Directional Stiffness of Electronic Component Lead

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2 Diectional Stiffness of Electonic Component Lead Chang H. Kim Califonia State Univesit, Long Beach Depatment of Mechanical and Aeospace Engineeing 150 Bellflowe Boulevad Long Beach, CA , USA Abstact It has been nown that the lead stiffness o compliance of suface mounted electonic components is one of the e paametes in pedicting the long-tem solde joint eliabilit unde a themal cclic envionment. Thus, computing an accuate lead stiffness value is essential, especiall fo the cone lead stiffness along the diagonal diection of the component because the cone leads will epeience the most defomation. The angle measued fom the lead bod coodinate sstem to the diagonal diection of the components will be vaied depending on the component geomet, and thus, fomulation of stiffness vaiation with espect to the angle change is also highl desiable. Such off-ais stiffness is geneall nown as the diectional stiffness. An accuate closed-fom solution to compute the diectional lead stiffness of the suface mounted electonic components will be pesented hee. The solution will be based on two in-plane stiffness values along the lead bod coodinate sstem paallel to the substate. The compaison between the theoetical and computational solutions is shown to be in ecellent ageement. 1. Intoduction One of the e paametes in lead design fo suface mounted components (SMC) is the stiffness o compliance of the lead unde the themal ccling envionment. Due to the themal mismatch between the SMC and its substate, such as a pinted cicuit boad (PCB), the inteacting stess ma ise and tansmit to the weae solde joint that in tun ma fail due to fatigue. It is geneall nown that stiffe leads tend to educe the numbe of themal ccles equied to fail a solde joint, and thus, shotens the themal life epectanc of the SMC [1-9]. The effots to compute lead stiffness continued. Gee and van Kessel appoimated the stiffness of the cuved lead b using simple beam bending theo [7] while Kotlowitz et al computed the lead stiffness of vaious sizes and shapes b using classical elastic stain eneg methods [-6]. Si stiffness values pe lead end can be obtained along its bod coodinate sstem whee Lau and Hains used FEA technique to povide a full 11 stiffness mati of a lead which could elate stess esultants to the defomation field at both ends of the lead [9]. When the SMC and the PCB epand at thei own ates duing themal ccling, the cone leads undego the lagest dimensional changes since the ae at the fathest distance awa fom the geometic cente of the SMC. Since the cone leads will epeience the most defomation, the ae consideed to be the citical leads. The will defom along the diection fom the geometic cente of the SMC to the location of the cone lead position. This diection is at an angle to the lead bod coodinate sstem. Such off-ais stiffness will be called the diectional stiffness. It is impotant to compute the accuate diectional stiffness of the cone leads whee the off-ais angle depends on the geomet of the components. Substate waping duing low-fequenc tempeatue ccling is assumed to be negligible. Kotlowitz fomulated the diectional stiffness in []. Howeve, the diectional stiffness along the diagonal of a SMC was shown to have 6% deviation fom the FEA esult. The effot to upgade the diagonal stiffness accuac can be seen in [3], but simila diffeences still eisted. The pima objective is to povide an accuate fomulation to compute the diectional stiffness of the cone leads. In fact, the geneal fomulation and its concept can be applicable to man othe stuctual elements. The validit of the fomulation is tested with a given SMC lead geomet b the finite element method. It will be shown that the theoetical pediction matches ve well with the coesponding finite element solutions. 1846

3 . Diectional Lead Stiffness.1. Geneal Concept cos (3) The bod coodinate sstem fo a stuctual element such as a lead of a SMC is shown in Fig. 1 whee the and ais ae paallel to the substate, and the z-ais is defined pependicula to the substate. Out of 6 stiffness values, two stiffness values, and, ae used to compute the diectional stiffness,. The stiffness, and, epesent in-plane stiffness of the lead along the and diections, espectivel, and the diectional stiffness,, epesents the stiffness along the - diection. The main objective is to fomulate the diectional stiffness ( ) based on nown in-plane stiffness, and, and the given -diection. And, let tan()=r, tan R (4) Afte substituting δ fom (1) into (), and ewiting the equation in tem of R, sin R 1R Similal fo (3), cos 1 1R (5) (6) It is also noted that the esultant foce (F ) induced b δ in the -diection is elated to its component foces (F and F ) in the and diections. Thus, F F F whee b definition (7) (8a) F Fig. 1. Lead bod coodinate sstem at the lead end. The and -aes ae in-plane to the substate, and the z-ais is pependicula to the substate. Fom Fig. 1, the -diection is defined to be at an angle () fom the -ais. While the uppe end of the lead is held fied, the othe lead end is displaced b δ along the -diection. Then, (1) whee δ and δ ae defomations along the and diections, espectivel. The following elations can also be established fom Fig. 1, sin () F (8b) F (8c) Afte substituting (8) into (7), and then dividing b δ using the elation shown in (1), (5), and (6), can now be deived as follows, R 1R (9) The equation shown in (9) states that fo a given stuctual element, when in-plane stiffness, and, and R ae nown, the diectional stiffness can be found. It can also be deduced fom (9), the diectional stiffness is same fo and with espect to the -ais due to R tem. 1847

4 As R 0 (o the angle appoaches 0 ), becomes, and as R (o the angle appoaches 90 ), becomes. Fo R1 (o the angle appoaches 45 ), Radius (lb/in) Theo FEA Result L=0.07 Coss-Sectional Aea= Angle Angle () (φ) Radius 0.03 Fig. 3. Compaison between theoetical and FEA solution. ( =3.15 lb/in and =3.59 lb/in) Fig.. Stuctual model fo S-shaped (gullwing tpe) lead geomet A simplified S-shaped lead geomet of the gullwing tpes is shown in Fig. which will be used fo the upcoming illustations. The lead oveall height is appoimatel 0.13 and its coss-sectional aea is shown to be The simple finite element beam model was ceated whee the fied bounda condition is applied at one end of the lead, and the unit displacement is pescibed at the othe end. The lead mateial, Kova, with elastic modulus of.10 7 psi and Poisson s atio of 0.35, is chosen. Fom the FEA, the stiffness value fo the given lead geomet can be computed simpl b dividing the eaction load b the pescibed displacement in the desied diection. Fist, the in-plane stiffness values, and, of the lead must be found. The can be obtained b eithe FEA o the classical elastic stain eneg methods given in [,3]. Fo simplicit, the inplane stiffness values fo =3.15 lb/in and =3.59 lb/in ae computed. Howeve, these values ae veified to be within 0.5% diffeence between the FEA and the classical methods fom [,3]. Since the diffeence is acceptable fo this engineeing application, =3.15 lb/in and =3.59 lb/in will be used to compute. Fig. 3 plots the diectional stiffness obtained b (9) with espect to the inclined angle. Five additional FEA stiffness values ae computed at =10, 30, 45, 60, and 75. Fo compaison, the FEA esults ae also plotted in Fig. 3 which shows ecellent ageement with the theoetical pediction. The diffeence between the theo and computation solution is shown to be less than 0.016% at =45. Similal, when the computational esult at =45 is compaed to the diectional stiffness calculated b the method given in [3], it onl shows a diffeence of 0.8% at =45. Howeve, this is because both in-plane stiffness values ae compaable, =3.15 lb/in and =3.59 lb/in. Fo a lead that has dissimila in-plane stiffness values, the diffeence between the method fom [3] and computational solutions will become significant. Anothe eample can be illustated b simpl changing the coss sectional aea fom to Then, =4.7 lb/in and =8.93 lb/in ae obtained fo the lage coss sectional aea. In this case, the diectional stiffness at =45 calculated b the method shown in [3] is unde-pedicted b 13.5% when compaed to the FEA esult. A few data points ae tabulated in Table 1 fo futhe compaison. The diffeence between the FEA esults and theoetical pediction b (9) is shown to be negligible. 1848

5 TABLE I Diectional Stiffness Compaison ( =4.7 lb/in and =8.93 lb/in).. Application to Suface Mounted Component A suface mounted component (SMC) comes in man diffeent sizes and shapes. Such a tpical SMC can be seen in Fig. 4 whee the u-ais and v-ais epesent the SMC coodinate sstem o simpl the u-v coodinate sstem. Since the cone leads undego the lagest defomation, two epesentative cone leads ae shown in Fig. 4 and 5. The cone lead position 1 in Fig.4 shows that the lead bod coodinate sstem is paallel to the component coodinate sstem. The angle 1 is inclined fom the -ais and as well as fom u- ais, and tan( 1 ) can be found b its coodinate (u 1,v 1 ) measued fom the oigin of the u-v coodinate sstem. tan Angle (φ) () Diectional Stiffness (lb/in) Eq. (9) FEA Ref. [] Ref. [3] R 1 1 v 1 u1 (10) And thus, the coesponding diectional stiffness at the cone lead position 1 can be witten diectl fom (9), Fig. 4. The geomet of the cone lead at position 1. The coodinate (u 1, v 1 ) ae measued fom the oigin of the u-v coodinate sstem. Fig. 5. The geomet of the cone lead at position. The coodinate (u, v ) ae measued fom the oigin of the u-v coodinate sstem., position 1 R 1R 1 1 (11) Fig. 5 shows the location of the cone lead position with its elated geomet. The lead bod coodinate sstem at position is otated b 90 degees fom the u-ais, and the angle is shown to be inclined fom the -ais of the lead bod coodinate sstem. Similal, tan v R u (1) whee (u, v ) is the coodinate measued fom the oigin of the u-v coodinate sstem fo the cone lead position. Afte e-deiving the diectional stiffness as 1849

6 shown befoe, the diectional stiffness at the cone lead position can now be witten as follows,, position R 1R (13) The fomulation in (13) can also be deived fom (10) and (11) b simpl eplacing 1 =90 and R 1 =1/R. The definition of R 1 and R as shown in (10) and (1) ae essentiall the same, and thus, R can eplace R 1 and R fo simplicit. 3. Closing Rema The mathematical fomulation in pedicting the diectional stiffness of the stuctual element, such as electonic component leads, has been significantl impoved. An ecellent ageement was shown when compaing theoetical and computational solutions fo the diagonal stiffness values of a suface mounted component lead. 4. Refeences [1] W. Englemaie and A. I. Attawala Sufacemount attachment eliabilit of clip-leaded ceamic chip caies on FR-4 cicuit boad, IEEE Tan. Components, Hbids, and Manufactuing Technolog, vol. 1, no., June. 1989, pp [] R. W. Kotlowitz, Compaative compliance of epesentative lead designs fo suface mounted components, IEEE Tan. Components, Hbids, and Manufactuing Technolog, vol. 1, no. 4, Dec. 1989, pp [3] R. W. Kotlowitz, Compliance metics fo suface mount component lead design, Poceedings 1990 IEEE Electonic Components and Technolog Confeence, Las Vegas, NV, Ma 1-3, 1990, vol., pp [4] R. W. Kotlowitz and L. R. Talo, Compliance metics fo the inclined gull-wing, spide J-bend, and spide gull-wing lead designs fo suface mount components, IEEE Tan. Components, Hbids, and Manufactuing Technolog, vol. 14, no. 4, Dec. 1991, pp [5] R. W. Kotlowitz and G. Gosen, Compliance metics fo the genealized S-bend lead design fo suface mount components, Poceedings 199 IEEE Electonic Components and Technolog Confeence, San Diego, CA, Ma 18-0, 199, pp [6] R. W. Kotlowitz and I. M. Nevaez, Compliance metics fo the S-bend lead design fo suface mount components with application to clip-leads, Poceedings 1993 IEEE Electonic Components and Technolog Confeence, Olando, Fl, June 1-4, 1993, pp [7] S. A. Gee and C.G.M. van Kessel, Stiffness and ielding in PLCC J lead, IEEE Tan. Components, Hbids, and Manufactuing Technolog, vol. CHMT-10, no. 3, Sept. 1987, pp [8] W. E. Jahsman and P. Jain, Compaison of pedicted and measued lead stiffnesses of suface mounted pacages, Poceedings 40 th Components and Technolog confeence, 1990, pp [9] J. H. Lau and C. G. Hains, Stiffness of gullwing leads and solde joints fo a plastic quad flat pac, IEEE Tan. Components, Hbids, and Manufactuing Technolog, vol. 13, no. 1, Ma. 1990, pp