Failure Mechanisms Driven Reliability Models for Power Electronics: A Review

Power modules play a key role in delivering flexible and efficient energy conversion. Tougher environmental protection laws and the ever growing need to cut down greenhouse gas emissions have led to the rising demand for high performance power electronics, especially for aerospace and automotive applications [1]. This is due to expansion of power solution from a predominately secondary system toward a significantly higher energy requirement to power not only vehicle entertainment systems, but also environment control devices, electric motors, safety systems, and sensors in vehicles. Figure 1 depicts schematics of a hypothetical power module.

Diode and insulator gate bipolar transistor (IGBT) with nickel/gold metallization both on front and back side allows for soldering process, to be implemented. This facilitated the development of wire-less power module. By replacing the Al wire on the traditional with copper spacer and copper clip, the electric, thermal performance, and reliability can be improved [2]. Several factors such as thermomechanical stress caused by coefficient of thermal expansion (CTE) mismatch, environmental induced degradation, fatigue, electromigration as well as their combine effects complicate failure mechanisms and thereby, pose reliability or lifetime prediction difficulties [1,3].

Reliability models based on traditional methods contained in standard handbooks such as MIL-HDBK 217F, 217-Plus, PRISM, Telcordia, FIDES, and CNET, are strongly discouraged as a reference material for reliability prediction purposes [3]. Mainly, because these handbooks assume components to have constant failure rates that can be modified using separate modifiers to account for a various operating, quality, and environmental conditions. Many studies have enumerated concerns associated with this type of reliability modeling approaches [3–6]. Generally, reliability prediction models derived from these handbooks are inaccurate and provide highly misleading predictions, with potential to result in inferior designs as well as product decisions.

IEEE 1413 standards and its associated guidebook, IEEE 1413.1 are regarded as improvement to the previously named handbooks, because they provided reliability prediction assessment methods based on field data as well as information on the benefits of reliability prediction using physics of failure (PoF). Reliability models based on PoF [7,8] are generally preferred, because it puts emphasis on failure analysis, root cause of failure, as well as failure mechanisms [6–10]. This paper, review's reliability modeling activities related to power electronics components based on failure mechanisms. In Ref. [2] electronics failure mechanisms were classified into six. That is fatigue, electromigration (EM), corrosion, conductive filament formation (CFF), stress-driven diffusion voiding, and time-dependent dielectric breakdown (TDDB). Numerous research efforts have been carried out on each of these failure mechanisms. For instance, Zhao et al. [9], studied the effects of lead-free solder joints aging on their reliability using various pitch sizes and ball arrangement. The study shows that the degradation rate slows with aging time and the reliability degrades up to 70% after two years of aging at elevated temperature.

Xu et al. [10], carried out an accelerated EM test on four types of interconnect structure comprising of conventional ball grid array (BGA); solder ball with a copper via on top; an individual copper via in the substrate; and an individual copper plated-through-hole (PTH). The result shows higher probability of EM on the copper via in the substrate when placed in the vicinity of the solder ball. The effect of the humidity and temperature cycling on corrosion-based reliability was assessed by quantifying the leakage current (LC) on interdigitated test comb patterns, precontaminated with sodium chloride [11]. The results showed that the temperature cycling led to significant variation in the water–vapor concentration. In the work of Sood and Pecht [12], it was shown that smaller conductor spacing lowers CFF time to failure.

GaN power device TDDB was studied with various substrates [13]. The results show a decreasing shape parameter and an increase in scale parameter under positive substrate biases. In the study of stress induced voiding [14], combined electromigration as well stress migration to develop a unified model. Although some past studies have conducted review on specific power electronics failure mechanisms such as solder fatigue [15] and electromigration [16], a comprehensive review of reliability modeling efforts that captures the six failure mechanisms, with the view to highlight future expectation is to the best of our knowledge lacking. This paper, therefore, seeks to fill this gap. The remaining of this paper is organized as follows. In Sec. 2, reliability modeling based on fatigue failure mechanism is reviewed. In Secs. 3 and 4 reliability models based on electromigration and corrosion are discussed, respectively. In Secs. 5 and 6 reliability models based on CFF and SIV failure mechanisms are discussed, respectively. In Sec. 7, TDDB failure mechanism is discussed, and Sec. 8 concludes the study.

Power electronics devices are usually exposed to mechanical vibration and thermal cyclic loads. The effects of these loads include fatigue crack initiation, propagation, and finally fracture. In Ref. [3] die attach, wire bond/tab, solder leads, bond pads, traces, via/PTHs, and interfaces were identified as the major fatigue associated failure site in electronic packaging. For over four decades, numerous PoF-based fatigue life prediction models have been developed for these fatigue prone failure sites [17–22]. In Ref. [15], it was reported that the properties of the solder material play a prominent role in the life of the solder joint. A detailed classification of the common materials used for solder joint can be found in Ref. [23]. Generally, based on health and environmental concern, there is strong shift from the well-known lead-tin (PbSn) solder to the lead-free solders such as the tin-silver-copper (SAC) family as well as its doped variants such as innolot. Rare earth elements have equally been shown to be a promising dopant [24,25]. Due to cost, melting temperature, and mechanical strength of SAC solder, the next generation of lead-free solder alloy will focus on doped solder alloy [24].

Successful prediction of fatigue failure is often based on the ability to accurately model the solder joint. Understanding the crack initiation and propagation mechanism in solder joint is critical to efficient fatigue-based life modeling. Apparently, it is quiet challenging to track and monitor the initiation as well as propagation of fatigue cracks in electronics packaging. Hence, a lot of fatigue failures models often adopt failure criteria appropriate to the purpose of their study. Lee et al. [26] carried out a review of solder joint life prediction model. Subsequently, Su et al. [15], provided an updated review on solder joint life models, capturing some fatigue models not covered in Ref. [26]. In this work, some new models with emphasis on recent incorporation of microstructural effects are covered with the view of highlighting prevailing challenges as well as direction of future research on electronic packaging fatigue life modeling. Section 2.1 discusses solder joint failure models.

Solder joint fatigue life prediction models are generally categorized into four, comprising plastic-strain, creep-strain, energy, and damage accumulation models. These categories are based on the mechanism used to induce failure. In the strain-based models, thermal induced strain is applied, leading to stresses within the system [15]. The strain could be plastic, shear, or a combination of plastic and shear. Generally, the strain effect is either time-dependent plastic or creep-based [26]. For energy-based models, the overall stress–strain hysteresis energy of the solder joint is used as a basis of the model development. Fracture mechanics or creep and fatigue mechanisms often used to compute damage accumulation caused by fatigue crack propagation is the basis of damage accumulation models. Past reviews of these models can be found in Refs. [15] and [26]. Figure 2 and Table 1 represent the classification of these fatigue modeling methods. The parameters associated with each model are defined where they appear. In this section emphasizes is place on recent direction of research, associated with each of the solder joint failure model categories.

where $ho$ and $a$ represents the material strain hardening parameters. $s̃$ denotes a coefficient of saturation, and $n$ represents the saturation value of deformation resistance strain rate sensitivity. The nine material parameters, such as $A, Q, m, n, j, s̃, a, ho,$ and $s$ can be easily determined from extensive experimental tests and are often available from manufacturer data sheet. In Zhang et al. [32], Anand and Engelmaier models were combined to predict the fatigue life of Sn-Ag-Cu-Zn lead-free solder joints in a chip-scale packaging device. It was found that the use of Zn as a dopant improves the solder fatigue life. In Refs. [22] and [33], Anand model assigned from abaqus was combined with Engelmaier model to investigate the fatigue life of PBGA under temperature cycling. It was shown that solder height and temperature ramp rate significantly affected fatigue life. Also, the joint corner was assumed to determine the life of the joint. In Ref. [34] C–M model and machine learning were used to assess the failure life prediction of wafer level package. In a recent study, FEA and strain-based models (C–M, Eugelmaier, Solomon, and Syed) were used to assess the fatigue life of ball grid array (BGA) joints comprising of various alloy compositions [35,36]. The results show lack of consistency in the predicted values among the strain-based models compared. The study attributed the lack of consistency to the critical role played by damage parameters as well as the diverse failure modes associated with fatigue damage.

Although, many FEA software such as ansys and abaqus depend on steady-state constitutive model to model creep behavior, the prediction accuracy is believed to be less than optimal. To increase the prediction accuracy, FEA has recently been combined with heuristic algorithms. To illustrate, Chen et al., [44] combined ansys and artificial intelligent (AI) method for solder joint fatigue life prediction in WLCSP. Similarly, Zhang et al. [44], evaluated the reliability of WLCSP using a combination of FEA with ANN. In both studies modified C–M model was used for the fatigue life prediction. Zhao et al. [46], reported that analytical life prediction without incorporating microstructural effects due to aging or impurities may be erroneous. In Morooka and Yoshiharu, [20] this concept was considered in a fatigue life prediction of a BGA solder joints. Validation of the microstructural effect requires more studies. Therefore, constitute interesting area to concentrate on creep-based fatigue life prediction models [47,48]. Also, constitutive models that integrate microstructural effects due to recrystallization during aging or variation in test sample quality will equally be an interest area to consider in the future.

The Ag in the models represents %Ag content by weight. Geometry plays a key role in the energy-based fatigue models [38]. The complexity of FEA implemented in an energy-based fatigue analysis is dependent on the size and shape of the solder joint. The accuracy of recently developed energy-based fatigue model will require further study. Most importantly, extension of the single element variation is currently accounted for in Eqs. (27) and (28) to more than one element will be expected, to account for multiple doped solders.

In Ref. [71] fatigue life model for solder joints under corresponding failure rate (⁠$F$⁠) based on Weibull equation was proposed from thermal cycling tests using Eq. (41). After careful review fatigue related publications, we observed that there is lack of clear definition of solder joint fatigue. Some model definition for solder joint is based on JESD22-A122A [72] for power cycling, which stated that failure criteria shall include, but not be limited to, hermeticity for hermetic devices, parametric limits, functional limits, and mechanical damage resulting in failure of the test point of interest. In the case of IPC JSTD change is resistance suffix [73]. Some others use mechanical behaviors like amplitude stress. Clearly, lack of global fatigue failure standard for all kinds of fatigue test, could result in misleading fatigue life comparison among various testing condition. Although microstructural effect has been recent capture in some fatigue models, a lot of research activities, is required to enhance their prediction accuracy.

Electromigration (EM) is a mass movement of atoms, caused by the momentum transfer between conducting electrons and metal atoms. Migration of atom along a line, often results in flux divergences. At sites of flux divergences, material accumulation (hillock) or depletion (void) takes place [74]. Typically, damage caused by voids is much more probable than damage caused by extrusions. Within a power device, electromigration predominantly occurs along interconnect lines. For wire bonds, it occurs either at the attachment spot or at the middle of the wire between two attachment points, while for solder balls it occurs along the interphase between the solder and intermetallic compound. Figure 3 depicts electromigration induced void in an interconnect line, wire bond, and solder ball.

Typically, the formation and growth of voids cause a significant increase in the resistance in a line and, finally, leads to open circuit. Material, temperature, grain structure, stress gradients current density are the common sources of flux divergence [78]. For over 50 years EM reported by the Fik's and Huntington has been an area of active research [79,80]. This trend has been driven by integrated circuit (IC) miniaturization to nanoscale, which often results in to increase in current density. Despite numerous research articles already published on EM, persistent miniaturization of electronic devices constantly presents the need for EM induced failure evaluation due to complex stresses and stress interaction that exist at nanoscale [80]. With the growing shift from traditional EM-based models to physics-based models as well as the availability of finite element analysis tools like ansys and comsol, clarity and prediction accuracy of EM failure mechanism is growing. Many review articles on the EM have been published [16,78]. It is not the intention of this section to reproduce the content already available in those articles. Rather this work will highlight notable progress made in electromigration reliability model development up to the time of writing this paper. We note that not citing a paper does not diminish its significance. During the EM process, atomic flux diffusion (AFD) varies with diffusion paths and time. Generally, reduction in the AFD, increases interconnects life. Based on the concept of AFD, we categorized EM reliability models into two; the diffusion path model and the driving force model.

where the subscript s, b, i, p, and gb denote surface, bulk, interface, pipe, and grain boundary, while $fq(q=s,b,i,p, and gb)$ which depends on the interconnect geometry and structure is the proportion of atoms diffusing through a given path. $Ω$ is the atomic volume. At temperature less than 400 °C, bulk and pipe diffusion are basically negligible. Hence, surface, interphase, and grain boundary diffusion dominate in most line interconnect. Concise description of diffusion path reported in literature with respect to commonly used interconnect line materials is provided. Due to many triple points peculiar to aluminum microstructure, grain boundary activation energy (AE) is lower, compared to the AE at its high protective surface or interphase. Hence, grain boundary diffusion is the predominant diffusion path in aluminum line [81]. On the contrary, copper with less protective surface, exhibits lower activation energy at its interface compared to order paths. Other electromigration studies, affirm that surface migration is the most rapid diffusive pathway, even faster than both grain boundary [82,83] and interface diffusion [84] in copper and its alloys-based interconnect. Due to the high rise in copper line resistance associated with miniaturization, strong research efforts are currently channeled toward materials such as cobalt, ruthenium as well as topological metals [85,86]. Cobalt interconnects have already been implemented in advanced nodes [85]. The attractive feature of these new materials is their ability to maintain or experience only very low resistance rise as the line thickness is reduced to nanoscale. While, grain boundary diffusion has been reported as the predominant diffusion path in cobalt and ruthenium [87], in topologically metals the fastest diffusion path is bulk [85]. Table 2, depicts interconnect material and the predominant diffusion path.

Generally, reliability models based on diffusion approach, is known to be insufficient, as other factors such as stress gradient, thermal gradient as well as impurities, and resistivity scaling are known to facilitate EM. Developing a reliability model which captures other EM contributory factors, facilitated a lot of research attention to driving force-based reliability models.

Atomic flux diffusion has been described as the primary cause of EM. Several factors, such as electron wind force, stress gradient, thermal gradient, and atomic concentration gradient have been reported to drive EM, which has led to numerous reliability models [89–94]. In this study, we classify these models into traditional and physics-based models. Table 3 summarizes the major driving force inspired by EM reliability models found in literature. It is important to note that Table 3 does not capture all related references mentioned in-text.

Lloyd and Kitchin [95] implemented numerical method and found that the current density exponent associated with Black's model is also two. Many of the traditional models have faced overwhelming criticism due to conservativeness and their applicability to single wire segment. In addition, stress contributed by other connected wires, or temperature variations is often handled by overestimating the EM effect. To address these problems with the view to enhance prediction accuracy, for multisegment interconnect facilitated the development of physics-based EM models.

Physics EM models: EM models based on PoF offers the benefit of better reliability prediction in terms of accuracy. In this paper, physics-based models found in literature are classified into five. That is, Korhonen's model, three phase compact model, voltage-based model, saturated volume-based, and void based. All other models which do not fall under the above-mentioned five are classified as other model.

Korhonen's model: Pioneering physics-based EM modeling could be traced to a model developed by Korhonen et al. [96], which is currently referred to as Korhonen's model. To illustrate the basis of their model development, consider the dual damascene interconnect depicted in Fig. 4(a). Electrons flow from the (M1) interconnect line to M2 interconnect line. In this structure, M2 is separated from M1 using Ta barrier layer. After some time, rise in hydrostatic stress and stress gradient acting counterforce to atomic migration occurs due to unidirectional electrical load. Generally, the longer the line, the higher the tendency for the stress to reach critical level, thereby resulting in a void nucleation at the cathode or hillock at the anode.

The expression of $σ$ for finite line with and without void under constant diffusion coefficient as well as case of stress-dependent diffusion coefficient can be found in Ref. [95]. Based on Korhonen's model many hydrostatic stress-based kinetics models, which are generally more accurate than traditional model have been developed [96–103]. Although Korhonen's model is fundamental to the development of EM physics of failure, it was only applied to a single wire segment. In addition, recent studies show that void nucleation does not cause increase in resistance or failure, except it grows to a critical size often corresponding to the diameter of via or cross-sectional area of the interconnect [97,98].

To capture void incubation and growth period facilitated the development of three phase compact EM models. This model which has been experimentally validated is based on the principle that a nucleated void must grow to a critical size, often the cross-sectional area of the interconnect before current will flow over the interconnect layer, which results in high current density as well as joules heating. Experimental plot verifying these three regions can be found in Ref. [99]. Figure 5 depicts these phases, and the resultant resistance rises with time. During the nucleation phase, a void is not formed until time $tnc$⁠. Therefore, the resistance remains constant. During the incubation phase, defined by the time from $tnc$ to $ti$⁠, the void has nucleated, but its size is not significant. Similarly, the resistance remains basically unchanged. The incubation time (⁠$ti$ − $tnc$⁠) for single and multisegment interconnect is expressed as the following equations, respectively.

where $α$ denotes the line CTE, $∇σ, and ∇T$ are the stress and thermal gradient, respectively. $v$ denotes the Poisson ratio. A key merit of the mass divergence model is that it considers the effect of other migration mechanisms such as stress migration and thermo-migration nearly impossible to isolate from EM.

Other EM models, have also been reported. Most of these models are based on some of the above-described variants, with modification in the solution solving technique. For instance, in Ref. [114] semi-analytical technique, based on separation of variables (SOV) method was used to model EM reliability for multiline interconnect. Similarly, in Ref. [115] semi-analytic solution based on accelerated separation of variable (ASOV) method was implemented to solve Korhonen's equation for multiline interconnects. In Refs. [116] and [117], analytical solutions, which can be applied to multiline interconnect were used to solve EM reliability problem for a variety of interconnect such as single, T, and cross-shaped lines. EM dynamic models with capability to model recovery effects under time varying current density and temperature changes were proposed in other studies [118–120]. Some other studies reported that the recovery effects consideration at system level could facilitate improvement in EM lifetime [121,122]. In Refs. [123] and [125] the stochastic behavior and EM impact of power grid and signal line interconnect carrying AC currents was investigated. In Ref. [126] a detailed AC EM analysis for signal interconnect based on Monte Carlo method was presented. In Ref. [127], EM-susceptible wires were tracked using a hierarchical EM mortality check algorithm. They compared their result with Korhonen's model for a wire with a finite and semifinite length and reported that Korhonen's model may not be accurate for very long interconnect line. In Ref. [128], power grids stochastic EM analysis, was proposed using the Hermite polynomial chaos-based stochastic analysis. In Ref. [129] thermo-mechanical stress and EM stress on the array of vias for copper wires was proposed and showed that a via in a via array has a different lifetime due to layout dependency. Recently, in Ref. [130] two methods were implemented to trigger interconnect failure. In the first method, an active wire segment is converted to a passive sink, while in the second method, a passive sink is converted to an active sink. In Ref. [131], the two methods described in Ref. [130] were modified by a direct conversion of an active wire segment into an active sink. This approach facilitated easy mortality monitoring of the interconnect structure during operation by simply changing the direction of current flow in the sink segment. Finite different method (FDM) and finite element method (FEM) are well known to be very accurate, but inefficient for very large interconnect wires analysis. To address these FDM and FEM deficiencies, an analytic approach, which basically used eigenfunction to solve Korhonen's equation was proposed in Ref. [121]. Their method has potential to give the exact solution of stress evolution for multiline interconnect for both nucleation and growth phases at a specified time.

Notwithstanding over three thousand articles already published on EM, most experimental data collection effort has mainly concentrated on only current density and temperature as the acceleration stress factors, even though a lot of research works have recognized mechanical stress as a significant EM accelerating factor. To address that, in Ref. [132], a test vehicle designed to apply mechanical stress, current density, and temperature was built. In the study, reliability data were collected based on change in resistance. However, physics-based analysis was not carried out to augment experimental effort. We believe that future research effort will standardize EM three stress factors test plan as well as develop more physics-based models that correctly represent the type of data collected. Also, despite numerous publications affirming the inaccuracy of Black's model for EM time to failure prediction, JEDEC standards [133–136], for testing and time to failure estimation are still based on Black's model. In addition, little effort was found to be channeled toward the assessment of the effect of stress factor interaction on the reliability metric for EM. Not considering stress interaction for multistress prevailing would likely reduce the accuracy of any estimation of interest.

Solution pH greatly affects metal corrosion. The pH-potential diagrams depicted in Fig. 6, are a plot of equilibrium potential (E) against pH for Aluminum. Even though Fig. 6, provides limited information on the corrosion process kinetics, it clearly shows the oxide layer thermodynamic stability boundaries.

The pH–potential diagram for aluminum comprises of three regions: immunity (I), passivation (III), and corrosion (II and IV). Pure aluminum in the present water develops aluminum hydroxide $(Al(OH)3)$ coating on its surface, which facilitates outstanding oxidation resistance [145,146]. From, the pH diagram, $Al(OH)3$ thermodynamic stability is only between pH 4–9. The $Al(OH)3$⁠, can react with an acid or a base [147]. It oxidizes to form Al³⁺-ions in an acid solution. Al³⁺-ions are unstable as well as possess low affinity to migrate [141]. At the cathode, it forms aluminates when it reacts with hydroxide ions.

Figure 7(b) depicts the electrochemical migration failure mechanism. The potential difference of metals plays a major role on the rate of corrosion. For galvanically connected metal, the higher the difference in potential, the higher the magnitude of the driving force. Table 4 shows the potential for most metals used in electronic devices.

In general, corrosion process basically involves three steps: oxidation, metal ion migration, and reduction [148]. It is well known to be affected by the humidity, temperature, pH, electric field, process, and service-related contaminants, as well as intermetallic compound [149,150]. Based on the corrosion predominant stress factors, many reliability models have been developed. We classify these models into two: classical models and physics-based models. Table 5 summarizes some notable corrosion-based reliability models found in literature. In Ref. [140] other corrosion classical models were reported. We observed that they are basically a repetition of one of the models given in Eqs. (60)–(64), with slight variation in model parameters. Hence, were ignored because the intension of this review was not to repeat an already published review, but rather to capture newly models developed since Pecht et al. [140] was published.

where $ΔR/Ro$ is the change in wirebond resistance, $ko$ is the surface reaction rate constant, and $Pcl2$ is the concentration of gaseous chlorine. Compared to fatigue and electromigration failure mechanisms, physics-based corrosion models have not received a lot of attention. We feel that insufficient understanding of mathematical linkage between critical aspects dealing with a wide range of potentially relevant corrosion degradation factors, as well as difficulty in addressing the existence of nondeterministic (uncertain) modeling parameters, are among factors affecting the low attention given to corrosion mechanism-based reliability models. In addition, JESD22-A107B [163] as well as other standard on corrosion mainly focus on test protocol. Lack of reliability-based prediction model based on corrosion failure mechanism, incorporated into standards may cast doubt on the validity of prediction models found in literature. Nonetheless, more research activities are required in this area to facilitate development of more robust physics-based models.

In Sec. 4 reliability models associated with corrosion failure mechanism in electronics devices were described. Most of the models in Sec. 4, didn't consider the effect of electric field. In this section, a failure mechanism driven by the combined presence of an applied electric field and liquid medium known as CFF is reviewed. This failure mechanism was first observed in 1955, by researchers at Bell Laboratories [164] on silver. In their investigation, silver in contact with insulating materials was found to be removed from the anode and deposited in a different location, which resulted in breakdown of the insulating material. In Refs. [165–167], Au, Cu, Ni, Sn, and Pb were found to migrate, which led to microcircuits insulation breakdown. The failure mode for this mechanism includes formation of shorts that grows through the substrate and between conductors of same size as a substrate [168]. Generally, CFF is known to occur in two steps: organic material delamination and moisture absorption at the interface and metal migration leading to loss of insulation resistance. Several reliability models for time to failure due to CFF have been reported and are subsequently discussed.