Time-dependent Failure Research Articles

TEM Investigation of Time-Dependent Dielectric Breakdown Mechanisms in Cu/Low-k Interconnects

The time-dependent dielectric breakdown (TDDB) in on-chip interconnect stacks is one of the most critical failure mechanisms for microelectronic devices. The aggressive scaling of feature sizes, on both devices and interconnects, poses serious challenges to ensure the required product reliability. Conventional reliability tests and postmortem failure analysis provide only limited information about the physics of failure mechanisms and degradation kinetics. Therefore, it is necessary to develop new experimental approaches and procedures to study the time-dependent failure mechanisms and degradation kinetics, in particular. In this paper, comprehensive transmission electron microscopy (TEM), particularly an in situ experimental methodology, is demonstrated to investigate the TDDB degradation and failure mechanisms in Cu/low-k interconnect stacks. A dedicated “tip-to-tip” test structure is designed in the 32-nm complementary metal–oxide–semiconductor (CMOS) technology node, to restrict the failure site, and is the key basis for the in situ and ex situ TEM investigations. High-quality imaging and chemical analysis are used to identify the failure mechanism and study the kinetic process. The in situ electrical test is also integrated into the in situ TEM investigation, to provide an elevated electric field to the dielectrics. Electron tomography is utilized to characterize the directed Cu diffusion in the insulating dielectrics. These experimental approaches open a different possibility to study the TDDB failure mechanism in interconnect stacks of microelectronic products, and it could also be extended to other structures in active devices.

Downhill progressive landslides in long natural slopes: triggering agents and landslide phases modeled with a finite difference method

A large landslide in Tuve (Gothenburg, Sweden, 1977) initiated the development of a model for slope stability analysis taking the deformation-softening of soft sensitive clays into consideration. The model studies triggering agents and five phases in progressive slope failure are identified: (1) in situ, (2) disturbance, (3) unstable “dynamic”, (4) transitory (or permanent) equilibrium, and (5) “global” failure. The clay resistance in these phases may differ widely; mostly due to different rates of loading. Two time-dependent failure criteria are defined: (i) the triggering load condition in the disturbance phase 2 and (ii) the transitory equilibrium in phase 4, indicating whether minor downhill displacements or a veritable landslide catastrophe will occur. The analysis explains why downhill landslides tend to spread over vast areas of almost horizontal ground further downslope. The model has been applied to landslides in Scandinavia and Canada. Three case studies are briefly discussed. The model is a finite difference approach, where local downhill deformations caused by normal forces is maintained compatible with deviatory shear deformations above — and, if relevant, below — the potential (or the established) failure surface. Software and an easy-to-use spreadsheet are introduced as well as recent developments.

Maximum probable life time analysis under the required time-dependent failure probability constraint and its meta-model estimation

Time-dependent reliability (failure probability) aims at measuring the probability of the normal (abnormal) operation for structure/mechanism within the given time interval. To analyze the maximum probable life time under a required time-dependent failure probability (TDFP) constraint, an inverse process corresponding to the time-dependent reliability is proposed by taking the randomness of the input variables into consideration. The proposed inverse process employs the monotonicity between the TDFP and the upper boundary of the given time interval which reflects the life time, and an adaptive single-loop sampling meta-model for the time-dependent limit state function is presented to estimate the TDFP at the given time interval flexibly. Since the TDFP is generally monotonic to the upper boundary of the given time interval, thus by adjusting the probable upper and lower boundaries of the time interval in which the corresponding TDFPs include the required TDFP constraint, the proposed approach can always search the maximum probable life time at the required TDFP by the dichotomy. By introducing the time variable as an input which is the same level as the input random variables and constructing the adaptive single-loop sampling meta-model for the time-dependent limit state function in a longer time interval with the TDFP bigger than the required TDFP, the TDFP in any subintervals of the time interval involved in the constructed meta-model can be estimated as a byproduct of the constructed meta-model without any additional actual limit state evaluations. Then the efficiency for analyzing the maximum probable life time is improved by the dichotomy and the unified meta-model of the time-dependent limit state function. Two examples are employed to illustrate the accuracy and the efficiency of the proposed approach.

Experimental observation of TDDB-like behavior in reverse-biased green InGaN LEDs

This paper reports the outcome of a series of reverse-bias experiments performed on commercial GaN-based green LEDs. The experimental results showed that green LEDs submitted to reverse bias i) show a time-dependent failure when they are submitted to constant (reverse) voltage stress, at a bias point smaller than the BDV; ii) experience an increase of the reverse-bias electro-luminescence signal, well-correlated with the increase of the reverse leakage current; iii) the TTF (Time-To-Failure) related to the time-dependent breakdown process has an exponential dependence on stress voltage; iv) the TTF is Weibull distributed. This work provides the first experimental demonstration of time-dependent failure of GaN LEDs.

Study of the stability of e-mode GaN HEMTs with p-GaN gate based on combined DC and optical analysis

This paper investigates the robustness of normally-off High Electron Mobility Transistors (HEMTs) with p-GaN gate submitted to forward gate bias overstress. By means of combined DC and spectral analysis we demonstrate the following results: (i) the devices demonstrate a time-dependent failure mechanism; (ii) time to failure (TTF) can be described by a Weibull distribution with a shape factor higher than 1, suggesting a wear-out failure; (iii) the devices have an estimated 20-years lifetime for a gate voltage of 7.2V; (iv) TTF is temperature-dependent, with an activation energy of 0.5eV; (v) emission microscopy reveals the presence of hot spots, whose emission originates from yellow luminescence and/or hot electron radiation.

Time-dependent brittle creep-relaxation failure in concrete

In real-world engineering applications, concrete is usually subjected to both creep and stress relaxation. Observations are necessary to understand this coupling process. This paper presents the results of brittle creep-relaxation experiments performed on concrete. Instead of tending to an asymptotic value, the stress in all the test specimens dropped sharply with a rapid increase in the strain before failure, when the boundary displacement was kept constant. The acceleration in the tertiary stage exhibited power-law behaviour, with the exponent − α being − 0·58 ± 0·13 for the stress rate and − 0·56 ± 0·12 for the strain rate. For each specimen, the time-to-failure exhibited power-law dependence on the secondary creep (relaxation) rate, with the exponent being 0·97 ± 0·09 for strain and 0·98 ± 0·09 for stress. These results suggest that it should be possible to predict the time-to-failure of concrete by monitoring its behaviour during the steady and critical stages.

A modified GO-FLOW methodology with common cause failure based on Discrete Time Bayesian Network

The GO-FLOW methodology is a success-oriented system reliability modelling technique for multi-phase missions involving complex time-dependent, multi-state and common cause failure (CCF) features. However, the analysis algorithm cannot easily handle the multiple shared signals and CCFs. In addition, the simulative algorithm is time consuming when vast multi-state components exist in the model, and the multiple time points of phased mission problems increases the difficulty of the analysis method. In this paper, the Discrete Time Bayesian Network (DTBN) and the GO-FLOW methodology are integrated by the unified mapping rules. Based on these rules, the multi operators can be mapped into DTBN followed by, a complete GO-FLOW model with complex characteristics (e.g. phased mission, multi-state, and CCF) can be converted to the isomorphic DTBN and easily analyzed by utilizing the DTBN. With mature algorithms and tools, the multi-phase mission reliability parameter can be efficiently obtained via the proposed approach without considering the shared signals and the various complex logic operation. Meanwhile, CCF can also arise in the computing process.

Time-Dependent Failure of GaN-on-Si Power HEMTs With p-GaN Gate

This paper reports an experimental demonstration of the time-dependent failure of GaN-on-Si power high-electron-mobility transistors with p-GaN gate, submitted to a forward gate stress. By means of combined dc, optical analysis, and 2-D simulations, we demonstrate the following original results: 1) when submitted to a positive voltage stress (in the range of 7–9 V), the transistors show a time-dependent failure, which leads to a sudden increase in the gate current; 2) the time-to-failure (TTF) is exponentially dependent on the stress voltage and Weibull-distributed; 3) the TTF depends on the initial gate leakage current, i.e., on the initial defectiveness of the devices; 4) during/after stress, the devices show a localized luminescence signal (hot spots); the spectral investigation mainly reveals a peak corresponding to yellow luminescence and a broadband related to bremsstrahlung radiation; and 5) 2-D simulations were carried out to clarify the origin of the degradation process. The results support the hypothesis that the electric field in the AlGaN has a negligible impact on the device failure; on the contrary, the electric field in the SiN and in the p-GaN gate can play an important role in favoring the failure, which is possibly due to a defect generation/percolation process.

Molecular and morphological studies to understand slow crack growth (SCG) of polyethylene

Slow crack growth (SCG) is a time-dependent brittle-type failure that polyethylene (PE) pipes suffer from when under low stress levels. This study discusses the relation of morphological, molecular weight and molecular weight distribution, rheological, thermal and tensile properties of different PE materials with SCG behavior obtained from the crack round bar (CRB) test, strain hardening (SH) test, and notched pipe (NPT) test. It was observed that increasing the molecular weight and its distribution, short-chain branches, co-monomer content and length, as well as lateral lamellar area increased the SCG resistance and the subsequent time to failure. This was attributed to the enhanced interlamellar entanglement and tie molecules that resisted deformation for a longer time. In addition, SCG resistance was found to decrease with decreasing lamella thickness and degree of crystallinity (within similar molecular weight range). A decrease in the SCG resistance was observed on increasing the onset degradation temperature. Despite the lack of correlation established from tensile tests in the elastic region, SH and CRB values were found to be directly related. As strain hardening modulus increased, time to failure also increased. Zero-shear viscosities also reflected the SCG resistance properties of the samples, as CRB values increased with increasing zero-shear viscosity.

Automotive Water Cooling System Analysis Subject to Time Dependence and Failure Issues

In an automobile engine, the heat transfer cannot be possible without cooling system support. The cooling system has a great importance in the engines. It coolants overheat of the engine, and prevents it from breakdown, that's why a highly reliable cooling system is the necessity of every engine but there are many failure issues with a cooling system which are time dependent. This paper investigates the performance of a water cooling system with the consideration of their significant components by taking the attention of three types of time dependent failure issues while the water cooling system is maintained by the sufficient repair facility. It is obvious that in the lack of maintenance, failure issues in water cooling system lead with the increment of time. Maintenance and operating costs of water cooling system affect the economy of overall engine very much, so, it is necessary to be aware about overheating of engines during peak ambient conditions when it is operated with full capacity. Hence, a Mathematical model of water cooling system is proposed by using the Markov process and supplementary variable technique.

Development of the APSRA+ Methodology for Passive System Reliability Analysis and Its Application to the Passive Isolation Condenser System of an Advanced Reactor

Research in the field of passive system reliability analysis is garnering sharp interest in the nuclear community. Passive systems are being utilized extensively in current- and future-generation reactors for their normal operations as well as for safety critical operations during any accidental conditions. In this paper, we present a methodology called Analysis of Passive System ReliAbility Plus (APSRA+) for evaluating reliability of passive systems. This methodology is an improved version of the existing APSRA methodology. The methodology has been applied to the passive isolation condenser system (ICS) of the AHWR (Advanced Heavy Water Reactor). With the help of the APSRA+ methodology, the probability of the passive ICS failing to maintain the clad temperature under 400°C is estimated to be of the order 1×10−10.Important features of APSRA+ are the following. First, it provides an integrated dynamic reliability method for the consistent treatment of dynamic failure characteristics such as multistate failure, fault increment, and time-dependent failure rate of components of passive systems. Second, this methodology overcomes the issue of process parameter treatment by just the probability density function or by root cause analysis, by segregating the parameters into dependent and independent process parameters and then giving a proper treatment to each of them separately. Third, the methodology treats the model uncertainties and independent process parameter variations in a consistent manner.In APSRA+, the important parameters affecting the passive system under consideration are identified using sensitivity analysis. To evaluate the system performance, a best-estimate system code is used with due consideration of the uncertainties in empirical models. A failure surface is generated by varying all the identified important parameters; variation from the nominal values of these parameters affects the system performance significantly. These parameters are then segregated into dependent and independent categories. For dependent parameters, it is attributed that the variations of process parameters are mainly due to malfunction of mechanical components or control systems, and hence, root cause analysis is performed. The probability of these dependent parameter variations is estimated using a dynamic reliability methodology based on Monte Carlo simulation. The dynamic failure characteristics of the identified causal component/system are accounted for in calculating these probabilities. For the treatment of independent process parameters, using APSRA+ suggests adopting and integrating classical data-fitting techniques or mathematical models. In the next steps, a response surface-based metamodel is formulated using the generated failure points. The probability of the system being in the failure zone is estimated by sampling and analyzing a sufficiently large number of samples for all the dependent and independent process parameters based on the probability of variations of these parameters, which were estimated using dynamic reliability methodology.

A Realistic Method for Time-Dependent Dielectric Breakdown Reliability Analysis for Advanced Technology Node

This paper proposes a methodology to determine a realistic time-dependent dielectric breakdown failure rate. The in-die constant voltage stress was performed to determine the chip level Weibull shape ( $\beta _{\mathrm{die}})$ and voltage acceleration factor, while a voltage ramp (Vramp) is performed in production line (inline Vramp) to determine the via-to-line and line-to-line spacing distributions. We found that for the chip population with spacing ( $s$ ) smaller than 4 nm, the in-die voltage accelerations based on power-law and sqrt-V models do not lead to a significant difference in the lifetime prediction. For the chips with large spacing, the stress voltage ( $\sim 20$ V) is significantly higher than the operating voltage (1 V). The extrapolation using the power law results in an infinitely long lifetime, which could lead to an overoptimistic reliability prediction. In this paper, a new method is introduced for a more realistic failure rate calculation, which is the superposition of the failure rates of chips with small spacing ( $s nm) and the failure rates of chips with large spacing, by using different voltage acceleration models.

Block-Layer Reliability Method for Distribution Systems under Various Operating Scenarios

This paper formulates a block-layer method for the reliability assessment of distribution systems. The characteristics of the method include: 1) identifying the impact of distribution component reliability on the system and load points using a block-layer structured assessment; 2) incorporating time-dependent failure parameters; and 3) taking account of the topological, seasonal, and meteorological features of the distribution systems under analysis. The proposed method first identifies the three critical parts of the distribution system: main supply, feeder, and secondary substation. It can also include reserve connections and distributed generation. Second, the method frames these parts into the layered structure, each corresponding to the zone of total load curtailment. To verify this reliability technique, this paper simulates distribution feeders assembled in a number of topologies and compares them with the state sampling technique. Data provided by the local utility company are processed to model the equipment and load for the base year. The results show that the proposed method can provide a wide range of partial and system indices. These values assist in the identification of parts of the distribution system and scenarios with low reliability and to determine possible remedial actions.

機器の状態遷移および経時的変化の影響を考慮したPRA手法の提案

機器の状態遷移および経時的変化の影響を考慮したPRA手法の提案

A review of fracture in viscoelastic materials

This review is written in honor of Max L. Williams who not only started this International Journal of Fracture (the author’s Ph.D. advisor. Originally the Journal was called International Journal of Fracture Mechanics) but who had a seminally fundamental influence on the course of fracture mechanics in general, and specifically as applied to the time dependent failure of elastomers/polymers. In view of that background this article reviews developments over more than 50 years, as colored by my own experiences in regard to this topic. It seems appropriate to include a historical perspective that starts during pre-journal times and addresses the need for understanding time dependent processes governing fracture in rate sensitive materials. To the largest extent, the rate dependence is important where polymers are involved, though under more limited conditions metals and igneous solids as well as ligneous ones exhibit time dependent fracture characteristics. Such facts notwithstanding, the major discussion in this contribution is devoted here to the time dependent fracture of polymeric materials, and elastomeric ones in particular. The emphasis will be thus on time dependent issues governed primarily by the fracture processes in elastomeric solids, which have evolved largely in parallel to problems devoted to the more rigid polymers. Because consideration of fracture of the rigid polymers has often, if not usually, minimized the time dependence, only cursory attention is paid to these, in spite of the fact that they constitute a very important class of materials in the modern engineering community. From an engineering perspective this review is motivated also by an exposition of a persistent lack of knowledge concerning time dependent fracture issues. Most of the work attached to the notion of viscoelastic fracture is—intentionally or by omission—associated with the phenomenon of crack growth under steady state conditions with the expectation that this understanding leads implicitly to resolution of problems governed by transient loadings. Besides reviewing the historical evolution of the knowledge in this field over the past half century, it is a main purpose of this paper to offer information that has either been ignored or has not been explored (this includes the work of the author), but which contradicts this “popular” perception. It is thus an intentionally large part of this presentation which documents compelling motivation for addressing fracture aspects, that are generally important from an engineering design and analysis point-of-view: specifically, it is intended to illustrate the remarkable degree by which the steady state solution to crack propagation deviates from experimental information when transient conditions prevail, and the large range of time scales over which this failure behavior is observed.

PROBABILISTIC CONDITION ASSESSMENT TECHNIQUE FOR TIMBER POWER POLES

Timber poles are extensively used in Australia to support overhead electric and telecommunication facilities. The strength of the pole degrades over time, and pole failure can have serious safety and economic implications. The failure occurs when stresses exceed the remaining strength of the timber element. In this paper, a probabilistic framework is developed to estimate the remaining life of the timber power pole system. The developed framework permits the user to consider the variability in the capacity of the timber pole and cross-arm, loading and deterioration processes, and to propagate the uncertainty associated in each stage of the assessment procedure. Further, the time-dependent failure rate of the pole system is estimated to develop the risk matrix to improve the current renewal and replacement decision making process used by the utility companies in Australia.

Separable Monte Carlo 방법을 적용한 부식배관 신뢰도평가

A deterministic stress-based methodology has traditionally been applied in pipeline design. Meanwhile, reliability based design and assessment (RBDA) methodology has been extensively applied in offshore or nuclear structures. Lately, the release of ISO standard on reliability based limit state methods for pipelines ISO16708 indicates that the RBDA methodology is one of the newest directions of natural gas pipeline design method. This paper presents a case study of the RBDA procedure for predicting the time-dependent failure probability of pipelines with corrosion defects, where separable Monte Carlo (SMC) method is applied in the reliability estimation for corroded pipeline instead of traditional, crude Monte Carlo(CMC) Method. The result shows the SMC method take advantage of improving accuracy in reliability calculation.

Time-dependent statistical failure of fiber networks.

Numerical simulations of time-dependent stochastic failure of fiber network have been performed by using a central-force, triangular lattice model. This two-dimensional (2D) network can be seen as the next level of structural hierarchy to fiber bundles, which have been investigated for many years both theoretically and numerically. Unlike fiber bundle models, the load sharing of the fiber network is determined by the network mechanics rather than a preassigned rule, and its failure is defined as the point of avalanche rather than the total fiber failure. We have assumed that the fiber in the network follows Coleman's probabilistic failure law [B. D. Coleman, J. Appl. Phys. 29, 968 (1958)] with the Weibull shape parameter β=1 (memory less fiber). Our interests are how the fiber-level probabilistic failure law is transformed into the one for the network and how the failure characteristics and disorders on the fiber level influence the network failure response. The simulation results showed that, with increasing the size of the network (N), weakest-link scaling (WLS) appeared and each lifetime distribution at a given size approximately followed Weibull distribution. However, the scaling behavior of the mean and the Weibull shape parameter clearly deviate from what we can predict from the WLS of Weibull distribution. We have found that a characteristic distribution function has, in fact, a double exponential form, not Weibull form. Accordingly, for the 2D network system, Coleman's probabilistic failure law holds but only approximately. Comparing the fiber and network failure properties, we found that the network structure induces an increase of the load sensitivity factor ρ (more brittle than fiber) and Weibull shape parameter β (less uncertainty of lifetime). Superimposed disorders on the fiber level reduce all these properties for the network.

Analysis of two-machine lines with finite buffer, operation-dependent and time-dependent failure modes

An analytical model for evaluating the throughput of two-machine lines, characterised by intermediate buffer with finite capacity, deterministic processing times and multiple failure modes for each machine is presented in this paper. Both operation-dependent failure and time-dependent failure are captured in a unique model as extension of the existing literature that was dealing with either one of them. Each machine has two failure modes, one is operation-dependent and the other is time-dependent. Time to failure and time to repair are assumed to be geometrically distributed. The presented method calculates the steady-state probabilities of the manufacturing system with a computational effort that depends only on the number of failure modes and not on the buffer capacity. A performance comparison of the proposed model with existing techniques is also reported, the aim is to show the error introduced by an analytical model that considers the operation-dependent failure mode as approximation of the time-dependent one.

Extensive Investigation of Time-Dependent Breakdown of GaN-HEMTs Submitted to OFF-State Stress

This paper reports the experimental demonstration of time-dependent dielectric breakdown in GaN-based high-electron mobility transistors (HEMTs) submitted to OFF-state stress. Based on combined breakdown measurements, constant voltage stress tests, and 2-D simulations, we demonstrate the following relevant results. First, GaN-based HEMTs with a breakdown voltage higher than 1000 V (evaluated by dc measurements) may show time-dependent failure when exposed to OFF-state stress with $V_{\mathrm {DS}}$ in the range 600–700 V. Second, time-to-failure (TTF) is Weibull-distributed, and has an exponential dependence on the stress voltage level. Third, time-dependent breakdown is ascribed to the failure of the SiN dielectric at the edge of the gate overhang, on the drain side. Fourth, 2-D simulations confirm that—in this region—the electric field exceeds 6 MV/cm, i.e., the dielectric strength of SiN. Finally, we demonstrate that by limiting the electric field in the nitride through epitaxy and process improvements, it is possible to increase the TTF by three orders of magnitude.