Nagraj S Kulkarni

Large Discrete Resistance Jump at Grain Boundary in Copper Nanowire

Copper is the current interconnect metal of choice in integrated circuits. As interconnect dimensions decrease, the resistivity of copper increases dramatically because of electron scattering from surfaces, impurities, and grain boundaries (GBs) and threatens to stymie continued device scaling. Lacking direct measurements of individual scattering sources, understanding of the relative importance of these scattering mechanisms has largely relied on semiempirical modeling. Here we present the first ever attempt to measure and calculate individual GB resistances in copper nanowires with a one-to-one correspondence to the GB structure. Large resistance jumps are directly measured at the random GBs with a value far greater than at coincidence GBs and first-principles calculations. The high resistivity of the random GB appears to be intrinsic, arising from the scaling of electron mean free path with the size of the lattice relaxation region. The striking impact of random GB scattering adds vital information for understanding nanoscale conductors.

Simultaneous measurement of tracer and interdiffusion coefficients: an isotopic phenomenological diffusion formalism for the binary alloy

In this paper, a new development of the classic Onsager phenomenological formalism is derived using relations based on linear response theory. The development concerns the correct description of the fluxes of the atomic isotopes. The resulting expressions in the laboratory frame are surprisingly simple and consist of terms coming from the standard interdiffusion expressions and from Fick’s first law, where the tracer diffusion coefficient is involved thus providing a better understanding of the relationship between the two approaches – Fick’s first law and the Onsager phenomenological formalism. From an experimental application perspective, the new development is applied to the binary alloy case. The formalism provides the means to obtain the interdiffusion coefficient and tracer diffusion coefficients simultaneously from analysis of the interdiffusion composition profiles in a single experiment.

The Harrison diffusion kinetics regimes in solute grain boundary diffusion

Knowledge of the limits of the principal Harrison kinetics regimes (Types A, B and C) for grain boundary diffusion is very important for the correct analysis of depth profiles in a tracer diffusion experiment. These regimes for self‐diffusion have been extensively studied in the past by making use of the phenomenological lattice Monte Carlo (LMC) method with the result that the limits are now well established. However, the relationship of these self‐diffusion limits to the corresponding ones for solute diffusion in the presence of solute segregation to the grain boundaries remains unclear. In the present study, the influence of solute segregation on the limits was investigated with the LMC method for the well‐known parallel grain boundary slab model by showing the equivalence of two diffusion models. It is shown which diffusion parameters are useful for identifying the limits of the Harrison kinetics regimes for solute grain boundary diffusion. It is also shown how the measured segregation factor from the diffusion experiment in the Harrison Type‐B kinetics regime may differ from the global segregation factor.

Diffusion Couple Investigation of the Mg-Zn System

Growing use and development of lightweight Mg alloys has been the catalyst for more fundamental research in Mg based material systems to be completed. Zinc is one of the most common alloying elements in Mg alloys. Phase layer growth and interdiffusion in the binary Mg-Zn system was investigated utilizing solid-to-solid diffusion couples. Anneals were carried out at 295°, 315° and 325°C for 384, 168 and 120 hours, respectively. The diffusion microstructures that developed were examined by optical and scanning electron microscopy (SEM). Concentration profiles were determined using X-ray energy dispersive spectroscopy (XEDS) and electron microprobe analysis (EPMA). The phases observed were the Mg solid solution, Mg2Zn11, MgZn2 and Mg2Zn3 in all three couples as well as the high temperature, Mg51Zn20 phase in the 325°C couple. The MgZn2 phase was observed to grow the thickest layer, followed by the Mg2Zn3 and the Mg2Zn11 phases. Parabolic growth constants were determined for each phase. Activation energies for the growth of the intermetallic phases were calculated as 105 kJ/mol for the Mg2Zn3 phase and 207 kJ/mol for the MgZn2 phase.

Simultaneous tracer diffusion and interdiffusion in a sandwich-type configuration to provide the composition dependence of the tracer diffusion coefficients

In this paper, a new formalism of a combined tracer and interdiffusion experiment for a binary interdiffusion couple is developed. The analysis requires an interdiffusion couple that initially contains a thin layer of tracers of one or both of the constituent elements at the original interface of the couple (sandwich interdiffusion experiment). This type of interdiffusion experiment was first performed in 1958 by J.R. Manning. The theoretical analysis presented in this paper is based on a newly developed phenomenological theory of isotopic interdiffusion combined with the Boltzmann–Matano formalism. This new analysis now provides the means to obtain the composition dependent interdiffusion coefficient and tracer diffusion coefficients simultaneously from analysis of the interdiffusion and tracer profiles in a single sandwich interdiffusion experiment. The new analysis is successfully applied to the results of Manning’s original ‘sandwich interdiffusion’ experiment in the Ag–Cd system (six couples in total) and is validated with an independent determination of the Ag and Cd tracer diffusion coefficients by Schoen using the conventional thin film technique. Suggestions for further development of the sandwich interdiffusion experiment and analysis to the case of multicomponent alloys are provided.

Growth Kinetics of γ‐Al12Mg17 and β‐Al3Mg2 Intermetallic Phases in Mg vs. Al Diffusion Coupes

Increasing use and development of lightweight Mg-alloys have led to the desire for more fundamental research in and understanding of Mg-based systems. As a strengthening component, Al is one of the most important and common alloying elements for Mg-alloys. In this study, solid-to-solid diffusion couple techniques were employed to examine the interdiffusion between pure Mg and Al. Diffusion anneals were carried out at 300°, 350°, and 400°C for 720, 360, and 240 hours, respectively. Optical and scanning electron microscopies (SEM) were employed to observe the formation of the intermetallics γ-Al12Mg17 and β-Al3Mg2, but not e-phase. Concentration profiles were determined using X-ray energy dispersive spectroscopy (XEDS). The growth constants and activation energies were determined for each intermetallic phase.

Structural Dependence of Grain Boundary Resistivity in Copper Nanowires

We report the direct measurement of individual grain boundary (GB) resistances and the critical role of GB structure in the increased resistivity in copper nanowires. By measuring both intra- and inter-grain resistance with a four-probe scanning tunneling microscope, large resistance jumps are revealed owing to successive scattering across high-angle random GBs, while the resistance changes at twin and other coincidence boundaries are negligibly small. The impurity distributions in the nanowires are characterized in correlating to the microstructures. The resistance of high symmetry coincidence GBs and the impurity contributions are then calculated using a first-principle method which confirms that the coincidence GBs have orders of magnitude smaller resistance than the high-angle random GBs.

Low Temperature Plasma Etching of Copper for Minimizing Size Effects in sub-100 nm Features

A low temperature plasma etching process for patterning copper interconnects is proposed as a solution to the size effect issue in the resistivity of copper. Key features of this etching process based on a previous thermochemical analysis of the Cu-Cl-H system are discussed. Potential benefits of a subtractive etching scheme based on this process in comparison with the damascene scheme for copper-based interconnect processing in sub-100 nm features are presented in the context of the ITRS roadmap. Preliminary experimental work on plasma etching of Cu thin films using the proposed process is discussed.

Direct measurement of grain boundary resistance in copper nanowires

As interconnect dimensions decrease, the resistivity of copper increases dramatically because of electron scattering from surfaces, impurities, and grain boundaries (GBs), and threatens to stymie continued device scaling. Here we directly measure individual GB resistances in copper nanowires with a one-to-one correspondence to the GB structure. The resistance of high symmetry coincidence GBs is then calculated using a first-principle method. GB resistance is found to differ by orders of magnitude between different types of GB, with random GBs showing an intrinsically higher resistance compared to coincidence GBs.