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Void dynamics in copper-based interconnects
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10.1063/1.3611408
/content/aip/journal/jap/110/3/10.1063/1.3611408
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/3/10.1063/1.3611408

Figures

Image of FIG. 1.
FIG. 1.

Voids in an interconnect segment terminating in a cathode via below the test segment. (a) Voids most readily nucleate at the Cu/cap interface, and grow at the site where the electromigration-induced tensile stress is highest. (b) Voids are sometimes observed at the base of vias, where they may have nucleated or where they may have drifted from other locations. Voids are sometimes observed at locations other than directly at the cathode via. These voids can drift toward the via (c) or grow in place (d) to cause failure.

Image of FIG. 2.
FIG. 2.

Voids in an interconnect segment terminating in a cathode via above the test segment. (a) Voids most readily nucleate at the Cu/cap interface, and grow where the electromigration-induced tensile stress is highest. Voids are sometimes observed at locations other than directly at the cathode via. These voids can drift toward the via (b) or grow in place (c) to cause failure.

Image of FIG. 3.
FIG. 3.

(a) Void nucleation and growth at boundaries is favored when the atomic diffusivity at the Cu/cap interface of the cathode-side grain is lower than the diffusivity of the anode-side grain. (b) Once voids have grown to a critical size, they can de-pin from boundaries and drift toward the cathode. The drift rate is determined by the magnitude of the diffusivity on the surface of the void relative to the interface diffusivity.

Image of FIG. 4.
FIG. 4.

(Color online) Stress profiles of a 50 μm-long interconnect after four 100-min intervals and after the last step at 10,000 min, when the evolution stops due to a balance of the electron wind force and the back stress (j = 0.5 MA/cm2, T = 350 °C). In the case shown at the top, the interconnect has a constant diffusivity of D = 4.5 × 10−16 m2/s throughout, while in the case shown at the bottom, diffusivities of either D/2, D, or 2D are randomly assigned to 50 1 μm-long grains (such that the average diffusivity of the interconnect is D).

Image of FIG. 5.
FIG. 5.

(Color online) Stress profile evolution of a 50 μm-long interconnect that has a 2 μm-long high diffusivity grain located 20 μm away from the cathode via. The diffusivity of the grain is 100D while the diffusivity everywhere else along the interconnect is D (j = 0.5 MA/cm2, T = 350 °C). Notice that the cathode edge of the high diffusivity grain quickly reaches a local maximum stress that is initially higher than the stress at the cathode via, but that the stress at the cathode via eventually exceeds this local maximum stress.

Image of FIG. 6.
FIG. 6.

(Color online) Stress profile evolution of a 50 μm-long interconnect with a cluster of grains, which is 5 μm in length and located 3 μm away from cathode via. The cluster of grains is assigned with higher diffusivity, whereas the diffusivity everywhere else along the interconnect is set at D (j = 0.5 MA/cm2, T = 350 °C). The diffusivity of the high-diffusivity grain cluster is 40D in the top plot and 4D in the bottom plot. The tensile stress reaches σnuc first at the cathode edge of the cluster in the top case and first at the cathode via in the bottom case.

Image of FIG. 7.
FIG. 7.

(Color online) Stress profile evolution at the cathode end of a 1000 μm-long interconnect that has a pre-existing void at 5 μm in the top plot and 2 μm away from the cathode via in the bottom plot (j = 3.0 MA/cm2, T = 350 °C). The interconnect has a uniform diffusivity of D throughout. In the case of the top plot, the stress at the cathode via reaches σnuc and the stress in the region between the void and the cathode via quickly relaxes to zero. In the case of the lower plot, the stress stops evolving when a force balance develops, and a void does not nucleate at the cathode via.

Image of FIG. 8.
FIG. 8.

(Color online) Top plot: Stress profile evolution at the anode end of a 1000 μm-long interconnect that has a pre-existing void located at 5 μm away from the anode. Bottom plot: Changes in void volume of the pre-existing void as a function of time for voids at different distances La from the anode via (j = 3.0 MA/cm2, T = 350 °C). The interconnect has uniform diffusivity D throughout.

Image of FIG. 9.
FIG. 9.

(Color online) Change in the volume as a function of time of a pre-existing void located at the middle of a 50 μm-long interconnect. The grain on the anode side of the void is 0.6 μm long and the diffusivity of the grain is varied from D/2 to 2D, while the diffusivity everywhere else along the interconnect is D (j = 3.0 MA/cm2, T = 350 °C).

Image of FIG. 10.
FIG. 10.

(Color online) Change in void volume as a function of time of pre-existing voids at different distances from the cathode via Lc (j = 3.0 MA/cm2, T = 350 °C). The interconnect has uniform diffusivity D throughout. In the top plot, where Lc  >  Lc , cr , void growth saturates. In the bottom plot, where Lc  < Lc , cr , voids continue to grow during stressing.

Image of FIG. 11.
FIG. 11.

(Color online) Change in the volume as a function of time of a pre-existing void located at 2 μm away from cathode via. The grain on the anode side of the void is 0.6 μm long and the diffusivity of the grain is either D/2, D, or 2D, while the diffusivity everywhere else along the interconnect is D (j = 3.0 MA/cm2, T = 350 °C).

Tables

Generic image for table
Table I.

Parameters used for simulations.

Generic image for table
Table II.

Length of a high diffusivity grain cluster required in order for the stress to reach the critical value at the cathode-end grain boundary before it is reached at the cathode via.

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/content/aip/journal/jap/110/3/10.1063/1.3611408
2011-08-02
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Void dynamics in copper-based interconnects
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/3/10.1063/1.3611408
10.1063/1.3611408
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