Engineers in the manufacturing industries have used accelerated test (AT) experiments for many decades. The purpose of AT experiments is to acquire reliability information quickly. Test units of a material, component, subsystem, or entire systems are subjected to higher-than-usual levels of one or more accelerating variables such as temperature or stress. Then the AT results are used to predict life of the units at use conditions. The extrapolation is typically justified (correctly or incorrectly) on the basis of physically motivated models or a combination of empirical model fitting with a sufficient amount of previous experience in testing similar units. The need to extrapolate in both time and the accelerating variables generally necessitates the use of fully parametric models. Statisticians have made important contributions in the development of appropriate stochastic models for AT data (typically a distribution for the response and regression relationships between the parameters of this distribution and the accelerating variable(s)), statistical methods for AT planning (choice of accelerating variable levels and allocation of available test units to those levels), and methods of estimation of suitable reliability metrics. This paper provides a review of many of the AT models that have been use successfully in this area.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1027&context=stat_las_preprints

A Review of Accelerated Test Models

Miniaturization has steadily increased the economic usefulness of digital electronics through the past two decades. A variety of physical arguments are brought to bear on the question of how far miniaturization can be extended. The implications of the laws of quantum mechanics and thermodynamics for information storage are examined. The need for power dissipation in electrical information processing is demonstrated and the limits set on miniaturization by the problems of removing the heat thereby produced are estimated. limits with origins in properties of the materials used to make electronic devices are reviewed. The potential performance of various technologies based on nonsemiconductor phenomena is estimated and compared with the limits found for planar silicon technology. Attempts are made to guess at all of the many unknown parameters that enter into broadly applicable quantitative expressions of the properties of logic circuitry so that actual values of the limits can be estimated.

Physical limits in digital electronics

Electromigration studies on Cu interconnects are reviewed. Some history and more recent results are discussed along with a description of the present interpretations of the active mass transport mechanisms involved in Cu electromigration. The issue of the dual-damascene process and its potential effect on EM reliability is described with special focus on the peculiarities of the dual-damascene interconnect architecture compared to more conventional subtractively etched Al-based interconnects. Experiments performed on dual-damascene interconnects that highlight electromigration reliability issues such as early failure, a tentative explanation for via electromigration failure, and the Blech effect, are summarized. Emphasis is placed on an experimental methodology that uses large interconnect ensembles in a multi-link configuration. Such a large scale study of nearly 10000 interconnects has shown statistical evidence of bimodal failure behavior consistent with the presence of a weak and strong failure mode, which have been identified as voiding, respectively, within the via and the trench at the cathode end of an interconnect. A multi-link approach has also demonstrated a length-dependent distribution of failures that yields a (j/spl middot/L)/sub c/ product value of about 9000 A/cm in dual-damascene Cu/oxide interconnections and is consistent with mass transport that is controlled by the presence of extended defects within Cu such as grain boundaries, interfaces, and/or surfaces. The study of dual-damascene Cu has demonstrated the importance of statistics in analyzing EM reliability.

Electromigration reliability issues in dual-damascene Cu interconnections

In recent years it has become well established that fast diffusion along grain boundaries plays a key role in many important metallurgical processes including cases where net mass is transported along boundaries which act as sources and/or sinks for the fluxes of atoms. In addition, considerable advances have been made in understanding grain boundary structure, and new techniques have become available for studying kinetic phenomena in grain boundaries. This lecture will attempt to review our current knowledge of the atomistic mechanisms responsible for these grain boundary diffusion phenomena. Relevant aspects of the structure of grain boundaries and the point and line defects which may exist in grain boundaries are described first. The important experimental observations are then discussed. Diffusion models are then taken up, and it is concluded that the atomic migration occurs by a point defect exchange mechanism which, in at least the vast majority of boundaries in simple metals, most likely involves grain boundary vacancies. The grain boundary sources and/or sinks required to support divergences in the atomic (vacancy) fluxes are grain boundary dislocations. Phenomena therefore occur which resemblethe Kirkendall Effect in the bulk lattice in certain respects. Additional topics are discussed which include effects of boundary structure on boundary diffusion and the question of whether or not boundary diffusion is faster along migrating than stationary boundaries.

F.M. D'heurle

Papers

Electromigration in Thin Films