Numerical Analysis of Vacancy Transport by Residual Stress in Electromigration on LSI Interconnects
The L \text{i multiplication method for the driving force induced particle migration equation was proposed to solve numerically the stress and electric fields induced vacancy migration equation. On the basis of this method, vacancy migration behaviors were found to be predicted under the competitive...
Saved in:
| Published in | Japanese Journal of Applied Physics Vol. 49; no. 2; pp. 024301 - 024301-7 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
The Japan Society of Applied Physics
01.02.2010
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | The L \text{i multiplication method for the driving force induced particle migration equation was proposed to solve numerically the stress and electric fields induced vacancy migration equation. On the basis of this method, vacancy migration behaviors were found to be predicted under the competitive relationship between stress and electric field. When a residual stress is dominant, vacancies concentrate around the maximum hydrostatic stress region, such as elastic--plastic boundary. On the other hand, when the electric field is dominant, vacancies do not concentrate around the maximum hydrostatic stress region, but move from the cathode end to the anode end. An in situ observation of electromigration on AlCuSi interconnect was conducted to verify the simulation results. A void nucleated and grew at the tip of a notch on an AlCuSi line without passivation film, while many voids appeared and grew in cathode side in a line with passivation film. Greater hydrostatic stress gradient is considered to occur in the line without passivation film, owing to a small scale of yielding, and this leads to concentrate void formation at the tip of the notch. These results indicate that numerical analysis of electromigration is valid to represent the experimental result. Based on results mentioned above, various failure modes in interconnects cased by electromigration are predictable by the proposed L \text{i multiplication method. |
|---|---|
| Bibliography: | Two dimensional physical model of interconnection with an initial circular void. Hydrostatic Stress distribution around a round-shaped defect. Distribution of hydrostatic stress from the tip of the round-shaped defect in the normal direction of line. Calculation method of the mean value of hydrostatic stress. Interpolation method of hydrostatic stress obtained by FEA at the nodes $i$ and $i-1$ to the grids of the finite differential method for vacancy diffusion. Vacancy distribution around an initial round-shaped defect stress = 0 MPa and current density = $7.0\times 10^{6}$ A/cm 2 . Vacancy distribution around an initial round-shaped defect stress = 400 MPa and current density = $7.0\times 10^{6}$ A/cm 2 . Vacancy distribution around an initial round-shaped defect stress = 400 MPa and current density = $2.0\times 10^{6}$ A/cm 2 . Vacancy distribution around an initial round-shaped defect stress = 400 MPa and current density = 0 A/cm 2 . Electric potential distribution around a round-shaped defect. Hydrostatic stress distribution around a round-shaped defect. Voids and hillock growth without passivation film (10 min 15 s). Voids growth on the line with passivation film (10 min 15 s). Stress field around the round-shaped defect: (a) line with passivation film and (b) line without passivation film. |
| ISSN: | 0021-4922 1347-4065 |
| DOI: | 10.1143/JJAP.49.024301 |