2.2
25.5 0.0 57.4 37.1 28.8 1.0 0.05 78.2
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O. Hölck et al. / Microelectronics Reliability 52 (2012) 1285–1290 Table 2 Work of adhesion as derived by Eq. (8) from experimental contact angles. Material or liquid
SiO2 (m J/m2)
H2O (m J/m2)
MI (m J/m2)
Glycerol (m J/m2)
SiO2 SiO2 (lit.) EPN EPNF 212
– –
121.3 124.2 72.7 83.0 160.8
81.9 90.8 84.2 87.3 86.3
153.6 167.9 86.8 84.1 210.5
80.5 79.1 168.5
2
0.20
SiO2 (lit.) EPN
0.15
0.30
F
EPN 212
SiO2
0.25
0.10
wad / J/m
0.05 0.00
0.15 0.10
SiO2
H2O
MI
Glyc
material/ liquid
0.05
Fig. 3. Work of adhesion wad between different materials calculated from contact angle measurements.
der Waals forces (mainly London-Lifshitz dispersion forces) and the Lewis acid–base (electron-donor–acceptor) interactions. Both contribute to the specific surface energy of a solid cS:
qffiffiffiffiffiffiffiffiffiffiffi
cS ¼ cdS þ 2 cþS cS
ð3Þ
where superscript d indicates the dispersive (Lifshitz –van der Waals) contribution and superscript + and the polar interaction (Lewis acid and base, respectively). When depositing a drop of a liquid upon a plane solid surface, the angle of contact h between liquid and solid (see Fig. 2) will form according to the balance of forces acting at the interface, which are the surface tension of the liquid in contact with vapor-saturated air cL, the surface tension of the solid cS and the interfacial tension cSL. Their relation is given by the Young equation:
cL cos h ¼ cS cSL
ð4Þ
According to van Oss et al. [9], Eq. (4) can be rewritten in terms of Lifshitz-van der Waals and Lewis-acid–base contributions as follows:
cL ð1 þ cos hÞ ¼ 2
EPN 212
0.20
2
wad / J/m
Fig. 4. Principle of copying the complete model and separate materials by deleting material 1 or 2.
SiO2
qffiffiffiffiffiffiffiffiffiffi
cc þ d d S L
qffiffiffiffiffiffiffiffiffiffiffi þ S L
c c þ
qffiffiffiffiffiffiffiffiffiffiffi þ S L
c c
0.00
SiO2
MI
H2O
Glyc
material / liquid
Fig. 5. Work of adhesion wad between SiO2, EPN and 212 and to different liquids calculated from molecular dynamics simulations.
origin are additive, the following forces will act on that volume per unit area:
c1 ¼ c1
qffiffiffiffiffiffiffiffiffiffi
cd1 cd2 þ
qffiffiffiffiffiffiffiffiffiffiffi
cþ1 c2 þ
qffiffiffiffiffiffiffiffiffiffiffi
c1 cþ2
ð6Þ
where c1 is the surface tension of material 1, acting towards material 1. The term in brackets, acting toward material 2, consists of the contributions of dispersive and polar (acid–base) interactions, each of which is in accordance with a geometric mean rule [9,17]. The same argumentation will hold for a volume element of material 2, so that in total the trans-interface-tension c12 may be written as
c12 ¼ c1 þ c2 ¼ c1 þ c2 2
qffiffiffiffiffiffiffiffiffiffi
cd1 cd2 þ
qffiffiffiffiffiffiffiffiffiffiffi
cþ1 c2 þ
qffiffiffiffiffiffiffiffiffiffiffi
c1 cþ2
ð7Þ
Rearranging Eq. (7) and comparing to Eq. (2) yields the work of adhesion between material 1 and 2:
wad ¼ 2
qffiffiffiffiffiffiffiffiffiffi
cd1 cd2 þ
qffiffiffiffiffiffiffiffiffiffiffi
cþ1 c2 þ
qffiffiffiffiffiffiffiffiffiffiffi
c1 cþ2
ð8Þ
ð5Þ
Eq. (5) contains the three unknown variables of Eq. (3). Using three different liquids with well documented parameters cd, c+, c and corresponding contact angle h on the surface S, the surface tension of the solid surface can be obtained. The parameters and surface tensions taken from literature and measured experimentally in this work are compiled in Table 1. The experimental error has been determined not to exceed 10% but is in general well below 5%. Once the surface tensions of two solids 1 and 2 are obtained, it is possible to calculate the work of adhesion by following the treatment of Comyn [16]. If we consider a volume element of material 1 at the interface to material 2 and assume that forces of different
Using the parameters derived from contact angle measurements on the free surfaces which are compiled in Table 1, the work of adhesion between the investigated materials EPN, EPNF and 212 to the SiO2 surface are shown in Fig. 3 and tabulated in Table 2 along with that of the test-liquids. 4. Molecular dynamics simulations One way to obtain the thermodynamic work of adhesion by simulation is the construction of interfacial models in atomic detail, utilizing molecular dynamics simulations. In a previous publication [2], we have detailed our approach on the construction of bulk and interface models of 3D-crosslinked epoxy materials.
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and E2 and of the complete model E12 by following the procedure described by Yarowsky and coworkers [19,20]:
Table 3 Work of adhesion as derived by Eq. (12) from molecular models. Material or liquid SiO2 (m J/m2) H2O (m J/m2) MI (m J/m2) Glycerol (m J/m2) SiO2 EPN 212
– 189 ± 16 187 ± 3
233 ± 6 212 ± 12 249 ± 28
151 ± 7 148 ± 15 133 ± 7
274 ± 7 262 ± 6 266 ± 22
Main feature of the models was the validated periodic connectivity of the models. Based on the interface models of SiO2 and EPN reported in [2], we have performed an extensive investigation of interfacial energies between these materials and the test-liquids used for contact angle measurements reported above. In the same manner interface models of 212/SiO2 were constructed and investigated. It is beyond the scope of this work to give a full introduction to the methodology of molecular dynamics simulations, and therefore we will only repeat the features which are most important for this work. A more thorough introduction can be found in e.g. [18]. In molecular dynamics simulations, an ensemble of atoms is described by the individual positions ri within a simulation cell, the bond information between the atoms and a vector vi describing the current velocity of each atom. The dynamics of the system may now be determined using the force field information which describes the interactions of bonded atoms (bond-lengths, -angles, conformation) and non-bonded interactions (van der Waals, electrostatic). Force fields thus allow the calculation of the potential energy E of an ensemble of N atoms, as a function of their coordinates (r1...rN):
P
Eðr1 rN Þ ¼
P
In this procedure we have used the convenient possibility in molecular modeling to copy models and delete selected atoms or groups of atoms. In this way, an energy sum may be calculated which comprises of all bonded and non-bonded contributions according to the force field used. Thus in Eq. (12), all intra-material contributions (bonded or non-bonded) cancel out, while only interfacial contributions remain (which are of course non-bonded in nature, Eq. (10)). Note that in a 3D-periodic model without vacuum layer, two interfaces need to be regarded and layer thicknesses need to be larger than potential-cutoffs in order to avoid interactions across two layers. Three models of SiO2/EPN and SiO2/212 were independently constructed and equilibrated at T = 298 K, following the scheme reported in [2]. Based on the separated models sketched in Fig. 4, models of the materials in contact with the test-liquids (H2O, MI, Glycerol) were constructed by filling the vacuum with molecules of the liquid at the respective density. These models were further equilibrated at T = 298 K and 1 bar pressure in an NpT-simulation for 500 ps. Afterwards the energy calculation described above was repeated on all models. In total, of each material combination 3 independent models were evaluated adding up to a total of 33 models. The results of the investigated material combinations calculated from Eq. (12) along with the error from the averaging procedure are compiled in Table 3 and plotted in Fig. 5.
5. Discussion
nonbonded interaction
ð9Þ
atompairs
The details of the bonded interaction contributions (usually represented by anharmonic oscillators) are described in [18]. The non-bonded interactions between all pairs of atoms ij are expressed in the applied force field by a van derWaals term with a 9,6-potential and a Coulomb-term:
Enb ij ðr ij ; qi ; qj Þ ¼
ð12Þ
bonded deformation
bonds; angles
þ
wad ¼ ðE1 þ E2 E12 Þ=2A
Aij Bij r 9ij r6ij
! þ
qi qj e0 rij
ð10Þ
where Aij and Bij are parameters describing the strength of the repulsive and attractive force, rij, qi and qj are the distance and partial charges of the interacting atoms i and j; 0 is the vacuum permittivity. For a given molecular structure, the force field results in a potential energy surface. Integration of the Newtonian equations of motion
Fi ¼ rri Ei ðr1 rN Þ ¼ mi €ri
ð11Þ
Leads to a new velocity of each particle which can be extrapolated over the time step of the simulation to determine the new coordinates ri. The force Fi, acting on a particle i of mass mi, results from the gradient of the potential energy Ei (Eq. (11)) determined by the force field Eq. (9). Besides the simulation of the dynamics of the system, the force field enables an evaluation of the potential energy of the system at any time during the simulation by taking a ‘‘snapshot’’ of the system (positions ri) and evaluating Eq. (9). In a bimaterial layered model as depicted in Fig. 4 the interfacial energy may then be calculated from energy calculations of the separated materials E1
The work of adhesion between a native silicon-oxide surface (SiO2) and an epoxy-phenol novolac (EPN) as well as a model epoxy (212) was determined experimentally by contact angle-measurement as well as by molecular dynamics simulation of interface models. Fig. 3 shows the results of the experimentally determined results. From these, the following observations can be made: The best defined and reproducible surface SiO2 yields results that are in good agreement with the literature, giving confidence in the method. Both materials, unfilled (EPN) and filled epoxy (EPNF) show the same results within experimental uncertainty, suggesting the filler particles (silica) to be sufficiently covered by the epoxy even after polishing. The thermodynamic work of adhesion of the interface between EPN and EPNF and a SiO2 surface is of similar magnitude as to the test-liquids. The work of adhesion between 212-material and SiO2 is predicted to be stronger and the behavior of the liquids on 212 and SiO2 surfaces shows very similar tendencies. Fig. 5 shows the results obtained by molecular simulations, permitting the following statements: The two materials EPN and SiO2 behave similarly in molecular interfacial models. The thermodynamic work of adhesion of the interface between EPN and a SiO2 surface is of similar magnitude as to the test-liquids. The surface of 212 seems more attracted to water and less so to MI compared to EPN. However, differences are relatively small.
O. Hölck et al. / Microelectronics Reliability 52 (2012) 1285–1290
normalized wad / %
175
fat-free surfaces. A minimum of 5 drops of each test-liquid (1–3 ll) were placed on the cleansed surfaces in a DataPhysics OCA 20 to derive an average value for the contact angle. Contact angles were determined from camera snapshots five seconds after settling of the drops. All molecular modeling simulations were performed using the Materials Studio software of Accelrys Inc., and COMPASS force field [21,22] was applied. Ewald summation method was used for van der Waals as well as Coulomb interactions. Berendsen thermostat and Andersen barostat were used where applicable.
SiO2 sim SiO2 exp
150
EPN sim EPN exp 212 sim 212 exp
125 100
1289
75 50 25 0
SiO2
H2O
MI
Glyc
material / liquid Fig. 6. Work of adhesion between different materials normalized to the value of SiO2/H2O for experimental and simulated results, respectively.
For a comparison of experimental and simulated results, caution has to be exercised regarding absolute values. For one thing, experimental contact angle determination varies between laboratories due to impurities of the test-liquids, deviation of test-equipment and different surface treatment. Secondly, in models at the atomic scale, interfaces are atomistically flat, allowing for perfect contact (wetting) of the interfaces. Furthermore, in the simulations performed in this work infinite multilayers of nanometer thickness are simulated. Finally, as Yarovsky points out [19], the interfacial energies depend on the force field used in the simulations. However, as Yarovsky also points out, trends in work of adhesion obtained from simulations are well reproduced experimentally. In this work, these statements can be confirmed. From Figs. 3 and 5 it is clear, that absolute values of the work of adhesion can not be compared directly between experiment and simulation. In order to properly compare the values in a qualitative way, we have normalized both experimental and simulated works of adhesion to the respective value of silicon oxide and water. In Fig. 6 it is now clearly seen, that the simulated results for the thermodynamic work of adhesion of a SiO2 interface to the test-liquids is in good qualitative agreement with the experiments (hatched columns). However, some disagreement remains regarding the results for the EPN epoxy. Finally, for the 212-epoxy both simulation and experimental results predict the strongest interaction between the materials. 6. Conclusions The thermodynamic work of adhesion of the material combinations SiO2/EPN and SiO2/212 were thoroughly analyzed by both experimental contact angle determination and molecular dynamics simulations. Both approaches are self-consistent and yield results in reasonable agreement to literature. Comparison of absolute values between experiment and simulation shows agreement on the same order of magnitude (factor of 2–3), which is a quite satisfying achievement, considering the differences of scales (time and space). Comparisons on a qualitative basis yield even better results. Further work will be done regarding other contributions (ii)–(iv) to interfacial delamination as discussed above. 7. Technical details For the contact angle materials, surfaces of the epoxy samples (filled and unfilled) were polished and oven-dried at 120 °C. Silicon with a small layer of native SiO2 were used as received. All samples were cleaned shortly with ethanol and dried in nitrogen flow for
Acknowledgments The authors thank the following colleagues: C. Menke and S. Todd of the Accelrys support team for close collaboration; K.M.B. Jansen of TU Delft and W. van Driel of NXP Semiconductors for providing samples of the epoxy; H. Kukuk-Schmid of Fraunhofer IZM for sample preparation; R. Mroßko of AMIC GmbH and J. Brückner of TU Chemnitz for help with the roughness analysis. The authors thank the European Commission for partial funding of this work under project NanoInterface (NMP-2008-214371) (http://nanointerface.eu). The authors thank the German Federal Ministry of Education and Research (BMBF) for partial funding of this work under project CoSiP (01M3186B) (http://cosip.de/).
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Contents lists available at SciVerse ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Comparative characterization of chip to epoxy interfaces by molecular modeling and contact angle determination O. Hölck a,b,⇑, J. Bauer a, O. Wittler a, B. Michel c, B. Wunderle a,b,c a
Fraunhofer Institute for Reliability and Microintegration (IZM), Gustav Meyer Allee 25, 13355 Berlin, Germany Chemnitz University of Technology, Materials and Reliability of Microsystems, Germany c Fraunhofer Institute for Electronic Nano Systems (ENAS), Germany b
a r t i c l e
i n f o
Article history: Received 15 November 2011 Received in revised form 15 February 2012 Accepted 6 March 2012 Available online 10 May 2012
a b s t r a c t An investigation of interfacial interaction has been performed between three epoxy molding compound materials and a native silicon dioxide layer (SiO2) usually found at chip surfaces. The epoxy materials were an industry oriented epoxy molding compound Epoxy Phenol Novolac (EPN), its filled variety EPNF (with silica particles) and a model aromatic epoxy1 (2 1 2). All systems are described in full in [1] and [2]. The free surfaces of the solid materials were experimentally analyzed by contact angle measurements of three different liquids (water, methylene-iodide (MI) and glycerol). Results are compared to interfacial energies obtained by analysis of the interfaces in bimaterial molecular models, yielding reasonable agreement. A qualitative prediction regarding the influence of water on the interfacial strength between chip and molding compound is attempted. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
2. Interface delamination
The investigation of the mechanisms of delamination or fracture between the interfaces of different materials is a challenging yet necessary task in microelectronic packaging. A lot of the failure modes that are detected in highly integrated System in Package (SiP) devices originate directly or indirectly in the failure of adhesive strength and thus causing loss of performance or function [3]. For a comprehensive reliability assessment of microelectronic components, the development of a physical understanding of the failure mechanisms is necessary (‘‘physics of failure’’ approach). The involved processes are complex in nature and therefore all scales involved need to be taken into account, that is, phenomena at system level and the level of surface finish (macro- and microscale), as well as phenomena on molecular and even atomic level (meso- and nanoscale) need to be investigated [4]. We present in this work delamination as a process consisting of several contributions. These are roughly estimated as to their magnitude and experimental or numerical possibilities of a more thorough treatment is given. The center of our attention lies on the investigation of the thermodynamic work of adhesion and a comparative analysis of molecular modeling and experimental contact angle results.
The critical energy release rate Gc, is a measure of interfacial strength between two materials. It may be obtained from fracture experiments like 3- or 4-point bending tests or mixed-mode bending tests, using fracture mechanics and beam theory [5–7]. This procedure is well established and of great practical value, however, it must be understood, that a macroscopical quantity for the interfacial toughness is obtained that consists of several mechanisms of different physical origin. In a first approximation, the contributions can be identified as follows:
⇑ Corresponding author at: Fraunhofer Institute for Reliability and Microintegration (IZM), Gustav Meyer Allee 25, 13355 Berlin, Germany. E-mail address: [email protected] (O. Hölck). 1 1,3-Bis(2,3-epoxypropoxy)-benzene and a 1,2 diamino(ethane)2 hardener in a 2:1 mixing ratio. 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.03.019
i. ii. iii. iv.
physical interaction: w12 chemical bonds: wchem mechanical interaction: u heat dissipation: Dh
By physical interaction (i) the interatomic or intermolecular forces across an interface are meant, which give the thermodynamic work of adhesion w12 between two materials 1 and 2. According to the theory of van Oss et al. [8,9], van der Waals forces and polar forces are mainly responsible for this interaction. In general, the thermodynamic work of adhesion is discussed in terms of this interaction energy per unit area of interface and can be related to the difference in system energy and the sum of free surface energy of each material (see discussion below), i.e. the energy needed to create ideal free surfaces. This contribution w12 to delamination will be discussed more thoroughly in a later paragraph.
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Fig. 1. Rough surface of a silicon chip measured by AFM and transfered to ANSYS for area calculation, leading to a correction factor u > 0. The z-axis is scaled by a factor of 10 compared to x and y.
If chemical bonds are formed across the interface (ii), these will need to be broken for delamination to occur and contribute as chemical interactions. Chemical bonds may be formed during or after the curing process of the molding compound, if the surfaces of the respective materials contain relevant groups. As a quick estimate we assume the formation of a carbon–oxygen bond between an epoxy group of the molding compound and an oxygen of a SiO2surface. C–O-bonds typically exhibit an energy of ECO = 350 kJ/mol [10]. If we further assume a density of one such bond per 400 Å2 (interface-area of our molecular models, see below). Equating these assumptions leads to a contribution to interfacial strength of the order of wchem 150 mJ/m2. Regardless of the accuracy of these assumptions, this estimation shows that if chemical bonds are likely to occur, their contribution to interfacial toughness are not to be neglected and it can be stated that chemical interaction wchem would contribute to the energy per unit area needed to separate the interface. We would like to note, that at room temperature TR, the thermal contribution to dissociation of covalent bonds Eth is negligible (Eth NAkBTR 2.5 kJ/mol with NA Avogadro and kB Boltzmann constants). Physical (i) and chemical (ii) interaction refer to a contribution per unit area of an ideal interface, meaning two materials in full contact with each other at ideally flat surfaces. However, real materials always exhibit a surface roughness, which leads to non-ideal contact, enlargement of the surface area A⁄ with respect to the apparent surface area A or mechanical interlocking of the interfaces (iii). In turn, this real interfacial area A⁄ = A(1 + u) will lead to change in the contribution of (i) and (ii) per unit apparent interface area, that is, the macroscopically measured interface area. Experimental values for the interface roughness may be obtained by atomic force microscopy (AFM). An example of such a measurement can be seen in Fig. 1. The AFM-scan of the area of 1 lm2 with resolution of 128 points on x and y-axis results in depth-profile with maximum height of about 20 nm. The values can be read into ANSYS and the resulting surface can easily be analyzed (note the scaled z-axis by a factor of 10 in Fig. 1). For our samples, a surface factor of (1 + u) = 1.002 results, revealing for this case negligible influence of the surface roughness. In the zone of fracture and especially at the crack-tip, where elastic theory would result in a singularity of the stress field, plastic deformation occurs in the materials (iv). In the process of irreversible material deformation energy is dissipated as heat Dh and thus adds to the sum of macroscopically observed fracture energy. In an attempt to quantify this energy, the mechanisms of irreversible plastic deformation (besides rupture of covalent bonds) need to be identified that possibly contribute to heat dissipation in the fracture zone. Let us assume that for an epoxy delaminating from a chip surface (native SiO2), no deformation in the SiO2 will take place. Furthermore it can be assumed that at room temperature, long-range cooperative motions as they appear in the glass
Fig. 2. Sessile drop of methylene-iodide (MI, see inlet) on a solid surface of EPNF for determination of the contact angle h.
transition exhibit too large relaxation times to play a major role at room temperature (order of days or weeks, depending on activation energy). However, short range cooperative motions as they appear in the b-relaxation [11–13] like a crankshaft-motion down to flips of aromatic rings seem possible candidates. If we roughly assume for the epoxy to contain one relaxable motion group in between two crosslinks, that is, the number-density of b-groups equals that of the crosslinks (qb qxl 4 kmol/m3), using up the average b-relaxation activation energy of Eb 50 kJ/mol, and further assuming the relaxation to take place up to d = 10 nm from the crack-tip (volume of the process zone dAd), the dissipating energy during the fracture process can be estimated as Dh = bb Eb d = 2 J/m2 (again neglecting the thermal contribution). In summary, the contributions i.–iv. can be expressed as
Gc ¼ ðw12 þ wchem Þð1 þ uÞ þ Dh
ð1Þ
we are aware that Eq. (1) and the above estimates present only a first approximation to assess the magnitude of the individual contributions. All of the contributions will need further consideration as they contain rather complex effects and phenomena. In this work, we will focus on the first contribution w12 and in the following we present results of evaluating the physical interactions at interfaces by way of molecular dynamics simulations validated by experimental contact angle measurements. 3. Contact angle measurement The thermodynamic work of adhesion per unit area w12 is a measure of the attraction between two surfaces of the materials 1 and 2. The well known Dupré equation [5] relates the work of adhesion to the specific surface energy of the materials ci:
w12 ¼ c1 þ c2 c12 ¼ wad
ð2Þ
where c12 denotes the specific interfacial energy. The surface energy of a solid may be obtained experimentally by contact angle measurements. Following the theory of van Oss and coworkers [8,9], interfacial interaction consists of a combination of the Lifshitz-van
Table 1 Surface-energy components of different materials and liquids. Material or liquid a
Water MI(CH2I2)a Glycerola SiO2b SiO2 EPN EPNF 212 a b
cL or cS (m J/m2) cd (m J/m2) c+ (m J/m2) c (m J/m2) 72.8 50.8 64.0 44.6 47.3 36.4 38.6 62.8
Literature values: Ref. [14]. Literature values: Ref. [15].
21.8 50.8 34.0 40.6 33.1 34.9 37.5 36.7
25.5 0.0 3.92 0.1 1.8 0.6 5.4 2.2
25.5 0.0 57.4 37.1 28.8 1.0 0.05 78.2
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O. Hölck et al. / Microelectronics Reliability 52 (2012) 1285–1290 Table 2 Work of adhesion as derived by Eq. (8) from experimental contact angles. Material or liquid
SiO2 (m J/m2)
H2O (m J/m2)
MI (m J/m2)
Glycerol (m J/m2)
SiO2 SiO2 (lit.) EPN EPNF 212
– –
121.3 124.2 72.7 83.0 160.8
81.9 90.8 84.2 87.3 86.3
153.6 167.9 86.8 84.1 210.5
80.5 79.1 168.5
2
0.20
SiO2 (lit.) EPN
0.15
0.30
F
EPN 212
SiO2
0.25
0.10
wad / J/m
0.05 0.00
0.15 0.10
SiO2
H2O
MI
Glyc
material/ liquid
0.05
Fig. 3. Work of adhesion wad between different materials calculated from contact angle measurements.
der Waals forces (mainly London-Lifshitz dispersion forces) and the Lewis acid–base (electron-donor–acceptor) interactions. Both contribute to the specific surface energy of a solid cS:
qffiffiffiffiffiffiffiffiffiffiffi
cS ¼ cdS þ 2 cþS cS
ð3Þ
where superscript d indicates the dispersive (Lifshitz –van der Waals) contribution and superscript + and the polar interaction (Lewis acid and base, respectively). When depositing a drop of a liquid upon a plane solid surface, the angle of contact h between liquid and solid (see Fig. 2) will form according to the balance of forces acting at the interface, which are the surface tension of the liquid in contact with vapor-saturated air cL, the surface tension of the solid cS and the interfacial tension cSL. Their relation is given by the Young equation:
cL cos h ¼ cS cSL
ð4Þ
According to van Oss et al. [9], Eq. (4) can be rewritten in terms of Lifshitz-van der Waals and Lewis-acid–base contributions as follows:
cL ð1 þ cos hÞ ¼ 2
EPN 212
0.20
2
wad / J/m
Fig. 4. Principle of copying the complete model and separate materials by deleting material 1 or 2.
SiO2
qffiffiffiffiffiffiffiffiffiffi
cc þ d d S L
qffiffiffiffiffiffiffiffiffiffiffi þ S L
c c þ
qffiffiffiffiffiffiffiffiffiffiffi þ S L
c c
0.00
SiO2
MI
H2O
Glyc
material / liquid
Fig. 5. Work of adhesion wad between SiO2, EPN and 212 and to different liquids calculated from molecular dynamics simulations.
origin are additive, the following forces will act on that volume per unit area:
c1 ¼ c1
qffiffiffiffiffiffiffiffiffiffi
cd1 cd2 þ
qffiffiffiffiffiffiffiffiffiffiffi
cþ1 c2 þ
qffiffiffiffiffiffiffiffiffiffiffi
c1 cþ2
ð6Þ
where c1 is the surface tension of material 1, acting towards material 1. The term in brackets, acting toward material 2, consists of the contributions of dispersive and polar (acid–base) interactions, each of which is in accordance with a geometric mean rule [9,17]. The same argumentation will hold for a volume element of material 2, so that in total the trans-interface-tension c12 may be written as
c12 ¼ c1 þ c2 ¼ c1 þ c2 2
qffiffiffiffiffiffiffiffiffiffi
cd1 cd2 þ
qffiffiffiffiffiffiffiffiffiffiffi
cþ1 c2 þ
qffiffiffiffiffiffiffiffiffiffiffi
c1 cþ2
ð7Þ
Rearranging Eq. (7) and comparing to Eq. (2) yields the work of adhesion between material 1 and 2:
wad ¼ 2
qffiffiffiffiffiffiffiffiffiffi
cd1 cd2 þ
qffiffiffiffiffiffiffiffiffiffiffi
cþ1 c2 þ
qffiffiffiffiffiffiffiffiffiffiffi
c1 cþ2
ð8Þ
ð5Þ
Eq. (5) contains the three unknown variables of Eq. (3). Using three different liquids with well documented parameters cd, c+, c and corresponding contact angle h on the surface S, the surface tension of the solid surface can be obtained. The parameters and surface tensions taken from literature and measured experimentally in this work are compiled in Table 1. The experimental error has been determined not to exceed 10% but is in general well below 5%. Once the surface tensions of two solids 1 and 2 are obtained, it is possible to calculate the work of adhesion by following the treatment of Comyn [16]. If we consider a volume element of material 1 at the interface to material 2 and assume that forces of different
Using the parameters derived from contact angle measurements on the free surfaces which are compiled in Table 1, the work of adhesion between the investigated materials EPN, EPNF and 212 to the SiO2 surface are shown in Fig. 3 and tabulated in Table 2 along with that of the test-liquids. 4. Molecular dynamics simulations One way to obtain the thermodynamic work of adhesion by simulation is the construction of interfacial models in atomic detail, utilizing molecular dynamics simulations. In a previous publication [2], we have detailed our approach on the construction of bulk and interface models of 3D-crosslinked epoxy materials.
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and E2 and of the complete model E12 by following the procedure described by Yarowsky and coworkers [19,20]:
Table 3 Work of adhesion as derived by Eq. (12) from molecular models. Material or liquid SiO2 (m J/m2) H2O (m J/m2) MI (m J/m2) Glycerol (m J/m2) SiO2 EPN 212
– 189 ± 16 187 ± 3
233 ± 6 212 ± 12 249 ± 28
151 ± 7 148 ± 15 133 ± 7
274 ± 7 262 ± 6 266 ± 22
Main feature of the models was the validated periodic connectivity of the models. Based on the interface models of SiO2 and EPN reported in [2], we have performed an extensive investigation of interfacial energies between these materials and the test-liquids used for contact angle measurements reported above. In the same manner interface models of 212/SiO2 were constructed and investigated. It is beyond the scope of this work to give a full introduction to the methodology of molecular dynamics simulations, and therefore we will only repeat the features which are most important for this work. A more thorough introduction can be found in e.g. [18]. In molecular dynamics simulations, an ensemble of atoms is described by the individual positions ri within a simulation cell, the bond information between the atoms and a vector vi describing the current velocity of each atom. The dynamics of the system may now be determined using the force field information which describes the interactions of bonded atoms (bond-lengths, -angles, conformation) and non-bonded interactions (van der Waals, electrostatic). Force fields thus allow the calculation of the potential energy E of an ensemble of N atoms, as a function of their coordinates (r1...rN):
P
Eðr1 rN Þ ¼
P
In this procedure we have used the convenient possibility in molecular modeling to copy models and delete selected atoms or groups of atoms. In this way, an energy sum may be calculated which comprises of all bonded and non-bonded contributions according to the force field used. Thus in Eq. (12), all intra-material contributions (bonded or non-bonded) cancel out, while only interfacial contributions remain (which are of course non-bonded in nature, Eq. (10)). Note that in a 3D-periodic model without vacuum layer, two interfaces need to be regarded and layer thicknesses need to be larger than potential-cutoffs in order to avoid interactions across two layers. Three models of SiO2/EPN and SiO2/212 were independently constructed and equilibrated at T = 298 K, following the scheme reported in [2]. Based on the separated models sketched in Fig. 4, models of the materials in contact with the test-liquids (H2O, MI, Glycerol) were constructed by filling the vacuum with molecules of the liquid at the respective density. These models were further equilibrated at T = 298 K and 1 bar pressure in an NpT-simulation for 500 ps. Afterwards the energy calculation described above was repeated on all models. In total, of each material combination 3 independent models were evaluated adding up to a total of 33 models. The results of the investigated material combinations calculated from Eq. (12) along with the error from the averaging procedure are compiled in Table 3 and plotted in Fig. 5.
5. Discussion
nonbonded interaction
ð9Þ
atompairs
The details of the bonded interaction contributions (usually represented by anharmonic oscillators) are described in [18]. The non-bonded interactions between all pairs of atoms ij are expressed in the applied force field by a van derWaals term with a 9,6-potential and a Coulomb-term:
Enb ij ðr ij ; qi ; qj Þ ¼
ð12Þ
bonded deformation
bonds; angles
þ
wad ¼ ðE1 þ E2 E12 Þ=2A
Aij Bij r 9ij r6ij
! þ
qi qj e0 rij
ð10Þ
where Aij and Bij are parameters describing the strength of the repulsive and attractive force, rij, qi and qj are the distance and partial charges of the interacting atoms i and j; 0 is the vacuum permittivity. For a given molecular structure, the force field results in a potential energy surface. Integration of the Newtonian equations of motion
Fi ¼ rri Ei ðr1 rN Þ ¼ mi €ri
ð11Þ
Leads to a new velocity of each particle which can be extrapolated over the time step of the simulation to determine the new coordinates ri. The force Fi, acting on a particle i of mass mi, results from the gradient of the potential energy Ei (Eq. (11)) determined by the force field Eq. (9). Besides the simulation of the dynamics of the system, the force field enables an evaluation of the potential energy of the system at any time during the simulation by taking a ‘‘snapshot’’ of the system (positions ri) and evaluating Eq. (9). In a bimaterial layered model as depicted in Fig. 4 the interfacial energy may then be calculated from energy calculations of the separated materials E1
The work of adhesion between a native silicon-oxide surface (SiO2) and an epoxy-phenol novolac (EPN) as well as a model epoxy (212) was determined experimentally by contact angle-measurement as well as by molecular dynamics simulation of interface models. Fig. 3 shows the results of the experimentally determined results. From these, the following observations can be made: The best defined and reproducible surface SiO2 yields results that are in good agreement with the literature, giving confidence in the method. Both materials, unfilled (EPN) and filled epoxy (EPNF) show the same results within experimental uncertainty, suggesting the filler particles (silica) to be sufficiently covered by the epoxy even after polishing. The thermodynamic work of adhesion of the interface between EPN and EPNF and a SiO2 surface is of similar magnitude as to the test-liquids. The work of adhesion between 212-material and SiO2 is predicted to be stronger and the behavior of the liquids on 212 and SiO2 surfaces shows very similar tendencies. Fig. 5 shows the results obtained by molecular simulations, permitting the following statements: The two materials EPN and SiO2 behave similarly in molecular interfacial models. The thermodynamic work of adhesion of the interface between EPN and a SiO2 surface is of similar magnitude as to the test-liquids. The surface of 212 seems more attracted to water and less so to MI compared to EPN. However, differences are relatively small.
O. Hölck et al. / Microelectronics Reliability 52 (2012) 1285–1290
normalized wad / %
175
fat-free surfaces. A minimum of 5 drops of each test-liquid (1–3 ll) were placed on the cleansed surfaces in a DataPhysics OCA 20 to derive an average value for the contact angle. Contact angles were determined from camera snapshots five seconds after settling of the drops. All molecular modeling simulations were performed using the Materials Studio software of Accelrys Inc., and COMPASS force field [21,22] was applied. Ewald summation method was used for van der Waals as well as Coulomb interactions. Berendsen thermostat and Andersen barostat were used where applicable.
SiO2 sim SiO2 exp
150
EPN sim EPN exp 212 sim 212 exp
125 100
1289
75 50 25 0
SiO2
H2O
MI
Glyc
material / liquid Fig. 6. Work of adhesion between different materials normalized to the value of SiO2/H2O for experimental and simulated results, respectively.
For a comparison of experimental and simulated results, caution has to be exercised regarding absolute values. For one thing, experimental contact angle determination varies between laboratories due to impurities of the test-liquids, deviation of test-equipment and different surface treatment. Secondly, in models at the atomic scale, interfaces are atomistically flat, allowing for perfect contact (wetting) of the interfaces. Furthermore, in the simulations performed in this work infinite multilayers of nanometer thickness are simulated. Finally, as Yarovsky points out [19], the interfacial energies depend on the force field used in the simulations. However, as Yarovsky also points out, trends in work of adhesion obtained from simulations are well reproduced experimentally. In this work, these statements can be confirmed. From Figs. 3 and 5 it is clear, that absolute values of the work of adhesion can not be compared directly between experiment and simulation. In order to properly compare the values in a qualitative way, we have normalized both experimental and simulated works of adhesion to the respective value of silicon oxide and water. In Fig. 6 it is now clearly seen, that the simulated results for the thermodynamic work of adhesion of a SiO2 interface to the test-liquids is in good qualitative agreement with the experiments (hatched columns). However, some disagreement remains regarding the results for the EPN epoxy. Finally, for the 212-epoxy both simulation and experimental results predict the strongest interaction between the materials. 6. Conclusions The thermodynamic work of adhesion of the material combinations SiO2/EPN and SiO2/212 were thoroughly analyzed by both experimental contact angle determination and molecular dynamics simulations. Both approaches are self-consistent and yield results in reasonable agreement to literature. Comparison of absolute values between experiment and simulation shows agreement on the same order of magnitude (factor of 2–3), which is a quite satisfying achievement, considering the differences of scales (time and space). Comparisons on a qualitative basis yield even better results. Further work will be done regarding other contributions (ii)–(iv) to interfacial delamination as discussed above. 7. Technical details For the contact angle materials, surfaces of the epoxy samples (filled and unfilled) were polished and oven-dried at 120 °C. Silicon with a small layer of native SiO2 were used as received. All samples were cleaned shortly with ethanol and dried in nitrogen flow for
Acknowledgments The authors thank the following colleagues: C. Menke and S. Todd of the Accelrys support team for close collaboration; K.M.B. Jansen of TU Delft and W. van Driel of NXP Semiconductors for providing samples of the epoxy; H. Kukuk-Schmid of Fraunhofer IZM for sample preparation; R. Mroßko of AMIC GmbH and J. Brückner of TU Chemnitz for help with the roughness analysis. The authors thank the European Commission for partial funding of this work under project NanoInterface (NMP-2008-214371) (http://nanointerface.eu). The authors thank the German Federal Ministry of Education and Research (BMBF) for partial funding of this work under project CoSiP (01M3186B) (http://cosip.de/).
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