6b-O,/- In large-scale integrated circuits, the interface between ceramic. modules and epoxy-glass circuit cards contains a large number of pin

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1 6b-O,/- Computer Microchip Interconnections T. W.Wu and J. T. Oden The University of Texas at Austin 1. Introduction In large-scale integrated circuits, the interface between ceramic modules and epoxy-glass circuit cards contains a large number of pin arrays. Usually one end of each pin is brazed to the module; the other end' of the pin is inserted into a plated through-hole in the card and then wave-soldered in place, as indicated in Fig. 1. Since the modules and the card are usually quite rigid, the interface. between the module and the card is commonly the weakest region in the module-card assembly system. A finite element study of the stress analysis in the card-pin-module system has recently been given by Kelly et al (1984 [1D. In their work, mechanical loadings in the actual processing steps and the thermal loading due to a uniform temperature drop were considered. In addition to the uniform temperature drop, the transient behavior in if. a real soldering process should draw equal attention as well. When a pin, is heated up rapidly, it may have no time to reach a steady state. In that case, a steady state solution may lead to an over stiff design. Also, some

2 ... local stress concentrations may be observed during the transient interval even if a steady state can be reached. All these phenomenashould be taken into account in designing the pin connections, The major thrust of this work is to analyze the transient behavior in the real soldering process by using finite element methods. All the materials are assumed to be isotropic and linearly elastic. Deformations are assumed to be infinitesimal. Although the card-pin-module system is actually a three-dimensional object, attention is focuse<j on an isolated pin, which can be represented by a body of revolution. ' Two results have been obtained by using the TEXVISC (1985[2]) computer program. The first one is the transient thermal stresses induced by the soldering process; the second one is the residual stresses due to a uniform temperature drop. It is hoped that such results will shed some light on the optimization of pin connection design. 2. Governing Equat ions The governing differential equation of heat conduction is at c - - \J. (k\j T ) ( 1) at where Ttemperature ttime cheat capacity kheat conductivity The boundary conditions can be a combination of the following three types: (0 Temperature: TT0

3 , at (j i) Flux:-k:'- - Cb an ȧt (iii) Radiation:-k-- an h (T-To) Equation (1) can be reformulated into a weak form and a semi-discritization finite element scheme can be used. After the heat conduction problem is solved, a therm~l stress analysis at any time step can be attempted. The equilibrium equation is CTij~ + fj - 0 (2) where CTjj f j stress tensor body force The stress-strain relationship for an isotropic linearly elastic material is ij ) E 1) CTiJ - ECTkk 6iJ + Q- l:::.t 6iJ (3) where 9J strain tensor E Young'smodulus 1) Poisson's ratio Q- coefficient of thermal expassion l:::.t temperature increment In the infinitesimal theory, strains are related to displacements by ~.. - (I L. + U.. ) /2 (4) ~J Vj,J JJ Equations (2), (3), and (4) can be combined together to form the governing differential equation in thermal elasticity. Like the heat conduction problem, the boundary conditions fall into three categories:

4 (I) Displacement: U. -.Uoi (ii) Traction' CT, n -t o. IJ J I (iii) Mixed' CT.. n - k (U _I L.). U J I ~I The governing differential equation formed by (2), (3), and (4) can be reformulated into a weak form and then the standard finite element technique can be applied. 3. Numerical Results Case 1: Soldering Process A pin-braze-module unit is cut out of a piece of module. The pin is then heated up. We assume the problem is axisymmetric and there is no flux across the far-field module boundary. A flux boundary condition is prescribed on the soldering boundary, while radiation boundary cond1tions are prescribed on all the free surfaces. For stress analysis purposes, we assume a fixed condition on the soldering boundary and a roller condition on the far-field module boundary. The finite element mesh can be shown in Fig. 2 and the material constants are given in Table 1. Ten time steps between to and t10 sec. were used to integrate the time derivative. The results are given in Figs. :3 to 7. Figure:3 is the temperature contours in the pin at t 10 sec. We can see that the temperature diminishes away from the soldering zone. Figure 4 contains the temperature profiles at three different times along the center line of the pin. The temperature goes up rapidly as expected. The deformed configuration can be shown in Fig. 5; Figures 6 and 7 give the equivalent

5 stress contours at tlo sec. i~ the pin and braze joint, respectively. The most highly stressed region is found to be around the soldering zone, where a fixed boundary condition is prescribed. Case 2: Uniform Temperature Drop After the pin is soldered to the card, the temperature will drop slowly. We assume a uniform temperature drop throughout the module-pin-card unit. Furthermore, a fixed condition on the far-field card boundary and a roller condition on the far-field module boundary are also assumed. The finite element mesh can be shown in Fig. 8 and the material constants are given in Table 2. No transient analysis is needed in this case because the temperature wi 11eventually drop to the environmental temperature. The results are given in Figs. 9 to 12. Figure 9 shows the deformed configuration after the temperature drop. 'The equivalent stress contours in the pin, solder, and braze joint are given in Fig. 10, Fig. 11, and Fig. 12, respectively. The most stressed region is found in the braze joint.

6 References [1) Kelly, J. H., Lim, C. K., and Chen, W. T., "Optimization of Interconnections between Packaging Levels," IBM J. Res. Develop., Vol. 28, No.6, 1984, pp [2] Collingwood, G. A, Ratte, A M., Becker, E. B., and Miller, T., "User's Manual for the TEXVISC Computer Program," BMDATC, U A, 1985.

7 Table 1 Material constants used in case 1 c (J/m 3 k) k (W/mk) E (Gpa) 1) Q- ( 11k) Pin 3.0X Xl0-6 Braze 4.0X X 10-7 MLC 1.OX X10-6 Table 2 Mater1al constants used in case 2 E (Gpa) 1) Q- (1 /k) Pin X10-6 Braze OX10-7 MLC X10-6 Solder OX10-7 Card X 10-6

8 a. //,/ card..,// // b. - 1 braze joint card Fig. 1 a. Module-p;n-card b. An isolated unit assembly

9 '"....., '" '" I... I.. I... I.. N.. N.. N.. N ~ I I I ~ ~ BeUNDARY CBNDITISNS 12 UR I! 31 FIX.: I!. I! Fig. 2 Finite element mesh for case 1

10 AUT0MATIC CBNTBURING INCREMENT.1000E~Ql SYH o ED m LEVEL.4900E E E E E+02 mi.3400e e e+02 Fig. 3 Temperature contour at t 10"

11 U) _ - d d r- -I- NON LULUlU 000 0_0 0('/")0 -(0_... - ('I") _ d II) U) 0 d U) d II) II) o Q S - - d d II) ḇ "0 6 IT t C» - C' - U) -.. d c::: II) ra -:z ls.1 1"1 d I- ~ d.. U a: 0 ls.1 d -.J 0 II) 0 -.J 0 '" II a: d X ra a: rn Q.l L- a. Q.l L- :J... ra L- Q.l a. E Q.l l- ('I") - V en ū X dw:31

12 I I I - - Fig. 5 Deformed configuration at t 10"

13 AUTIHATIC CINTIURING INCREHENT.2000E+02 SYH. LEVEL.2S00E+03 o. 1900E+03 $. 1300E+03 Ell.7000E E+02 un1t: N/mm 2 Fig. 6 Stress contours in the pin at t 10"

14 AUT0HATIC C0NT0URING INCREHENT.3GOOE+Ol SYH o o LEVEL.2000E+02.llOGE+02 unit: N/mm 2 Fig. 7 Stress contours in the braze joint at t-1 0"

15 Ṇ.. Ṇ.. I, N j Ṇ..,,I Ṇ..,I Ṇ. ~ ~,, I I I 12 UR 31 FIX. I I l-. I ::. I N... N... I IN I ". : Fig. 8 Finite element mesh for case 2

16 I I I r- -,... - fig. 9 Deformed configuration

17 AUTI"ATIC CINTIURING INCRE"ENT.7000E-02 SYH LEVEL (4 F0'.S70DE-Ol o.i60de-dl $.2S0DE-Ol B ioooe-02 UI oj :::2.., lit... UI a I... Q ~.. oj :. VI Col.: VI Q VI. c > )C : II. ~ ~.:.: VI.:.:.:::I cr: -... ~.. u.: z a I.: ::I Col \ Fig. 10 Stress Contours in the Pin

18 AUT6HATIC CONTOURING INCREHENT :.1000E+Ol SYH LEVEL o.4200e+02 o.3900e+02 $.3600E+02 m.3300e+02 ~.3000E+02 mi.2700e+02 unit: N/mm 2 Fig. 11 Stress contours in the solder

19 AUT0HRTJC C0NT0URING INCREMENT.2000E~02 SYH o o LEVEL.11 OOE~ E~02 unit: N/mm 2 Fig. 12 Stress contours in the braze joint

Using MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup,

Using MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup, Introduction to Finite Element Analysis Using MATLAB and Abaqus Amar Khennane Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business