Temperature Cycling: Predicted Time-to-failure

Temperature cycling has become the main accelerated test vehicle in microelectronics (see, for example, [88-98]). While low-cost and short time-to-market are the main driving forces in commercial electronics, operational reliability is of paramount importance in aerospace, military, medical, long-haul communications, and other areas of electronic engineering, when the consequences of failure might be dramatic. Adequate operational reliability is therefore critical in these industries and cannot be assured if the underlying physics of failure is not understood. Since nothing is perfect and the probability of failure is never zero, this probability should be predicted and, if possible, even specified on the probabilistic basis. The recently suggested PDfR concept (see Chapter 11) makes the art of producing reliable electronic products into a reliability-physics and applied-probability-based science. The concept has its experimental foundation in a highly focused and highly cost-effective FOAT designed and conducted for the most vulnerable material(s) and structural element(s) of the device (solder joints, for instance) and geared to a simple and physically meaningful predictive model. The BAZ equation can be employed in this capacity. Let us show how the probability P of nonfailure of a solder joint interconnection experiencing inelastic strains during temperature cycling can be determined using the BAZ equation.

Let us seek this probability, considering the general formula (10.6), as follows:

Here, U₀ is the stress-free activation energy viewed as material property and characterizing the material’s propensity to fracture, W is the damage caused by a single temperature cycle and measured for the solder material experiencing inelastic deformations, in accordance with Hall’s concept [67-69], by the inelastic-strain-energy hysteresis loop area (see Figure 10.1 [99]), T is the absolute temperature (say, the cycle’s mean temperature), n is the number of cycles, к is the Boltzmann constant, t is time, R is the measured electrical resistance at the joint locations (this monitored resistance is viewed as a suitable criterion of the material failure), and у is the sensitivity factor.

The distribution (10.11) makes physical sense. Indeed, the probability P of nonfailure is equal to “one” at the initial moment of time 1 = 0 and/or when the measured electrical resistance R is next-to-zero. This probability decreases with time because of a material’s aging and structural degradation (and, not necessarily only because of temperature cycling); is lower for higher electrical resistance; materials with higher activation energy U₀ have a higher probability of nonfailure; the increase in the number n of cycles lowers the effective activation energy U = U_f)-nW and, hence, the probability of nonfailure.

FIGURE 10.1 Hall’s hysteresis loop for a single temperature cycle of a solder interconnection. (From C. Hillman, N. Blattau, M. Lacy, “Predicting Fatigue of Solder Joints Subjected to High Number of Power Cycles,” IPC APEX EXPO, 2014.)

There is an underlying entropy-related consideration for the distribution (10.11). From (10.11), we have

w'here H(P) = -P In P is the entropy of the distribution (10.11). The result (10.12) indicates that the suggested distribution reflects a physically meaningful assumption that the change in the probability of nonfailure with time is proportional to the entropy (uncertainty) of this distribution and is inversely proportional to the elapsed time. As

dH 1

has been showm earlier, the condition — = -lnP* -1 = 0 yields P, = H(P*) = -. The

dP e

maximum entropy takes place for the MTTF

The level of the entropy of the distribution (10.11) is the maximum at this time. Mechanical failure occurs when n = In such a situation, the temperature in the

denominator in equation (10.12) becomes irrelevant, and this equation results in the following formulas for the probability P, of nonfailure and the MTTF x_f of the solder material:

If, for example, 20 devices have been temperature cycled and the resistance R_f = 450Q, considered as a suitable indication of failure, w'as detected in 15 of them, then Pf = 0.25. If the number of cycles at failure was, say, n_f = 2000 and each cycle lasted, say, for 20 min = 1200 s, then the time at failure is t_f = 2000 x 1200 = 24 x 10^s and formulas (10.14) yield

According to Hall [19], the inelastic strain energy of a single cycle should be evaluated experimentally by conducting a specially designed test.

Let, for example, the measured area of the hysteresis loop in such tests is W = 4.5 x lO^eV = 7.200 x lO'²³./.

Then the stress-free activation energy is U₀ = 2000x4.5 x 10"⁴eV = 0.9 eV = 1.440 x КГ¹⁹./. When assessing the number of cycles to failure in actual operation conditions, one could assume that the temperature range in these conditions is, say, half the FOAT range, and that the area W of the hysteresis loop is proportional to the temperature range. Then the number of cycles to failure becomes

n_f = — = ———_T = 2000. If the duration of one cycle is one day, then the pro- ^f W 4.5 xlO"^{4 J J} ^

jected lifetime of the materials (time to failure) is t_f = 2000 days = 5.8 years. Future work should include, first of all, improved Hall’s type measurements, considering today’s state of the art in experimental electronic materials science; actual FOAT data; and trustworthy information about the actual operation conditions and lifetimes.

Incentive for Mechanical Prestressing of Accelerated Test Specimens

Background/Incentive

Accelerated testing of soldered assemblies, such as, for example, temperature cycling, is usually conducted in a wider range of temperatures than is expected to take place in actual operation conditions (see, for example, [100-125]). Since the mechanical and electrical properties of electronic materials are temperature sensitive, such testing might generate deviations of the material properties from the properties that they possess in actual operations conditions, and the results of such accelerated testing might be misleading: they might trigger mechanisms and modes of failure that will never occur in the field conditions. In such a situation, mechanical prestressing of the accelerated test specimens [102] might be a promising way to go. FOAT specimens are particularly vulnerable since the temperature range in these tests should be broad enough to eventually lead to failures, and if a shift in the modes and mechanisms of failures takes place during significant temperature excursions, the physics of such failures might be quite different than in actual operation conditions. An appropriate mechanical prestressing can be an effective means for narrowing the range of temperature excursions during accelerated testing and, owing to that, for obtaining consistent and trustworthy test data. If such a prestressing is considered and implemented, the ability to predict/model the thermo-mechanical stresses in the test specimen is certainly a must.

Application of mechanical prestressing could be an effective means for achieving a failure-mode-shift-free “destructive ALT effect” in electronic and photonic devices and micro-electro-mechanical systems (MEMS). A simple, physically meaningful, and easy-to-use analytical (“mathematical”) predictive model has been developed to assess the magnitude and the distribution of stresses in a bimaterial assembly subjected to the combined action of thermally induced (considered by the ALT design) and external (“mechanical”) prestressing. Such a compressive prestressing is applied to the assembly component that is expected to experience thermal compression. The model is an extension and a modification of the author’s

1986 and 1989 “bi-metal thermostat” models suggested as a generalization of the classical 1925 Timoshenko’s theory. The objective of the analysis carried out in this section is not so much to add to the existing knowledge in the field of thermal stress modeling, but rather to indicate the feasibility of using mechanically prestressed test specimens, when there is a need to avoid the “shift” in the modes and mechanisms of failure in electronic, photonic or MEMS assemblies subjected to thermal loading during accelerated life testing. When planning and conducting such testing, there is always a temptation to broaden (enhance) as far as possible the temperature range to achieve the maximum “destructive testing effect” in a shortest period of time. There exists, however, one major pitfall: a possible shift in the modes and mechanisms of failure as a result of broadening the temperature range; enhanced accelerated testing conditions may hasten failure mechanisms that are quite different from those that could possibly occur in actual service.

The likely pitfalls include, but might not be limited to, the change in materials properties at high or low temperatures; time-dependent strain due to diffusion; enhanced creep at elevated temperatures; brittle fracture at low temperatures; generation and movement of dislocations caused by an elevated thermal stress; and occurrence of a bimodal distribution of failures. Because of the possibility of such pitfalls, it is always necessary to establish the appropriate narrow enough temperature limits in order to prevent the distortion of the actual (real-life) dominant failure mechanism(s). Therefore, there is an obvious incentive for trying to find ways of increasing the induced stresses without broadening the ALT temperature range. One way to enhance the “destructive ALT effect” without compromising the acceptable temperature limits is to mechanically prestress the test specimens prior to conducting thermal ALT. For instance, a low expansion silicon chip attached to a high-expansion polymeric substrate will experience thermally induced compression, when the bimaterial chip-substrate assembly manufactured at an elevated temperature is subsequently cooled down to a low (say, room) temperature. This compression can be enhanced, and the interfacial stresses will be increased, if the chip is mechanically pre-stressed in compression. The objective of our analysis is to develop a simple, easy-to-use, and physically meaningful predictive model for the evaluation of the thermo-mechanical stresses in a mechanically prestressed bimaterial specimen. Although our model is an approximate engineering model that is not aimed at the most accurate prediction of the induced stresses, it seems nonetheless acceptable for engineering evaluations and applications. Some additional details of the suggested methodology are given in Appendices A and B.