Sah C-T, Jie B.B.
University of Florida, US
Keywords: Black formula, electromigration, electron-windless model
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 [1] in gold wire, and empirically modeled by the 1969 Black formula [2] 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 [3]. Since the first Landauer theoretical analysis in 1957 [4], 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 [5] 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 [6] 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.
Journal: TechConnect Briefs
Volume: 3, Nanotechnology 2008: Microsystems, Photonics, Sensors, Fluidics, Modeling, and Simulation – Technical Proceedings of the 2008 NSTI Nanotechnology Conference and Trade Show, Volume 3
Published: June 1, 2008
Pages: 782 - 782
Industry sector: Sensors, MEMS, Electronics
Topic: Compact Modeling
ISBN: 978-1-4200-8505-1