Electromigration Failure Distributions of Cu/Low-$k$ Dual-Damascene Vias: Impact of the Critical Current Density and a New Reliability Extrapolation Methodology

Analysis of critical-length data from Electromigration failure studies

“…Using eqns (8) and (12), it is now a simple matter to reinterpret the results of references [3,[5][6][7][8][9][10][11][12][13][14]. [5][6][7][8] (jL) Fig.…”

“…This case, which is valid for unpassivated lines [4], has also been used consistently in the case of passivated lines [3,[5][6][7][8][9][10][11][12][13][14]. In passivated lines, unless the anode is steadily leaking copper into the surrounding dielectric stack, the steady-state occurs only when 0  drift v .…”

“…This is known as the short line effect, and can be vital in Electromigration-aware chip design as, by daisy chaining long interconnects, say in M1 and M2 sections, all lines can conceivably be made sufficiently short that EM ceases, this defines a critical or Blech length. In recent years a number of studies of the short line effect in DD copper have been reported [3,[5][6][7][8][9][10][11][12][13][14] some of which have indeed daisy chained interconnects of different lengths to increase the efficiency of the experiment. The purpose of this paper is to analyse that work using what might be described as standard theory for Electromigration [1].…”

“…In references [3,[5][6][7][8][9][10][11][12][13][14] it is assumed that a rupture pins the anode stress at  rup . Should that happen the void will continue to grow until the flux leaking into the dielectric stack can be brought to a halt; this can only In references [11,13,14] only void growth is considered, although a critical value of the jL product (implying nucleation or rupture) is sought rather than jL 2 , which is relevant to void growth [2].…”

“…In references [3,[5][6][7][8][9][10][11][12][13][14], and in most analysis V cr is assumed fixed which for now we do also. Bu contrast in lines close to L B , it is clearly vital to also include the effects of the anode stress, which we do now.…”