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Application of electronic speckle-pattern interferometry to measure in-plane thermal displacement in flip-chip packages
Materials Science and Engineering A 380 (2004) 231–236
Application of electronic speckle-pattern interferometry to measure in-plane thermal displacement in flip-chip packages Baik-Woo Lee a,∗ , Woosoon Jang a , Dong-Won Kim a , Jeung-hyun Jeong a , Jae-Woong Nah b , Kyung-Wook Paik b , Dongil Kwon a a
School of Materials Science and Engineering, Seoul National University, San 56-1, Shinrim-dong, Kwanak-gu, Seoul 151-744, Republic of Korea b Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Republic of Korea Received 12 January 2004; received in revised form 22 March 2004
Abstract Electronic speckle-pattern interferometry (ESPI) was applied for noncontact, real-time evaluation of thermal deformation in a flip-chip package. The spatial resolution of ESPI was increased to submicron scale by magnifying the areas studied in order to measure the deformation of such small-scale components as the solder in the flip-chip package. Thermal deformation in the horizontal and vertical directions around the solder joints was measured as two-dimensional mappings during heating from 25 to 125 ◦ C. ESPI was successful in obtaining information on the complicated deformation field around the solder joints. Furthermore, the shear strain could also be calculated using the measured thermal deformation around each solder joint. The applicability of ESPI to flip-chip packages was verified by comparing the ESPI results with those of finite-element analysis (FEA). © 2004 Elsevier B.V. All rights reserved. Keywords: Electronic speckle-pattern interferometry (ESPI); Flip-chip package; Shear strain; Finite-element analysis (FEA); Coefficient of thermal expansion (CTE)
1. Introduction Flip-chip packages are produced by an interconnection technique in which the active area of a chip is mounted by various interconnecting materials on a multilayer substrate [1]. While flip-chip technologies have progressed rapidly and are now widely used, they present special reliability concerns [2–4]. A large thermal expansion mismatch between the chip and the substrate increases the likelihood of fatigue failure in solder joints under cyclic thermal loading [2,3]. In addition, the thermal mismatch often results in the delamination of interfaces between two materials, which eventually leads to mechanical and/or electrical failure [4]. Thus, it is of great interest to measure the thermomechanical deformation of flip-chip packages. Noncontact optical methods are desirable in measuring such thermomechanical deformation because they allow real-time, whole full-field measurement during operation.
∗
Corresponding author. Tel.: +82-2-880-8404; fax: +82-2-886-4847. E-mail address: [email protected] (B.-W. Lee).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.03.068
Different but complementary optical methods include holographic interferometry [5], moiré interferometry [4–6] and electronic speckle-pattern interferometry (ESPI) [5,7]. Among these methods, ESPI is one of the most promising for measuring thermal deformation in a flip-chip package in that it requires little or no special specimen preparation and can measure in-plane and out-of-plane deformation with high sensitivity. It is based on the interference of two speckle-patterns recorded before and after deformation. The speckle-patterns arise by the interference of two incident beams, an object beam and reference beam; here the object beam is reflected on the specimen and then goes to a CCD camera, while the reference beam goes directly to the camera. As the specimen deforms, the resulting surface deformation changes the phase difference between the object and reference beam and thus alters the speckle-pattern. Subtracting the deformed speckle-pattern from the undeformed one produces correlation fringes that yield a displacement field through the well-known relationship between fringe order and displacement. An ESPI system was applied to measure in-plane thermal displacement in a flip-chip package consisting of a Si
232
B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
chip, FR-4 substrate, and Sn–36Pb–2Ag solder joints, which have tiny observation areas and submicron deformation. The spatial resolution of the ESPI system was improved to submicron scale and then horizontal and vertical deformation was measured independently around the solder balls. The experimental findings were verified by comparison with the results of finite-element analysis (FEA).
Mirror Object beam
Beam expander
Specimen
Beam splitter Laser
β din
CCD
α
PZT
2. Experimental procedures A Si chip was attached face down on the substrate (FR-4) by reflowing solder balls on metallized terminals on the chip and substrate [8]. The under-bump metallurgy (UBM) was constructed by sequentially plating copper (2 m), nickel (3 m), and gold (0.1 m) for both the chip and substrate. The solder was the widely used Sn–36Pb–2Ag of 500 m diameter. Only the right half of the flip-chip was investigated by ESPI, since deformation is symmetric about the central solder joint. A cross-section was created through the outermost row of solder balls and polished with 200-grit paper. To improve the spatial resolution of ESPI, a long-workingdistance microscope (lens 1, focusing distance 325 mm and magnification 10×) and zoom lens (lens 2, maximum magnification 2×) were attached in front of the CCD camera (Fig. 1). By adjusting the arrangement of the two lenses, images 20 times larger than previously obtainable were generated, and the optimal focus distance and light intensity could be controlled by the zoom lens and iris. Here, the ESPI optics was set up in in-plane deformation measurement mode, as shown in Fig. 2. In case of in-plane deformation measurement, two object beams are used and one of them functions as a reference beam. Displacement d is calculated from the correlation fringe by the relation d = Nλ/(sin α + sin β) (shown geometrically in Fig. 2(b)) [5], where N is the fringe order at the measuring points, λ the wavelength, and α and β are incidence angles of two object beams. Because the angles are fixed during the experiment, the deformation can be measured just from the fringe order. Most measurements
Fig. 1. Long-working-distance microscope (lens 1) and zoom lens (lens 2) attached to ESPI system.
Beam expander Object beam
(a)
Mirror
β
dinsinβ
dinsinα
(b)
α
din
Fig. 2. Schematic drawing of (a) ESPI optics setup for in-plane displacement measurement and (b) phase difference between two incident beams.
are made with the aid of an image-processing computer. In addition, a phase-shift technique significantly improved the precision, convenience and usefulness of the interferometry by precisely altering the phase angle of the two incoming coherent beams by a mirror mounted on a piezoelectric transducer (PZT) in the reference beam [5]. A thermal vacuum chamber with an optical window was manufactured to produce thermal loading conditions. An optical window of 210 mm diameter was fitted to the front of the chamber to accommodate the laser beam of the ESPI system. To avoid any alteration in the laser route due to thermal circulation, a vacuum of about 10−2 Torr was maintained. Measurements were made every minute while heating from room temperature (25 ◦ C) to 125 ◦ C at a rate of 5 ◦ C/min. The temperature was monitored by a thermocouple attached around the solder joints. The FEA model used to simulate the experimental procedure is illustrated in Fig. 3. Because of geometrical symmetry, only half of the flip-chip was simulated. A three-dimensional eight-node linear hexahedral element was used for the model (7512 elements and 10814 nodes). The material properties of the chip (Si), substrate (FR-4) and various UBMs are listed in Table 1 [9]. Elastic behavior was assumed for the chip and substrate and elastoplastic behavior for the solder. The true stress–strain curve of Sn–37Pb solder was used for the solder [3]. A commercial finite-element code, ABAQUS, was employed for modeling [10].
B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
233
Fig. 3. 3D finite-element model for half of the flip-chip specimen. Table 1 Material properties of the constituents of the flip-chip assembly Material Substrate FR-4 Chip Si Cu Ni Solder Sn–36Pb–2Ag
Elastic modulus (GPa) (25 ◦ C)
22.8 19.3 (125 ◦ C) 130 (25 ◦ C) 129 (125 ◦ C) 126 (25 ◦ C) 120 (125 ◦ C) 204 (25 ◦ C) 199 (125 ◦ C) 40.6 (25 ◦ C) 35.1 (125 ◦ C)
CTE (ppm) (25 ◦ C)
20 20 (125 ◦ C) 2. 68 (25 ◦ C) 3.06 (125 ◦ C) 16.6 (25 ◦ C) 17.3 (125 ◦ C) 13.0 (25 ◦ C) 13.8 (125 ◦ C) 23.8 (25 ◦ C) 24.7 (125 ◦ C)
Poisson ratio 0.2 0.22 0.33 0.28 0.39 (25 ◦ C) 0.40 (125 ◦ C)
3. Results and discussion 3.1. Thermal deformation measurement The horizontal (U) and vertical (V) displacement was measured around the solder ball as the temperature was increased from 25 to 125 ◦ C. Fig. 4 shows the fringe patterns generated by the speckle interference (representing the thermal U displacement) in the chip and substrate at several temperatures. The number of fringes increased with increasing temperature, meaning that the U displacement increased; the difference in the number of fringes between the chip and substrate is of course due to the difference in CTE between the two components. This U displacement mismatch between chip and substrate gives rise to severe shear deformation in solder balls that connect the chip mechanically and electrically to the substrate, and the deformation becomes more significant as the temperature increases. Here the solder joints constrain the thermal deformation of the chip and substrate, an effect attested by the shape of the fringe patterns in Fig. 4: the fringe is not exactly vertical but slightly inclined. Due to the constraint of the solder joint, the U displacement of the chip is larger locally near the solder ball than predicted from its CTE but that of the substrate is smaller, as shown in Fig. 4. These observations help us get a rough understanding of the thermal deformation behavior and a quantitative evaluation of the local displacement of the flip-chip specimen.
Fig. 4. Fringe patterns at (a) 50 ◦ C, (b) 75 ◦ C, (c) 100 ◦ C and (d) 125 ◦ C.
The local U displacement over the cross-sectional specimen was calculated from the fringe information in Fig. 4 by the relation of displacement versus fringe order stated previously. Fig. 5 (a) shows the U displacement field generated during heating from 25 to 125 ◦ C. Here the solder ball in the center of the ball arrays is used as a reference point and only the right-hand half of the center ball was investigated. Also, we know from the deformation distribution of Fig. 5(a) that as the package deforms thermally,
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Fig. 5. Two-dimensional maps of (a) horizontal (U) displacement and (b) vertical (V) displacement during heating from 25 to 125 ◦ C.
the stresses are concentrated around the outermost solder ball. The V displacement given in Fig. 5(b) was measured by the same procedure as the U displacement, except for a small configurational difference in the specimen and optics: the heating stage over which the specimen is located was rotated by 90◦ so that its vertical direction is coincident with the U direction in the optics setup, since only one-dimensional analysis is available in the ESPI system used here. We can see that the V deformation is larger in the outer solder ball than in the central one, meaning that concave bending arises in the chip and substrate. This bending is related to the deformation gradient in the chip and substrate along the thickness direction due to the constraint of solder joint. As
described above, the ESPI measurement is very effective in determining two-dimensionally the thermal deformation around solder joints. 3.2. Finite-element analysis (FEA) Finite-element analysis (FEA) was performed to simulate the thermal deformation of flip-chip package from 25 to 125 ◦ C; the results are compared with ESPI results in Fig. 6. The data in Fig. 6 on U and V displacements were obtained by subtracting the value of the chip from that of the substrate, each taken just above and under the solder ball, respectively. The deformation measured by ESPI are in good agreement with those obtained by FEA except for a small
B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
235
Si chip
+
FR-4 substrate (a)
-
+
(b) Fig. 7. The effect of two modes of (a) horizontal (U) and (b) vertical (V) deformation contributing to the shear deformation of solder joint.
shear deformation due to the CTE mismatch between the chip and substrate arises in two modes (horizontal and vertical deformation), as shown in Fig. 7. The shear strain γ is given approximately by γ=
Fig. 6. Deformation differences between directly above and under solder joint in (a) horizontal (U) and (b) vertical (V) directions, as obtained by ESPI and FEA.
deviation around the outermost solder ball (see Fig. 6(a)) that can be attributed to uncertainties in the substrate material properties, particularly the elastic modulus [11]. Our results support the validity (within experimental accuracy) of the solder deformation measurement for the flip-chip package. More accurate stress distribution and level can also be predicted by combining the ESPI measurement technique with FEA.
∂U ∂V x y + ≈ + ∂y ∂x h w
(1)
where h and w are the height (320 m) and width (521 m) of the solder joint, respectively, and x and y are the deformation in the width and height direction, respectively. In addition to the U shear strain component, there was also a considerable V deformation gradient, implying that the shear strain has a V component as well. The sign of U shear strain component was opposite that of the V component. Fig. 8 shows the calculated shear strain in each solder ball. The outermost solder ball has maximum shear strain and will fail easily by thermal fatigue. The shear strain of the outermost solder ball determined by ESPI can be applied to predict the
3.3. Calculation of shear strain Many practical analyses of solder joint lifetimes require the shear strain distribution. Average shear strains for the solder balls were calculated using the deformation differences in the U and V directions as given in Fig. 6, since some noise is still involved in direct ESPI measurements of the local deformation inside solder balls. The shear strain in the solder joint can be calculated from the displacement distribution of the chip and substrate measured by ESPI. The
Fig. 8. Shear strain at solder joints with locations from center to outermost.
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B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
lifetime of the flip-chip package by using a fatigue governing equation such as the Coffin–Manson equation [12,13].
oratory Program and also partly by Grant No. R01-1999000-00195-0 from the Basic Research Program of the Korea Science and Engineering Foundation.
4. Conclusions References Electronic speckle-pattern interferometery (ESPI) was applied in an in-plane measurement mode to evaluate the thermal deformation of a flip-chip package heated from 25 to 125 ◦ C. The spatial resolution of ESPI was improved to submicron scale by magnifying the area studied with a long-working-distance microscope and a zoom lens. The thermal displacement distribution of the chip (Si) and substrate (FR-4) in the horizontal (U) and vertical (V) direction was obtained as a two-dimensional mapping by this improved ESPI system. The results let us understand the local and global behaviors of the whole deformation field in the flip-chip package. The results of a 3D finite-element (FEA) analysis for U and V displacement were very similar to the ESPI results, meaning that ESPI is sufficiently valid for use in inspecting microscale systems such as solder joints. In addition, the shear strain distribution of solder joint, one of the most important factors in determining the lifetime of thermal-cyclic fatigue failure, can be calculated by using the value of the chip and substrate around solder joint from the two-dimensional deformation map.
Acknowledgements This work was supported by the Korean Ministry of Science and Technology as a part of the National Research Lab-
[1] M. Pecht, A. Dasgupta, J.W. Evans, J.Y. Evans, Quality Conformance and Qualification of Microelectronic Packages and Interconnects, 1st ed., Wiley, New York, 1994, pp. 207–235. [2] J.H. Lau, Y.-H. Pao, Solder Joint Reliability of BGA, CSP, Flip Chip, and Fine Pitch SMT Assemblies, 1st ed., McGraw-Hill, New York, 1997, pp. 219–296. [3] J.H. Lau, Low Cost Flip Chip Technologies for DCA, WLCSP and PBGA Assemblies, 1st ed., McGraw-Hill, New York, 2000, pp. 223–262. [4] H. Xie, A. Asundib, C.G. Boayb, L. Yunguangb, J. Yub, Z. Zhaoweib, B.K.A. Ngoib, Microelectron. Reliability 42 (2002) 1219–1227. [5] G.L. Cloud, Optical Methods of Engineering Analysis, 1st ed., Cambridge University Press, New York, 1995, pp. 453–491. [6] K. Verma, S.-B. Park, B. Han, W. Ackerman, IEEE Trans. Comp. Packag. Technol. 24 (2001) 300–307. [7] S. Dilhaire, S. Jorez, A. Cornet, E. Schaub, W. Claeys, Microelectron. Reliability 39 (1999) 981–985. [8] J.-W. Nah, K.-W. Paik, IEEE Trans. Comp. Packag. Technol. 25 (2002) 32–37. [9] MPDB Software, Temperature Dependent Elastic and Thermal Properties Database, JAHM Software, Massachusetts, 2002. [10] ABAQUS/Standard, Hibbitt, Karlsson and Sorensen, Inc., RI, 1998. [11] J.-H. Zhao, X. Dai, P.S. Ho, in: Proceedings of the 48th Electronic Components and Technology Conference, Seattle, Washington, 1998, pp. 336–344. [12] W.W. Lee, L.T. Nguyen, G.S. Selvaduray, Microelectron. Reliability 40 (2000) 231–244. [13] C.S. Desai, R. Whitenack, J. Electron. Packag. 123 (2001) 19– 32.
Application of electronic speckle-pattern interferometry to measure in-plane thermal displacement in flip-chip packages Baik-Woo Lee a,∗ , Woosoon Jang a , Dong-Won Kim a , Jeung-hyun Jeong a , Jae-Woong Nah b , Kyung-Wook Paik b , Dongil Kwon a a
School of Materials Science and Engineering, Seoul National University, San 56-1, Shinrim-dong, Kwanak-gu, Seoul 151-744, Republic of Korea b Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Republic of Korea Received 12 January 2004; received in revised form 22 March 2004
Abstract Electronic speckle-pattern interferometry (ESPI) was applied for noncontact, real-time evaluation of thermal deformation in a flip-chip package. The spatial resolution of ESPI was increased to submicron scale by magnifying the areas studied in order to measure the deformation of such small-scale components as the solder in the flip-chip package. Thermal deformation in the horizontal and vertical directions around the solder joints was measured as two-dimensional mappings during heating from 25 to 125 ◦ C. ESPI was successful in obtaining information on the complicated deformation field around the solder joints. Furthermore, the shear strain could also be calculated using the measured thermal deformation around each solder joint. The applicability of ESPI to flip-chip packages was verified by comparing the ESPI results with those of finite-element analysis (FEA). © 2004 Elsevier B.V. All rights reserved. Keywords: Electronic speckle-pattern interferometry (ESPI); Flip-chip package; Shear strain; Finite-element analysis (FEA); Coefficient of thermal expansion (CTE)
1. Introduction Flip-chip packages are produced by an interconnection technique in which the active area of a chip is mounted by various interconnecting materials on a multilayer substrate [1]. While flip-chip technologies have progressed rapidly and are now widely used, they present special reliability concerns [2–4]. A large thermal expansion mismatch between the chip and the substrate increases the likelihood of fatigue failure in solder joints under cyclic thermal loading [2,3]. In addition, the thermal mismatch often results in the delamination of interfaces between two materials, which eventually leads to mechanical and/or electrical failure [4]. Thus, it is of great interest to measure the thermomechanical deformation of flip-chip packages. Noncontact optical methods are desirable in measuring such thermomechanical deformation because they allow real-time, whole full-field measurement during operation.
∗
Corresponding author. Tel.: +82-2-880-8404; fax: +82-2-886-4847. E-mail address: [email protected] (B.-W. Lee).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.03.068
Different but complementary optical methods include holographic interferometry [5], moiré interferometry [4–6] and electronic speckle-pattern interferometry (ESPI) [5,7]. Among these methods, ESPI is one of the most promising for measuring thermal deformation in a flip-chip package in that it requires little or no special specimen preparation and can measure in-plane and out-of-plane deformation with high sensitivity. It is based on the interference of two speckle-patterns recorded before and after deformation. The speckle-patterns arise by the interference of two incident beams, an object beam and reference beam; here the object beam is reflected on the specimen and then goes to a CCD camera, while the reference beam goes directly to the camera. As the specimen deforms, the resulting surface deformation changes the phase difference between the object and reference beam and thus alters the speckle-pattern. Subtracting the deformed speckle-pattern from the undeformed one produces correlation fringes that yield a displacement field through the well-known relationship between fringe order and displacement. An ESPI system was applied to measure in-plane thermal displacement in a flip-chip package consisting of a Si
232
B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
chip, FR-4 substrate, and Sn–36Pb–2Ag solder joints, which have tiny observation areas and submicron deformation. The spatial resolution of the ESPI system was improved to submicron scale and then horizontal and vertical deformation was measured independently around the solder balls. The experimental findings were verified by comparison with the results of finite-element analysis (FEA).
Mirror Object beam
Beam expander
Specimen
Beam splitter Laser
β din
CCD
α
PZT
2. Experimental procedures A Si chip was attached face down on the substrate (FR-4) by reflowing solder balls on metallized terminals on the chip and substrate [8]. The under-bump metallurgy (UBM) was constructed by sequentially plating copper (2 m), nickel (3 m), and gold (0.1 m) for both the chip and substrate. The solder was the widely used Sn–36Pb–2Ag of 500 m diameter. Only the right half of the flip-chip was investigated by ESPI, since deformation is symmetric about the central solder joint. A cross-section was created through the outermost row of solder balls and polished with 200-grit paper. To improve the spatial resolution of ESPI, a long-workingdistance microscope (lens 1, focusing distance 325 mm and magnification 10×) and zoom lens (lens 2, maximum magnification 2×) were attached in front of the CCD camera (Fig. 1). By adjusting the arrangement of the two lenses, images 20 times larger than previously obtainable were generated, and the optimal focus distance and light intensity could be controlled by the zoom lens and iris. Here, the ESPI optics was set up in in-plane deformation measurement mode, as shown in Fig. 2. In case of in-plane deformation measurement, two object beams are used and one of them functions as a reference beam. Displacement d is calculated from the correlation fringe by the relation d = Nλ/(sin α + sin β) (shown geometrically in Fig. 2(b)) [5], where N is the fringe order at the measuring points, λ the wavelength, and α and β are incidence angles of two object beams. Because the angles are fixed during the experiment, the deformation can be measured just from the fringe order. Most measurements
Fig. 1. Long-working-distance microscope (lens 1) and zoom lens (lens 2) attached to ESPI system.
Beam expander Object beam
(a)
Mirror
β
dinsinβ
dinsinα
(b)
α
din
Fig. 2. Schematic drawing of (a) ESPI optics setup for in-plane displacement measurement and (b) phase difference between two incident beams.
are made with the aid of an image-processing computer. In addition, a phase-shift technique significantly improved the precision, convenience and usefulness of the interferometry by precisely altering the phase angle of the two incoming coherent beams by a mirror mounted on a piezoelectric transducer (PZT) in the reference beam [5]. A thermal vacuum chamber with an optical window was manufactured to produce thermal loading conditions. An optical window of 210 mm diameter was fitted to the front of the chamber to accommodate the laser beam of the ESPI system. To avoid any alteration in the laser route due to thermal circulation, a vacuum of about 10−2 Torr was maintained. Measurements were made every minute while heating from room temperature (25 ◦ C) to 125 ◦ C at a rate of 5 ◦ C/min. The temperature was monitored by a thermocouple attached around the solder joints. The FEA model used to simulate the experimental procedure is illustrated in Fig. 3. Because of geometrical symmetry, only half of the flip-chip was simulated. A three-dimensional eight-node linear hexahedral element was used for the model (7512 elements and 10814 nodes). The material properties of the chip (Si), substrate (FR-4) and various UBMs are listed in Table 1 [9]. Elastic behavior was assumed for the chip and substrate and elastoplastic behavior for the solder. The true stress–strain curve of Sn–37Pb solder was used for the solder [3]. A commercial finite-element code, ABAQUS, was employed for modeling [10].
B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
233
Fig. 3. 3D finite-element model for half of the flip-chip specimen. Table 1 Material properties of the constituents of the flip-chip assembly Material Substrate FR-4 Chip Si Cu Ni Solder Sn–36Pb–2Ag
Elastic modulus (GPa) (25 ◦ C)
22.8 19.3 (125 ◦ C) 130 (25 ◦ C) 129 (125 ◦ C) 126 (25 ◦ C) 120 (125 ◦ C) 204 (25 ◦ C) 199 (125 ◦ C) 40.6 (25 ◦ C) 35.1 (125 ◦ C)
CTE (ppm) (25 ◦ C)
20 20 (125 ◦ C) 2. 68 (25 ◦ C) 3.06 (125 ◦ C) 16.6 (25 ◦ C) 17.3 (125 ◦ C) 13.0 (25 ◦ C) 13.8 (125 ◦ C) 23.8 (25 ◦ C) 24.7 (125 ◦ C)
Poisson ratio 0.2 0.22 0.33 0.28 0.39 (25 ◦ C) 0.40 (125 ◦ C)
3. Results and discussion 3.1. Thermal deformation measurement The horizontal (U) and vertical (V) displacement was measured around the solder ball as the temperature was increased from 25 to 125 ◦ C. Fig. 4 shows the fringe patterns generated by the speckle interference (representing the thermal U displacement) in the chip and substrate at several temperatures. The number of fringes increased with increasing temperature, meaning that the U displacement increased; the difference in the number of fringes between the chip and substrate is of course due to the difference in CTE between the two components. This U displacement mismatch between chip and substrate gives rise to severe shear deformation in solder balls that connect the chip mechanically and electrically to the substrate, and the deformation becomes more significant as the temperature increases. Here the solder joints constrain the thermal deformation of the chip and substrate, an effect attested by the shape of the fringe patterns in Fig. 4: the fringe is not exactly vertical but slightly inclined. Due to the constraint of the solder joint, the U displacement of the chip is larger locally near the solder ball than predicted from its CTE but that of the substrate is smaller, as shown in Fig. 4. These observations help us get a rough understanding of the thermal deformation behavior and a quantitative evaluation of the local displacement of the flip-chip specimen.
Fig. 4. Fringe patterns at (a) 50 ◦ C, (b) 75 ◦ C, (c) 100 ◦ C and (d) 125 ◦ C.
The local U displacement over the cross-sectional specimen was calculated from the fringe information in Fig. 4 by the relation of displacement versus fringe order stated previously. Fig. 5 (a) shows the U displacement field generated during heating from 25 to 125 ◦ C. Here the solder ball in the center of the ball arrays is used as a reference point and only the right-hand half of the center ball was investigated. Also, we know from the deformation distribution of Fig. 5(a) that as the package deforms thermally,
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B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
Fig. 5. Two-dimensional maps of (a) horizontal (U) displacement and (b) vertical (V) displacement during heating from 25 to 125 ◦ C.
the stresses are concentrated around the outermost solder ball. The V displacement given in Fig. 5(b) was measured by the same procedure as the U displacement, except for a small configurational difference in the specimen and optics: the heating stage over which the specimen is located was rotated by 90◦ so that its vertical direction is coincident with the U direction in the optics setup, since only one-dimensional analysis is available in the ESPI system used here. We can see that the V deformation is larger in the outer solder ball than in the central one, meaning that concave bending arises in the chip and substrate. This bending is related to the deformation gradient in the chip and substrate along the thickness direction due to the constraint of solder joint. As
described above, the ESPI measurement is very effective in determining two-dimensionally the thermal deformation around solder joints. 3.2. Finite-element analysis (FEA) Finite-element analysis (FEA) was performed to simulate the thermal deformation of flip-chip package from 25 to 125 ◦ C; the results are compared with ESPI results in Fig. 6. The data in Fig. 6 on U and V displacements were obtained by subtracting the value of the chip from that of the substrate, each taken just above and under the solder ball, respectively. The deformation measured by ESPI are in good agreement with those obtained by FEA except for a small
B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
235
Si chip
+
FR-4 substrate (a)
-
+
(b) Fig. 7. The effect of two modes of (a) horizontal (U) and (b) vertical (V) deformation contributing to the shear deformation of solder joint.
shear deformation due to the CTE mismatch between the chip and substrate arises in two modes (horizontal and vertical deformation), as shown in Fig. 7. The shear strain γ is given approximately by γ=
Fig. 6. Deformation differences between directly above and under solder joint in (a) horizontal (U) and (b) vertical (V) directions, as obtained by ESPI and FEA.
deviation around the outermost solder ball (see Fig. 6(a)) that can be attributed to uncertainties in the substrate material properties, particularly the elastic modulus [11]. Our results support the validity (within experimental accuracy) of the solder deformation measurement for the flip-chip package. More accurate stress distribution and level can also be predicted by combining the ESPI measurement technique with FEA.
∂U ∂V x y + ≈ + ∂y ∂x h w
(1)
where h and w are the height (320 m) and width (521 m) of the solder joint, respectively, and x and y are the deformation in the width and height direction, respectively. In addition to the U shear strain component, there was also a considerable V deformation gradient, implying that the shear strain has a V component as well. The sign of U shear strain component was opposite that of the V component. Fig. 8 shows the calculated shear strain in each solder ball. The outermost solder ball has maximum shear strain and will fail easily by thermal fatigue. The shear strain of the outermost solder ball determined by ESPI can be applied to predict the
3.3. Calculation of shear strain Many practical analyses of solder joint lifetimes require the shear strain distribution. Average shear strains for the solder balls were calculated using the deformation differences in the U and V directions as given in Fig. 6, since some noise is still involved in direct ESPI measurements of the local deformation inside solder balls. The shear strain in the solder joint can be calculated from the displacement distribution of the chip and substrate measured by ESPI. The
Fig. 8. Shear strain at solder joints with locations from center to outermost.
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B.-W. Lee et al. / Materials Science and Engineering A 380 (2004) 231–236
lifetime of the flip-chip package by using a fatigue governing equation such as the Coffin–Manson equation [12,13].
oratory Program and also partly by Grant No. R01-1999000-00195-0 from the Basic Research Program of the Korea Science and Engineering Foundation.
4. Conclusions References Electronic speckle-pattern interferometery (ESPI) was applied in an in-plane measurement mode to evaluate the thermal deformation of a flip-chip package heated from 25 to 125 ◦ C. The spatial resolution of ESPI was improved to submicron scale by magnifying the area studied with a long-working-distance microscope and a zoom lens. The thermal displacement distribution of the chip (Si) and substrate (FR-4) in the horizontal (U) and vertical (V) direction was obtained as a two-dimensional mapping by this improved ESPI system. The results let us understand the local and global behaviors of the whole deformation field in the flip-chip package. The results of a 3D finite-element (FEA) analysis for U and V displacement were very similar to the ESPI results, meaning that ESPI is sufficiently valid for use in inspecting microscale systems such as solder joints. In addition, the shear strain distribution of solder joint, one of the most important factors in determining the lifetime of thermal-cyclic fatigue failure, can be calculated by using the value of the chip and substrate around solder joint from the two-dimensional deformation map.
Acknowledgements This work was supported by the Korean Ministry of Science and Technology as a part of the National Research Lab-
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