Zhu Wu Jian Lu Mem. ASME Laboratory of Mechanical Systems and Concurrent Engineering (LASMIS), Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes, France e-mail: [email protected]

Yifan Guo Mem. ASME Packaging Mechanics, Semiconductor Products Sector, Motorola, 2100 East Elliot Road, Tempe, AZ 85284

A Study of Process-Induced Residual Stress in PBGA Packages Process-induced residual stresses can play a significant role in the reliability of electronic components and packages. In this paper, a practical method is developed to determine residual stresses for electronic packaging. In this method, blind holes are drilled into the specimens and relationships are established, between the released surface displacements and the corresponding residual stress, by introducing a set of calibration coefficients. A multilayer 3D-FEM model is established to determine the relevant calibration coefficients. This methodology, which combines moire´ interferometry and the incremental hole drilling method, can provide an accurate determination of residual stresses in materials and structures by precisely controlled incremental blind-hole drilling and an accurate determination of the surface in-plane displacement fields in the hole drilling region. The methodology is implemented by investigating the residual stress in the Plastic Ball Grid Array (PBGA) packages. The tensile residual stresses are determined in both the plastic molding compound and the glass/epoxy laminate chip carrier. The method is accurate, simple, convenient, and practical. More applications, in residual stress determinations and in process evaluations in electronic packaging, are anticipated. 关S1043-7398共00兲00103-1兴

Introduction Plastic Ball Grid Array 共PBGA兲 packages are cost-effective surface mounting packages with a high density interconnection, low profiles, and lightweight. They are currently used in many electronic products including portable telecommunication and computing products 共Freyman 关1兴, Lau 关2兴兲. A typical structure in a PBGA package consists of four layers: plastic molding compound, a silicon chip, a chip attach adhesive layer, and an organic chip-carrier. Due to the coefficient of thermal expansion 共CTE兲 mismatch between the silicon chip, the plastic compound and the organic chip carrier, considerable residual stresses are developed in the package during the assembly process. The residual stresses can impact the package reliability in many aspects. They can cause cracks in the molding compound and the chip and delaminations at the interface 共Wu 关3兴, Lau 关2兴兲. They can also cause planarity and dimension stability problems in package assembly processes 共Guo 关4兴兲. Recently, theoretical analyses and numerical simulations were used in predictions of thermal residual stresses 共Jung 关5兴, Lau 关6兴兲. However, the residual stresses induced in an electronic package are highly dependent of the assembly process which varies significantly for different packages. Therefore, it is difficult for the theoretical or numerical analyses to predict accurate residual stress values in the packages. There is a need for an effective experimental method which can determine the process induced residual stresses for the purpose of both understanding the phenomena and verifying the theoretical and numerical results. As moire´ interferometry features high sensitivity, whole field observation, and real-time measurement, it was recently applied to the residual stress investigations on PBGA packages 共Dai 关7兴, Guo 关8兴, Guo关9兴兲. In these studies, cross sections of PBGA specimens were prepared; the specimen grating was replicated at an elevated temperature; the thermal strains in the plastic layer, the silicon chip, the chip carrier, the solder joints and the PCB board were obtained from moire´ fringe patterns by in-situ observations when the temperature was maintained at constant levels Contributed by the Electrical and Electronic Packaging Division for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received by the EEPD April 20, 1999; revised manuscript received December 8, 1999. Associate Technical Editor: J. Lau.

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inside an oven. As the techniques for specimen grating replication under high temperatures was relatively sophisticated, some uncertainties may have emerged in the process. The above method requires a cross section of the specimens, which changes the stress state significantly. Moreover, the results on cross-sections will not represent the stresses inside the packages. Consequently, it is difficult to establish the qualitative relationship between the residual stresses and the thermal deformations 共Guo 关9兴, Zhu 关10兴兲. The traditional strain gage hole drilling method has been widely applied in residual stress measurement for many engineering materials 共Lu 关11兴兲. However, the size of a standard strain rosette is too large to be adopted for most electronic packages including PBGA packages. X-ray diffraction method and neutron diffraction method which were widely used for multi-crystal materials are also unsuitable for the plastic compound and the PCB board in a PBGA package. A newly-developed technique, combining moire´ interferometry and incremental hole drilling device, has sufficient accuracy for many residual stress problems 共Wu 关12,13兴兲. The moire´ fringe patterns of U x and U y displacement fields due to the relaxation of residual stresses were generally localized in a small region around the hole and featured high signal-to-noise ratio even in the regions very close to hole boundary, hence, it is a suitable means for determining residual stresses in electronic packages.

Relationship Between Displacement and Residual Stress When residual stresses exist in a single homogeneous material, a blind hole solution was proposed by Schajer 关14兴. The solution which was applied in the holographic interferometry hole-drilling method 共Nelson 关15兴, Makino 关16兴兲 can be expressed as u r 共 r, ␪ 兲 ⫽A 共 ␴ xx ⫹ ␴ y y 兲 ⫹B 关共 ␴ xx ⫺ ␴ y y 兲 cos 2 ␪ ⫹2 ␶ xy sin 2 ␪ 兴 (1) where, A, B are calibration coefficients; u r (r, ␪ ) is surface radial displacement in the cylindrical coordinate system; ␴ xx , ␴ y y , and ␶ xy are in-plane residual stress components in the Cartesian coordinate system. In moire´ interferometry 共Post 关17兴兲, the surface in-plane displacement fields U x and U y can be expressed as

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U x⫽

1 N 2f x

U y⫽

Table 1 Material properties for the PBGA electronic packages

1 N 2f y

(2)

where N x and N y are fringe orders in U x and U y fields, respectively. In routine practice, a frequency of 1200 lines/mm is used, providing a contour interval of 0.417 ␮m/fringe order. The in-plane radial displacements U r can be calculated from U x and U y . For in-plane biaxial residual stress problems, by combining Eq. 共1兲 and 共2兲, the relationship between the fringe orders of U x and U y displacement fields and the corresponding residual stresses can be expressed as 关 N ix 共 x k ,y k 兲

N iy 共 x k ,y k 兲兴

A ⫺B cos 2 ␪ k ij

ij

冋 册

i

cos␪ k ⫽ 2 f 关 A i j ⫹B i j cos 2 ␪ k sin␪ k j⫽1

兺

冋册

␴ ixx i 2B sin 2 ␪ k ] ␴ y y , i ␶ xy ij

k⫽1,2,3;

i⫽1,2, . . . ,n

(3) ij

ij

where, n is the total number of incremental steps; A , B are the calibration coefficients of the jth layer after the ith incremental step has been drilled; N ix (x k ,y k ) and N iy (x k ,y k ) are the total fringe numbers of U x -field and U y -field obtained from moire´ interferometry, respectively, after the ith incremental step has been drilled; f s is the frequency of the specimen grating; ␴ ixx , ␴ iy y , j and ␶ xy are the residual stress components of the previous and the current layers, respectively. In Eq. 共3兲, the calibration coefficients A i j , B i j were determined by 3-D FEM analysis, in which two specific residual stress fields were used: 共1兲 ␴ xx ⫽ ␴ ; ␴ y y ⫽ ␶ xy ⫽0, an uniaxial residual stress field, which is equivalent to the harmonic distributions of the normal stress ␴ rr ⫽⫺ ␴ cos2␪ and the shearing stress ␶ r ␪ ⫽ ␴ /2 sin 2 ␪ acting on the hole side surface; 共2兲 ␴ y y ⫽ ␴ , ␴ xx ⫽ ␶ xy ⫽0, another uniaxial residual stress field, which is equivalent to the harmonic distributions of the normal stress ␴ rr ⫽ ⫺ ␴ sin2␪ and the shearing stress ␶ r ␪ ⫽⫺ ␴ /2 sin2 ␪ acting on the hole side surface.

Application in PBGA Packages For isotropic and homogeneous materials, the calibration coefficients A i j , B i j in Eq. 共3兲, which are determined by threedimensional finite element method using two specific loading cases, are generally believed suitable for any in-plane uniform residual stress fields. However, since a PBGA package structure consists of four layers of different materials, it needs to be proved whether this coefficient-calibration-method is still valid in the analysis of the PBGA structure. The cross-sectional dimensions of the PBGA sample are drawn in Fig. 1. The material properties are given in Table 1. The chip carrier is made of glass/epoxy laminate with cross plies, which can be treated as in-plane isotropic material. A blind hole with a diameter of 2.0 mm was used. In the analysis, a three dimensional finite element model was established as shown in Fig. 2共a兲. The

Fig. 1 A cross section of the plastic ball grid array packaging

Journal of Electronic Packaging

FEM model has a fixed boundary condition only at the far-ends, so that the boundary effect can be ignored. The above-mentioned two specific loading cases were applied to simulate the relaxation of residual stresses when a blind-hole was drilled. The commercial FEM-code, ABAQUS 5.6 was used in the analysis. The results of deformed shape, the surface strain and displacement fields are shown in Fig. 2共b–d兲, respectively. The calibration coefficients at the points (1.2r 0 , ␪ ) for the single step hole-drilling solution in Eq. 共3兲 were determined as: A⫽1.682 ⫻10⫺5 mm3/N; B⫽1.871⫻10⫺5 mm3/N. Thus, Eq. 共3兲 can be rewritten as: u r 共 r, ␪ 兲 ⫽1.682⫻10⫺5 共 ␴ xx ⫹ ␴ y y 兲 ⫹1.871⫻10⫺5 关共 ␴ xx ⫺ ␴ y y 兲 cos2 ␪ ⫹2 ␶ xy sin 2 ␪ 兴 (4) Considering an arbitrary residual stress field: ␴ xx ⫽100 MPa, ␴ y y ⫽40 MPa, ␶ xy ⫽⫺60 MPa, Eq. 共4兲 can be further expressed as: u r 共 r, ␪ 兲 ⫽2.3548⫻10⫺3 ⫹1.1226⫻10⫺3 cos 2 ␪ ⫺2.2452⫻10⫺3 sin 2 ␪

(4a)

The distribution of u r along the hole boundary against angle ␪ of 0 to 2␲ is plotted in Fig. 3. On the other hand, by using the coordinate transformation, the arbitrary residual stress field: ␴ xx ⫽100 MPa, ␴ y y ⫽40 MPa, ␶ xy ⫽⫺60 MPa can be also expressed with a cylindrical coordinate as:

␴ r 共 ␪ 兲 ⫽70⫹30 cos 2 ␪ ⫺60 sin 2 ␪ ␴ ␪ 共 ␪ 兲 ⫽70⫺30 cos 2 ␪ ⫹60 sin 2 ␪

(5)

␶ r ␪ ⫽⫺30 sin 2 ␪ ⫺60 cos 2 ␪

Fig. 2 Three-dimensional finite element to determine the calibration coefficients for PBGA packages by using equibiaxial stress field. „a… A 3-D finite element model, „b… deformed shape, „c… surface strain field ⑀ 11 , „d… surface displacement field, u 1 .

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orders, consequently, the maximum possible error in residual stress determination is 0.6193 MPa. Therefore, the method has sufficient accuracy in residual stress analysis for electronic packaging.

Test Specimens

Fig. 3 Distributions of surface radial displacements on the circle r Ä1.2r 0 , for an assumed arbitrary uniform residual stress field calculated by using two methods: the coefficientcalibration method and the direct FEM method

To simulate the relaxation of the residual stress for this arbitrary residual stress field, the normal nodal force P i , calculated from ␴ r in Eq. 共5兲 and the shearing nodal force T i , calculated from ␶ r ␪ in Eq. 共5兲 were applied at the surface of the hole, respectively. The established FEM model for determining calibration coefficients was used again only with the different loading cases. The surface radial displacement u r was then determined and the distribution of u r along the circumferential direction is also plotted in Fig. 3. It is obvious that the displacements u r calculated from two methods coincide very well. This indicates that the residual stressdisplacement relationship established by Eq. 共3兲 is applicable to PBGA packages and other multilayer structures when the corresponding calibration coefficients are determined.

Accuracy Analysis There are two main error sources in the method. 共1兲 Errors from the coefficient-calibration process due to the inaccuracy of material properties and geometrical parameters. As an example, when the Young’s modulus used in the FEM model is 10 percent smaller than the real one, the residual stress calculated by Eq. 共3兲 will be also 10 percent smaller than the real residual stress value. The dimensions of a specimen can often be measured accurately. However, errors may occur in hole diameter and hole depth, which highly depend on the incremental hole-drilling system and will have significant effect on residual stress determination. The combined system used in the experiment has been proved very accurate for incremental hole-drillings. 共2兲 Errors due to fringe order counting at the coefficient-calibration points. Although in moire´ interferometry, a half fringe order can be readily determined, this is not sufficient for accurate determination of residual stresses when residual stress levels are relatively low or holedrilling increments are relatively small. Thus, displacements at the calibration points may be smaller than a whole fringe order and would not coincide with the locations of integer or half fringe orders. Moire´ interferometry features high signal-to-noise ratio. With the aid of intensity distribution analysis or phase-shifting technique for images captured by a high resolution CCD camera, 0.1 fractional fringe orders can be resolved. Consequently, the maximum possible error in fringe order determination would be ⫾0.05 fringe orders, which corresponds to ⫾0.02 ␮m in displacement measurement. As an example, assuming an equibiaxial residual stress field in the plastic layer of the PBGA package which was used in the previous coefficient-calibration analysis, the residual stress can then be expressed by Eq. 共3兲 as:

␴ a⫽

Nx 4 f sA

(6)

Assuming a specimen grating f s ⫽1200 lines/mm and the maximum possible error in fringe order determination is 0.05 fringe 264 Õ Vol. 122, SEPTEMBER 2000

Two types of PBGA packages were studied in the experiments. The samples were named A and B. Apart from the size difference of the silicon chips, the outline dimension and the manufacturing process were similar. The cross-sectional drawing is shown in Fig. 1. The dimensions of silicon chip for package A were: 8 mm in length, 6 mm in width and 0.38 mm in thickness; and for package B were: 15 mm in length, 8 mm in width, and 0.38 mm in thickness. The silicon chip was attached to the chip carrier by a layer of epoxy adhesive. The chip carrier was made of glass/epoxy laminate with cross piles. The chip was molded by the plastic compound at a high temperature. The material properties of the PBGA packages have been given in Table 1. The purpose of the experiments is to determine the residual stresses developed during the assembly process.

Experimental Procedure The newly-developed system, combining moire´ interferometry and incremental hole-drilling device 共Wu 关3兴兲, was implemented in determining 共1兲 the average residual stress in the plastic layer for the packages A and B, and 共2兲 the average residual stress in the chip carrier of package B. In order to replicate specimen gratings, the convex solder balls on the bottom surface of the package B were polished. However, the top surface of the packages was only polished slightly so that no residual stress can be released. Specimen gratings with a frequency of 1200 lines/mm were replicated at room temperature on the top surface of the package A and on both the top and the bottom surfaces of package B, respectively. The directions of the grating lines were set to coincide with the outlines of the specimens. After the specimen grating was replicated, the sample was adhered slightly onto a flat metal plate so that the mounting of the specimen did not induce any deformation. The metal plate was in turn mounted tightly onto the fixing plate in the hole-drilling device. The optical system was preadjusted to produce an initial null field condition, which was devoid of fringes. The drilling machine subassembly was locked into the U-shaped base and the XY translation stage was adjusted to locate the drill bit at the center of the package. The diameter of the drill bit used in the experiment was 2 mm. The drilling process

Fig. 4 U x and U y fringe patterns obtained from the PBGA packages A and B, when a blind hole was drilled throughout the plastic molding compound; hole radius, r 0 Ä1.0 mm and hole depth, h Ä0.4 mm

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Fig. 5 U x and U y fringe patterns obtained from the PBGA package B, when a blind hole was drilled by two steps hole drilling with identical increment throughout the chip carrier; hole radius, r 0 Ä1.0 mm and hole drilling increment, ⌬ h Ä0.3 mm

was controlled accurately by a computer program. Only a single step of hole drilling throughout the plastic layer was performed for packages A and B on the plastic side, whereas, two steps of hole-drilling with an identical increment of 0.3 mm were performed on the chip carrier side, also as shown in Fig. 1. The drilling machine subassembly was then removed and the U x displacement field in the region around the hole was recorded by moire´ interferometry. The experiment continued, the specimen being rotated by 90 deg and the corresponding U y displacement field was obtained. For the second step hole-drilling on the chip carrier side, the specimen was repositioned precisely to its original U x field. The drill bit re-entered the hole and the fringe recording process was repeated. The U x and U y field moire´ fringes patterns obtained from the plastic side of the packages A and B, and from the chip carrier side of the package B are shown in Fig. 4 and Fig. 5, respectively, where a contour interval was 0.417 ␮m per fringe order.

Fig. 6 Magnified view of U x fringe pattern of the PBGA package B

Fig. 7 Average values of residual stresses in the plastic molding compound of the PBGA packages A and B

Analysis and Results The plastic compound can be treated as an isotropic and homogeneous material in a macro scale. Following to the analysis in the previous section, Eq. 共3兲 was used to determine residual stress in the plastic layers. As moire´ interferometry provided the continuous displacement fields in the hole-drilling region, fringe orders of three points, used in Eq. 共3兲, can be chosen relatively arbitrary. In order to improve the fringe counting accuracy and to simplify coefficients calibrating process, points on a concentric circle of the hole with a radius of 1.2r 0 were suggested. Moreover, in order to minimize the condition number of Eq. 共3兲, some characteristic points: (1.2r 0 , 45°兲, (1.2r 0 , 0°兲 and (1.2r 0 , ⫺45°兲; (1.2r 0 , 0°兲, (1.2r 0 , 45°兲 and (1.2r 0 , 90°兲; (1.2r 0 , 135°兲, (1.2r 0 , 180°兲 and (1.2r 0 , 225°兲; (1.2r 0 , 90°兲, (1.2r 0 , 135°兲 and (1.2r 0 , 180°兲 . . . were routinely chosen in the analyses. In this experiment, with the aid of intensity distribution analysis, the fringe orders at the three points (1.2r 0 , 0°兲, (1.2r 0 , 45°兲 and (1.2r 0 , 90°兲 were counted accurately as shown in Fig. 6. The average levels of residual stresses throughout the plastic layer for packages A and B were determined and plotted in Fig. 7. It is evident that: 共1兲 the shearing residual stresses in the plastic layers were very small and thus the normal residual stresses ␴ xx and ␴ y y can be regarded as principal stresses; 共2兲 the normal residual stresses in the plastic layers are tensile stress; 共3兲 as the Journal of Electronic Packaging

Fig. 8 Average values of residual stresses in the chip carrier of the PBGA package B

chip size in package B was larger than that in package A, the average level of tensile residual stresses in package B was 1.5 times larger than with package A. Due to the local nonuniformity in the glass/epoxy chip carrier, the irregular fringes were found in the regions very close to the hole boundary, as shown in Fig. 5. However, the effect of the local non-uniform residual stresses attenuates very fast and the regular displacement contours were found in the regions r ⬎1.4r 0 , where the displacement fields represented the relaxation SEPTEMBER 2000, Vol. 122 Õ 265

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of the average residual stresses. Therefore, in this experiment, the calibration points were chosen on the concentric circle, r ⫽1.5r 0 , of the hole, where Eq. 共3兲 is used for the average residual stress determination. By using the same fringe counting procedure as presented above, the residual stresses in the chip carrier were determined as shown in Fig. 8. It can be seen that: 共1兲 the shearing residual stresses in the chip carrier were also very small and thus the normal residual stresses ␴ xx and ␴ y y can be regarded as principal stresses; 共2兲 the residual stresses in the chip carrier were tensile stresses.

Conclusions In this study, a new experimental methodology was developed. This method provided a practical way for experimental determination of residual stresses in electronic packages. The accuracy of the method has been proved sufficient for electronic packaging applications even in the packages which have relatively low residual stress levels. In the two PBGA packages studied, as the chip size of package A was smaller than that of package B, a tensile residual stress of 13.0 MPa was found in the plastic molding layer of package A and 19.0 MPa in package B. The tensile residual stress in the chip carrier layer is 12.0 MPa for the first 0.3 mm layer and 18.0 MPa for the second 0.3 mm layer. This advanced technique can be applied to many residual stress problems for different types of electronic packages. The method is also anticipated in studding the residual stress variations with temperatures or after certain thermal cycles.

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关11兴 关12兴 关13兴 关14兴 关15兴 关16兴 关17兴

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