Previous work on planning accelerated life tests has assumed that the scale parameter σ for a location-scale distribution of log lifetime remains constant over all stress levels. This assumption is, however, inappropriate for many applications, including accelerated tests for metal fatigue and certain electronic components. This article extends the existing maximum likelihood theory for test planning to the nonconstant σ model and presents test plans for a large range of practical testing situations. The test plans are optimum in that they minimize the asymptotic variance of the maximum likelihood estimator of a specified quantile at the design stress. The development and discussion in the article, as well as the theory given in the Appendix, applies to accelerated-life-test models in which the log time-to-failure can be modeled as a location-scale distribution. The test setup assumes simultaneous testing of units with time censoring. We give particular numerical results for the Weibull failure-time distr...

Optimum Accelerated Life Tests Wth a Nonconstant Scale Parameter

The term “stress migration” in Al lines in ICs is used in a broad sense to described thermally induced void formation and resulting failures, i.e. open circuits and increases in resistance, which occur in high-temperature processes, such as insulating film deposition on Al lines in IC fabrication, and during storage tests at elevated temperatures for evaluating the reliability of fabricated ICs. Stress migration degrades the IC production yield and reliability. The problem becomes more serious as the linewidth decreases. This paper reviews stress migration-induced void formation and resulting failures in Al lines, and is intended to clarify current experimental and theoretical knowledge of their characteristics. The main topics discussed are classification and characteristics of stress migration, accelerated life test results and failure prediction, Al line stress, void formation models and countermeasures for reducing failures.

Stress-induced void formation in metallization for integrated circuits

Electromigration threshold was measured in oil bths at the temperature range 100–280°C, approaching operation temperature of integrated circuits. For uncovered unannealed films, threshold was constant in the temperature range below 200°C, yielding a low threshold value of about 420 A/cm (42 μm × 105 A/cm2) for the product of current density and stripe length. Annealing does not affect temperature behavior, but threshold values grow with increasing annealing temperatures. Threshold does not depend on annealing atmospheres, such as N2, O2 and N2/H2. Different film compositions like Al, Al/Si and Al/Si/1% Cu are equivalent concerning threshold. Elevated, slightly temperature-dependent threshold values were measured using covering SiO2 films. The threshold of covered films depends on test conditions. Reduced current densities and stress times result in increasing values which may be beneficial for electromigration reliability. Moreover, electromigration test results can be influenced by threshold, which has to be considered. The discrepancy to former threshold results is assumed to be due to N2/H2 test ambients, reducing electromigration mass flow. The reason for threshold is suggested to proceed from different bond energies for the transition from grain boundaries to surface.

Electromigration threshold in aluminum films

Electromigration‐induced failure mechanisms were investigated by means of extremely sensitive resistance change measurements and simultaneous observations using scanning electron microscopy. Abrupt changes in resistance (ACRs), classified into three types: downward steps, upward steps, and oscillations, were found to occur frequently during the dc current stressing test. It was conspicuously observed that there was a rapid void annihilation associated with an abrupt increase in resistance, and a rapid void formation with a decrease in resistance. ACRs are considered to be caused by a rapid change in the number of excess vacancies concomitant with void annihilations or formations. The thermodynamical analysis on the stability of a void strongly suggests that the change of a local stress from tensile to compressive causes a rapid annihilation of voids, and the opposite one causes a rapid formation. Temperature dependence of the intensity of ACRs exhibited an activation energy of 0.43 eV, which implied that ...

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Electromigration-induced abrupt changes in electrical resistance associated with void dynamics in aluminum interconnections

An interconnection structure using a TiN/Al-1% Si-0.5% Cu/TiN/Al-1% Si-0.5% Cu/TiN/Ti multilayer conductor was investigated as a quarter-micrometer interconnection candidate for 256-Mb DRAMs. It was found that intermetallic compounds such as TiAl/sub x/ were formed at both grain boundaries of Al-Si-Cu and interfaces between Al-Si-Cu and TiN of the multilayer, resulting in both increase in Vickers hardness and suppression of stress relaxation. The multilayer conductor strip, which was covered with plasma-enhanced chemical vapor deposition silicon nitride (P-SiN), suppressed stress-induced voiding after heat treatment at 500 degrees C. Electromigration tests for quarter-micrometer wide multilayer strips indicated the improvement in the mean time to failure and the increase of the standard deviation. >

A quarter-micrometer interconnection technology using a TiN/Al-Si-Cu/TiN/Al-Si-Cu/TiN/Ti multilayer structure

The activation energy E g for electromigration along aluminum grain boundaries has been examined intensively by many authors and different methods. However, the common techniques yield very contradictory results, with E g ranging between 0.3 and 1.2 eV. For clarifying these contradictions, the present work examines the validity of the different test methods and their basic assumptions. It is shown that for most of these techniques the test quantity being measured is given by time dependent divergences which cause local stripe variations from scarcely detectable voids up to stripe interruptions. This means that constant conditions are not maintained during the test period, thus yielding more or less incorrect activation energies. A well defined measurement of the mass transport and the activation energy is practicable only if the divergence of the electromigration is both constant for a fixed test condition and proportional to the flux for different test conditions. Additionally, all other diffusion terms except electromigration must be negligible, especially the diffusion term based on pressure gradients. These preconditions are satisfied for the direct measurement of the drift velocity of an aluminum front on a TiN stripe, proper test conditions provided. That is why this technique is applied here extensively for clarifying several contradictions. Other techniques were performed for comparison yielding different results. The here obtained valid values of E g and their variation between 0.43 and 0.47 eV are smaller than generally reported, even for extremely different evaporation and sputtering conditions. In contrast to former results obtained by improper test methods, the activation energy is temperature independent in the examined temperature range between 140 and 280°C, and E g is not dependent on grain size even for most different fabrication conditions, yielding grain sizes from 0.3 up to 3 μm.

Electromigration measuring techniques for grain boundary diffusion activation energy in aluminum

Besides high lifetimes and a low standard deviation of failure times, the electromigration drift velocity is an important parameter for metallization reliability. Here, lifetimes should be high and drift velocity low. For pure Al films, only properly chosen and optimized sputter conditions yield good film quality and electromigration data comparable to evaporated stripes. Annealing and oxide covering improve lifetime and reduce drift velocity of pure Al structures. For redundant AlTiAl multilayers, annealing yielded an enormous lifetime enhancement of 3 orders of magnitude. However, these stripes are not suited for practical applications because of whisker formation and of an increased drift velocity! These disadvantages do not appear for a lifetime-improving TiN intermediate layer instead of Ti. A further method of lifetime enhancement is Cu-addition which reduces the drift of stripes. Finally, for (Al + Cu)TiN(Al + Cu)-structures, lifetime is improved even further in combination with low drift velocity.

Lifetime and drift velocity analysis for electromigration in sputtered Al films, multilayers, and alloys

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Electromigration measuring techniques for grain boundary diffusion activation energy in aluminum

Lifetime and drift velocity analysis for electromigration in sputtered Al films, multilayers, and alloys