Accelerated Testing of Solder Joint Interconnections: Incentive for Using a Low-Temperature/Random- Vibrations Bias



Although promising ways exist to avoid inelastic strains in solder joints of the second-level interconnections in IC package designs, it still appears more typical than not that the peripheral joints of a package/PCB assembly experience inelastic strains. This takes place at low-temperature conditions, when the deviation from the high fabrication temperature is the largest and the induced thermal stresses are the highest. On the other hand, it is well known that it is the combination of low temperatures and repetitive dynamic loading that accelerate dramatically the propagation of fatigue cracks, whether elastic or inelastic. Accordingly, a modification of the recently suggested multiparametric BAZ model is developed for the evaluation of the remaining useful lifetime (RUL) of the second-level solder joint interconnections whose peripheral joints experience inelastic strains. The experimental basis of the approach is the highly focused and highly cost-effective FOAT. The FOAT specimens have been subjected in our methodology (which is “reduced to practice”) to the combined action of low temperatures (not to elevated temperatures, as in the classical Arrhenius model) and random vibrations with the given input energy spectrum.


The suggested methodology is viewed as a possible, promising, effective, and attractive alternative to temperature cycling tests. As long as inelastic deformations are inevitable, it is assumed that it is these deformations that determine the fatigue lifetime of the solder material, and the state of stress in the elastic midportion of the assembly does not have to be accounted for. The roles of the size and stiffness of this midportion have to be considered, however, when determining the very existence the inelastic zones at the peripheral portions of the design and establishing their size. The general concept is illustrated by a numerical example. Although this example is carried out for a ball-grid array (BGA) design, it is applicable to highly popular column-grid array (CGA) and quad-flat no-lead (QFN) designs as well. It is noteworthy that it is much easier to avoid inelastic strains in CGA and QFN structures than in the addressed DGA design. The random vibrations are considered in the developed methodology as a white noise of the given ratio of the acceleration amplitudes squared to the vibration frequency.

Reduction to Practice

The suggested model is confirmed by accelerated testing. Testing was carried out for two PCBs, with surface-mounted packages on them, at the same level (with the mean value of 50 g) of 3D random vibrations. One board was subjected, concurrently with random vibrations, to the low temperature of-20°C = 253K and another one - to -100°C = 173K. It has been predicted, by preliminary calculations using the developed model that the solder joints at the -20°C will still perform within the elastic range, while the solder joints at -100°C will experienced static inelastic strains. No wonder that no failures were detected in the solder joints of the board tested at -20°C while the joints of the board tested at -100°C failed after several hours of testing. Some results of such an accelerated testing are addressed, described, and commented on. Here is how FOAT could be implemented in the problem in question.

Calculation Procedure

Let us assume that the failure rate of the solder material, which characterizes the rate of propensity of the material or the device to failure, could be monitored determined by the level of the measured electrical resistance: у = yKR. Using the BAZ model (10.7) and considering the combined action of low temperature T (that supposedly leads to elevated thermal stresses in the solder material) and external random vibrations characterized by their spectrum S, one can seek the probability of the material nonfailure after FOAT for the time t in the form

where the у values reflect the sensitivities of the material to the corresponding stimuli (stressors), and R is the continuously measured/monitored electrical resistance for the peripheral joints. Although only two stimuli (stressors) were selected in this model—low temperature and random vibrations—the model can be easily made multiparametric, that is, generalized for as many stimuli as necessary. The units for the sensitivity parameter yK are obviously Q 'h~l if the measured electrical resistance of the peripheral solder joints is measured in ohms, and the elapsed time t is measured in hours. The unites of the sensitivity parameter ys are eVm~2s~3 if the stress-free activation energy U0 is measured in eV and the power spectral density (PSD) amplitudes are measured in (m/s2)2/Hz = m2s3. The physical meaning of this distribution could be seen from the formulas

where H(P) = -P P is the entropy of the probability P of nonfailure. Thus, the change in the probability of nonfailure always increases with an increase in the entropy (uncertainty) of the distribution and decreases with an increase in the monitored (measured) electrical resistance and the elapsed time. As to the sensitivity factor ys, it can be found as the ratio


of the (negative) derivative —— of the probability of nonfailure with respect to the


level of the vibration excitation (power spectrum) to the ratio of the entropy of the probability of nonfailure to the level of the thermal energy kT. It should be emphasized that the temperature T in the aforementioned formulas is, unlike in Boltzmann’s statistics or in the Arrhenius formula, a parameter, not an argument. It is the threshold of the low temperature, below which the inelastic strains in the peripheral solder joints occur. This temperature/threshold should be determined and established based on the procedures addressed in the “Inelastic strains in solder material” section in chapter 4. The expression for the probability of nonfailure contains three empirical parameters: the stress-free activation energy U0 and two sensitivity factors, yK and Ys. Here is how these parameters can be obtained from the conducted highly focused and highly cost effective FOAT data.

At the first step, one should run the FOAT for two different temperatures 7j and T2, keeping their levels unchanged during the experiment. Unlike in the original Arrhenius or Zhurkov’s experiments, these levels should be established and kept low enough so that inelastic strains in the peripheral solder joints of the pack- age/PCB assembly could occur. These temperatures could/should be obtained from the preliminary thermal stress analysis already described. Recording the percentages (values) P, and P2 of nonfailed samples (or values Q, = 1 - fl and Q2 = 1 - P2 of the failed samples) and assuming a certain criterion of failure (say, when the level of the measured electrical resistance, because of the “opens” in the failed joints, exceeds a certain level R,) one could obtain the following two relationships:

Since the numerators U0-ysS (effective activation energies) in these relationships are kept the same during the FOAT, the following equation must be fulfilled for the sought sensitivity factor yK of the electrical resistance:

Here, t and t2 are times at which the failures defined as the moments of time when the level R> of the continuously measured electrical resistance were observed. Equation (10.78) has the following solution:

It is expected that more than two series of FOAT tests and at more than two temperature levels should be conducted, so that the sensitivity parameter yK could be established with a high enough degree of accuracy and certainty.

At the second step, FOAT tests at two spectra levels 5, and S2 should be conducted for the same temperature T. This leads to the relationship

Note, that the ys value is independent, in this approach, of the resistance P* threshold and the sensitivity factor yK. Finally, the stress-free activation energy can be computed, for the determined factors yK and ys as

for any consistent vibration spectrum level, temperature threshold and time values. After the sensitivity factors and the loading (stressor) free activation energy are determined for the tested combinations of the input data, the aforementioned formula could be used, but should be checked (validated), of course, for other physically meaningful combinations of the FOAT parameters. The fatigue lifetime can be found for the induced temperature below the temperature, at which the inelastic strains occur from the basic formula for the probability of nonfailure as follows:

This formula makes physical sense. Indeed, the RUL increases with an increase in the probability P of nonfailure, and with an increase in the level of the effective activation energy U = U0-ysS. The RUL decreases with an increase in the acceptable level R, of the electrical resistance of the damaged joints, with an increase in the sensitivity factor yR and the level kT of the thermal energy. This level is higher for lower thermal energies.

Numerical Example

Input data:

Structural Element





Element’s Number




Effective Young’s Modulus, E. kg/mnr




Poisson’s Ratio, V




Shear Modulus, G, kg/mnr




CTE. 1 / °C




Thickness, mm




Estimated yield stress of the solder material in shear: xY =1.825 kg/mnr Soldering Temperature: 158°C = 43 Г К

Testing Temperatures: 7] = -20°C = 253°K. T2 = -100°C = 173°K Changes in Temperature: Д/i = 178°C = 178°K. Дь = 258°C = 258°K The “external” thermal strains: 6| = ДаДО = 151.3 x 10_s, e? = ДаАЬ = 219.3 x 10~s Half Package Length / = 15 mm;

Electrical Resistance Threshold at Solder Failure [52]: R> = 450f 2

Computed data:

Axial compliances of the assembly components:

Flexural rigidities of the assembly components:

Total axial compliance of the assembly:

Interfacial compliances:

Parameter of the interfacial shearing stress

The product kl = 0.9890 x 15.0 = 14.8350 is significant, and therefore the maximum interfacial shearing stress can be evaluated assuming infinitely large assembly.

For the board tested at -20°C this stress is

and is somewhat below the yield stress of the solder material, so that no inelastic strains are likely to occur. For the board tested at -100°C this stress is

and the lengths of the inelastic zones in this case are

The temperature boundary between the elastic and inelastic states of stress is characterized by the temperature change of

and, with the soldering temperature of-158°C, is -24.6°C.

Here is a hypothetical example of how the parameters of the BAZ equation can be determined when testing is conducted until failure. Note that has not been the case for the two PCBs whose testing is described in Section 10.6.6, since only the solder joints in the PCB tested at -100°C have failed, while the joints in the board tested at -20°C have not exhibit any failure after many hours of testing. Let, for example, the FOAT is carried out until the resistance threshold is reached. Half of the specimen population failed at the first stage of testing at the temperature of 7j = -30°C = 243°K after ?, = 200 hrs of testing. When testing was conducted at the temperature of T2 = -10°C = 263°K, half of the specimen population failed after t2 = 300 hrs of testing. The level of the vibration power spectrum density S was kept the same in both sets of the tests and therefore did not affect the factor y„. Then, the equation for the sensitivity parameter yR yields

The thermal energy is A7j = 8.6176x 10 5 x 243° = 2.0941 x 10 2eV, when testing is carried out at the temperature 7j =-30°C= 243°K. and is кЪ = 8.6176 x 10~5 x 263° = 2.2664 x 10“2eV, when testing is carried out at the temperature T2 = -10°C = 263°K. Let the testing at the second stage of testing be carried out until 99% of the tested specimens failed, so that P = 0.01, and that this took place after = 500 hrs of testing at the temperature of 7j = -30°C = 243°K and at the vibration level of Sj = 2 x 1 O'* mm2 sec"3 and after Г, = 650 hrs of testing at the temperature of T2 = -10°C = 263°K and at the vibration level of S2 = l()',lmm2sec'2. The effective activation energy is

when testing was carried out at the temperature 7] = -30°C = 243°K, and is

when testing was performed at the temperature T2 = -10°C = 263°K. Clearly, since the thermal strain and/or the region occupied by the inelastic stresses in the solder material are higher at the lower temperature condition, the remaining effective activation energy is lower at this temperature.

From the last two equations, considering that the zero-stress activation energy should be loading independent, we have the following formula for the vibration sensitivity factor:

Then, the stress-free activation energy can be computed as or as

The RUL can be computed for any probability of nonfailure, low temperature, and vibration spectral density as

If, for example, P = 0.9, T = -20°C = 253°K, and S = 103mm2 sec'3, then the predicted RUL of the solder material is

Testing Facility and Procedure

The actual testing has been carried out at the Reliant Labs. Inc., 925 Thompson Place, Sunnyvale, California. Two PCB boards, serial numbers QFN-P-07 and QFN- P-08, provided by the customer, were tested. Qualmark OVS 2.5LF HALT/HASS Chamber (model # 2.5LF) was used to accommodate the test specimens (one at a time). Omega thermocouples were used to measure temperature, and a Dytran accelerometer control was used to measure the applied accelerations. All test equipment that requires periodic calibration was in current calibration at time of test.

The test results could be summarized as follows. Board #l was tested at the temperature of-20°C and the (identical) board #2 at the temperature of-100°C. In both cases the established level of the random 3D vibrations was 50 g.

The reason why these temperatures were chosen, is that, according to these calculations, the -20°C temperatures were not expected to lead to inelastic static strains, while the -100°C temperature was supposed to result in appreciable plastic deformations and, hence, in a considerably shorter fatigue life of the solder material. Electrical resistance was continuously measured in four corner packages of each board. Prior to testing, all the joints showed resistance of about 0.15(xQ For board #1 (tested at -20°C), this level of resistance has not changed after 5 hours of testing. For board #2 (tested at -100°C), opens in two packages were detected after about

1.5 hours of testing, and an increase in the resistance to about 0.9£2 was detected for the remaining two corner packages after about 3.5 hours of testing. The total time of testing of board #2 was about 4 hours. Hence, the test results have confirmed the general concept that low temperatures in combination with random vibrations might be an attractive accelerated test vehicle for electronic materials and packages, and that there is a significant difference in the fatigue lifetime (RUL) for the solder material that remains within the elastic region (when subjected to moderately low temperatures) and the material that is stressed above this region at significant low temperatures. The tests were not continued beyond the above times, since no substantial new information was expected if they would be. It should be emphasized, however, that the FOAT should be always conducted if there is an intent to quantify the RUL. For materials that failed within the elastic region, the probabilistic Palmgren-Miner “rule of the linear accumulation of damages” can be used to predict the RUL.


The carried out analyses explain how the predictive modeling approach can be used in predicting and prevention of failures of solder joints in electronic products in which high reliability is imperative.

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