Study of Fracture Mechanics in Testing Interfacial Fracture of Solder Joints

Transcription

1 Journal of ELECTRONIC MATERIALS, Vol. 37, No. 4, 2008 DOI: /s Ó 2008 TMS Special Issue Paper Study of Fracture Mechanics in Testing Interfacial Fracture of Solder Joints W.H. BANG, 1,2 M.-W. MOON, 1 C.-U. KIM, 2,4 S.H. KANG, 1 J.P. JUNG, 3 and K.H. OH 1 1. School of Materials Science and Engineering, Seoul National University, Seoul , Korea. 2. Department of Materials Science and Engineering, University of Texas at Arlington, Arlington, TX, USA. 3. Department of Materials Science and Engineering, University of Seoul, Seoul , Korea choongun@uta.edu This paper is concerned with the mechanics of interfacial fracture that are active in two common testing configurations of solder joint reliability. Utilizing eutectic Pb-Sn/Cu as a reference system and assuming the presence of a predefined crack size in the intermetallic compound (IMC) layer, stress intensity factors (K I and K II ) at the crack are numerically calculated for the two given configurations. The analysis of the tensile test configuration reveals that the fracture occurs by the crack-opening mode (K I mode), as anticipated, but that it is greatly assisted by the viscoplasticity of the solder. With nonuniform viscoplastic deformation across the joint, K I is found to increase much more rapidly than it would without the solder, decreasing the critical crack size to the micron scale. The same mechanism is also responsible for the development of a K II comparable to K I at the crack tip, that is, K I /K II 1. It is also found that the predominant fracture mode in the bump shear configuration is crack opening, not crack shearing. This is an unexpected result, but numerical analyses as well as experimental observations provide consistent indications that fracture occurs by crack opening. During shear testing, bump rotation due to nonzero rotational moment in the test configuration is found to be responsible for the change in the fracture mode because the rotation makes K I become dominant over K II. With rotational moment being affected by the geometry of the bump, it is further found that the fracture behavior may vary with bump size or shape. Key words: Solder joint reliability, intermetallic layer, tensile test, bump shear test, stress intensity factors (K I and K II ) INTRODUCTION Sn-based solder alloys are widely used in electronic packaging applications as they offer several advantageous properties, including low processing temperatures and excellent wetting of common Cu metallization components. With the continuing thrust toward smaller and higher-performance packaging, however, the alloys are becoming a source of critical reliability concerns. In advanced (Received April 13, 2007; accepted January 16, 2008; published online February 13, 2008) packaging, solder joints are required to endure increasingly punishing mechanical load conditions, and thus they are increasingly prone to physical failures. Of these physical reliability failures, one of the most troubling is fracture at the interface between solder and metallization. The interface is known to be the weakest mechanical link in all solder joints because the presence of brittle Sn-Cu intermetallic compounds (IMC, Cu 6 Sn 5 or Cu 3 Sn) weakens the overall resistance against fracture and also creates a point of stress singularity at which cracks can initiate. 1 6 In order to enhance the overall reliability of the solder joint, it is therefore 417

2 418 Bang, Moon, Kim, Kang, Jung, and Oh critical to prevent or retard the interface fracture, and this has been the main focus of recent studies in this field. Progress in this area demands a more indepth investigation of interface fracture mechanics. There are two common methods of characterizing the mechanics of interface fracture: the joint tensile test and the bump shear test. 5,7 10 The tensile test requires the induction of interfacial fracture by exerting a load in a direction normal to the interfacial layer, while the bump shear test requires the application of a force in a direction parallel to the interfacial layer. The simplicity of these methods, combined with their ability to provide quantitative information and fractography, has made them the most popular approaches for the investigation of interface fracture in solder joints. However, such studies produce data with clear limitations. Real solder joints are subjected to complex load conditions and, as a result, their fracture may proceed by significantly different mechanisms than the ones found in the tensile or bump shear test. Further, because of the time-dependent mechanical properties of the solder, the fracture mechanism under differing load conditions of a single test method (bump shear or tensile joint) may be sufficiently different to lead to the need for nonsimplistic methods of analysis. In order to extrapolate information from the common test configurations to real solder joints, it is imperative to investigate more carefully how fracture occurs in each of these two methods. This quest requires the study of fracture mechanics in the IMC layer to determine the fracture criteria, including the critical crack size and the fracture mode under a given load condition. 11,12 This paper presents the results of our investigation on the interface fracture mechanics of the bump shear and joint tensile test methods. Specifically, this paper investigates the fracture mode by conducting numerical analysis of the stress intensity factors (K) at the crack tip in the IMC layer for each method. The cases simulated here are fractures at the brittle IMC layer created by a reaction between the Sn-Pb eutectic solder and Cu substrate under geometrical constraints and load conditions relevant to the tensile test and a bump shear test. Our analysis yields several interesting and somewhat surprising results of practical importance. We find that the fracture behavior for the two methods, that is, the crack-opening (K I ) mode for the tensile and the crack-shearing mode (K II ) for the bump shear testing, are not as simple as each method intends to produce. In the case of the tensile test condition, it is found that the viscoplastic deformation and Poisson contraction of the solder matrix have a significant influence on the stress field around the crack tip. With viscoplastic deformation of the solder, K I increases much more rapidly than without solder, making the IMC more prone to cracking. Furthermore, Poisson contraction causes the crack in the IMC to develop a K II value with a magnitude comparable to that of K I. Even more unexpected is the result that the crack propagation in the bump shear test condition occurs by the K I mode not by the K II mode. It is found that the K I mode prevails because of bump rotation during crack propagation. This result is surprising but our experimental investigation produces supporting evidence. The rotation of solder bumps in the shear direction is clearly seen, resulting in the fracture site being lifted up from the substrate and the development of crack opening (K I ) during shearing. These results strongly suggest that any characterization of the interface fracture of solder joint, especially characterization conducted with the two common methods, needs to include careful consideration of the solder deformation and rotation with variations in geometrical and load conditions. BACKGROUND AND NUMERICAL AND EXPERIMENTAL PROCEDURES Background While there exist a few experimental results for solder joint fracture in tensile tests, the study of Sn- Pb/Cu joints is most comprehensive and thus provides the data needed for our modeling work. The data used in our modeling is taken from Sn-Pb/Cu tensile testing conducted by Lee et al., Prakash et al., and Quan. 7 9 Table I shows the summary of the tensile test data along with the experimental conditions used in these studies. While there are differences in the experimental details, such as the tension rate and specimen configuration, the tests show reasonable agreement in the fracture strength value of 80 MPa. In spite of this agreement, Prakash et al. and Quan report somewhat different observations on the crack propagation path. Quan notes that the fracture proceeds through the IMC layer (Cu 6 Sn 5 ) and therefore attributes the data to the fracture strength of the IMC layer. On the other hand, Prakash et al. suggest, based on the fractography showing the mixture of IMC and solder Table I. Tensile Testing Results of Cu/Sn-Pb/Cu Joints (As-Soldered Samples) Fracture Strength Joint Thickness Cross Section of Joint Tensioning Rate IMC Thickness Lee et al MPa 750 lm 3 mm (diameter) 0.6 mm/min 1 lm Prakash et al MPa lm 10 mm 3 mm 0.5 mm/min (0.66 MPa/s) 2.5 lm Quan 9 83 MPa 1.0 mm 7.6 mm 2.8 mm 0.05 mm/min (0.47 MPa/s) 1 3 lm

3 Study of Fracture Mechanics in Testing Interfacial Fracture of Solder Joints 419 matrix, that the measured fracture strength may be related to the decohesion strength between the solder and the IMC layer. However, since such fractography can result from the cracks repeatedly switching between the solder and the IMC layer, and in such cases the brittle IMC phase would limit the overall fracture strength of the joints, it seems reasonable to assume that the measured fracture strength is attributable to the fracture strength of the IMC layer. The tensile load (stress) displacement (strain) curves presented by Prakash et al. and Quan also provide supporting evidence for this assessment. In both cases, an abrupt drop in load after its maximum is visible. This is not possible without rapid crack growth through a brittle phase. While numerous studies using the bump shear method have correlated the test results to IMC fracture, the resulting data requires consideration of its complexity. The difficulty of analyzing the fracture mechanics of this method stems mainly from the fact that the test load is imparted to the interface area through a bump that is softer than the IMC phase at the interface. As is well pointed out by Huang et al. and Kim et al. in their finite element method (FEM) analysis, 13,14 the viscoplasticity of the bump in such a case may play a critical role in the fracture at the interface. Perhaps more importantly, shearing load, imparting nonzero rotational momentum to the bump, may result in physical motion of the bump that changes the mechanical constraints at the crack tip. This possibility has been proven to exist in our experimental and numerical studies. It is therefore necessary for fracture analysis to include consideration of the viscoplasticity as well as the bump movement. FEM Modeling Our numerical analysis of the fracture mechanics begins with the assumption that the fracture initiates and proceeds predominantly through the brittle IMC layer in both configurations, which is a reasonable assumption as previously mentioned. Consequently, the modeling requires calculation of the stress intensity factors, K, at the crack tip in the IMC layer under the two different test configurations while the fracture strength of the IMC layer is set to 80 MPa. For this numerical analysis, we use a commercial FEM program, ABAQUS 6.3 with the finite element mesh structure shown in Fig. 1a and b. As is shown in these figures, the IMC layer between the eutectic Sn-Pb solder and Cu is assumed to be 1-lm-thick Cu 6 Sn 5. 2,9 Table II lists the mechanical properties of the materials used in our FEM analysis. It is further assumed that the test is conducted at room temperature, 300 K, in order to be consistent with the existing data and common testing practice. This temperature is a high homologous temperature for eutectic Sn-Pb solder, 0.65T m, and thus the viscoplastic characteristics of eutectic Sn-Pb are incorporated into the finite Fig. 1. Finite element models and crack mesh for estimating stress intensity factors, K, at the crack tip in the IMC layer during joint tensile and bump shear tests: (a) FEM meshes for joint tensile analyses; (b) FEM meshes for bump shear analyses with calculations performed for different bump sizes, R; and (c) the crack tip mesh defined in the IMC layer in the dashed-circle area in (a) and (b). Table II. Mechanical Properties Used in the FEM Analysis 15 Elastic Modulus PoissonÕs Ratio, m Copper 117 GPa 0.35 Cu 6 Sn 5 85 GPa 0.31 Eutectic Sn-Pb 30 GPa 0.40 FR4 substrate 22 GPa 0.28 Steel shear bar 220 GPa 0.3 element calculation. The viscoplastic constitutive equation used is: _e pl ¼ 2: ½rŠ 3:2 69 kj=mol exp RT þ 1: ½rŠ 6:2 64 kj=mol exp ; RT (1)

4 420 where _e pl is the plastic strain rate, r (MPa) is the stress, R is the gas constant, and T is the temperature. 16 Figure 1c shows the mesh structure for a predefined crack in the IMC layer for the calculation of the stress intensity factors in the joint tensile and bump shear tests. The K factors are evaluated at five finite element contours surrounding the crack front from one crack face to the opposite crack face. 17 The detailed description of Fig. 1a c and our FEM analysis procedure follow. Tensile Analysis The two-dimensional finite elements in Fig. 1a are a simplification of the butt-joined tensile specimen used in QuanÕs experiment. 9 A quarter section is modeled using symmetric boundary conditions along the transverse and longitudinal directions. Considering the fact that the specimen width is far greater than the joint thickness, a plane-strain condition is employed. 9,18,19 From the tensile-load development curve and data presented by Quan, the applied tensile rate was determined to be 0.3 MPa/s and this value is used for our main calculation. Further, since the outer edge of the joint is the most likely place for crack initiation, being subjected to the highest interfacial stress singularity, 6,20 the crack tip mesh in the IMC layer is placed at the end (indicated by a dashed circle in Fig. 1a). In this way, the calculation of the K factors with variation in the size of predefined crack is performed. Bump Shear Analysis The finite element model in Fig. 1b is a cross section of a eutectic Sn-Pb bump reflowed on a copper pad. The crack mesh in the IMC layer is defined at the bump corner (indicated as a dashed circle in Fig. 1b), as this is the expected place for crack initiation. The development of the K factors with shear displacement is calculated for a given size of predefined crack. In our calculation, the interfacial area is fixed and we include the shape and size of the bump as variables, as they may vary in real testing situations and also have a significant influence on shear stress development at the crack tip. Table III details the shape and size of the bump considered in our simulation, expressed in terms of Table III. Geometrical Parameters in Fig. 1b at Different Bump Sizes U DX R 25 deg 35 lm 360 lm 30 deg 50 lm 375 lm 35 deg 75 lm 400 lm* 40 deg 100 lm 425 lm 45 deg 135 lm 460 lm *R 400 lm is a case when a 760-lm-diameter solder ball ideally wets on a 650-lm-diameter copper pad (the solder bump configuration used in our bump shear experiment) Bang, Moon, Kim, Kang, Jung, and Oh the geometrical parameters U, DX, and R. The definition of these parameters can be found in Fig. 1b. The key variation in these parameters is the radius R. The others are adjusted based on the wetting behavior of the bump for the given size of the interfacial area. Bump Shear Test Instead of analyzing published data, we conducted the bump shear test for a selected case in order to acquire the information needed for our analysis. This test is especially necessary to identify any bump motion during the test. For this test, we prepared the eutectic Sn-Pb bump shear samples following standard procedures. The solder balls used in our experiment had a diameter of 760 lm. The balls are attached to the 650-lm-diameter Cu pad by reflow treatment at 215 C for 1 min. They were then subjected to the shear test while the load and displacement are recorded. For selected cases, position markers, in the form of small indentations, were made on top of the bump before shear testing for the purpose of tracing the bump movement. These markers, consisting of three consecutive indentations along the centerline of the bump, were made by creating a small impression using a microindenter. The marker position was then compared before and after shear testing using scanning electron microscopy (SEM, refer to Fig. 8). RESULTS Fracture Analysis in Joint Tensile Our numerical results reveal that the stress intensity factors in the butt-joint tensile test show radically different behaviors from those found in the ordinary situation in which homogeneous material is tested. Immediately noticeable is the fact that, in addition to the nominal tensile stress, a substantial amount of shear stress (in the direction of crack propagation) develops around the crack tip. It is in fact found that the level of K I and K II developed at any crack size and load stress is almost comparable, K II /K I 1. This behavior, i.e., almost equal development of K I and K II, is shown in Fig. 2 in which the stress intensity factors (K I as positive and K II as negative) are shown as a function of incremental tensile load for various sizes of predefined cracks. The loading rate used in this calculation was 0.3 MPa/s. It can be seen that, for any given crack size and comparable loading rate, the magnitude of K I and K II increases with the applied stress. The reason for the K II development shown in Fig. 2 is found to be nonuniform Poisson contraction in the transverse direction (normal to the axial load and parallel to the crack propagation direction). The elastic modulus and yield strength of the solder matrix are far lower than those of Cu and IMC, and therefore it is subjected to a large Poisson deformation upon axial loading. However, full-scale solder deformation can occur only in the area where there

5 Study of Fracture Mechanics in Testing Interfacial Fracture of Solder Joints 421 Fig. 2. The developments of K I and K II at the IMC crack tip for different crack lengths Da. Fig. 4. Crack opening degree (DD T ) and shearing degree (DD S )at the IMC crack tip during tensile test: DD T = tensile-direction coordinate of the upper crack-plane node () minus the tensile-direction coordinate of the lower crack-plane node (s); DD S = shear-direction coordinate of the upper-crack plane node () minus the transversedirection coordinate of the lower crack plane node (s). The upper crack-plane node () and the lower crack-plane node (s), at which data are derived, are 0.01 lm distant from the crack tip. Fig. 3. Transverse directional displacement contour in a solder joint at a tensile load level of 80 MPa (a quarter section model with y- direction boundary conditions along the bottom and x-direction boundary conditions along the left edge, refer to Fig. 1a). is little constraint imposed by the stiffer Cu and IMC. Therefore, the contraction of the solder is greater in the area distant from the interface, while it is practically limited to the level of the Poisson contraction of Cu (and IMC) near the interface. This nonuniform Poisson deformation field creates a large shear stress in the transverse direction, resulting in a high value of K II at the crack tip in the IMC. Figure 3 shows the displacement contour in the transverse direction of the joint under 80 MPa tensile load at the macroscopic scale. An uneven contraction deformation field in the joint is observed. Note that a significant transverse contraction occurs in the solder in the area distant from the IMC while it becomes smaller closer to the interface. Figure 4 shows the influence of the nonuniform Poisson contraction in the solder on the deformation field at the crack tip area. This figure compares the degree of axial opening displacement (DD T ) and transverse shearing displacement (DD S ) calculated in the crack tip area as a function of axial load. The displacements presented here are taken by selecting a nodal plane that is 0.01 lm behind the tip of a 0.5-lm-long crack and subsequently calculating the relative displacement of the nodes in the axial and transverse directions upon loading. Since the measurements are taken in close proximity to the tip, the absolute magnitude of the displacement in both directions appears small, but it should be noted that the axial and shear stresses developed by such a displacement are in reality extremely large. Even though the stress field around the crack tip in the IMC includes a considerable shear stress component, it is not likely that the fracture mode is significantly affected by it. K I is known to dominate fracture even when K I and K II are comparable. Furthermore, since our calculations find that K I is actually higher than K II at the crack tip, it is easy to conclude that IMC fracture occurs by the crackopening mode. Nevertheless, the mechanism leading to shear stress development at the crack, that is, the restriction of solder deformation near the IMC, causes the IMC fracture behavior to be substantially different from that expected from tensile testing of a single-phase material in two ways. The first, perhaps with the most significant practical importance, is the fact that the IMC phase becomes far more brittle than without the solder. A simple analysis of the critical crack size for IMC fracture may be helpful in elaborating our conclusion. According to the available data, 3,4,19 the critical K I (K IC ) for the fracture ofp the Cu 6 Sn 5 IMC ranges from 1.4 MPa to 2.4 MPa ffiffiffiffi m. The data in Fig. 2 then suggest that, at the assumed fracture strength of 80 MPa, K I would reach these critical values with just a 0.5lm to 0.8 lm crack. This means that a small crack of submicron dimensions would be sufficient to trigger fracture of the IMC layer in the solder joint. In contrast, in the case in which the IMC layer is not structurally associated with the

6 422 Bang, Moon, Kim, Kang, Jung, and Oh solder, the critical crack size is found to be much larger. If it is assumed that the IMC is purely elastic and tested as a homogeneous sample, the mode I stress intensity factor p developed at the crack tip should be given by r ffiffiffiffiffi pc. Under an identical fracture condition, that is K IC = 1.4 MPa to 2.4 MPa ffiffiffiffi m p and r f = 80 MPa, the critical crack size is estimated to be 98 lm to 290 lm, which is roughly two orders of magnitude longer than that for the IMC with the solder. Although simplified, our analysis suggests that the presence of the solder in the joint causes the crack in the IMC to propagate much more easily. It is our finding that the reduced critical crack size with solder stems from exaggerated crack opening caused by nonuniform solder deformation. Similar to the case of Poisson contraction, the axial deformation of the solder is restricted near the IMC but is not restricted further away. This nonuniform deformation in the axial direction induces a bending deflection at the IMC, making the crack open more than in the homogeneous case, as illustrated in Fig. 5a and b. These figures compare the deformation field at the crack in the case of homogeneous IMC (Fig. 5a) and the case of IMC with solder (Fig. 5b). Note that the crack opens considerably more with the solder present, causing K I to increase much more quickly upon loading. Therefore, it is not so surprising that the critical crack size for the IMC is far smaller in solder joints. The second impact of the restricted solder deformation near the IMC is found to be the relative insensitivity of fracture conditions to the strain rate. Since solder is a material with considerable viscoplasticity, it is not unreasonable to expect that fracture, even if it occurs at the IMC, would be influenced by the strain rate. However, as shown in Table I, experimentally measured fracture strength is remarkably insensitive to the tensioning rate used in these studies. As can be seen in Fig. 6, in which calculated K factors as a function of loading rate are presented, our numerical calculations appear to reproduce such insensitivity. The results shown here assume the presence of a 0.5-lm-long crack at the IMC and the application of a 80 MPa load stress. Note that the K factors remain nearly constant in the loading rates between 0.03 MPa/s and 3 MPa/s, while they start to show a noticeable decrease as the rate exceeds 3 MPa/s. Close inspection of the results, including the calculated deformation field in the joint, suggests that the loading rate insensitivity of the K factors up to 3 MPa/s stems from the quick saturation of the viscoplastic deformation of th solder near the IMC layer. As has been previously discussed, the K factors are strong functions of the crack-opening magnitude and are greatly affected by the deformation field in the solder. At the low and intermediate loading rate, the viscoplastic deformation contributes greatly to the total deformation field responsible for crack opening. However, after its quick development, viscoplastic deformation stops (saturates) because of the constraints from he stiffer Cu and IMC. Since the total solder deformation near the IMC is ultimately limited by the deformation of Fig. 5. Crack tip deformation at tensile stress of 80 MPa for two different structures: (a) homogeneous elastic material of Cu 6 Sn 5 ; (b) Cu 6 Sn 5 intermetallic layer formed between Sn-Pb and Cu. p Fig. 6. K factors (MPa ffiffiffiffi m ) at 80 MPa for tensioning rates ranging between 0.03 MPa/s and 16 MPa/s.

7 Study of Fracture Mechanics in Testing Interfacial Fracture of Solder Joints 423 the Cu and IMC, the total amount of plastic deformation, and thus the degree of crack opening, remains unchanged when the applied strain rate is low enough. This results in near-constant K factors regardless of the loading rate, between 0.03 MPa/s and 3 MPa/s. The K factors start to decrease when the strain rate is fast enough that viscoplastic deformation of the solder does not saturate, resulting in a lesser degree of crack opening. It should be noted that the strain rate insensitivity, seen in both the experimental work in Table I and the numerical K factor analysis, is possible because the critical crack size is small. If the critical size were much longer than that determined in our study, significant viscoplastic deformation should occur before the crack reaches the critical size, making K factors vary more sensitively with the strain rate and joint geometry. Fracture Analysis on Bump Shear Test Our investigation of fracture in bump shear tests includes both experimental characterization and numerical analyses of the fracture mechanics, and these studies also yield several new findings of practical importance. The most striking finding made in our investigation is probably the result that the fracture in bump shear tests does not proceed by the pure shear mode but occurs mainly by the crackopening mode. This mode I fracture in the bump shear test may be an unexpected result because the test induces fracture by exerting shear force to the bump. However, our investigation reveals that nonzero rotational moment in the test configuration makes the solder body rotate in the shear direction during testing, and thus results in significant change in K I than K II. This result, combined with the viscoplasticity of solder, causes the fracture analysis of bump shear testing to be much more complicated than desired, yet it produces several interesting results. Among these findings, the occurrence of solder bump rotation and its impact on the fracture process are detailed in this paper. Figure 7 displays an example of the load displacement results obtained in our experiments. This particular test is conducted using 760-lmdiameter solder ball reflowed on a 650-lm-diameter Cu pad with a shear probe displacement rate of 200 lm/s. While similar tests are conducted with variation of test conditions, including the bump size and displacement rate, they all show essentially the same trend, that is, a rapid increase of the load to saturation (30 lm in the considered in Fig. 7) followed by a gradual decrease of the load after some duration at saturation. The load displacement relationship shown in Fig. 7 is also consistent with the results obtained in many other studies in which the saturation load is attributed to the point of cracking. As the cracking appears to occur by shear loading, the saturation (maximum) load is typically reported relative to the shear strength or adhesion strength of the solder joint. However, our SEM observations reveal that fracture in bump shear Fig. 7. Shear load displacement in a bump shear test. tests does not occur by a simple shear process but involves a rotation of the solder body. Evidence for the bump rotation is shown in Fig. 8, which presents a series of SEM micrographs of bumps (760 lm diameter, 200 lm/s shear rate) after being sheared to four different distances: 50 lm, 150 lm, 300 lm, and 500 lm. The occurrence of bump rotation can be seen from the movements of the indentation markers on each bump. Their position shows a gradual increase in the rotation of the bump in the shearing direction. In the case in which the shear distance is small, the rotational motion of bump is not clear because it is too small to resolve under SEM. However, the rotation is clearly visible at the larger shear distances of 300 lm and 500 lm. The rotational motion of the bump seen in our experiment may appear to be an anomalous result; however, it is found that the rotation is in fact inevitable because the test configuration yields a nonzero rotational moment. If the test object had a uniform surface contact area with the shear probe, e.g., a cubic bump, the rotational moment would not exist. However, in the case of the bump test, the contact between the probe and the solder is not uniform but rather is sharp because the bump has a round surface. Because the exertion of the shear force is achieved by a small contact while the wholebody displacement of the bump is prevented by the soldered interface at the bottom, a rotational moment arises and the crack tip acts as a rotation axis. Our numerical analysis of the deformation field also provides supporting evidence for the existence of the rotational motion of the solder. Figure 9 show the displacement contour developed in the vertical direction at 20 lm shear of a R 400 lm size bump with a 0.5 lm crack located at the bump corner (indicated as a circle). Figure 9a shows clear evidence of this nonzero rotational moment, as it shows the development of vertical deformation contours during shear. In this case, the solder is assumed to

8 424 Bang, Moon, Kim, Kang, Jung, and Oh 50µ m shearing 150µ m shearing 300µ m shearing 500µ m shearing Side view of bump before shearing Side view of bump after shearing Rotated view of sheared bump Fig. 8. SEM observation of the mechanical motion of a solder bump in a bump shear test (the arrow in the first column indicates the shearing direction of the shear probe). Two important motions of the solder bump can be seen: the movements of the micro-indented mark at bump top indicate the rotation of the solder bump in the shearing direction; the arrows point to compressed areas of solder bumps due to contact with the shear probe. Fig. 9. Upward-displacement contour in bumps at a shear distance of 20 lm. Notice that the dashed circles indicate the location of the crack tip, which is lifted up from the substrate by the rotation motion of the bump in the shearing direction: (a) Perfect elastic bump: a result from the FEM model incorporating only the elasticity of Sn-Pb but not incorporating the viscoplasticity; (b) viscoplastic solder bump: a result from the FEM model that includes the viscoplasticity of Sn-Pb (Eq. 1). be purely elastic for simpler analysis and better visualization. Note that the displacement contour is consistent with what is expected from deformation with rotational motion, that is, the development of vertical tensile strain at the probe contact area, including near the crack tip, and compressive strain at the opposite end. Inspection of the deformation contour with varying shear distance reveals that the tensile component arises immediately with bump contact of the probe tip. The advancement of the shear probe increases the tensile strain as the bump rotates more in the shear direction. The viscoplasticity of solder does not change the general trend of bump rotation and its evolution with shear distance, but creates a more complex evolution of the strain field at the crack-tip area due to the addition of plastic mass flow. The initial displacement response of the bump is the same as in the elastic case. Upon contacting the probe tip, the bump starts to rotate and creates a tensile strain field at the crack-tip area. However, the continuation of the shear induces an increasing degree of plastic deformation in the area in contact with the tip (as seen in Fig. 8), which induces mass flow into adjacent areas and adds a compressive strain component to the total deformation field. The strain field near the crack tip is found to be the most significantly affected by such plastic flow. Our calculation shows that it decreases the overall rate of tensile strain development at the bump corner compared to the pure elastic case, and in some shear distance ranges the tensile strain shows a negative dependence on the probe displacement. The vertical displacement contour shown in Fig. 9b demonstrates the influence of the viscoplastic flow. It can be seen that, compared to the elastic contour shown in Fig. 9a, the bump corner area exhibits much smaller tensile deformation.

9 Study of Fracture Mechanics in Testing Interfacial Fracture of Solder Joints 425 Fig. 10. K developments at the IMC crack tip during shearing of a 400-lm-radius solder bump (refer to Fig. 1b and Table III). Fig. 11. K I values at a 0.5 lm crack tip for different bump sizes (see Fig. 1b) and Table III for detailed geometry descriptions). The most critical impact of the bump rotation is the fact that it promotes mode I fracture because the resulting deformation opens up the crack tip in the vertical direction and thus makes K I greater than K II. Figure 10 shows one of many examples evidencing K I dominance. This figure shows the stress intensity factors (K I and K II ) as a function of the shear distance for R 400 lm with a 0.5 lm crack in the IMC layer. Note that K I is far greater than K II and, at any shear distance, K I /K II 3. Similar calculations conducted with varying bump and crack sizesproducethesameresult.thedominanceofk I suggests that the fracture mechanics in bump shear testing is not much different from that in tensile testing, and that the crack propagation would commence p when K I exceeds K IC =1.4MPato2.4MPa ffiffiffiffi m. Another critical impact of the bump rotation is that it makes the interfacial fracture behavior sensitive to the bump size or shape. One of the main applications of the bump shear test is the quantitative characterization of interfacial adhesion strength. It is desired that the resulting data should ideally yield consistent interfacial strength without sensitivity to bump size as long as the interfacial area is the same. However, our analysis indicates that such consistency may not be possible in the bump test configuration due to intrinsic dependence of the K I development on bump size. Such sensitivity is shown in Fig. 11, in which K I development with shear distance is shown for different bump sizes. In this calculation, the interfacial area is kept constant, copper size 325 lm, while the bump radius varies from 360 lm to 460 lm (see Fig. 1b and Table III). Since the interfacial area is assumed to be the same, different bump size changes the bump shape, and its influence is included in our calculation, as indicated in Table III as the parameters U and DX. Also, the presence of a 0.5 lm crack at the bump corner is assumed in the calculation. The K I development shown in Fig. 11 presents a clear indication that the interface fracture is sensitively affected by the variation in bump size. It can be seen that the K I development with shear distance is much more rapid p in larger bumps (or longer DX). If K IC = 1.4 MPa ffiffiffiffi m is assumed for the IMC, the interfacial fracture would take a shear distance of about 6 lm for a 460-lm-radius bump (DX = 135 lm), while it takes almost 18 lm when the bump radius is reduced to 375 lm (DX =50lm). This result indicates that larger bumps become more brittle and are more prone to interfacial fracture. Bump rotation is the primary source of the size effect shown in Fig. 11. The decisive factor affecting K I at any given shear distance is the degree of crack opening at the crack tip. As previously discussed, crack opening occurs by bump rotation, and its magnitude is proportional to the rotational moment. Because the rotation axis is located at the crack tip, the rotational moment at any given time should be a linear function of the distance between the crack tip and probe tip. In this sense, the DX defined in Table III and Fig. 1b is a good measure of the rotational moment, as larger DX means larger crack tipto-probe distance. In a larger bump, DX is larger, making it subject to a higher rotational moment. As a result, the rate of K I increase with shear distance becomes higher in bigger bumps. This explains the result shown in Fig. 12, in which the K I data shown in Fig. 11 is normalized with DX and plotted as a function of shear distance. Notice that the normalization makes the K I of different bumps reasonably close. While the normalized K I values in Fig. 12 exhibit reasonable agreement for different bump sizes, there still exist minor but measurable differences. The difference is particularly significant for the smallest bump (R = 360 lm, DX = 35lm). Interestingly, unlike in other bumps, K I in this case does not increase monotonically with the shear distance but shows a sinusoidal dependence on the shear distance. Such a behavior in K I is a result of two

10 426 Bang, Moon, Kim, Kang, Jung, and Oh Fig. 12. Normalization of K I s in Fig. 11 by DX at various bump sizes. A relation between R and DX can also be seen in Table III. competing strain components at the crack tip. As previously described and also shown in Fig. 9b, the viscoplastic mass flow to the crack-tip area adds a compressive strain component to the total deformation. This compressive strain competes with the tensile strain from the bump rotation, working in the direction of reducing K I. However, such a contribution becomes influential in small bumps in which the strain from rotational moment is small enough to be affected by the strain from the viscoplastic mass flow. Furthermore, the contribution is not uniform but varies with shear distance. Such a mechanism may be better understood with the conceptual representation of the strain field displayed in Fig. 13. In this diagram, C + and C - represent the degree of crack opening by the tensile field and crack closing by the compressive field, respectively. A simple approximation based on the results shown in Fig. 12 finds that the crack opening by bump rotation may be expressed as: C þ / DXDu (2) where, Du is the shear distance. On the other hand, the dependence of C - on the shear distance may be approximated to be proportional to the contact arc length between the bump and a shear probe because it is related to the volume of the solder that is plastically displaced during shearing: C / R cos 1 R Du R ; (3) where R is the bump radius, and the negative sign represents crack closing. In the diagram, C - is displaced by Du in the shear direction because viscoplastic flow at small shear distances is localized to the bump/probe contact area and cannot affect the strain field at the crack tip of the bump corner (in addition, Du will be larger for larger bumps since the viscoplastic mass flow distance will be longer). Then, C + + C - determines the net rate of crack-tip Fig. 13. Schematic illustration of crack-tip opening by rotation, C +, and crack-tip closing by compressive deformation of solder bump, C -. In the C + diagram, the thick solid line provides the value for a large solder bump, while the thin solid line illustrates that for a small bump. This is also the case for the C - diagram. C + + C -, which provides the net crack-tip opening in degree, is displayed by the dashed (for large bump size) and dotted lines (for small bump size). opening with shear distance. As shown in the diagram, for large bumps, C + is predominant in determining the value of C + + C -, making it increase monotonically with shear distance. For small bumps C + is small enough to be affected by C -, and therefore the total opening of the crack (C + + C - ) shows a sinusoidal variation with shear distance (dotted line). Note the resemblance between the two cases of C + + C - with the K data for the 460 lm and 360 lm bumps shown in Fig. 11. It is therefore reasonable to conclude that the viscoplasticity of the solder causes the bump to resist fracture, especially when the bump is small. DISCUSSION It is our belief that the analysis presented in this investigation provides several insights that are useful in enhanced utilization of the two testing

11 Study of Fracture Mechanics in Testing Interfacial Fracture of Solder Joints 427 methodologies for solder joint evaluation. The most obvious conclusion of this study is that both the methods test the worst case of fracture resistance of the solder joint. In the case of tensile testing, the viscoplasticity of the solder and its restriction near the IMC layer create the greatest level of stress concentration at the IMC layer, making even micron-size cracks fatal. The shear test configuration also puts the IMC layer under the strongest possible fracture conditions because of the rapidly developing K I value due to bump rotation. Since these testing methods are often utilized to identify problematic areas in joint reliability and also to quantify the degree of reliability enhancement due to processing or material design, both of these methods can be highly successful in providing relevant information. Furthermore, the fact that fracture in the bump shear testing occurs by mode I fracture may increase its usefulness. Some of the greatest merits of the bump shear test are its simplicity in sample preparation and the proximity of the test to real solder configuration, yet its application has conventionally been limited to the evaluation of adhesion strength. Since the bump shear method shares similarity in fracture mechanics with tensile test method, the method has a potential for providing more information than just the adhesion strength, such as fracture toughness of the IMC layer. Nevertheless, our study indicates that more theoretical development is necessary to make bump testing more useful. In particular, the size effect seen in our study will pose significant challenges. As pointed out by our results, the critical shear distance (and therefore the fracture load) is sensitive to the bump size even if the adhesion area is the same. Since the mechanism responsible for the size effect is the rotational moment, variation can also happen with varying bump shape even if the starting solder ball is the same. Depending on the contact angle or soldering conditions, the DX value that determines the rotational moment can vary significantly. Because of all these variations, bump size and shape will exist within a sample population, the resulting fracture data may be difficult to deconvolute. This complication created by the size effect needs further study to resolve, part of which is ongoing in our laboratories. The finding that the critical crack for IMC fracture is micron sized under tensile testing configuration may have significant practical importance and deserve further attention. The very mechanism that makes the critical size such an extreme scale is the excessive crack-tip opening due to the nonuniform viscoplasticity of solder at the joint. This result suggests that the viscoplasticity of solder, unlike common expectation, may not be helpful in retarding joint fracture but, in fact, it may make joint more prone to fracture. With the complexity of stress conditions and also variation in the crack initiation location in real solder joints, the threat of IMC failure found in tensile tests may be masked. It should be noted that, even if a crack initiates at the solder, it becomes fatal once it encounters the IMC layer. The usual IMC thickness in real solder joints is in the micron range, i.e., it is in the same size range as the critical crack. Therefore, once a crack meets the IMC layer during its growth, it is likely to be close to or larger than the critical size. In this sense, engineering solutions for enhancing the reliability of solder joints may need to focus more on enhancing IMC properties. Finally, the analysis shown in this paper is not limited to the case of Pb-Sn eutectic solder. The fundamental conclusion is equally valid for other solder materials such as lead-free solder. All solders achieve adhesion with the substrate through the reaction between Sn and metallization layers such as Cu and Ni. While variations in material properties may exist, such variations do not change the fundamental fracture mechanics found in this study. It is therefore reasonable to expect that a simple extension of the current analysis would yield valid assessments of the fracture mechanics in joints made by other alloys as well as the identification of the critical factors affecting their reliability. CONCLUSIONS The analysis conducted in this study has focused on fracture mechanics that is active in two common solder joint reliability test configurations. With an assumption of a predefined crack in the IMC layer, the development of stress intensity factors at the crack tip is numerically calculated with variations in relevant contributing parameters such as crack size, the viscoplasticity of the solder, and testing conditions. The calculations assume the presence of a crack in the IMC layer. Therefore, the fracture mechanics calculated here appears to be valid only when the interface fracture is considered. It is found that the assumption of the IMC being the fracture site correctly represents fracture in real testing situations as well as in real solder joints. This is due to the fact that both of the configurations produce generic mechanical constraints that make the IMC layer the most susceptible to fracture. In the case of joint tensile testing, it is found that: (a) the critical crack size for IMC fracture is on the micron scale; (b) the brittleness of the IMC layer stems from the generic mechanical constraints in the test configuration that assist crack-tip opening; and (c) with the brittleness of the IMC as well as the restriction of the viscoplasticity of the solder near the IMC, the fracture is insensitive to loading rate in the range of practical importance. In the case of bump shear testing, the IMC layer is again the weakest link for fracture because: (a) the test load does not impart pure shear load on the interface but rather creates more of a crack-opening load because of bump rotation; (b) the bump rotation occurs with its axis located at the crack tip; and (c) because the bump rotation (and thus K I level) is proportional to

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