Proeedings o the World Congress on Engineering 2007 Vol II Reliability Estimation o Solder Joints Under Thermal Fatigue with Varying Parameters by using FORM and MCS Ouk Sub Lee, Yeon Chang Park, and Dong Hyeok Kim Abstrat One o major reasons o ailure o solder joints is known as the thermal atigue. Also, The ailure o the solder joints under the thermal atigue loading is inluened by varying boundary onditions suh as the material o solder joint, the materials o substrates(related the dierene in CTE), the height o solder, the Distane o the solder joint rom the eutral Point (DP), the temperature variation and the dwell time. In this paper, irst, the experimental results obtained rom thermal atigue test are ompared to the outomes rom theoretial thermal atigue lie equations. Seond, the eets o varying boundary onditions on the ailure probability o the solder joint are studied by using the probabilisti methods suh as the First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS). Index Terms FORM, Failure lie,, MCS, Solder Joints I. ITRODUCTIO The soldering is the most popular joining tehnology in the eletroni industry. The suessul estimation o lietime o solder joint highly depends on the degree o aurate modeling o the stress and strain related to the strength o the solder joint. The main ause o ailure in solder joints is onsidered to be thermo-mehanial stresses, aused by dierenes in the oeiient o thermal expansion (CTE) between the hip and the substrate. Also, the pakage variables inluding the die size, the pakage size, the ball ount, the pith, the mold ompound and the substrate material aet the ailure lie o solder joints.[] However, it is not easy to onsider all o the variables. In this study, the material o solder joint, the materials o substrates, the height o solder, the Distane o the solder joint rom the eutral Point (DP), the temperature variation and the dwell time were onsidered. Furthermore, experimental results obtained rom thermal atigue tests are ompared to that rom theoretial atigue ailure lie equations. The eets o varying boundary onditions on the ailure probability o the solder joint are also studied by using the probabilisti approah methods suh as the First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS). II. FATIGUE FAILURE MODELS A generalized atigue damage law or metals has been proposed on the basis o umulative stored viso-plasti strain energy density. The yli shear atigue lie is related to Δ W in a stabilized atigue yle by the equation[2] Where atigue dutility exponent yles-to-ailure Δ W () W W interept energy term, a material onstant Δ W viso-plasti strain energy density per yle The ollowing well-known Manson-Coin plasti strain-atigue lie relationship a speial stress limited ase o this generalized atigue damage untion. Δ γ (2) Where Δ γ yli shear strain range ε atigue dutility oeiient Where, and are deined below, respetively. Submitted date: April 28, 2007. This work was supported by the Brain Korea 2 projet in 2007.. O.S. Lee is with the Shool o Mehanial Engineering, InHa University, Inheon, Korea, 402-75 (e-mail: leeos@inha.a.kr).. Y.C. Park is with the Department o Mehanial Engineering, InHa University, Inheon, Korea, 402-75 (e-mail: yeonhang_park@yahoo.o.kr). D.H. Kim is with Department o Mehanial Engineering, InHa University, Inheon, Korea, 402-75 (e-mail: kdonghyeok77@yahoo.o.kr). 0.442 2 ε 0.65 (3) 6 0 4 T m +.74 0 2 360 ln + t D (4)
Proeedings o the World Congress on Engineering 2007 Vol II Where T m mean yli solder joint temperature t D hal-yle dwell time (min) The yli strain range is given by LD Δγ F Δα ΔT (5) h Where F empirial nonideal ator indiative o deviations o real solder joints rom idealizing assumptions and aounting or seondary and requently untratable eets F.27 or olumn-like leadless solder attahments, F. 0 or solder attahments utilizing ompliant leads L D Distane o the solder joint rom the eutral Point (DP) h solder joint height, solder diameter Δ α absolute dierene in oeiients o thermal expansion o solder joint and substrate, Δ CTE Δ T yli temperature swing Thus, rom ombining (2), and (5), the yli lie o surae mount solder attahment is obtained as [2] LD Δα ΔT F (6) h reliability index using the proedure shown in Fig.[4],[5]. The MCS tehnique is used to hek the auray o the results out o the FORM. Deine Deine LSF LSF and and assume assume initial initial Value Value o o the the design design Compute Compute mean mean and and standard standard deviation deviation O O equivalent equivalent standard standard normal normal spae spae Compute Compute partial partial derivate derivate At At the the design design Compute Compute partial partial derivate derivate In In the the standard standard normal normal spae spae Compute Compute new new values values at at the the Equivalent Equivalent standard standard normal normal spae spae Compute Compute The The reliability reliability index index Compute Compute the the new new Design Design Δ β < Yes Compute Compute the the ailure ailure probability probability o Fig. Proessing o omputing the reliability index III. FAILURE PROBABILITY MODELS The ailure probability is alulated using the FORM that is one o the methods utilizing reliability index. The FORM is denoted rom the at that it is based on a irst-order Taylor series approximation o the Limit State Funtion (LSF) [3], whih is deined as: Z R L (7) Where R is the resistane normal variable, and L is the load normal variable. Assuming that R and L are statistially independent normal-distributed random variables, the variable will also be normal-distributed. The event o ailure ours, when R < L (i.e. Z < 0 ). The ailure probability is given as below. [ < 0] PF P Z 0 Z μ Z exp σ 2π 2 σ Z Z (8) 2 dz Φ( β ) Where μ Z and σ Z are the mean and standard deviation o the variable Z, respetively. And β is the reliability index. Rakwitz and Fiessler proposed a method to estimate the Set Set up up a onventional Deterministi analysis Replae onstants with with probability Distributions or or variables Generate random numbers Aording to to probability Distribution o o variables Compute the the deterministi result result and and store store the the answer answer o Simulation number Yes Compute the the mean mean and and standard deviation o o the the olleted results results Compute ailure ailure probability P [ Z < 0 ] Fig.2 Proessing o omputing the ailure probability using the MC
Proeedings o the World Congress on Engineering 2007 Vol II L D (DP) (m) Solder Material Substrate Material Δ α (ppm/ o C ) Δ T Sample Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 735 735 0.076 0.076 0.006 0.006 92 92 Sn4Ag0.5C u Sn4Ag0.5Cu Sn4Ag0.5Cu 63SnPb 63SnPb 63SnPb 63SnPb 63SnPb BT BT FR4 FR4 FR4 FR4 FR4 FR4 7.5 7.5 4.5 7.6 7.6 7.6 7.6 7.6 ( o C ) 80 00 65 65 65 65 65 65 h (m) 035 035 075 075 0508 0508 0406 0508-0.40699-0.4599-0.449-0.449-0.449-0.40774-0.449-0.449 Dwell Time(min) Failure lie o equation (yles) Failure lie o test (yles) 5 5 5 5 5 2 5 5 6 254 278 996 228 358 005 733 620 70 436 722 305 320 500 00 Table. Random variables and parameters used in the ase study Most engineering MCSs are usually perormed by using the steps shown in Fig. 2 [4]. C.O. V F L D Δ α Δ T h 4 5 0.0 4 IV. THE STADARD OF FAILURE ESTIMATIO The ailure probability o the solder joint is aeted by varying boundary onditions and the LSF inluding varying boundary onditions may be deined to estimate the inluene o boundary onditions to the ailure probability aordingly. In this paper, the modiied Manson-Coin plasti strain-atigue lie relationship is used to ormulate the LSF given as below. Z Where S LD Δα ΔT F h s speiied atigue yles. V. CASE STUDY For estimating about reliability o solder joints, results o thermal atigue test o eight samples are utilized in this study. Eah sample has dierene variables. The random variables in Table have been utilized to estimate the ailure probability o the solder joint. The standard o ailure in this study is deined as the irst ailure lie yle.[],[6],[7],[8] S (9) Table 2. C.O.V o varying boundary onditions The C.O.Vs o varying boundary ondition listed in Table 2 are taken rom some reerene. [9] The C.O.V is deined as below with the standard deviation, σ Z and the mean, μ Z. C OV σ Z.. (0) μz VI. RESULTS AD DISCUSSIOS Fig. 3 shows the relationship between the ailure probability o the solder joint and the yli temperature swing. It is onirmed that the ailure probability inreases with inrease o the yli temperature swing. Fig. 4 shows that the relationship between the ailure probability and the dierene in CTE or solder material. It is ound that the ailure probability inreases with inrease o the dierene in CTE. The reliability o lead-ree solder joint (Sn4Ag0.5Cu) is estimated better than that o lead solder joint
Proeedings o the World Congress on Engineering 2007 Vol II 0.0 550 600 800 2000 2200 umber o Cyles Sample (MCS) Sample (FORM) Sample 2 (MCS) Sample 2 (FORM) Fig.3 the relationship between the ailure probability o the solder joint and yli temperature swing 0.0 800 850 900 950 000 050 00 50 200 250 300 umber o Cyles Sample 3 (MCS) Sample 3 (FORM) Sample 4 (MCS) Sample 4 (FORM) Fig.4 Relationship between the ailure probability and solder material (dierene in CTE) 0.0 000 050 00 50 200 250 300 umber o Cyles Sample 5 (MCS) Sample 5 (FORM) Sample 6 (MCS) Sample 6 (FORM) Fig.5 Relationship between the ailure probability and dwell time 0.0 800 850 900 950 400 450 500 550 600 650 700 umber o Cyles Sample 7 (MCS) Sample 7 (FORM) Sample 8 (MCS) Sample 8 (FORM) Fig. 6 Relationship between the ailure probability and solder joint height Failure lie(yles) MCS Table 3. Dierene ratio o the ailure probabilities obtained by using the FORM and the MCS. ; dierene ratio00 (FORM-MCS)/ FORM (63SnPb). Fig. 5 shows that the relationship between the ailure probability and the dwell time. It is ound that the ailure probability inreases with inrease o the dwell time. Fig. 6 shows the relationship between the ailure probability and the solder joint height. For this ase, it is noted that the relationship obtained by using the ailure lie o equation and the one estimated rom experimental ailure lie test do not agree eah other. Sample 7 and sample 8 have same variables exept the die size and the solder ball diameter.[] We speulate the mismath in Fig. 6 the exlusion o the die size in the atigue lie equation. Table 3 shows the dierene ratio o the ailure probabilities obtained by using the FORM and the MCS. It is reognized that the results by the FORM and the MCS are almost the same. The dierene ratios are ound to be less than 2.3 %. VII. COCLUSIO FORM Dieren e rate [%] Sample 580 69 693 26 Sample 2 2050 0.05594 0.05656.0962 Sample 3 20 0.03866 0.03884 0.4634 Sample 4 930 0.035 0.0383 2.338 Sample 5 50 0.0722 0.0726 0.237 Sample 6 250 232 0.4246 0.3297 Sample 7 950 0.03433 0.3465 0.9235 Sample 8 650 0.05764 0.0579 0.449 In this paper, reliability o solder joints under varying onditions is estimated by the FORM and MCS. The FORM is utilized to extrat useul tehnial inormation in arrying out the eetive ailure ontrol. The results obtained by the FORM are veriied by omparing to those rom the MCS. The ollowing results are obtained: ) The ailure probability inreases with inreases in number o thermal atigue yles. 2) The ailure probability dereases with derease in the yli temperature swing, the dierene in CTE and dwell time. 3) It is ound that the result rom the theoretial atigue ailure lie equation has similar trend with one rom experimental test exept the ase or the dierent height o solder joint. 4) The FORM is ound to be eiient tehniques to estimate the ailure probability o the solder joint under
Proeedings o the World Congress on Engineering 2007 Vol II temperature boundary onditions. It is veriied by omparing the results out o the MCS. REFERECES [] R. Darveaux, J. Hekman, A. Syed, A. Mawer, Solder joint atigue lie o ine pith BGAs- impat o design and material hoies, Miroeletronis Reliability 40, 2000, pp. 7-27 [2] J.H.Lau, Solder Joint Reliability Theory and Appliation, Van ostrand Reinhold, 99, pp. 556-563. [3] A. Haldar, S. Mahadevan, Probability, Reliability, and Statistial Methods in Engineering Design, John Wiley & Sons, In, 2000, pp. h7 [4] O.S. Lee, S.S. Choi and D.H. Kim, Eet o Varying Boundary Conditions on the Buried Pipelines, Solid State Phenomena, Vol. 0, 2006, pp. 22~230. [5] O.S. Lee, D.H. Kim Reliability o Buried Pipeline Using FORM and Monte Carlo Simulation, Key Engineering Materials, Vol. 32-323, 2006, pp. 543-547. [6] A. Guedon-Graia, E. Woirgard, C. Zardini, Correlation between Experimental Results and FE Simulations to Evaluate Lead-Free BGA Assembly Reliability, Miroeletronis Reliability 45, 2005, pp. 652-657 [7] http://www.amkor.o.kr/ [8] J.E. Ryu, T.K. Hwang, and S.B. Lee, The inluene o mirostruture development on the thermal atigue behaviors o BGA solder joint, unpublished [9] O.S. Lee, M.J. Hur, J.S. Hawong,.H. Myoung, and D.H. Kim, Reliability Estimation o Solder Joint by Using the, Key Engineering Materials, Vol. 326-328, 2006, pp. 62-624