PHYSICAL REVIEW APPLIED 10, 054052 (2018) Inverse Blech Length Phenomenon in Thin-Film Stripes Nalla Somaiah and Praveen Kumar * Department of Materials Engineering, Indian Institute of Science, Bangalore 560012 (Received 4 August 2018; revised manuscript received 20 October 2018; published 21 November 2018) For decades, thin-film interconnects have been designed considering that the electric-current-induced mass transport or electromigration in thin films decreases with the reduction in the length of the film. This phenomenon is often called the Blech length effect, which dictates the seizure of electromigration if the product of the current density and the film length is smaller than a critical value. We report a phenomenon in Cu film stripes fabricated as per Blech configuration, where we observe that the electric-current-driven mass transport at the cathode increases as the sample length is reduced. We call this phenomenon the “inverse Blech length effect.” Furthermore, the mass transport at the cathode in Cu film increases linearly with the inverse of the sample length. Finite-element analysis reveals an increase in the self-induced temperature gradients, which are very large to induce thermomigration in Cu, at the ends of Cu film with a decrease in the sample length. Therefore, the contribution of thermomigration increases in the overall mass transport at the cathode as the sample length is decreased. The ensuing electromigration-thermomigration coupling is used to qualitatively explain the observation of the inverse Blech length phenomenon. The findings in this work open avenues for the design of device-level interconnects in microelectronic devices. DOI: 10.1103/PhysRevApplied.10.054052 I. INTRODUCTION Electromigration, which transports matter directionally from one of the electrodes to another upon passage of electric current, is a major reliability issue associated with thin-film interconnects in integrated circuits (ICs) [1]. Electromigration often becomes important at very high current densities (e.g., > 10 8 A/m 2 ) and it results in mass depletion at the cathode and mass accumulation at the anode in most of the solid metals, such as Cu, Al, Au, etc. Because of the mass depletion and the mass accu- mulation at the cathode and the anode, respectively, open circuit and short circuit, respectively, occur at these two ends of the Cu (as well as Al) film. One of the methods for avoiding electromigration in thin film interconnects is fab- ricating shorter interconnects [2]. This method is based on the Blech length effect, named after Ian A. Blech, who pro- posed that the extent of the electromigration in a conductor would decrease with a decrease in the sample size so that it will completely seize when the product of the current den- sity j and the sample length l is smaller than a critical value [2,3]. For an application where the current density cannot be arbitrarily affixed to a lower value, the above guide- line translates into designing interconnects with a length smaller than a critical length l c , which is often called the Blech length [see Fig. 1(a)][2,3]. * praveenk@iisc.ac.in The Blech length effect is an outcome of the existence of a stress gradient, which is generated in response to the gra- dient of vacancies, created due to electromigration, from the anode to the cathode [2]. Accordingly, the anode is at a higher compressive stress, due to the depletion of the vacancies below the equilibrium concentration, as com- pared to the cathode. Therefore, the generated stress gra- dient acts in the direction opposite to the atomic transport due to the electromigration. Accordingly, as schematically shown in Fig. 1(b), the mass transports due to the electro- migration and the self-generated stress gradient are in the opposite directions, with a finite probability that the latter can inhibit the mass transport due to the electromigration. In the interconnects of the length equal to the Blech length (i.e., l c ), the force on atoms due to the stress gradient in the interconnect exactly matches the force due to the elec- tric field, and hence, these interconnects do not show any mass transport. This phenomenon suggests that electromi- gration will not occur in interconnects with length smaller than l c . However, it should be noted that the generation of the stress gradient is dependent on the electromigra- tion and, hence, the stress gradient (and, accordingly, mass transport) will not exist in the absence of electromigra- tion [3]. Interestingly, there are reports suggesting a need for finite electromigration before the stress gradient can be established and, hence, it is not possible to strictly avoid electromigration altogether [4]. However, electromigration can be greatly minimized due to the Blech length effect. Mathematically, the equilibrium between stress gradient and electromigration forces, which is responsible for the 2331-7019/18/10(5)/054052(10) 054052-1 © 2018 American Physical Society