Inverse Blech Length Phenomenon in Thin-Film Stripes

Abstract

In electronics, current-induced mass depletion at the cathode is often seen to decrease with decreasing sample length; this is called the $B\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}h$ $l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}h$ $e\phantom{\rule{0}{0ex}}f\phantom{\rule{0}{0ex}}f\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t$. However, in the presence of a self-induced temperature gradient in copper film with a geometry that allows current crowding, the authors observe strong coupling between thermomigration and electromigration, which $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}s$ mass depletion with decreasing sample length. This $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}e$ $B\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}h$ $l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}h$ phenomenon warrants a revision of design practices currently used to avoid current-induced damage in multilevel microelectronic devices.