2.1.2 1970s: Blech Effect

In the late 1960s, Blech and Sello [17] discovered that electromigration in aluminum thin films could be a leading source of failure in planar semiconductor ICs. After that observation, the interest as well as the direction of electromigration studies have shifted their focus of the investigation to the aspect of electromigration damage in thin film conductors [48]. Different from bulk materials, the analysis of electromigration in thin films has shown that grain boundaries are particularly relevant to damage formation [79]. From the incorporation of copper in aluminum-based interconnects, IBM found out that copper atoms block the fast diffusivity paths at grain boundaries [29]. Furthermore, at that time, the idea of electron-ion interactions as a driving force fascinated material scientists to start to formulate a quantum mechanical approach in order to understand the physical phenomenon. The interest in a quantum mechanical description of electromigration has continued to the present time.

With the development of new interconnect technologies, research activities at Bell Labs led I. A. Blech and his coworkers to discover "immortal wires" in 1976 [16]. They designed electromigration experiments on thin aluminum films deposited onto titanium nitride surfaces. The passage of high electric current through the sample is mostly carried by the conductor layer due to its lower resistivity. The resulting induced atom flow, parallel to the direction of the electron flow, is related to the atom drift velocity v_d as follows

\[\begin{equation} v_\text{d} = M e |Z^*| \rho j, \end{equation}\] (2.7)

where M is the mobility, and e|Z^*| is the effective charge of the ions. By measuring the drift velocity responsible for the movement of the aluminum islands, they observed that only one side of the stripe moved according to equation (2.7) so that its length shrank. In turn, at the other end of the line, hillocks were formed. They also found that no electromigration-induced drift occurs below a critical applied current density. In order to explain these observations, the concept of the "back flow" drift velocity v_b, which acts against the electromigration drift velocity influencing the net forward drift velocity v_n, was proposed as follows

\[\begin{equation} v_\text{n} = v_\text{d}-v_\text{b} = M e |Z^*| \rho j - \cfrac{M \Delta F}{l} \approx M e |Z^*| \rho j - \cfrac{M \Omega_\text{a} \Delta \sigma_\text{xx}}{l}, \end{equation}\] (2.8)

where ΔF is the free energy difference between line ends, l is the line length, Ω_a is the atomic volume, and Δσ_xx is the normal hydrostatic mechanical stress difference between line ends when voids and hillocks are formed. When the "back flow" of atoms, due to the presence of back stress in the line, equals the atom flow due to electromigration, the steady-state condition, so-called "Blech condition", is reached. Given the maximum stress σ_thr that the aluminum stripe can sustain before yielding, the critical product of current density and wire length for electromigration failure in thin aluminum films, the "Blech product", is given by

\[\begin{equation} (jl)_\text{C} = \cfrac{\Omega_\text{a} (\sigma_\text{thr}-\sigma_\text{0})}{e |Z^*| \rho}, \end{equation}\] (2.9)

where σ₀ is the stress at x=0. Blech and coworkers were able to determine the critical line length l_B, well known as the "Blech length", from their measurements. When a line shrinks to the critical value due to the application of a given current density j, the line end stops moving, and electromigration halts. The applied threshold current density j_C, which a line can withstand before electromigration failure, can be similarly obtained. By following this approach, it was also possible to estimate the interconnect resistance against electromigration [40], and two electromigration failure modes in interconnects were identified, namely open circuit due to void formation and short circuit due to hillock formation. Furthermore, Blech was the first one to consider stress-migration as an additional driving force acting in the opposite direction of electromigration. The origin, as well as the nature of the mechanical back stress in microelectronic structures, are strongly influenced by the presence of the residual stress coming from the fabrication process, which could give false values of the Blech length and maximum operating current density [103].