Electromigration

Electromigration (EM) has been the most persistent reliability issue in interconnects of microelectronic devices. Electromigration is the phenomenon of mass transportation due to momentum transfer from the electron flow in the high-density current. Such a mechanism results in open or short circuit modes of failure. The mechanism impacts both the design and manufacturing of metallization. For EM in metal, the driving force of the net atomic flux consists of two forces. They are (1) the electrostatic force, which is the direct action of electrostatic field on the diffusion atom, and (2) electron wind force, which is the momentum exchange between moving electrons and the ionic atoms. These two forces can be expressed as [23]

F = F_direct+ F_wind = Z^∗eE = (Z_el^∗ + Z_wd^∗ )eE Equation 1-1

Where Z^* is the effective charge number, e is the electron charge, and E is the electric field. The effective charge Z^* consists of two terms, Z_el^* and Z_wd^*. Z_el^* is positive and can be regarded as the nominal valence of the diffusion ion in the metal when the dynamic screening effect is ignored. When these positively charged metal ions are under the field effect, this so-called “direct force” draws atoms toward the negative electrode. On the contrary, Zwd*

, the wind force, is usually negative and represents the momentum effect from electron flow that pushes atoms towards the positive electrode.

Generally, the electron wind force dominates and is found to be on the order of 10 for a good conductor, such as Ag, Al, Cu, Pb, and Sn [10]. Z_wd^* can also be positive, but it is found only in transition elements with complex band structures [10]. The atomic flux is related to the electric field and thus the current density. The flux equation can then be expressed as follows:

J_em= C D

kTZ^∗eE Equation 1-2

E = ρj Equation 1-3

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Where C is the atomic concentration, D is the atomic diffusivity, k is Boltzmann’s constant, and T is temperature. ρ is the resistivity and j is the current density. The flux is a function of temperature. As shown in the equation below, the atomic diffusivity is exponentially dependent on temperature. flux maintains the same as long as the microstructure does not change significantly.

Electromigration (EM) was first observed in Al metal interconnects. Less than 0.2% of Cu atoms were added to the Al line to reduce the EM effect [10]. Blech first developed a structure of a short Al or Cu strip in the base line of TiN to conduct EM tests, as shown in Figure 1-3 (a) [25-27]. Because Al or Cu, with the exception of Ag, as electric field was applied on the two ends of the TiN line, the electric current in TiN took a detour and went along the strip of Al or Cu. After EM testing, a depleted region occurs at the cathode and an extrusion is observed at the anode. Figure 1-3 (b) is the SEM image of the morphology of a Cu strip tested for 99 hr at 350ºC with current density of 5 × 10⁵ A/cm². According to mass conservation, both depletion and extrusion should occupy the same volume. The drift velocity can then be calculated from the depletion rate.

In recent years, an impetus to study EM in very fine conductors has arisen from the development of very large-scale integrated circuits. The conductors are not only interesting in small dimensions; they are often assembled into multilayered structure with a certain combination of conductors and insulators. This gives rise to EM problems which is distinctly different from the simple single-level conductor. The

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metal layer is a two-dimensional conductor film that can be considered as an ensemble of grain boundaries and their intersections as illustrated in Figure 1-3 (c).

Experimental observations have indicated that in most cases, mass depletion and accumulation initiate at grain boundary intersection, such as triple junctions. Mass depletion would eventually lead to the formation of voids or cracks while mass accumulation would result in hillocks or whiskers. The reason why the grain boundary intersections are likely the failure sites is that they often represent the spots where the mass flux would diverge or converge most. At the grain boundary intersection, there could be abrupt changes in grain size, which produce a change in paths for mass movement. Moreover, there could also be a change in atomic diffusivity due to the change in grain boundary microstructure.

In recent years, damascene structure has been developed to form Cu interconnect.

Cu material is employed to replace Al due to its high electric conduction. Because Cu has higher melting temperature, its diffusion mechanism is surface diffusion instead of grain boundary diffusion [28]. As for solder joints with lower melting temperature, the diffusion mechanism is lattice diffusion for most solders at a typical operation temperature of an electronic device around 100ºC. Table 1-1 lists the melting temperatures of Al, Cu, and SnPb solder and their corresponding diffusion mechanisms.

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Figure 1-3 (a) Blech’s structure, showing an aluminum strip deposited on a TiN layer [2]; (b) morphology of a Cu strip tested for 99 hr at 350ºC with 5 × 10⁵ A/cm² current density [2]; and (c) two-dimensional conductor with grain boundaries and intersections [2].

Melting point (K) 373K/T_m Diffusivities at 373K (cm²/sec)

Cu 1356 0.275 Surface D_s = 10^-12

Al 933 0.40 Grain boundary Dgb = 6 × 10^-11

Pb 600 0.62 Lattice Dl = 6 × 10^-13

Eutectic SnPb 456 0.82 Lattice Dl = 2 × 10^-9 to 2 × 10^-10 Table 1-1 Melting temperatures, diffusivities, and diffusion mechanisms for Cu, Al, Pb, and SnPb solder [2].

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