for Advanced Interconnect Systems Technologies
Supported by SRC (Semiconductor
Corporation), New York State, and IBM. SRC funding
comes from semiconductor industry manufactures and their suppliers.
Electron Scattering at Cu-interconnect Surfaces
Daniel Gall and Hong Guo
Daniel Gall, Department of Materials Science, Rensselaer Polytechnic Institute, Troy , NY 12180
Hong Guo, Department of Physics, McGill University , Montreal , Quebec , Canada H3A 2T8
This is a combined theoretical and experimental study focusing on electron-scattering at the interfaces between Cu-interconnect and barrier layers. The resistivity will be calculated using ab inito density functional calculations based on a non-equilibrium Green’s function formalism. Complementary experiments measure electron scattering using single-crystal Cu-layers. The primary goal is to understand specular versus diffuse electron scattering and to propose and test novel barrier configurations that reduce the size effect, that is, yield high-conductivity Cu lines at reduced length scales.
1. Problem to be addressed:
The electrical resistivity of Cu interconnects increases with decreasing line width. This so called “size effect” becomes important when the line width reaches length scales comparable to the room-temperature electron mean free path, determined by electron-phonon scattering, which is 39 nm. The resistivity of Cu lines in the 45 nm technology node are expected to be a factor of two above the 1.67 μ W-cm bulk resistivity value, if no technologically viable schemes can be developed to reduce the size effect. This resistivity increase, which becomes even more dramatic for nodes beyond 45 nm, represents a major challenge for the continuous device scaling as specified in the International Technology Roadmap for Semiconductors. The proposed work will address some fundamental scientific issues that need to be resolved in order to suppress the size effect.
Electron scattering that contributes to the size effect can be divided into three processes: surface scattering, surface roughness, and grain boundary scattering. All three processes will need to be understood and controlled since each of them causes a contribution to the resistivity which is inversely proportional to the line width.
(a) Electron-surface scattering is not well understood and is the primary focus of the proposed investigation. In a classical (particle) view, the conduction electron follows a slightly curved trajectory (due to the applied field), scatters at the Cu surface (i.e. the Cu-Ta interface) and continues its path in a new direction. The scattering may be specular, that is, the electron momentum parallel to the surface is maintained. Alternatively, the scattering may be partially or completely diffuse, which means that the electron travels in a partially or completely random direction after scattering from the surface. The key issue for Cu-interconnect technology is to engineer surfaces which lead to specular rather than diffuse scattering. This will suppress the resistivity increase due to surface scattering.
Little is known about the quantum mechanical processes at the Cu surface that lead to specular versus diffuse scattering. The primary parameter of importance for such considerations is the distribution of the surface density of states (DOS) near the Fermi energy E f. Localized surface states with DOS(E f) > 0 are expected to yield non-specular scattering since momentum conservation is relaxed by the localization within the surface plane. A non-zero DOS(E f) outside of the Cu-line, as is the case with Ta adhesion/barrier layers, complicates the structure since scattering may occur not at the Cu surface but also within the barrier-layer, typically increasing the non-specular contribution as experimentally observed when comparing the effect of a Ta barrier layer with that of insulating Ta oxide. 5 In contrast, specular scattering occurs when coherent scattering from multiple centers within a plane causes constructive interference yielding momentum conservation parallel to the scattering plane. This process would be comparable to the reflection of light from a mirror. It requires a low probability for inelastic scattering at individual centers and also a planar distribution of scattering centers. It is the desired process for low-resistivity Cu-lines.
(b) Surface roughness increases the resistivity and becomes increasingly important as the line width decreases. This has been shown by Rossnagel and Kuan, 1, 2 using a Monte Carlo approach which is based on simple geometrical arguments to simulate classical electron trajectories. The simulation showed that a 5-nm-amplitude surface roughness will cause a ~30% increase in resistivity for a 60-nm-thick layer, but a 40% increase for a 20-nm-thick layer. Thus, it is clear that the surface roughness of Cu-interconnects will need to be controlled below a few nanometers in order to not compromise its good conductivity.
However, in addition to the geometrical effect of surface roughness mentioned above, there is also an atomistic effect of surface roughness that increases electron scattering. For example, a one-atom-high step at the surface will result in localized surface states which scatter conduction electrons. The surface step will also cause a strain-field which penetrates several atomic layers into the Cu-line and causes additional electron scattering. Almost nothing is known about the magnitude of this atomic-level roughness effect on resistivity. It will be addressed in the proposed investigation with the goal to provide (a) an estimate of its importance and (b) proposed ways to limit its effect.
(c)Grain boundary scattering increases with decreasing line width because the grain size typically scales with the feature width. This effect is a technological challenge and requires the growth of Cu grains that are longer than the line width, which may be achieved by secondary grain growth or directional (single-crystal) growth. Grain boundary scattering is, however, reasonably well understood and studied, , including recrystallization effects caused by Ostwald ripening 5 and the recently-reported low scattering coefficient on 111-twin boundaries. The proposed study will therefore not focus on grain boundary effects.
The overall objective of this research program is to develop a detailed understanding of electron scattering at the interface between the Cu line and various barrier-layers with the goal to provide the material and surface-structure requirements that lead to specular electron scattering.
The primary novelty of the proposed work is to provide a clear understanding, from both experimental and theoretical approaches, on the electrical resistivity of nano-meter scale Cu lines, including attached barrier layers, from an atomistic point of view. Our theory will be completely from first principles using density functional theory (DFT) and state-of-art quantum transport formalisms, and will be applied to explain and predict experimental resistivity data of epitaxial single-crystal Cu layers, including Ta and TaN x overlayers, with surfaces that have been characterized on an atomic level by in-situ scanning tunneling microscopy.
The calculation will provide the quantum mechanical insight into scattering at the Cu surfaces, in particular the requirements for specular scattering. Such calculations have not been done before because (a) most DFT approaches are not well suited to self-consistently treat non-equilibrium processes like the proposed conductivity simulation which includes an externally applied potential, and (b) the magnitude of the system, approximately 1000 atoms for a 10 ´10 ´0.3 nm 3 2D-slab and ~100,000 atoms for a 10 ´10 ´10 nm 3, is only now beginning to become computationally feasible, due to increasing computer power, the emergence of O(N) methods, and the integration of multiple length scale techniques.
The complementary strength of theory and experiment will be exploited in parallel to maximize cross-fertilization, stimulation, and fast advancement of the project. For example, the experimentally measured atomic-level surface roughness will be included in the simulation and the resistivity of the identical conductor will be both measured and simulated. Also, the calculation will show novel barrier materials or arrangements that dramatically increase the specular scattering. Such a prediction could be quickly checked by experiment and further optimization by both theory and experiment would then follow.
4. Technical approach
We will employ DFT calculations within the Kedysh nonequilibrium Green’s function (NEGF) formalism, which is the most promising atomistic modeling technique for nanoelectronics. This NEGF-DFT technique was first developed by one of the PIs (Guo) and allows parameter-free analysis of devices with up to ~1000 atoms in the active region. It has been successfully applied to quantitatively predict transport properties in molecular, metallic, and carbon nanowires, and has lead to an understanding for electronic levels in molecular devices, vibrational excitations in transistors, tunnel junctions, , and non-equilibrium charge distribution in nanocapacitors. 9 This formalism is well suited for the proposed simulations since the transport problem, including open boundaries and external bias can be solved fully self-consistently and since the calculation cost for the Hamiltonian operator scales only linearly with the number of atoms involved, making this approach ideal for the calculation of large systems like a Cu-wire.
To simulate even bigger systems of up to one million atoms, we will use a novel tight binding (TB) model where the TB parameters are extracted from our NEGF-DFT calculation of smaller devices at non-equilibrium. Thereby, they reflect the transport boundary condition and external fields. This new “environmental” dependent TB model is being developed in our laboratory and is expected to be operational by the summer of 2005.
The described atomistic simulation techniques are the most state-of-the-art for transport modeling at the nanoscale and can simulate arbitrary atomic arrangements with any elemental composition, like the proposed Cu wires with specified atomic-level surface roughness and various barrier layers. Calculations will be performed using our in-house 700 node 1.3 Tflop Beowulf cluster computer.
Resistivity measurements will be done on epitaxial single-crystal Cu layers which will be deposited by ultra-high vacuum (UHV) magnetron sputter deposition on MgO(001) substrates. We will build on our ( Galls) expertise in the epitaxial layer growth on MgO(001) substrates - and the growth of single-crystal and polycrystalline Ta and TaN x layers for use as adhesion and barrier layers. - Single-crystal layers simplify the analysis of the size effect on resistivity since the absence of grain boundary scattering allows to more directly probe surface scattering.
We will employ in-situ scanning tunneling microscopy (STM) to obtain atomic-level information on the surface roughness of the Cu and barrier layers. The surface roughness will be varied by the growth temperature as well as the ion-irradiation flux and energy during growth. These experiments are designed to measure the contribution of atomic-level roughness on the diffuse electron scattering at surfaces and interfaces which are expected to be related to localized electronic states as well as strain fields around surface irregularities.
We will utilize a UHV deposition system in Galls laboratory which is designed for epitaxial metal and nitride layer growth and also exhibits an attached STM chamber. It is very well suited for the proposed experiments which involve the deposition of Cu, Ta, and TaN x layers. The flexibility of the system, with ports for up to seven deposition sources, will allow to test new barrier layers that show promising specular electron scattering in the simulations.
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SRC BEP Needs Statement, www.src.org.
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Chao-Cheng Kaun, Brian Larade, and Hong Guo , “Electrical transport through oligophenylene molecules: A first-principles study of the length dependence,” Phys. Rev. B 67, 121411 (2003).
H. Mehrez, Alex Wlasenko, Brian Larade, Jeremy Taylor, Peter Grütter, and Hong Guo , “I-V characteristics and differential conductance fluctuations of Au nanowires,” Phys. Rev. B 65, 195419 (2002).
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C.-S. Shin, D. Gall, Y.-W. Kim, N. Hellgren , I. Petrov, and J. E. Greene, “Development of Preferred Orientation in Polycrystalline NaCl-structure δ -TaN Layers Grown by Reactive Magnetron Sputtering: Role of Low-Energy Ion/Surface Interactions”, J. Appl. Phys. 92, 5084 (2002).
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