Authors: C-T Sah, B.B. Jie
Affilation: University of Florida, United States
Pages: 782 - 782
Keywords: electromigration, electron-windless model, Black formula
Electromigration (EM) is the transport of atoms and ions in metals at high electrical current density (>100kA/cm^2) leaving behind voids. It was delineated in 1961 by Huntington  in gold wire, and empirically modeled by the 1969 Black formula  to fit the Time To Failure (TTF) experimental data of metal interconnect lines in integrated circuits with power law dependences of electron current density and sample temperature, and a thermal activation energy, TTF = AJ^-b*T^c*exp(-Ea/kT). Tan and Roy recently reviewed the 40 year applications . Since the first Landauer theoretical analysis in 1957 , theorists have attempted for 50 years to derive the Black formula by trying to justify the force of the electrons to move an atom, known as electron wind. Landauer concluded in 1989  that electron wind is untenable even at the most fundamental and complete many body quantum transport theory. Sah showed in his 1996 homework solution manual for undergraduate device core course  that the Black formula can be derived for a generic void model using the simple classical macroscopic transport theory, including drift, diffusion and the often if not always neglected generation recombination trapping (DDGRT) of the electrons or/and holes and the ions, without the empirical electron wind force. We review this windless model in this presentation.