Diffusional back flows during electromigration

doi:10.1016/S1359-6454(97)00446-1

Acta Materialia

Volume 46, Issue 11, 1 July 1998, Pages 3717-3723

https://doi.org/10.1016/S1359-6454(97)00446-1 Get rights and content

Abstract

Non-linear drift velocities have been reported when passing electrical currents through short metal lines. The aluminum drift velocity assumes very small values or disappears completely when metal lines are short. It was proposed that atoms moving by electromigration cause buildup of stress gradients (and in some cases concentration gradients) opposing their flow. Below a critical length there is no flow and above it, the drift velocity changes linearly with additional current. For aluminum lines with vertical grain boundaries it was suggested that the stress gradients are sufficient for calculating the back flow. By measuring the stress gradients in metal lines at or below the critical length, the value of the effective charge for aluminum was deduced. This value is quite low and does not agree with commonly accepted values. An original experiment is revisited, numerical calculations seem to substantiate the low value of the effective charge. Proposals for further experimentation are given.

Introduction

In the course of devising an experimental technique for measuring the electromigration drift velocity in thin films, current was passed through aluminum strips of various lengths deposited onto conducting TiN[1]. Most of the current was carried by the low resistivity aluminum causing it to migrate on top of the TiN in the direction of electron flow leaving a metal free area near the negative end of the strip and metal accumulation near the positive end.

It was discovered that the metal free area and hence, the drift velocity, was a function of the strip length. Longer strips showed a much higher drift velocity than shorter ones. In fact, at a given current density very short strips below a critical length did not drift at all. It was suggested that atoms transported by the electromigration are creating a stress and/or concentration differences between the strip ends causing a back flow counteracting the electromigration. The counterflow in short strips is higher since the stress and/or concentration gradients are higher leading to the slower observed drift velocity.

Both stress gradients and counterflows have been observed experimentally1, 2, 3. The separation between the effects of concentration and stress gradients remained elusive. The counterflow is in general a beneficial phenomenon as it tends to reduce the electromigration damage and in extreme cases prevent it altogether. For example, the increased lifetime at lower current densities was suggested to result from critical length effects4, 5. In fact any geometrical microstructural or temperature change that will lead to increased electromigration flow will immediately create a local opposing back flow.

The concept of critical length, counterflows as well as suggestions for further studies are discussed in the present paper.

Section snippets

Critical length

The unequal drifts of aluminum film deposited on TiN are clearly seen in Fig. 1, a micrograph first published in 1976[1]. Electrical current density of 3.7×10⁵ A/cm² was passed for 15 h at 350°C through a series of strips, the direction of electron (and atom) flow was from right to left. The strip on the right, 10 μm long, did not drift at all while the strip on the left, 90 μm long, drifted as much as 20 μm under the same conditions. The drift as a function of the inverse strip length is seen in

Local stress measurements

Changes in stress normal to the film grain boundaries were used to explain the observed drift behavior[2]. The free energy (or chemical potential) difference between the strip ends was assumed to originate from differences in the normal stress, $μ_{a} −μ_{v} =μ_{0} +Ωσ_{nn}$ where μ_a and μ_v are the chemical potentials of the atoms and vacancies, respectively, μ₀ is a constant, Ω is the atomic volume, and σ_nn the stress normal to the grain boundaries7, 8.

z* can be inferred by measuring the stress gradient along a

Suggestions for future work

Since the first report on critical length, a number of publications appeared which deal with drift velocity measurements9, 10. However, the relative roles of stress and vacancy/interstitial super saturation is still not clear.

If a free atom/vacancy exchange occurs on the grain boundaries than Eq. (7)is valid and the stress gradient is solely responsible for the back flow. The stress is in quasi equilibrium with the local vacancy concentration. When electrical current flows through a strip, some

Conclusions

The back flow observations are commensurate with stress as a driving force. The value of the effective charge for aluminum electromigration was found, by analyzing the back flow from a pad, to be about unity. The agreement with experimental results does not constitute a proof of the validity of the theory. The energy needed for driving the atoms back can also be provided chemically by super saturation of atoms (interstitials). Analyzing the back flow for this case yields a much higher effective

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Synchrotron X-ray study of electromigration, whisker growth, and residual strain evolution in a Sn Blech structure
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Synchrotron X-ray analysis of the Sn electromigration behavior and Sn whisker growth in a Blech structure using nano-X-ray fluorescence microscopy and white beam Laue nanodiffraction was conducted. Sn depletion at the cathode and whisker/extrusion formation at the anode were characterized in-situ, and the results obeyed the electromigration kinetics. This electromigration scenario gradually decayed because of the counterbalance between electron wind force and back stress. White beam Laue nanodiffraction analysis showed that a noticeable compressive deviatoric stress in the direction of electron flow built up at the anode of Sn strips, particularly in the roots of Sn whiskers, confirming that electromigration-induced atomic accumulation occurred downstream in a strip and that Sn whiskering was closely related to internal stress resulting from atomic accumulation in confined segments. Finally, a theoretical model based on fundamental electromigration theory revealed that Sn diffused predominately through lattice and grain boundary paths at Sn homologous temperature of 0.6.
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In this chapter, an overview of electromigration, which is an electric current driven diffusion controlled phenomenon, in solid pure metals, alloys, and liquid metals will be presented, along with the description of fundamental quantitative expressions. Effects of thermomigration–electromigration coupling and electromigration-induced back-stress in solid metal lines on the resultant mass transport will also be discussed. Since electromigration is a diffusion-controlled phenomenon that generates a stress gradient in a conductor, it may affect several stress directed diffusion controlled phenomena, such as whiskering, creep, etc. In this context, a brief introduction of whisker growth, especially in Sn coatings, will be presented. Finally, a correlation between electromigration and whiskering will be explored by using the link between the electromigration driven mass transport, back-stress, and the whiskering mediated relaxation of the generated stress.
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Fig. 3(c) shows a magnified image of the L0 = 20 μm case shown in Fig. 3(a), confirming that no Sn depletion or whisker was created in the short strip case. According to Eq. (1), the effect of the backflow generated by the stress gradient dσ/dx becomes increasingly important in short strips because dσ/dx inversely increases with the strip length [1,17]. Our observations provide a clear manifestation of the backflow effect on the short strips; specifically, the electromigration flux is balanced by the opposing backflow generated by dσ/dx during the testing.
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Diffusional back flows during electromigration

Abstract

Introduction

Section snippets

Critical length

Local stress measurements

Suggestions for future work

Conclusions

Thin Solid Films

Scripta metall.

J. Appl. Phys.

Appl. Phys. Lett.

Appl. Phys. Lett.