Statistical analysis of early failures in electromigration

Abstract

The detection of early failures in electromigration (EM) and the complicated statistical nature of this important reliability phenomenon have been difficult issues to treat in the past. A satisfactory experimental approach for the detection and the statistical analysis of early failures has not yet been established. This is mainly due to the rare occurrence of early failures and difficulties in testing of large sample populations. Furthermore, experimental data on the EM behavior as a function of varying number of failure links are scarce. In this study, a technique utilizing large interconnect arrays in conjunction with the well-known Wheatstone Bridge is presented. Three types of structures with a varying number of Ti/TiN/Al(Cu)/TiN-based interconnects were used, starting from a small unit of five lines in parallel. A serial arrangement of this unit enabled testing of interconnect arrays encompassing 480 possible failure links. In addition, a Wheatstone Bridge-type wiring using four large arrays in each device enabled simultaneous testing of 1920 interconnects. In conjunction with a statistical deconvolution to the single interconnect level, the results indicate that the electromigration failure mechanism studied here follows perfect lognormal behavior down to the four sigma level. The statistical deconvolution procedure is described in detail. Over a temperature range from 155 to 200 °C, a total of more than 75 000 interconnects were tested. None of the samples have shown an indication of early, or alternate, failure mechanisms. The activation energy of the EM mechanism studied here, namely the Cu incubation time, was determined to be Q=1.08±0.05 eV. We surmise that interface diffusion of Cu along the Al(Cu) sidewalls and along the top and bottom refractory layers, coupled with grain boundary diffusion within the interconnects, constitutes the Cu incubation mechanism.

Statistical Analysis of Electromigration Lifetimes and Void Evolution for Cu Interconnects

“…Hence, the question arises which line length is the correct choice to obtain lifetime distributions with truly lognormal behavior and not multi-lognormal characteristics, if such a length even exists. Gall et al [1999Gall et al [ , 2001 ruled out the Weibull distribution as a possible function to fit EM data. Since this is the only major distribution that actually scales, experimental results from EM tests with various numbers of links were examined with regard to a Weibull distribution fit.…”

A framework for reliability-aware design exploration on MPSoC based systems

“…The first is a set of random TGs with 5 to 15 tasks generated synthetically using TGFF. 10 The execution time of each task on the RISC/DSP is generated randomly between 100 and 1000. The second is an mpeg2 decoder example from [47] that consists of 13 tasks.…”

“…Based on large set of experiments, researchers proposed several empirical models. For example, EM and TDDB are usually considered to have lognormal and Weibull distributions, respectively [7,10]. Recent work [48] proposes a framework that integrates device, component and system level models.…”

A fuzzy TOPSIS and Rough Set based approach for mechanism analysis of product infant failure

“…A number of researchers about infant failure have focused on the estimation method of lifetime distributions from perspectives of traditionally statistical inferences (Kuo and Kim, 1999;Gall et al, 2001;Bebbington et al, 2009). However, only a few research works have been done on the mechanism analysis and root causes identification of product infant failure so far.…”

“…Quality improvement is a routine mission of the product engineering, and the optimization of product infant failure rate is the most important and difficult task (Köksal et al, 2011;Gall et al, 2001). Infant failures have often been referred to the quality problems occurred in the "infant" region of leftmost of bathtub curve of product life (Roesch, 2012), and infant failures are assumed to be caused mainly by design vulnerabilities and manufacturing defects (Jiang and Murthy, 2009).…”