Determination of failure criteria based upon grain boundary

Abstract

A critical temperature rise .DELTA.R is selected at a value for which electromigration of atoms in the metal conductive line deposited on a semiconductive substrate is predominantly a grain boundary electromigration. Selection of the critical resistance rise is made by performing a number of tests on different ones of a plurality of substantially identical bow tie conductive lines formed of alternating narrow and wide sections interconnected by tapering line sections. Temperatures for the selection of the critical resistance rise are calculated rather than measured so as to more accurately reflect the relatively high local temperature at the site of a void in the metallic conductive line. Plot of a plurality of line widths against temperature for a given current density enables selection of a minimum line width or maximum void depth that will occur in a condition of predominantly grain boundary electromigration and before a large amount of bulk electromigration occurs. Utilizing empirically selected line widths (or void depth) and calculated temperatures, a critical value of .DELTA.R resistance rise is calculated and structure of lines stressed to critical values of .DELTA.R is visually observed by a scanning electron microscope. The lines are electrically stressed at different values of current density until the selected critical value of resistance rise occurs and elapsed time for such occurrence recorded. The results are used to solve for Ea, A and N in Black's equation, MTTF=A(J).sup.-N exp (Ea/KT), also utilizing calculated temperature. Using a highest expected electrical current density and highest expected temperature with the calculated values of Ea, A and N, Black's equation is then solved for an expected mean time to failure (MTTF).