Performance of Cu–Ag Thin Films As Diffusion Barrier Layer

coatings

Article Performance of Cu–Ag Thin Films as Diﬀusion Barrier Layer

Po-Hsien Sung and Tei-Chen Chen *

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan; [email protected] * Correspondence: [email protected]

Received: 11 October 2020; Accepted: 11 November 2020; Published: 13 November 2020

Abstract: It is well-known that Cu–Sn intermetallic compounds are easily produced during reflow process and result in poor reliability of solder bump. Recently, amorphous metallic films have been considered to be the most effective barrier layer because of the absence of grain boundaries and immiscibility with copper. Since Cu–Ag alloys are characterized by their lower electrical resistivity and superior glass-forming ability, they are appropriate to be used as the diffusion barrier layers. In this study, molecular dynamics simulation was performed to investigate the effects of composition ratio and quenching rate on the internal microstructure, diffusion properties, and the strength of the interface between polycrystalline Cu and Cu–Ag barrier layers. The results showed that Cu40Ag60 and Cu60Ag40 present more than 95% of the amorphous at quenching rate between 0.25 and 25 K/ps, indicating a good glass-forming ability. Diffusion simulation showed that a better barrier performance can be achieved with higher amorphous ratio. For the sample of Cu20Ag80 with quenching rate of 25 K/ps, a void is initially generated in amorphous Cu–Ag layer during the tensile test. This indicates the strength of amorphous Cu–Ag is weaker than Cu–Ag/Cu interface and the polycrystalline Cu layer.

Keywords: amorphous; Cu–Ag; diﬀusion barrier layer; molecular dynamics

1. Introduction Recently, 2.5D integrated circuit (IC) flip chip assembly package with microbump was widely adopted in high-end niche applications [1]. In the meantime, copper is gradually replacing aluminum as a lead and trace material because of its much lower resistance. There are two basic solid state diffusion mechanisms: vacancy (substitutional diffusion) and interstitial diffusion. The major concern of using copper as metallization, however, is its much higher diffusion coefficient than aluminum due to smaller atomic size and lower activation energy [2,3]. Cu–Sn intermetallics compounds (IMCs) are easily formed by the reaction of copper and tin through diffusion effect even at temperature as low as 200 ◦C[4–7]. Generally, IMCs layer is the most brittle part in the solder joint and thus easily results in the failure of electronic devices during service. Hence, it is important to select a proper material as a diffusion barrier between copper and tin to prevent the formation of IMCs during the minimization progress of electronics devices. In the recent years, several kinds of materials, such as TiN [8–11], Ni [12–14], Ta [15], and amorphous Zr53Cu30Ni9Al8 [16], have been investigated as barrier layers to inhibit rapid copper diffusion in interconnect structures. Among these candidates, TiN, Ni, and Ta barrier layers are polycrystalline and cannot provide sufficient protection because grain boundaries can provide fast diffusion paths for copper and could react to form Cu–Sn IMCs. On the contrary, amorphous barrier layers exhibit superior behavior. These kinds of thin film metallic glasses (TFMGs) have been examined and regarded as the promising diffusion barriers in integrated circuits applications [17–22] because of the absence of grain boundaries and immiscibility with copper [23–25]. Amorphous coatings

Coatings 2020, 10, 1087; doi:10.3390/coatings10111087 www.mdpi.com/journal/coatings Coatings 2020, 10, 1087 2 of 14 also can be utilized for the purpose of corrosion resistance [26,27]. Their mechanical properties and fracture mechanisms in nano-scale have been investigated [28,29]. Compared to Zr53Cu30Ni9Al8 alloy, Cu–Ag alloys exhibit much lower electrical resistivity [30,31] and superior glass-forming ability. Recently, it has been considered as the candidate material of interconnection in high-field magnets [32,33]. Cu–Ag alloys can also be used in modern ultra-large-scale-integration interconnect applications. Their reliability can be enhanced by low grain boundaries, low interface diffusion, low electrical resistivity, and high mechanical strength by adjusting the composition ratio [34,35]. As a potential material of TFMGs barrier layer, the diffusion behavior of Cu–Ag and strength of this layered structure are crucial and need further detailed investigation.

2. Materials and Methods In this article, molecular dynamics (MD) simulation was adopted in analysis. The effects of composition ratio and quenching rate on the internal microstructure and diffusion properties of Cu–Ag alloy, as well as the strength of the barrier layer were systematically investigated. The large-scale atomic/molecular massively parallel simulator (LAMMPS, The large-scale atomic/molecular massively parallel simulator, version 27 Nov. 2018, Sandia National Laboratories, Albuquerque, NM, USA) [36] and the package of open visualization tool (OVITO, open visualization tool, version 2.9.0 (27 July 2017), Technical University of Darmstadt, Darmstadt, Germany) [37] were individually adopted as the analysis software and the scientific visualization for atomistic simulation data. Moreover, the embedded-atom method (EAM) potential was adopted to model the atomistic interactions among Cu and Ag atoms [38,39]. This potential has been successfully applied to accurately simulate the structure, surface, and transformation of amorphous metallic materials.

2.1. Amorphous Geometry Structure The amorphous structure of Cu–Ag at a temperature of 300 K was obtained by performing simulations with the following parameter settings and heat treatments. First, a crystal Cu–Ag alloy was created with a face-centered cubic copper lattice of 184,950 atoms and replaced enough copper atoms with silver to achieve the desired composition. Subsequently, a series of simulations of heat treatment was conducted within the isothermal isobaric ensemble (NPT) with an external pressure of zero. Three-dimensional periodic boundary conditions were applied to the simulation box. The velocities of atoms were adjusted in order to maintain them in an isothermal state with a speciﬁc temperature, obeying Newton’s second law. The model was initially relaxed under periodic boundary conditions at 300 K for 200 ps within a NPT ensemble. The system was heated from 300 to 2200 K at a constant heating rate of 5 1011 to 5 1013 K/s, which produced a liquid phase. To make the state of the × × system as natural as possible, the liquid system was relaxed for 20 ps at 2200 K. Finally, the system was quenched from 2200 to 300 K at a quenching rate of 5 1013 K/s, followed by relaxation for 20 ps at × 300 K. The amorphous alloy model, therefore, was prepared by performing the temperature history stages including heating state, holding state, and quenching state.

2.2. Procedures for Interface Model Preparation The simulation box constructed in this work was a two-layered structure, composed of the layer of Cu–Ag alloys (after quenching) and Cu layer (polycrystalline). The sizes of the former are 30 nm × 30 nm 5 nm in width (x-axis), height (z-axis), and thick (y-axis), respectively, while the latter is 30 nm × 10 nm 5 nm in width (x-axis), height (z-axis), and thick (y-axis), respectively. These two layers × × were located together along the interfaces of the x–y plane with a small separation distance of 3.5 Å based on the equilibrium bond lengths. After that, these two layers suddenly became in contact and bonded together automatically. It was reported that as long as the separation distance was appropriate, it did not aﬀect the results [40]. Coatings 2020, 10, 1087 3 of 14

2.3. Procedure for Diffusion and Deformation Models of Cu/Cu–Ag layered structures were adopted for both of the diffusion and deformation simulations. In the model of deformation simulation, two additional rigid regions of dimensions 30 nm width (x-axis) 5 nm height (y-axis) 12 nm thick (z-axis) were imposed at the top and bottom sides × × of the model, respectively. A uniform velocity along z-axis direction in the opposite direction was individually applied to these two rigid regions, approximately equal to the strain rate of 1 109 s 1. × − The condition of tensile test was simulated at a temperature of 300 K under NVT (constant-temperature and constant-volume) ensemble. Gear’s Predictor-Corrector integration algorithms [41] were adopted for the second-order differential equations of motion to correct all predicated positions. Moreover, a time step of 2 fs was selected. To avoid the phenomena of steric clashes and the formation of inappropriate geometries, the established configuration of the system was relaxed by energy minimization first. The convergence of the pressure, temperature, potential energy, and volume as the function of time was achieved when the time is longer than 100 ps. In other words, it means the simulation model already reached steady state. To confirm the correctness of the intermolecular potential functions, Table1 depicted the elastic constants of data by MD simulation and experiment, respectively [38,42]. Comparing the simulation data with experimental data, it was found that the errors between them were smaller than 2%, indicating the correctness of the potential functions. Since the elastic constants of Cu–Ag alloy are closely related to the ratio of composition, fabrication method, and microstructures, we did not find the elastic constants exactly equivalent to the microstructures of this study. However, it was reported in the literature [30] that the Young’s modulus of Cu20Ag80, prepared by co-sputtering technique, is around 95 GPa, in agreement with the data of 91.8 GPa (quenching rate 0.25 K/ps) of this study.

Table 1. Elastic constants of Cu and Ag via experimental and molecular dynamics (MD) simulation.

Elements Methods C11 (GPa) C12 (GPa) C44 (GPa) Experimental data [38] 168.4 121.4 75.4 Cu Calculated data by MD 168.5 120.8 75.2 Error (%) 0.06 0.49 0.27 Experimental data [42] 124.8 95.2 46.0 Ag Calculated data by MD 126.1 94.2 46.9 Error (%) 1.04 1.05 1.96

C11,C12,C44: elastic constants in anisotropic elasticity.

Some other verifications, such as atomic equilibrium distance, coefficient of thermal expansion, as well as glass transition temperature (Tg) are individually performed and discussed. To analyze the thermodynamic properties of Cu–Ag alloys with four different compositions (Cu20Ag80, Cu40Ag60, Cu60Ag40, and Cu80Ag20) and three different quenching rates (0.25, 2.5, and 25 K/ps), the relationship between volume and temperature is compared in this section. Figure1a,b shows the volume versus temperature curves of Cu20Ag80 and Cu40Ag60, respectively, at different quenching rates, which showed that glass transition temperature was dependent on the quenching rates. In order to acquire a more refined estimate of glass transition temperature, the data were captured with smaller increment in temperature, namely 1 K, from 2100 to 100 K. During the quenching process, the volume–temperature curves for Cu20Ag80 at a quenching rate of 0.25 K/ps, as shown in Figure1a, indicate that the slope change in estimation takes place at about 550 K, which indicates that glass transition occurs near this temperature. These results were similar to the literature [43,44]. As shown in Figure1, however, these curves are smooth for both Cu–Ag alloys at high quenching rates and are difficult to determine the glass transition temperature. Coatings 2020, 10, x 1087 FOR PEER REVIEW 4 of 14

(a) (b)

Figure 1. Volumes vary as a function of temperature at different quenching rates for (a) Cu20Ag80 and Figure 1. Volumes vary as a function of temperature at diﬀerent quenching rates for (a) Cu20Ag80 and (b) Cu40Ag60 alloys (glass transition temperature (Tg) of 550 K, can be approximately determined by (b) Cu40Ag60 alloys (glass transition temperature (Tg) of 550 K, can be approximately determined by extrapolation of two straight dotted lines below and above the transition until they intersect; and the extrapolation of two straight dotted lines below and above the transition until they intersect; and the alloys will transform to the glass state as the temperature is lower than Tg). alloys will transform to the glass state as the temperature is lower than Tg).

3. Results Results and and Discussion Discussion

3.1. Radial Radial Distribution Distribution Function Function (RDF) (RDF) To analyzeanalyze the the structural structural di ffdifferenceserences for for diff differeerent compositionsnt compositions and quenchingand quenching rates, therates, RDF the curves RDF curvesfor all configurationsfor all configurations were compared were compared in this section. in this The section. results The indicate results that indicate changes that in changes quenching in quenchingrates and di ratesfferent and composition different composition ratio have ratio significant have significant effects on effects the rearrangement on the rearrangement of Cu–Ag ofalloy. Cu– AgThe alloy. structure The ofstructure Cu40Ag of60 Cuwas40Ag studied60 was atstudied different at different quenching quenching rates of 0.25, rates 2.5, of and0.25, 25 2.5, K /andps to 25 follow K/ps tothe follow evolution the evolution of the atomic of the arrangements atomic arrangements during quenching, during quenching, as shown inas Figureshown2 a.in TheFigure first 2a. peaks The firstof Cu peaks40Ag 60ofpair Cu40 wereAg60 pair at 0.279 were nm at with0.279 300 nm K with and 300 0.241 K nmand with 0.241 50 nm K. with This result50 K. This was inresult agreement was in agreementwith the results with reportedthe results by reported Qi [43,44 by]. ForQi [43,44]. the RDF For curves the RDF of Cu curves60Ag40 of, theCu60 crystalAg40, the peaks crystal exceeding peaks exceedingthe second the one second gradually one disappear,gradually disappear, exhibiting aexhibiting short-range a short-range ordered and ordered long-range and long-range disordered disorderedfeature. When feature. the When atomic the ratio atomic of Cu:Ag ratio of is Cu:Ag close to is 1:1,close the to first1:1, the peak first is widerpeak is (full wider widths (full widths at half atmaximum half maximum (FWHM) (FWHM) of Cu20 Agof 80Cu, Cu20Ag40Ag80, Cu60,40 CuAg6060Ag, Cu40 60andAg40 Cu and80Ag Cu2080areAg about20 are about 0.7, 1.1, 0.7, 1.0, 1.1, and 1.0, 0.9 and nm, 0.9respectively) nm, respectively) and the secondand the andsecond third and peaks third are peaks merged are together. merged together. This represents This represents that the Cu that40Ag the60 Cuand40Ag Cu60 Agand40 Cuhave60Ag better40 have glass-forming better glass-forming ability than ability Cu20 Agthan80 andCu20 CuAg8080Ag and20 atCu the80Ag same20 at quenching the same quenchingrate, as shown rate, in as Figure shown2b. in Figure 2b.

(a) (b)

Figure 2. RadialRadial distribution distribution functions functions (RDFs) (RDFs) of of Cu–Ag Cu–Ag pairs pairs with with ( (aa)) different diﬀerent quenching rates of

Cu4040AgAg6060 andand (b (b) )different diﬀerent atomic atomic ratio ratio at at quenching quenching rates rates of of 25 25 K/ps. K/ps.

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Figure3a–c individually shows the RDF curves of Cu–Cu, Ag–Ag, and Cu–Ag pairs of Cu 40Ag60 as a function of temperature which drops from 1500 to 400 K under the quenching rate of 25 K/ps. It can be found from this figure that the second peaks of RDF curves become more explicit or splits as temperature decreases, which defines a common feature of the amorphous alloy. Therefore, the results confirm the structural change of microstructures caused to be in the short-range order under the fast quenching rates. However, the splits occur at different temperatures for RDF of different pairs. For this Ag-enriched near eutectic alloy Cu40Ag60, Cu–Ag, and Ag–Ag correlations are dominant. For the Cu–Cu pair, the split is already well developed at Tg and in fact it first occurs at about 800 K, which is above Tg. The temperature Tsplit (the temperature where a distinct peak splitting in RDF curve occurs) can be approximately determined by visual inspection of the RDF curve at different temperatures. While for Ag–Ag and Cu–Ag pairs, the splits occur at lower temperatures, which are 600 and 400 K, respectively. The results reveal that some substructures have formed atom pairs before reaching the final glassy state.

Figure 3. RDFs of Cu40Ag60 at various temperatures with quenching rates of 25 K/ps for (a) Cu–Cu pairs (b) Ag–Ag pairs and (c) Cu–Ag pairs.

3.2. Indexed of Glass Forming Ability Index of glass-forming ability (GFA) is an indication how easy a liquid metal can be made into amorphous solid by cooling. For example, index GFA 80 at a certain specific quenching rate means 80% amorphous solid can be achieved under this quenching rate. Figure4 indicates that the glass-forming ability (GFA) of binary Cu–Ag system with different quenching rate as the composition ranges from 20 at.% to 80 at.% Cu. From this figure, the predicted GFA of the Cu–Ag system indicated the glass-formation composition range of the Cu–Ag system as 40 at.%–60 at.% Cu with quenching rate of 0.25 K/ps. However, once the quenching rate reaches 2.5 K/ps, all the compositions that range from 20 at.% to 80 at.% Cu convert to amorphous. In addition, when the ratio of Cu and Ag atoms is nearly 1:1, the alloy shows better GFA. The glass-formation composition range of the Cu–Ag system provides further evidence for the reliability of the present simulations, and they could offer helpful guides to search for alloys with superior physical, chemical, or mechanical properties. The common neighbor analysis (CNA) of Cu20Ag80 and Cu60Ag40 alloys at two different quenching rates is shown in Figure5. The gray, green, red, blue, and yellow balls represent amorphous, FCC (body-centered cubic), HCP (hexagonal closest packed), BCC (body-centered cubic), and ICO structures, respectively. It can be seen in Figure5b that crystalline phases appear significantly in Cu20Ag80 at low quenching rate of 0.25 K/ps, while amorphous is dominating in Cu20Ag80 at high quenching rate of 25 K/ps, as shown in Figure5a, and in Cu 60Ag40 within the quenching rate of 0.25–25 K/ps, as shown in Figure5c,d. These results are well consistent to the GFA in Figure4.

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The common neighbor analysis (CNA) of Cu20Ag80 and Cu60Ag40 alloys at two different quenching rates is shown in Figure 5. The gray, green, red, blue, and yellow balls represent amorphous, FCC (body-centered cubic), HCP (hexagonal closest packed), BCC (body-centered cubic), and ICO structures, respectively. It can be seen in Figure 5b that crystalline phases appear significantly in Cu20Ag80 at low quenching rate of 0.25 K/ps, while amorphous is dominating in Cu20Ag80 at high quenching rate of 25 K/ps, as shown in Figure 5a, and in Cu60Ag40 within the quenching rate of 0.25–25 K/ps, as shown in Figure 5c,d. These results are well consistent to the GFA Figure 4. Relationship between glass forming ability, quenching rate, and composition of elements. in Figure 4.

(a) (b) (c) (d)

Figure 5. DistributionDistribution of of common common neighborneighbor analysis analysis (CNA) (CNA) of Cu of 20CuAg20Ag80 alloy80 alloy with with quenching quenching rate rate of of(a) ( 25a) 25 K/ ps,K/ps, and and (b )(b 0.25) 0.25 K/ ps;K/ps; Cu Cu60Ag60Ag40 40alloy alloy with with quenching quenching rate rate of of (c )(c 25) 25 K /K/ps,ps, and and (d ()d 0.25) 0.25 K /K/ps.ps. 3.3. Honeycutt–Anderson (HA) Bond Pair Analysis 3.3. Honeycutt–Anderson (HA) Bond Pair Analysis The analysis of the transformation between local structures of Cu–Ag layer at different temperatures The analysis of the transformation between local structures of Cu–Ag layer at different was performed by Honeycutt–Anderson (HA) [45]. Based on the definition of the HA bond-type index, temperatures was performed by Honeycutt–Anderson (HA) [45]. Based on the definition of the HA different pairs of atoms under consideration in a system can be completely described by four numbers bond-type index, different pairs of atoms under consideration in a system can be completely i, j, k, l. If they are bonded in the root pair, the first integer i is 1, otherwise i is 2. The number of near described by four numbers i, j, k, l. If they are bonded in the root pair, the first integer i is 1, otherwise neighbors shared in common was described by the second integer j. The third number k represented i is 2. The number of near neighbors shared in common was described by the second integer j. The the number of bonds among the shared neighbors. However, these three numbers were still insufficient third number k represented the number of bonds among the shared neighbors. However, these three to characterize a diagram uniquely. A fourth integer l, therefore, was required to resolve the ambiguity numbers were still insufficient to characterize a diagram uniquely. A fourth integer l, therefore, was about the arrangement of the atomic bonds. By using this HA bond-type index, the bond-types between required to resolve the ambiguity about the arrangement of the atomic bonds. By using this HA bond- two atoms can be identified clearly. As mentioned in the literature [45], eleven kinds of normalized type index, the bond-types between two atoms can be identified clearly. As mentioned in the abundance of pairs in bulk system are involved, i.e., 2211, 2101, 1421, 2441, 1422, 2331, 1551, 1541, 1321, literature [45], eleven kinds of normalized abundance of pairs in bulk system are involved, i.e., 2211, 2321, and 1311. For example, the HA indexes of FCC and HCP crystal structures are 1421 and 1422, 2101, 1421, 2441, 1422, 2331, 1551, 1541, 1321, 2321, and 1311. For example, the HA indexes of FCC respectively. Indexes 1431, 1541, and 1551 represented the icosahedral local structures, which occupied and HCP crystal structures are 1421 and 1422, respectively. Indexes 1431, 1541, and 1551 represented the largest fraction in the amorphous or liquid state. Among these three indexes, the 1551 pair was the icosahedral local structures, which occupied the largest fraction in the amorphous or liquid state. particularly characteristic of the icosahedral ordering; while the 1541 and 1431 were the indexes for the Among these three indexes, the 1551 pair was particularly characteristic of the icosahedral ordering; defect icosahedra and FCC defect local (or distorted icosahedra) structures, respectively. Moreover, while the 1541 and 1431 were the indexes for the defect icosahedra and FCC defect local (or distorted indexes 1661 and 1441 were used to identify the local BCC structure. Finally, the indexes 1321 and 1311 icosahedra) structures, respectively. Moreover, indexes 1661 and 1441 were used to identify the local denoted the packing related to rhombohedral pairs, or the side product accompanying icosahedral BCC structure. Finally, the indexes 1321 and 1311 denoted the packing related to rhombohedral pairs, atomic packing. The fractions of seven main bond-types for alloys of Cu Ag and Cu Ag at or the side product accompanying icosahedral atomic packing. The fractions20 of80 seven main60 bond-40 different quenching rates (0.25, 2.5 and 25 K/ps) were as shown in Figure6a,b, respectively. It can types for alloys of Cu20Ag80 and Cu60Ag40 at different quenching rates (0.25, 2.5 and 25 K/ps) were as be found that most of the defect and disorder icosahedral local structures (1541 and 1431 pairs) and shown in Figure 6a,b, respectively. It can be found that most of the defect and disorder icosahedral the icosahedral short-range order (1551 pair) were created in Cu Ag in comparison with Cu Ag . local structures (1541 and 1431 pairs) and the icosahedral short-range60 40 order (1551 pair) were created20 80 This indicated that Cu60Ag40 has higher proportion of amorphous structure, while a significant ratio of in Cu60Ag40 in comparison with Cu20Ag80. This indicated that Cu60Ag40 has higher proportion of crystalline phase still remains in Cu20Ag80 at low temperature under low quenching rate of 0.25 K/ps. amorphous structure, while a significant ratio of crystalline phase still remains in Cu20Ag80 at low On the other hand, the effects of temperature on the fraction of various bond-types of Cu Ag alloy at temperature under low quenching rate of 0.25 K/ps. On the other hand, the effects of temperature80 20 on quenching rate of 0.25 K/ps were depicted in Figure6c. It can be seen that the e ffects of the temperature the fraction of various bond-types of Cu80Ag20 alloy at quenching rate of 0.25 K/ps were depicted in on the different bond-types were insignificant when the temperature was above 800 K, and their Figure 6c. It can be seen that the effects of the temperature on the different bond-types were insignificant when the temperature was above 800 K,1 and their variation trends were almost the same. However, as the temperature decreases continually from 800 to 300 K, the effects of temperature on the fraction of various bond-types became remarkable, especially on the 1421 and 1431 bond-types. At 300 K of final stage, the crystalline structures were formed at low quenching rate of 0.25 K/ps in the systems with 1421 and 1422 bond-types as the dominant types, and the amorphous structures are formed at higher quenching rate in the systems with 1431 and 1541 and 1551 bond-types as the

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variation trends were almost the same. However, as the temperature decreases continually from 800 to 300 K, the effects of temperature on the fraction of various bond-types became remarkable, especially on the 1421 and 1431 bond-types. At 300 K of final stage, the crystalline structures were formed at low quenching rate of 0.25 K/ps in the systems with 1421 and 1422 bond-types as the dominant types, Coatings 2020, 10, x FOR PEER REVIEW 7 of 14 and the amorphous structures are formed at higher quenching rate in the systems with 1431 and 1541 and 1551 bond-types as the dominant types. The fractions of 1441 and 1661 pairs only changed dominant types. The fractions of 1441 and 1661 pairs only changed slightly from 1500 to 800 K and slightly from 1500 to 800 K and remained almost constant until 350 K. From all these results, similar to remained almost constant until 350 K. From all these results, similar to those obtained for other cases those obtained for other cases [46–49], it can be seen that the effects of different quenching rates on [46–49], it can be seen that the effects of different quenching rates on the microstructures of liquid the microstructures of liquid and super-cooled states were insignificant. However, the effects of them and super-cooled states were insignificant. However, the effects of them on solid (crystal) states were on solid (crystal) states were more significant and can only be fully displayed near the liquid–solid more significant and can only be fully displayed near the liquid–solid transition points [50]. transition points [50].

(a) (b)

(c)

FigureFigure 6. 6. Honeycutt–Anderson (HA) (HA) indices indices vary vary as as a function a function of ofquenching quenching rates rates at 300 at 300K for K ( fora)

Cu(a)20 CuAg2080Ag, (b80) ,(Cub)60 CuAg6040Ag, (c40) HA,(c) HAindices indices vary vary as a as function a function of oftemperature temperature for for Cu Cu2020AgAg8080 atat quenching quenching raterate of of 0.25 0.25 K/ps. K/ps.

3.4.3.4. Diffusion Diffusion between between Cu–Ag Cu–Ag and and Cu Cu InIn order order to to understand understand the the diffusion diffusion behavior behavior between between copper copper and and various various Cu–Ag Cu–Ag alloys, alloys, the interfacethe interface between between Cu and Cu Cu–Ag and Cu–Ag alloys alloys has been has investigated been investigated at various at various time steps. time Figure steps. 7 Figure shows7 shows the cross-section snapshots of Cu Ag /Cu interface under two different quenching rates after the cross-section snapshots of Cu20Ag80/Cu20 interface80 under two different quenching rates after 2000 ps2000 equilibration ps equilibration process. process. The crosso The crossoverver profiles profiles in this in this figure figure clearly clearly display display the the inter-diffusion inter-diffusion of of thesethese atoms atoms occurring occurring near near the the Cu Cu and and Cu–Ag Cu–Ag alloy alloy interfaces interfaces during during the the thermal thermal process. process. When When the the Cu Ag is produced at quenching rate of 0.25 K/ps, a high ratio of crystalline structure still can Cu2020Ag8080 is produced at quenching rate of 0.25 K/ps, a high ratio of crystalline structure still can be foundbe found in the in material. the material. This kind This of kind crystalline of crystalline structure structure cannot cannot effectively effectively block the block diffusion the diff ofusion Cu atomsof Cu atomsacross acrossthe interface the interface between between Cu and Cu andCu–Ag Cu–Ag layers layers especially especially at atelevated elevated temperature. temperature. Consequently,Consequently, there there exists exists significant significant interfacial interfacial diffusion diffusion between between Cu Cu and and Cu–Ag Cu–Ag as as the the temperature temperature reachesreaches 700 700 K. K. Figure 7 7aa showsshows that that more more than than 7000 7000 atoms atoms of of Cu Cu di diffuseffuse from from Cu Cu layer layer into into the the Cu–Ag Cu– Aglayer layer at 700at 700 K afterK after 2000 2000 ps. ps. These These phenomena phenomena of of di diffusionffusion can can be be seenseen inin FigureFigure8 8.. TheThe interatomic interaction already leads to some local atomic movement at the interface. Some Cu atoms diffuse into the Cu–Ag layer and blends with it. The region of interface becomes fuzzy. This is two-way diffusion and the domain where such crossover occurs termed as the inter-diffusion zone. However, the situation changes significantly when the quenching rate reaches 25 K/ps. No significant diffusion behavior is observed between the Cu and Cu20Ag80 interface since a significant ratio of amorphous phase is produced at this high quenching rate. As shown in Figure 7b, only a few atoms of Cu deviate from their original lattice positions and diffuse into the Cu–Ag layer. On the other hand, when the

Coatings 2020, 10, 1087 8 of 14 interaction already leads to some local atomic movement at the interface. Some Cu atoms diffuse into the Cu–Ag layer and blends with it. The region of interface becomes fuzzy. This is two-way diffusion and the domain where such crossover occurs termed as the inter-diffusion zone. However, the situation changes significantly when the quenching rate reaches 25 K/ps. No significant diffusion behavior is observed between the Cu and Cu20Ag80 interface since a significant ratio of amorphous phase is produced at this high quenching rate. As shown in Figure7b, only a few atoms of Cu deviate from their original lattice positions and diffuse into the Cu–Ag layer. On the other hand, when the Cu40Ag60 alloy is produced with quenching rate between 0.25 and 25 K/ps, no significant diffusion behavior is observed because of the effect of amorphous phase. Between the Cu and Cu40Ag60, only few Cu atoms deviate from their original lattice positions, and the interface still remains clearly. In addition, as the temperature increases, the inter-diffusion layer becomes thicker. This indicates the thickness of the Cu/Cu–Ag interface strongly depends on the thermal process temperature, i.e., the higher the temperature, the thicker the interface.

CoatingsFigure 2020, 10 7., x TheFOR PEER cross-section REVIEW of Cu20Ag80/Cu interface under quenching rate of (a) 0.25 K/ps,9 of 14 and (b) 25 K/ps (700 K after 2000 ps equilibration process).

(a) (b)

Figure 8. Concentration distributionsdistributions ofof CuCu2020Ag80/Cu/Cu quenched quenched at at ( (aa)) 0.25 0.25 K/ps, K/ps, and ( b) 25 K/ps K/ps along thethe didiffusionﬀusion couplecouple ((zz-axis)-axis) directiondirection (700(700 KK afterafter 20002000 psps equilibrationequilibration process).process).

ToFigure further 9 shows characterize the MSD quantitatively of Cu and Cu–Ag the di ffasusion a function process, of thetime concentration at various temperatures. profile is acquired. From Figurethis figure,8 shows it can the be concentration clearly observed distributions that the ofslop Cues and of MSD Cu 20 profileAg80 atoms are generally along the larger diffusion at a couplehigher (temperaturez-axis) direction and obtained the MSD at 700values K after of Cu–Ag 2000 ps alloy with dimadefferent from quenching slower rates.quenching A region rate is are defined larger, as interfacialindicating regionthe mobility if the concentration of atoms in ofCu–Ag Cu and alloy Cu–Ag made are from both slower over 5 at.%.quenching Thus, therate thickness is higher of than the interfacialthose made region from canhigher be estimatedquenching from rate. the On concentration the other hand, curves. the MSD The values profiles of of Cu concentration20Ag80 and Cu curves80Ag20 inare Figure generally8a show larger the than case Cu of40 CuAg2060Ag and80 Cuwith60Ag the40, slowest indicating quenching the mobility rate of of 0.25 atoms K/ps. in more The thickness crystalline of thestructure interfacial is higher region than grows those and with reaches more 7~8 amorph nm atous 2000 structures. ps, which canFor betime seen below from 0.1 the ps, coordinates the MSD ofis theproportional diffusion zoneto the boundaries square of time, or fronts. t2, as Asexpected shown for in Figureballistic8b, motion the thickness [54]. For of longer the interfacial times the region MSD becomesincreases approximatelylinearly with time, 1~2 nmindicating only when the phenomenon the quenching of rate long-range increases diffusion to 25 K/ps. [55]. This The indicates MSD is thatlinear there to the is delay no obvious time in di theffusion long-time between limit, Cu so and the Agself-diffusion atoms. In addition,coefficients Figure of Cu8 aand also Cu–Ag shows alloys that can be derived from the slopes of MSD profiles by the Einstein equation.

1 (a) (b)

Figure 9. The mean-square displacement (MSD) of Cu and (a) Cu20Ag80, and (b) Cu60Ag40 as a function of time under various temperatures at different quenching rates.

The total diffusion coefficients near the Cu/Cu–Ag interface at different temperatures are shown in Figure 10. It can be inferred that the diffusion coefficients of both Cu and Cu–Ag significantly increase with the increasing temperature when the system temperature exceeds the glass transition temperature. The values of these diffusion coefficients range between 1 × 10−12 and 1 × 10−10 m2/s, which has the same order than those found in the experimental measurement for the bulk inter- diffusion region. It is worth noting that the MSD calculated by the MD may be slightly lower than the experimental value. This is due to the MD is relatively unable to consider the satiation of bulk materials, such as defects and so on. Perfect structure in MD leads to the considerable cage effect,

Coatings 2020, 10, 1087 9 of 14 the interfacial region consists of rich-Cu and rich-Cu–Ag phases, and the thickness of rich-Cu–Ag phase is larger than that of the rich-Cu phase. This indicates that the main diffusion is from Cu to Cu–Ag. This phenomenon is similar as pure copper diffuses to pure silver [51]. The mean-square displacement (MSD) profiles at temperatures ranging from 300 to 900 K for Cu–Ag amorphous metal were used to investigate their dynamical properties. The MSD is defined by a function of time as shown in Equation (1): PN 2 [ri(t) ri(t0)] MSD = i − (1) N where ri(t) represents the position of atom i at delay time t, and ri(t0) indicates the reference position of the corresponding atom at reference time t0; N represents the total atom number of the investigated system. Generally, the MSD profile is linear to the delay time over the long-time limit, the slopes of the MSD profile are generally larger with the increasing temperature. The diffusion coefficients of Cu and Cu–Ag alloys at the interface can be derived from the slopes of MSD profiles with a longer delay time by the Einstein equation: [52,53] 1 d D = lim MSD (2) 6N n dt →∞ where D is the diffusion coefficient, and N is the number of atoms. Figure9 shows the MSD of Cu and Cu–Ag as a function of time at various temperatures. From this figure, it can be clearly observed that the slopes of MSD profile are generally larger at a higher temperature and the MSD values of Cu–Ag alloy made from slower quenching rate are larger, indicating the mobility of atoms in Cu–Ag alloy made from slower quenching rate is higher than those made from higher quenching rate. On the other hand, the MSD values of Cu20Ag80 and Cu80Ag20 are generally larger than Cu40Ag60 and Cu60Ag40, indicating the mobility of atoms in more crystalline structure is higher than those with more amorphous structures. For time below 0.1 ps, the MSD is proportional to the square of time, t2, as expected for ballistic motion [54]. For longer times the MSD increases linearly with time, indicating the phenomenon of long-range diffusion [55]. The MSD is linear to the delay time in the long-time limit, so the self-diffusion coefficients of Cu and Cu–Ag alloys can be derived from the slopes of MSD profiles by the Einstein equation.

Figure 9. The mean-square displacement (MSD) of Cu and (a) Cu20Ag80, and (b) Cu60Ag40 as a function of time under various temperatures at diﬀerent quenching rates.

The total diffusion coefficients near the Cu/Cu–Ag interface at different temperatures are shown in Figure 10. It can be inferred that the diffusion coefficients of both Cu and Cu–Ag significantly increase with the increasing temperature when the system temperature exceeds the glass transition temperature. The values of these diffusion coefficients range between 1 10 12 and 1 10 10 m2/s, which has the × − × − same order than those found in the experimental measurement for the bulk inter-diffusion region. It is

Coatings 2020, 10, 1087 10 of 14 worth noting that the MSD calculated by the MD may be slightly lower than the experimental value. This is due to the MD is relatively unable to consider the satiation of bulk materials, such as defects and so on. Perfect structure in MD leads to the considerable cage effect, which causes the backflow of atoms when an atom interacts with atoms of local structure, resulting in jumping back to its initial position and lowering diffusivity. For reasons outlined above, introduction of amorphous diffusion barrier is then considered to be the best mitigation strategy to prevent the interdiffusion between Cu and Sn. Therefore, TFMGs of Cu–Ag alloys are considered to be the promising diffusion barrier.

Figure 10. Diffusion coefficient between Cu and layers of (a) Cu20Ag80,(b) Cu60Ag40 under various temperatures at different quenching rates.

3.5. Tensile Behavior In order to understand the mechanical behavior of amorphous and crystalline states, the deformation and fracture mechanism of a bilayer structural specimen (Cu/Cu20Ag80) with different amorphous ratios made by different quenching rate under tensile stress were compared as shown in Figure 11. Figure 11a represents the stress–strain response of the Cu/Cu20Ag80 produced at both higher 25 K/ps and lower 0.25 K/ps quenching rates under mode-I loading at a temperature of 100 K and strain rate of 1 109 s 1. For Cu Ag produced at slower quenching rate (0.25 K/ps), in which crystalline × − 20 80 and amorphous phases coexist, the stress reaches a higher maximum and then suddenly drops. This is followed by a more steady flow regime during which some serrations are evident. The sudden drops are caused by the formation of voids near the Cu/Cu20Ag80 interface. However, for samples produced with higher quenching rate (25 K/ps), in which amorphous is major phase, the stress–strain curves are smoother and the behavior is close to the ideal elastic-perfectly-plastic response. This phenomenon is quite different from the single crystal metallic of dislocations undergoing slippage along the slip plane [39,45]. The void nucleation is attributed to the fact that there exist more defects in this local region, and they are generally formed by the coalescences of the free volume present in the metallic glass system [56], which becomes the weakness during the tensile deformation. Figure 11b,c depict the atomic position snapshots of the interface model captured at different strains till fracture under quenching rates of 25 and 0.25 K/ps, respectively. In comparison with these two figures, it reveals that for the specimen produced at faster quenching rate (25 K/ps), the initial position of the void tends to move from the Cu/Cu20Ag80 interface to the middle of the Cu–Ag, which indicates that the Cu/Cu20Ag80 interface is stronger than Cu20Ag80 alloy. In addition, it was observed that larger voids are created in the samples of Cu20Ag80 with quenching rate of 25 K/ps than with 0.25 K/ps at about 13% strain. We also found that when the Ag content of the specimens ranges between 40 at.% and 60 at.%, voids tend to occur at higher strain values (15% strain), or the plasticity behavior is more significant. From the microstructure side, by quenching the model at different quenching rates, different degree of structural ordering of the ordered clusters can be produced. The fraction of icosahedra in the as-quenched Cu–Ag MG sample increases considerably with decreasing quenching rate. The increasing

Coatings 2020, 10, 1087 11 of 14

Coatings 2020, 10, x FOR PEER REVIEW 11 of 14 number of icosahedral clusters forms a more extended and stronger elastic backbone, leading to higher observations are in good agreement with our prior simulations and the results conducted in the stiﬀness (Young’s modulus) and yield strength. The above observations are in good agreement with literature [57–59]. our prior simulations and the results conducted in the literature [57–59].

(a)

(b) (c)

20 80 Figure 11. ((a)) Stress–strain plot of thethe CuCu/Cu/Cu20Ag80 interfaceinterface model model under under mode-I mode-I loading; atomic position snapshots (I), can snapshots (II), and atomic strain snapshots (III) of the interface captured

with C 20AgAg8080 underunder quenching quenching of of (b (b) )0.25 0.25 K/ps K/ps and and (c (c) )25 25 K/ps K/ps at at different diﬀerent strains strains (300 (300 K). K).

4. Conclusions Conclusions The local atomic pairing arrangement of of Cu–Ag system with different diﬀerent quenching rates was simulated by MD simulation method. The The following following conclusions conclusions can be reached from this study:

• Cu20AgAg80 isis 50% 50% amorphous amorphous at at quenching quenching rate rate of of0.25 0.25 K/ps, K/ps, whereas whereas Cu Cu40Ag60Ag, Cu,60 CuAg40,Ag and, • 20 80 40 60 60 40 Cuand80Ag Cu2080 Agare20 moreare morethan than95% 95%amorphous amorphous at quenching at quenching rate ratebetween between 0.25 0.25K/ps K and/ps and25 K/ps. 25 K/ ps.In otherIn other words, words, Cu–Ag Cu–Ag alloys alloys exhibit exhibit excellent excellent GFA GFA except except Cu Cu20Ag20Ag80. 80. • A diffusion diffusion region of of 1 1 to to 2 2 nm nm at at 700 700 K K occurs occurs between between copper copper and and Cu Cu40AgAg60, or, orCu Cu60AgAg40, or, • 40 60 60 40 Cuor Cu80Ag8020Ag as20 quenchedas quenched within within the therange range from from 0.25 0.25 to 25 to K/ps. 25 K/ ps.However, However, a diffusion a diffusion region region of approximatelyof approximately 7 to 7 8 to nm 8 nm takes takes place place at 700 at 700K between K between copper copper and andCu20 CuAg2080Ag quenched80 quenched by 0.25 by K/ps.0.25 K In/ps. other In other words, words, the layer the layer with with higher higher ratio ratio of amorphous of amorphous exhibits exhibits a better a better performance performance of diffusionof diffusion barrier. barrier. • Simulation resultsresults ofof tensile tensile test test show show that that the th stress–straine stress–strain curves curves of Cu–Ag of Cu–Ag alloys alloys having having higher • higherratio of ratio amorphous of amorphous (for instance, (for instance, Cu20Ag80 Cuproduced20Ag80 produced at higher at quenching higher quenching rate 25 K /rateps, and 25 K/ps, other andratios other of Cu–Ag ratios of alloys Cu–Ag at quenching alloys at quenching rate 0.25–25 rate K /0.25–25ps) are smootherK/ps) are andsmoother the behavior and the isbehavior close to isthe close ideal to elastic-perfectly-plastic the ideal elastic-perfectly-plastic response. resp Theonse. void initiatesThe void in initiates the Cu–Ag in the layer Cu–Ag first layer and thenfirst and then gradually enlarges. This phenomenon indicates that the Cu/Cu–Ag interface is stronger than Cu–Ag alloy. For the Cu20Ag80 alloy produced at slower quenching rate (0.25 K/ps), in which both crystalline and amorphous phases exist together, as the strain increases, its stress

Coatings 2020, 10, 1087 12 of 14

gradually enlarges. This phenomenon indicates that the Cu/Cu–Ag interface is stronger than Cu–Ag alloy. For the Cu20Ag80 alloy produced at slower quenching rate (0.25 K/ps), in which both crystalline and amorphous phases exist together, as the strain increases, its stress gradually reaches a higher maximum and then suddenly drops. This is followed by a steady ﬂow regime during which some serrations are evident. The sudden drops are caused by the formation of voids near the Cu/Cu20Ag80 interface. This phenomenon of sudden drop in stress is diﬀerent from the crystal metallic of dislocations undergoing slippage along the slip plane.

Author Contributions: For P.-H.S. and T.-C.C. conceived and proposed the conceptualization and methodology; P.-H.S. applied the software, performed the simulations and experiments, and drew the figures; P.-H.S. and T.-C.C. performed the validation, formal analysis, data, as well as writing in the stages of original draft preparation, review and editing, and visualization; T.-C.C. conducted the supervision, project administration, and funding acquisition. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology of Taiwan, Grant number MOST Nos. 107-2221-E-006-122- and 108-2221-E-006-191-. Conflicts of Interest: The authors declare no conflict of interest.

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