A Second-Level SAC Solder-Joint Fatigue-Life ... - IEEE Xplore

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IEEE TRANSACTIONS ON DEVICE AND MATERIALS RELIABILITY, VOL. 8, NO. 1, MARCH 2008

A Second-Level SAC Solder-Joint Fatigue-Life Prediction Methodology Walter Dauksher

Abstract—An acceleration model is developed for relating existing second-level fatigue-life data of tin–silver–copper solder joints to untested environments. The acceleration model retains the familiar canonical form of the Norris–Landzberg equation. Model parameters are obtained through calibration with an extensive set of published empirical data. The model will find use in making rapid assessments of a product’s potential solder-joint field life based on accelerated product tests.

life will require both a mapping of accelerated test results to use conditions and a means to define (for example, through choices in the thermal and power management solutions) an acceptable set of product use conditions. This paper proposes an acceleration model for the lead-free solder alloy with the nominal composition 95.5Sn−3.8Ag−0.7Cu, which is henceforth referred to as the SAC alloy.

Index Terms—Fatigue, lead-free, reliability, solder.

II. B ACKGROUND OF THE NL E QUATIONS I. I NTRODUCTION

S

OLDER-JOINT reliability is often assessed under accelerated environmental conditions. With the goal of producing solder-joint fatigue failures within months of testing, thermal fatigue subjects board-mounted parts to extreme temperature changes at frequencies in excess of those seen by products. As an example, testing may cycle the mounted parts between 0 ◦ C and 100 ◦ C more than 30 times per day, whereas in service, the product may be thermally cycled once per day between room temperature and 60 ◦ C. For leaded solders, the most common acceleration model for relating the environmental test results to the product environment is the Norris–Landzberg (NL) [1] equation 1.9 1/3 ∆T1 1414 f2 1414 N2 = exp MAX − MAX (1) AF = N1 ∆T2 f1 T2 T1 where AF is the acceleration factor, N is the number of cycles to a specified cumulative failure, ∆T is the range of temperature change, f is the thermal cycling frequency, and T MAX is the maximum temperature in an environment. The subscripts 1 and 2 indicate separate environments. Typically, environment 1 may be the accelerated test environment, and environment 2 is the product service environment. The NL equation appears in several forms in the literature with most differences among forms seen in the maximum temperature term. As the microelectronics industry transitions to lead-free solders, an understanding of the acceleration factor between the accelerated tests and solder-joint fatigue failure in the field will be necessary. Manufacturers of electronic assemblies need a field reliability that surpasses warranty requirements and customer expectations. Achieving adequate solder-joint field

Manuscript received August 20, 2007. The author is with Avago Technologies, Fort Collins, CO 80525 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TDMR.2007.912253

The Coffin–Manson formulation [2], [3] predicted that the fatigue life of certain structural steel and nickel alloys was directly related to the plastic strain amplitude through N = C(∆εP )−α

(2)

where ∆εP is the plastic strain range, and α and C are parameters. Goldman [4] proposed the substitution of the temperature range ∆T for the plastic strain range ∆εP and demonstrated a correlation between the predictions of the modified Coffin–Manson equation using an exponent of 1.9 and the test results on high-lead solder joints. Norris and Landzberg [1] subsequently modified Goldman’s equation with two additional terms to account for the time and temperature dependence seen in Pb–Sn solder fatigue. The first corrective term was derived from the frequency-dependent fatigue lives of acid lead (at 43 ◦ C) and lead–antimony (at 30 ◦ C) as determined over cyclic frequencies between approximately 0.005 and 7 cycles per minute. The frequency effects were shown to obey a power law with an exponent of 1/3. The second corrective term, which is the exponential term in the NL equation, was added to reflect an expected decrease in fatigue life as the temperature increases. This term was based on the fatigue life of 95Pb5Sn measured between −50 ◦ C and 150 ◦ C at 1800 cycles per minute and 0.03% strain. Note that in addition to the NL equation, other refinements of the Coffin–Manson equation have been developed for the leaded solders. Notably, simple modifications for the frequency dependence [5] and the temperature dependence of the exponent [6], [7] have been proposed. While these formulations may also be valid starting points for a SAC alloy fatigue model, they are not the focus of this paper. The empirically based NL equation lacks a rigorous fracture mechanics and a material property foundation. Nevertheless, the NL equation, due to its inherent simplicity, is commonly used for quick estimates of the solder-joint fatigue life under a new set of use conditions or as projected from the accelerated test results. For product projections based on accelerated fatigue

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DAUKSHER: SECOND-LEVEL SAC SOLDER-JOINT FATIGUE-LIFE PREDICTION METHODOLOGY

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tests, a factor of safety (FS) from 1.5 to 2 is commonly used to derate the field life. III. A PPROACH At the time of this writing, there is a significant body of experimental data detailing accelerated part-on-board solder-joint fatigue test results. In particular, some of these data [8]–[23] examine the contributions of one or more of the environmental effects, specifically temperature range, cyclic frequency, and maximum temperature, which are the terms of the NL equation. The approach taken is to presume that the acceleration model for the SAC alloy follows the canonical form of the NL equation. The SAC acceleration model is obtained through a fitting of the experimental data to the form of the NL equation AF =

N2 = N1

∆T1 ∆T2

M

hot N

t1 thot 2

exp

Q Q − MAX T2MAX T1

Fig. 1. Response for ε = 0.001 T /100 for 0 ◦ C ≤ T ≤ 100 ◦ C.

(3)

where a solution is sought for the activation energy Q and the exponents M and N that fit the experimental data. Following Pan et al. [12], the frequency terms of the NL equation have been replaced with the thot terms which account for the time per cycle that the component is hot. By noting that frequency is inversely proportional to the period, hence cycle time, the substitution of time for frequency is consistent with the traditional NL equation form. Under the presumptions that the temporal aspect of creep damage is captured in the time term and that creep occurs only at higher temperatures, the thot terms include only the ramp-to-hot and hot dwell times per cycle. Finally, the use of the thot term, as discussed, produced a superior fit to the test data when compared with a traditional frequency term. A. Evaluation of the Time Term The frequency term in the NL equation accounts for the temporal dependence of creep fatigue damage. It is generally recognized that longer dwell times impart greater creep damage than shorter dwell times and result in a smaller number of cycles prior to fatigue failure. Creep damage is also known to saturate over suitably long time periods due to stress relaxation. Generally, this creep saturation is not realized during the accelerated testing but may be common in field use with power on/off cycles on the order of days or more. As a result of the saturation of creep damage, the direct use of the NL equation may lead to conservative estimates. Work performed at Hewlett-Packard [24] demonstrated that these saturation effects in leaded solders were appropriately represented with a saturation frequency from 4 to 6 cycles per day. The current industry practice with lead solders is to use the greater of the cyclic frequency or 6 cycles per day for each frequency term (e.g., the frequency used for a product that experiences 1 temperature cycle per day would be 6 cycles per day). The saturation frequency was developed, in part, with load relaxation experiments performed on CBGA, PBGA, and TSOP packages.

Fig. 2. Select normalized creep-strain energies.

As for the lead-solder NL equation, a maximum value of thot , representing a saturated creep response, must be used with the lead-free NL equation. This value is designated as thot− max and is evaluated through an examination of the creep of SAC solder within the range of temperatures and strains experienced by board-mounted components. The steady-state creep of the SAC alloy may be represented by the Garafalo–Arrhenius equation ∆ε = A [sinh(κσ)]p exp ∆t

−q kT

(4)

where A is 500 000 s−1 , κ is 10−9 Pa−1 , σ is in Pascals, p is five, q is 0.5 eV, k is Boltzmann’s constant, and T is in ◦ K [25]. By understanding that the solder-joint loading is principally fixed displacement, the creep response of a uniaxial member with a temperature-dependent displacement-based end strain provides a basis for examining the creep response. By noting that σ = Eε, ε = εO − εCR and that ∆εCR ≈ (∂ε/∂t)∆T , where E is Young’s modulus, εO is the initial elastic strain due to the imposed displacement, εCR is the creep strain, and ∆T is a time increment, the creep equation is numerically integrated through time. Morrow [26] has proposed that fatigue life is inversely proportional to the accumulated inelastic work. The accumulated creep-strain energy density W CR = σ∂eCR is

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TABLE I TEST DATA

determined from the numerical solution as W CR = Σσ · eCR and taken as the metric for the deleterious effects of time and creep damage. Fig. 1 shows the calculated response of a SAC bar subject to a thermally imposed strain. The bar is strain-free at 0 ◦ C. Over the course of a 10-min ramp, the temperature of the bar is raised to 100 ◦ C, and a linearly coincident end displacement is applied such that eO = 0 at 0 ◦ C and that eO = 0.001 at 100 ◦ C. The temperature and the end displacement are then held for a 24-h period. During the ramp and the dwell, the creep continuously alleviates the mechanical strain. Fig. 1 shows the select components of the structural response. Stress increases, due to the increasing end displacement, from an initial zero value to a maximum during the ramp period. Creep, which is active during the entire analysis, begins to substantially participate in the structural response at ∼60 ◦ C, which is the coincident with the maximum reported stress in the figure. Throughout the remaining 4 min of the ramp and the 24-h dwell, the creep actively alleviates the mechanical strain, hence the axial stress. The measure of creep damage W CR has the greatest change

over the course of the first few hours followed by an asymptotic increase during later times. For a fatigue situation where multiple loading cycles each impart the damage seen in the figure, it can be argued that the effects of time per cycle become negligible after the point of saturation, beyond which there is no substantial accumulation of the creep-strain energy. Through examination of Fig. 1, thot− max may be estimated to be ∼2 h for the particular loading examined. The SAC solder fatigue in electronic assemblies will, however, experience a broad range of imposed strains and temperature ranges. The preceding analysis was performed on an extensive and reasonably encompassing range of initial strains and temperature ranges in order to evaluate thot− max for use in (3). Imposed strain values of 0.01, 0.005, and 0.001 were imparted in the thermal environments −25 ◦ C–125 ◦ C, 0 ◦ C–100 ◦ C, and 25 ◦ C–75 ◦ C. In all cases and as before, the strain and the temperature were ramped during the initial 10 min and then held for 24 h. Fig. 2 shows the select bounding cases from the analysis. In order to evaluate the saturation time, W CR for each analysis is normalized to the value at the


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TABLE I (Continued.) TEST DATA

end of the analysis, which is assumed to be fully saturated. By choosing the criterion that the creep energy contribution is saturated when W CR (t) ≥ 0.995W CR (24 h), thot− max is set to be 240 min for use in (3). B. Experimental Data Table I presents the experimental data used in determining the SAC acceleration factor. The tests cover a wide range of package types (CBGA, PBGA, TSOP, CSP, FCOB, LCCC, etc.), temperature ranges as shallow as 40 ◦ C–100 ◦ C and as deep as −65 ◦ C–150 ◦ C, dwells ranging between 3 and

350 min, characteristic lives between 15 and 10 000 cycles, and a wide combination of solder-joint pitches and printed circuit board thicknesses. A least squares procedure is used to determine the unknown parameters Q, M , and N . By noting that the NL equation is only used to project the solder-joint fatigue life of a package and board combination in an untested environment given the fatigue data on the same package and board combination in a known environment, the fitting of test data is performed on groups of the same package tested under differing environmental conditions. In the table, these package groups correspond, generally, to a package type reported by each author.

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Fig. 4.

Components of the sample problem’s acceleration factor.

Fig. 3. Correlation between the experimental and predicted characteristic lives η.

V. E XAMPLE C. Resulting Acceleration Factor Through fitting the canonical form of (3) to the data and through the evaluation of creep saturation, the SAC NL equation is 1.75 hot 1/4 ∆T1 1600 t1 N2 1600 = exp − MAX N1 ∆T2 T2MAX T1 thot 2

(5)

hot

is the lesser of the ramp-to-hot time plus the hot where t dwell time or 240 min, and the temperature terms are in ◦ K. The quality of the SAC NL equation is shown in Fig. 3. For each data set, the case which is closest to cycling between 0 ◦ C and 100 ◦ C with 10-min ramps and holds is used to project the remaining cases. The figure demonstrates a very good correspondence between prediction and test, which is, on average, ±16%.

IV. R ESTRICTIONS Equation (5) is a simple empirical model rather than a rigorous description of the complex thermomechanical behavior of the SAC solder joints subject to thermal fatigue loads. The model should not be used with unusual solder-joint geometries or load conditions. The acceleration model, however, is suited for rapid estimates of product life under new or field conditions and when a minimum of package and thermal environment conditions is available. When using (5) to estimate the field life, the predicted cycles N2 are often reduced by the FS which provides a design margin on the prediction and may account for inaccuracies in the acceleration model, the known test data, or the product environment. The common practice with the traditional NL equation is to use the FS from 1.5 to 2 to derate the product field-life projections from the accelerated test data. By considering the limited field experience with the SAC material, an FS that is equal to two is recommended for the field-life projections obtained with (5).

Consider a product that has demonstrated a solder-fatigue characteristic life of 1000 cycles in accelerated thermal cycle testing. The test consisted of 10-min ramps and dwells over the temperature range 0 ◦ C–100 ◦ C. The product is used in an office environment, where the maximum solder-joint temperature is 60 ◦ C during the course of an 8-h workday. The product is turned off over the evening, rapidly cooling to the 20 ◦ C office ambient. By using an FS of two, the characteristic office life is N2 =

1.75 1/4 100 − 0 20 60 − 20 240 1600 1600 − × exp = 2235 cycles. 60 + 273 100 + 273

1 1000 2

By ignoring the FS, the acceleration factor for this case is 4.47. Fig. 4 shows the contribution of each term to the aggregate acceleration factor. As expected, the temperature range and maximum temperature terms are greater than one, indicating that the service-environment temperatures are less severe than the test temperatures. The thot term is less than one, reflecting the increased damage that occurs during the long service dwells when compared with those of the test environment. VI. C ONCLUSION An acceleration model, which retains the familiar form of the NL equation, has been developed for relating the existing second-level fatigue-life data of SAC joints to the untested environments. The model parameters were derived from an extensive set of published empirical data and from an analytic evaluation of the likely times for creep-damage saturation in typical environments. The model may find greatest utility in quickly relating the accelerated board-level thermal cycling data to the potential solder-joint field reliability. R EFERENCES [1] K. Norris and A. Landzberg, “Reliability of controlled collapse interconnections,” IBM J. Res. Develop., vol. 13, no. 3, pp. 266–271, May 1969. [2] L. F. Coffin, “A study of the effects of cyclic thermal stresses on a ductile metal,” Trans. ASME, vol. 76, no. 6, pp. 931–950, 1954.


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Walter Dauksher received the Ph.D. degree in mechanical engineering from the University of Washington, Seattle. He was a Structural Analyst with the Rockwell International and The Boeing Company and a Reliability Engineer with the Hewlett-Packard and the Agilent Technologies. He is currently a Reliability Engineer with Avago Technologies, Fort Collins, CO, where he specializes in the use of mechanical modeling to evaluate packaging and silicon technologies. His refereed and conference publications deal primarily with the accuracy of numerical methods and with the electronic packaging issues, particularly solder-joint reliability. He has also coauthored four U.S. patents. Dr. Dauksher is a Registered Professional Engineer.