Local strains measured in Al lines during thermal cycling and electromigration using convergent-beam electron diffractio
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C.A. Volkert Max Plank Institute for Metals Research, Stuttgart, Germany; and Forschungszentrum Karlsruhe, Karlsruhe, Germany (Received 19 November 2004; accepted 15 March 2005)
In situ local measurement of sub-threshold strains generated during the electromigration of a 0.3-m-wide Al interconnect was performed for the first time using convergent-beam electron diffraction (CBED) in a transmission electron microscope (TEM). Thermal strains were also analyzed and provided verification for the electromigration analysis. Spatially averaged strains resulting from thermal cycling and electromigration quantitatively agree with models and data from previous studies. However, the local strains exhibited variations as large as 2 × 10−3. After eliminating other possible mechanisms, the strain inhomogeneity is attributed to local plasticity through source-limited dislocation activity. I. INTRODUCTION
Large stresses and strains are often present in small metal structures due to their large flow stresses and thermal mismatch with surrounding materials. One way to measure strains is with convergent-beam electron diffraction (CBED). Although this transmission electron microscopy (TEM) based technique always offered excellent spatial resolution (20–100 nm), it initially suffered from insufficient strain resolution. Fortunately, recent technique improvements have overcome the critical barriers. The most significant hardware development was the energy filter, which removed the inelastic scattering responsible for the diffuse background and broad Higher Order Laue Zone (HOLZ) lines in CBED patterns.1 Recent software developments have enabled precise HOLZ line position determination, an algorithm for correcting the line shifts induced by dynamical scattering, and automation of the extensive process necessary to calculate the strains.2 As a result of these improvements, strain measurement resolution for Al increased roughly an order of magnitude from 10−3 to 10−4. Since commercially pure Al yields at a strain of approximately 10−3, this improved resolution enables the evaluation of elastic strains prior to and after yielding.3 The stresses and strains generated in Al films and lines
Address all correspondence to this author. a) e-mail: [email protected] b) Present address: Department of Materials Science and Engineering, University of California at Santa Barbara, Santa Barbara, CA DOI: 10.1557/JMR.2005.0231 J. Mater. Res., Vol. 20, No. 7, Jul 2005
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during thermal cycling4–7 and electromigration8–11 have long been measured. Temperature cycling creates strains because of the difference in thermal expansion coefficients between the Al and the substrate. Electromigration creates strains due to the transport of atoms along the interconnect; atoms are depleted from the cathode (negative) end of the segment and are accumulated at the anode (positive) end when a critical current density is exceeded.12 Experiments have confirmed the models for stress evolution during electromigration,12,13
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