Nakashima et al.: Warpage Mechanism of Thin Embedded LSI Packages (1/10) [Technical Paper] Warpage Mechanism of Thin Embedded LSI Packages Yoshiki Nakashima*, Katsumi Kikuchi*, Kentaro Mori*, Daisuke Ohshima**, and Shintaro Yamamichi* *Device Platforms Research Laboratories, NEC Corporation, 1120 Shimokuzawa, Sagamihara 229-1198, Japan **System Jisso Research Laboratories, NEC Corporation, 1120 Shimokuzawa, Sagamihara 229-1198, Japan (Received June 29, 2010; accepted October 1, 2010) Abstract The warpage mechanism of a thin embedded LSI package with a thick Cu plate was investigated for various Cu plate thicknesses. The package warpage increased gradually as the Cu plate was made thinner. Even structures with a balanced Cu and resin layer configuration for the top and bottom portions of the embedded chip showed substantial warpage, especially in the chip region, that was greater than that for an unbalanced layer configuration. This indicates the existence of other warpage factors as well as unbalanced residual stress between the top and bottom of the chip. A ‘Birth & Death’ finite element method simulation showed that the thermal residual stresses induced by the coefficient of thermal expansion mismatch for the LSI chip and embedding resin were concentrated in the resin surrounding the lateral sides of the chip and that the stresses increased with decreasing Cu thickness. The release of these tensile stresses resulted in package warpage. Keywords: Advanced Packaging, Embedded Device Technology, SiP, Simulation, Residual Stress and SIRRIUS packages are shown in Table 1. While 1. Introduction LSI packaging technologies are needed for fabricating several organizations have been developing packaging thinner and higher-pin-count LSI packages to meet the technologies that have structures similar to that of market demands for thinner, smaller, and more functional SIRRIUS,[6–9] SIRRIUS features the ability to embed a high- mobile devices.[1] One way to achieve a thinner, higher- pin-count LSI with a comparably thin structure and suffi- pin-count LSI packaging structure is to realize a thinner cient reliability. alternative to conventional flip-chip ball-grid array A reference FCBGA package and a SIRRIUS package (FCBGA) packaging. Our ‘SIRRIUS’ (seamless intercon- were prepared for LSI chips with the same specifications. nect for re-routing LSI using substrate) technology,[2–5] The total vertical thicknesses of these packages were 1.9 for example, is well suited to fabricating those alternatives, and 0.71 mm, respectively. This remarkable reduction in as shown in Fig. 1. The specifications of the embedded LSI thickness was achieved by using a thinner LSI chip (only 50 μm), a coreless structure, and seamless copper posts Table 1 SIRRIUS package specifications. Size (mm) LSI Thickness (μm) LSI pad count LSI pad pitch (μm) Size (mm) BGA pad count Package BGA pad pitch (mm) Fig. 1 Comparison of (a) Structure A, reference FCBGA package and (b) Structure B, our SIRRIUS package. Wiring layer BGA ball size (mm) 9×9 50 1500 160 (staggered area array) 27 × 27 625 1.0 (area array) 3 0.6 47 Transactions of The Japan Institute of Electronics Packaging Vol. 3, No. 1, 2010 for the interconnections instead of solder bumps. than half the original thickness. There are two factors that However, the continuing market trend makes it neces- make Structure C susceptible to warpage: the structure is sary to examine the possibility of making the SIRRIUS vertically asymmetric, so there is a vertical imbalance in structure even thinner. Thinning or removing the charac- the residual thermal stresses caused by the coefficient of teristic 500-μm-thick Cu plate is a valid approach to making thermal expansion (CTE) mismatch; and there is little in the package thinner. However, since the plate is used to the structure besides the Cu plate to keep the package flat control package warpage and remove LSI heat, research and stiff. into ways to make the SIRRIUS package thinner must The next structure fabricated, Structure D, is not address the control of package warpage with a thinner Cu affected by these two warpage factors. It is compared with plate. Structure C on the same scale in Fig. 3. Vertical asymme- We have now investigated several SIRRIUS package try was eliminated by introducing ‘balance resin’ and structures with thinner Cu plates or without any Cu plate ‘remaining Cu’ layers above the chip. The remaining Cu in order to clarify the warpage mechanism. We performed layer was only 10 μm thick, approximately the same thick- a ‘birth & death’ finite element method (FEM) analysis for ness as that of the first wiring layer. A glass cloth (GC) further discussion on fabrication process flows and struc- sheet was added to the same layer as the LSI chip to tures, though this thermal stress analysis is conventionally reinforce that layer so as to improve flatness and stiffness. used to predict reliability after fabrication.[10, 11] We The fabrication process flow for Structure C is shown in found that the Cu plate thickness reduction created resid- Fig. 4. Note that the direction of the cross-sectional illus- ual tensile stress in the resin layers surrounding the chip, trations is upside-down compared with Figs. 1 to 3. The mainly in the areas lateral to the chip. The release of these LSI chips were pre-processed to form Cu posts on the LSI tensile stresses, along with the release of the compressive pads by semi-additive metallization. This was followed by stress in the chip, caused the package to warp. back-grinding to make them 50 μm thick, 20-μm-thick adhesive layer lamination on the backside, and dicing to 2. Structures and Experimental Processes form 9-mm-square chips. The first process step was LSI As mentioned above, one approach to thinning the struc- chip mounting, as shown in Fig. 4 (a). The chips were sta- ture is to thin or remove the Cu plate while retaining the bilized by curing the adhesive layer. The CTE for the adhe- embedding resin and wiring structure, as shown in Fig. 2. sive layers was 80 ppm. The chips were then embedded in We used this approach to fabricate several structures for 90-μm-thick epoxy resin using a simple vacuum lamination evaluation. The first structure, ‘Structure C’ in Fig. 2 (b), process, as shown in Fig. 4 (b). The CTE for the epoxy had three wiring layers on the lower side of the LSI chip layer was 60 ppm. The Cu posts were then exposed by and a thinner or no Cu plate on the upper side of the chip, grinding the epoxy resin surface, as shown in Fig. 4 (c). A with an adhesive layer between the plate and the chip. The microscopic photo of the exposed Cu posts is shown in thickness of the thinned Cu plate was set to slightly less Fig. 5 (a). Next, the wiring layers were fabricated. The first Fig. 2 Comparison of (a) Structure B, our initial SIRRIUS Fig. 3 package and (b) Structure C, our SIRRIUS package with with thinned or removed Cu plate and (b) Structure D, anti- thinned or removed Cu plate. warpage structure. 48 Comparison of (a) Structure C, our SIRRIUS package Nakashima et al.: Warpage Mechanism of Thin Embedded LSI Packages (3/10) Fig. 4 Steps in fabrication of Structure C. forcement layer,’ which had a CTE of 24 ppm. The epoxy resin sheet, which is called the ‘cover resin’ layer, was composed of the same material as the ‘balance resin’ layer. Once the LSI chips had been embedded into the resin layers, the Cu posts were exposed using the same grinding process as that used for Structure C, as shown in Fig. 6 (d). A microscopic photo of the posts is shown in Fig. 7 (a). The cover resin layer thickness is the same as the Cu post Fig. 5 Photos of Structure C: (a) microscopic photo of exposed Cu posts; (b) photo of first wiring layer. thickness between the surface of the chip passivation film (PF) resin and the surface of the cover resin. We measured the cover resin layer thicknesses at the center of four chips after the grinding. The thicknesses of the four fan-out wiring layer was fabricated using semi-additive chips selected near the four edges of the work were 10.5, metallization, as shown in Fig. 4 (d). A photo of the wiring 12.1, 13.1 and 13.4 μm respectively. The variation of the layer is shown in Fig. 5 (b). Then, the second and third fan- thickness is within approximately 3 μm. Next, the first wir- out wiring layers were fabricated, with resin layers that ing layer was fabricated using the same process as that had the same physical properties as the cover resin and used for Structure C, as shown in Fig. 6 (e). A photo of the balance resin layers. This process was followed by solder layer is shown in Fig. 7 (b). We omitted the second and resist (SR) formation and package dicing, as shown in third wiring layer formation processes for Structure D Figs. 4 (e) and (f), respectively. The last process was Cu because the vertical balance effect was the focus in this plate etching, as shown in Fig. 4 (g). experiment. In the last step, the Cu plate was etched so The fabrication process flow for Structure D is shown in that a Cu layer about 10 μm thick remained, as shown in Fig. 6. The first step was balance resin layer lamination, as Fig. 6 (f). The resulting structure is basically unsusceptible shown in Fig. 6 (a). The same resin used for chip embed- to the warpage factors. ding with Structure C was laminated on the Cu plate by We measured the average thicknesses of the balance simple vacuum lamination to a thickness of 20 μm. Next resin layer, cover resin layer, reinforcement layer, adhe- was LSI chip mounting. The chips were the same as those sive layer, and LSI layer with PF resin in Structure D at the used for Structure D. The next step, resin-GC sheet and center, at the chip edge, and at the package edge after the cover resin lamination started with the formation of square process flow. As shown in Table 2, the cover resin layer holes for the chips on 50-μm-thick resin-GC sheets, or was thicker at the package edge than at the center while epoxy resin sheets reinforced by GC. Then the resin-GC the balance resin layer was thicker at the center than at the sheet and a 20-μm-thick epoxy resin sheet were laminated, package edge. This tendency is explained by the shrink- and the LSI chips were embedded in the layers, as shown age of the Cu plate, which causes the chips to take an arch in Fig. 6 (c). The laminated resin-GC sheet created a ‘rein- form, after step (c) in Fig. 6. 49 Transactions of The Japan Institute of Electronics Packaging Vol. 3, No. 1, 2010 Fig. 6 Steps in fabrication of Structure D. Fig. 8 Two partial warpage definitions: (a) package warpage Wp is larger than chip region warpage Wc; (a) Wc is larger Fig. 7 Photos of Structure D; (a) microscopic photo of than Wp. exposed Cu posts; and (b) photo of first wiring layer. Table 3 Average warpage for Structures C and D after Cu Table 2 Average layer thicknesses for Structure D. Layer Cover Resin Thickness (μm) Structure PKG Edge Chip Edge Center Average 16.2 16.8 12.7 plate etching. 15.3 Cu plate thickness (μm) Structure-C 250 100 Structure-D 0 135 362 316 Warpage [Wp or Wc] (μm) [Wp] [Wp] [Wc] 10 370 [Wc] LSI (w/PF) – 62.8 61.7 62.3 Adhesive – 20.1 19.8 19.9 Reinforcement 84.0 82.9 – 83.4 pages differed for the fabricated Structure C and Structure Balance Resin 13.8 18.7 19.3 17.2 D samples. When warpage Wp exceeds warpage Wc, the 113.9 118.4 113.6 115.3 warpage for the package was defined as Wp, as shown in Total Fig. 8 (a), and vice versa, as shown in Fig. 8 (b). The warpages for Structures C and D, as measured after Cu plate 3. Results and Discussion 3.1 Structures C and D etching using the shadow Moiré technique and a stylus surface profiler, respectively, are shown in Table 3. The To enable detailed discussion of the warpage, we defined common warpage measurement line for both structures is two partial warpage values (Fig. 8). Warpage ‘Wp’ is com- shown in Fig. 9. In these measurements, the fan-out wiring plete-package warpage and is the vertical distance between layer side was up, as shown in Figs. 4 (g) and 6 (f). the highest and lowest points, excepting the embedded LSI The warpage profiles after Cu-plate etching for Structure chip region. Warpage ‘Wc’ is embedded-chip-region war- C, with Cu plate thicknesses of 250, 100, and 0 μm, and for page and is the vertical distance between the highest and Structure D, with a 10-μm-thick copper layer, are shown in lowest points of the region. The directions of the two war- Figs. 10 (a) and (b), respectively. 50 Nakashima et al.: Warpage Mechanism of Thin Embedded LSI Packages (5/10) Fig. 9 Common warpage measurement line. Fig. 11 Other two warpage factors investigated: imbalance in thermal history and thermal stress in adhesive layer. Fig. 10 Warpage forms for (a) Structure C and (b) Structure D samples. during the cooling phase following curing. Moreover, there was no stiff material to suppress the warpage after the Cu plate etching. These configuration and physical The warpage for Structure C with Cu plate 100 μm thick or less was significant. When the Cu plate thickness was properties explain the observation of the large concave Wc. 100 μm or more, the concave warpage, Wp, exceeded the For Structure D, the resin layers for the chip-embedding convex warpage, Wc. This indicates that, with Cu plates, region were on the upper and lower sides of the chip and the CTE mismatch between the resin for the three fan-out had the same thickness. Therefore, if the resin layers wiring layers and the Cu plate was the dominant factor shrank during the cooling phase, the shrink force should causing warpage. In contrast, without the Cu plate, the have been balanced. Moreover, the chip layer was rein- concave warpage, Wc, exceeded convex warpage, Wp. forced to suppress warpage. Therefore, the larger warpage This indicates that the CTE mismatch between the LSI than for Structure C needed more explanation. chip and the resin in the three fan-out wiring layers was We thus considered other factors which might explain the dominant factor causing the warpage. These results for the results for Structure D. Structure C were as expected. 3.2 Factor Analysis and Discussion of Other Possi- The warpage for Structure D was also remarkable, as ble Warpage Factors shown in Fig. 10 (b). Convex warpage, Wc, exceeded con- We considered two other possible warpage factors for cave warpage, Wp. Comparing warpage Wc for Structure C Structure D, which are illustrated in Fig. 11: the imbalance without the Cu plate with that for Structure D, we see that in the thermal history of the resin layers and the thermal the warpage for Structure D, 370 μm, was larger than that stress in the adhesive layer. The balance resin layer was for Structure C, 316 μm, as shown in Table 3. In our dis- first laminated and cured on the Cu plate. Next, after LSI cussion here of warpage Wc, we focus on the thermal mounting, the reinforcement layer and cover resin layer residual stress factors of the chip-embedding 9 × 9 mm were laminated and cured, as was the balance resin layer. central region of the 27 × 27 mm package. Therefore, the balance resin layer was cured twice while For Structure C, the main warpage factor, especially for the upper two layers were cured only once, resulting in an the chip-embedding region, should be the imbalance imbalance in the thermal history. The thermal stress in the between the Si for the LSI chip and the resin for the three adhesive layer likely caused the layer to shrink, resulting fan-out wiring layers. The resin for the fan-out layers was in convex warpage of the chips. To investigate the effect of 140 μm thick, and they were only on the upper side of the these two factors, we performed an additional factor analy- LSI chip, as shown in Figs. 4 (g) and 6 (f). The CTE for the sis experiment in which the wiring layer was not included. resin is much larger than that for the Si, which would Cross-sectional illustrations of the two structures fabri- result in comparable shrinkage for the three resin layers cated for the experiment are shown in Fig. 12. Both struc- 51 Transactions of The Japan Institute of Electronics Packaging Vol. 3, No. 1, 2010 Table 4 Pros and cons of three possible structures for FEM analysis. Pros ➘ Realization for the fabrication Cons ➘ Known warpage mechanism discussion Fig. 12 Cross-sectional illustrations of (a) Structure E and (b) Structure F. ➘ Realization for the fabrication ➘ Further warpage ➘ Remaining two mechanism factors’ and further discussion warpage mechanism discussion ➘ No realization for the wiring fabrication Obviously, Structure D was warped by another mechanism. To identify candidate factors, we performed a FEM simulation. 4. Fig. 13 Results of factor analysis experiment: (a) warpage form for Structure E and (b) for Structure F. FEM Simulation First, we identified an appropriate structure for the FEM simulation. The pros and cons for possible structures are listed in Table 4. Structure E was not considered because its process flow and resin configuration are the same as tures had embedded bare Si chips, simulating LSI chips. those for Structure D. As shown in Table 4, the fabrication They were the same thickness and size as the LSI chips process flow for Structure C has already been developed, used for Structures C and D. The control sample structure, so fabrication is not a problem. However, the measured ‘Structure E,’ is shown in Fig. 13 (a). It had the same resin warpage is basically explained already, so this structure is configuration and was fabricated in the same way as Struc- not suitable for further warpage investigation. The fabrica- ture D. The experimental structure, ‘Structure F,’ is shown tion process flow for Structure D has also been developed. in Fig. 13 (b). It was fabricated using a ‘simultaneous lam- Moreover, the warpage factor for this structure is not fully ination’ process to eliminate the two remaining factors. explained by a known mechanism. Additionally, with this First, bare Si chips and a reinforcement layer with chip structure, we can discuss the other two factors. The war- holes were set in place. Then, the two resin layers were page mechanism for Structure F is also unknown, but a laminated onto the upper and lower sides of the chip and fabrication process with wiring has not been developed. reinforcement layer simultaneously. Next, the entire pack- We thus used Structure D for our thermo-mechanical FEM age was cured all at once. As a result, the thermal history simulation using ANSYS mechanical. was balanced, and there was no need for an adhesive layer. The model used for the simulation is illustrated in Figs. The warpage profiles for Structures E and F are shown 14 and 15. The subject of the simulation was a work of sev- in Fig. 13. As these warpage were too large for a stylus sur- eral 27 × 27 mm packages, and by setting symmetric face profiler or the shadow Moiré technique, we used a boundaries in the simulation model, we calculated the microscope that enabled us to measure the vertical level of model of one package in a practical manner. the focus point and focused on certain points on the mea- We set the fan-out wiring layer on the top, just as illus- surement line (Fig. 9). The warpages for the two struc- trated in Fig. 6. As shown in Fig. 14, we divided the first tures were almost the same. They exceeded warpage Wc fan-out wiring layer (CAD design shown in Fig. 14 (a)) in for both structures. These results indicate that these two the model into nine parts, and set the physical properties other factors, imbalance in the thermal history of the resin of the parts between Cu and air on the basis of the area layers and thermal stress in the adhesive layer, were not ratio of the wirings, as shown in Fig. 14 (b). The cross- the main factors in the package warpage. section line on the model shown in Fig. 14 (b) defines the 52 Nakashima et al.: Warpage Mechanism of Thin Embedded LSI Packages (7/10) there is no insulation material but air between the Cu wirings. We used the ‘birth & death’ method [12] to simulate the fabrication process flow. In this method, insulator materials such as resin and adhesive layers appear (are ‘born’) at the same time that these components are cured in the actual procedure, as shown in Table 5. The Cu plate disappears (‘dies’) when it is etched out in the actual procedure. Fig. 14 (a) Top view of Structure D package wiring layer and Other materials, such as Cu and Si, appear (are ‘born’) (b) top view of FEM model for ANSYS mechanical analysis, with the insulator materials, or between processes. In this which is divided into nine parts on basis of Cu area ratio of wir- simulation, the physical properties of the material, such as ing. Young’s modulus, the CTE values, the Poisson ratio, and the glass transition temperature, were used as parameters in the calculation. However, the chemical shrinkage factors of the resins were not parameterized. Therefore, we were unable to verify the thermal history imbalance in this simulation. The points labeled I–VII on the thermal condition chart in Table 5 are the process points at which the residual stresses were observed. Three observation points were set for the Cu plate etching process to enable detailed analysis of the warpage mechanism. Contour maps of the residual stresses at the observation points (I–VII) are shown in Figs. 16 and 17 as seen from the cross section line in Fig. 14 (b). The scale for the residual stress is shown to the right of Fig. 16. The black and white shadings correspond to compressive and tensile residual stress, respectively. Fig. 15 Cross-sectional views of embedded LSI components: The first residual stress map, Fig. 16 I, is for the room (a) material configuration defined using ANSYS mechanical temperature point after curing the balance-resin layer. The and (b) actual component configuration. resin layer showed about 300–400 MPa tensile stress due to shrinkage. The second map, Fig. 16 II, is for the room cross-sectional maps of the residual stress contour maps. temperature point after mounting the LSI. Due to the CTE Figure 15 shows cross-sectional views of (a) the actual gap between Cu and Si, the Cu plate showed 0–600 MPa components in the LSI chip margin area and (b) the mate- tensile stress, and the LSI chip showed −100 to 0 MPa rials defined for the simulation. The first fan-out wiring compressive stress. The third map, Fig. 16 III, is for the layer, labeled ‘9’ in Fig. 15 (a), corresponds to the ‘Cu + air’ room temperature point after lamination and curing of the material in Fig. 15 (b), which means that, in this layer, reinforcement and cover-resin layers. The reinforcement Table 5 ‘Birth and Death’ simulation processes for Structure D. 53 Transactions of The Japan Institute of Electronics Packaging Vol. 3, No. 1, 2010 Fig. 18 Residual stress contour maps of cross-sectional views Fig. 16 Residual stress contour maps of cross-sectional views with enhanced vertical deformation for last two process points for process points I (balance resin layer lamination), II (LSI shown in Fig. 17: (a) VI and (b) VII. mounting), and III (LSI embedding). Fig. 17 Residual stress contour maps of cross-sectional views for process points IV–VII (Cu plate etch-out). Fig. 19 Overhead views of Structure D at process point after Cu plate etch out: (a) complete package simulation model, (b) layer showed 0–100 MPa tensile stress. Maps IV–VII show the residual stress distributions for the Cu plate-etching process. At the earlier points of the maximum principal stress vector map for central region, middle layer meshes of chip and surrounding resin, and (c) enlarged and simplified figure of nearside edge of (b). process (IV-V), there was 100–200 MPa tensile stress for the reinforcement layer. At the following point (VI), 100– chip showed tensile stress of between 600 and 700 MPa for 200 MPa tensile stress remained in almost all regions of both maps, so this part also had little effect on the war- the reinforcement layer; however, in the vicinity of the LSI page. chip, tensile stress was greater than 400 MPa. At the last However, lateral to the chip, the tensile stress distribu- point (VII), there was almost zero stress in the reinforce- tion was clearly different. Along with the Cu-etching pro- ment layer while there was stress greater than 500 MPa cess, the upper parts of the lateral sides of the chip showed near the LSI chip. stronger tensile stresses while the lower parts of the lateral These results indicate that compressive stress in the LSI sides showed weaker tensile stresses. This means that the chip and/or Cu plate, caused by reinforcement layer tensile stresses on the lateral sides of the chip were shrinkage, gradually concentrated in the vicinity of the LSI released in the lower parts. This caused the chip to warp chip as the Cu plate was etched. The compressive stresses convexly on its lateral side, as shown in Fig. 18 (b). were mainly balanced by the reaction force of the thick Cu plate before point V. To discuss the directions of the stress in the chip itself and in its vicinity, as shown in Fig. 18 (b), we use Fig. 19 Figures 18 (a) and (b) shown enlarged images of the VI (a), which shows an overhead view of the ANSYS simula- and VII contour maps, with vertically enhanced deforma- tion model for the entire Structure D package after Cu- tion or warpage. Figure 18 (a) shows the contour map for plate etching. The chip and its surrounding region are a sample with a Cu plate one-third the original size, and enlarged in Fig. 19 (b) and shown as a map of the maxi- Fig. 18 (b) shows the map for a sample without a Cu plate. mum principal stress vectors for each mesh of the model. The lower side of the LSI chip showed tensile stress of The meshes in the map are located in the central region of around 600–700 MPa for both maps, meaning that this part the middle layer of the package, including the LSI chip had no effect on the warpage. The upper side of the LSI meshes. The principal stress vectors are set to be positive 54 Nakashima et al.: Warpage Mechanism of Thin Embedded LSI Packages (9/10) in tensile, and negative in compressive, just as for Figs. 16, that the stresses increased with decreasing Cu-plate thick- 17, and 18. Figure 19 (c) shows an enlarged and simplified ness, and that the warpage was caused by the release of illustration of four meshes at the near edge of the map in these tensile stresses, along with the compressive stress in Fig. 19 (b). The mesh with ‘Vector A’ is for a part of the the chip. Therefore, simple structural considerations are chip, and the other three meshes are for parts of the sur- insufficient for obtaining a reduced-warpage structure. In rounding resin-GC area. As these vectors in Fig. 19 (c) this study, when the Cu plate thickness was 100 μm or show, the resin-GC meshes have tensile stresses parallel less, we did not find a package without substantial war- to the chip side as maximum principal stresses. In con- page, which was the case with Structures D and F as well. trast, the maximum principal stress for the chip mesh is The material properties should also be considered, which compressive stress in the vertical direction (‘Vector A’). could change these balanced structures into reduced- This means that the minimum and middle principal warpage structures. One possible consideration for the stresses for the chip, which should be larger compressive material properties is the use of a resin with less tensile stresses than the maximum principal stress shown as stress in the areas lateral to the LSI chips. The resin could ‘Vector A’, are in horizontal directions. be stiffer to reduce the CTE mismatch or softer to reduce In short, these tensile stresses were caused by the the elastic modulus. shrinkage of the resin and GC surrounding the LSI chip., For the stress balance of these tensile stresses, the com- Acknowledgments pressive stresses were generated in the chip horizontally. We thank Dr. Yasunori Mochizuki, Mr. Kazuhiro Baba, Therefore, from Fig. 18 (b), we can understand that the Mr. Tomoo Murakami, Mr. Masanobu Hashimoto, and Dr. tensile stresses surrounding the chip (Figs. 19 (b) and (c)) Takashi Harada of NEC Corporation, and Dr. Hideki were partially released in the lower parts of the structure Sasaki of Renesas Electronics Corporation for their lateral to the chip after Cu-plate etching. This stress encouragement and useful feedback and suggestions. We release created substantial convex warpage in the region also thank Mr. Seiicihro Ohkawa and Ms. Keiko Kishino of surrounding the chip. Also, the compressive stresses cre- NEC Informatec Systems Ltd. for their guidance on the ated in the chip caused the entire chip to warp convexly, simulation. as shown in Fig. 18 (b). 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