Electron Transport in Anisotropic Conductors for Sub-10nm Interconnects

The Interconnect Scaling Challenge

As semiconductor technology scales below 10 nm, the resistance of copper (Cu) interconnects increases dramatically due to electron scattering at surfaces and grain boundaries. This resistivity size effect — where the effective resistivity of a metal line rises sharply as its cross-sectional dimensions approach the electron mean free path (MFP) — has become one of the most pressing bottlenecks in advanced BEOL (back-end-of-line) integration.

The Fuchs-Sondheimer (FS) model and the Mayadas-Shatzkes (MS) model provide the theoretical framework for understanding this size effect. The FS model describes how electron scattering at film surfaces increases resistivity as thickness decreases, while the MS model accounts for grain boundary scattering. Together, these models predict that for a wire with thickness comparable to the bulk MFP, resistivity can increase by a factor of 2–5× over the bulk value.

My dissertation research addresses this challenge by investigating alternative conductor materials whose intrinsic electronic structure may provide inherent resistance to surface scattering — specifically, anisotropic and directional conductors where the electron Fermi surface geometry naturally channels current with reduced surface interactions.

Materials Under Investigation

Ruthenium (Ru)

Ruthenium is a leading Cu-alternative candidate for sub-10nm interconnects due to its low bulk resistivity (~6.7 µΩ·cm), resistance to electromigration, and compatibility with established BEOL processes. My work on epitaxial Ru(0001) thin films grown on sapphire(0001) substrates via UHV magnetron sputtering quantifies the electron surface scattering specularity parameter p using the Fuchs-Sondheimer model.

Key findings include the relationship between surface roughness and specularity. Through systematic AFM surface roughness measurements correlated with in-situ and ex-situ resistivity measurements at thicknesses ranging from 5 nm to 330 nm, we established that atomically smooth Ru surfaces can achieve specularity parameters as high as p = 0.5–0.6, significantly reducing the resistivity size effect compared to polycrystalline films where p ≈ 0.

Delafossites: PtCoO₂ and PdCoO₂

The metallic delafossites PtCoO₂ and PdCoO₂ are remarkable materials with the highest in-plane conductivity of any known oxide — their room-temperature resistivities of ~2.1 and ~2.6 µΩ·cm respectively rival that of elemental metals. Their layered crystal structure produces a highly two-dimensional Fermi surface, meaning electrons preferentially conduct along the Pt/Pd layers with an extremely long in-plane MFP exceeding 10 µm at low temperatures.

This extreme Fermi surface anisotropy is potentially transformative for interconnect applications: if a wire is oriented with the high-conductivity direction along its length, the electron MFP perpendicular to the confining surfaces may be very short — effectively making the wire electrically "thick" even at nanometer dimensions. My research uses single crystals provided by collaborators at NIMS (Japan) and the Max Planck Institute to measure the anisotropic resistivity size effect and determine whether this directional transport advantage persists at the nanoscale.

CoSn (Kagome Metal)

CoSn is a kagome lattice metal featuring flat electronic bands and Dirac crossings that create a highly directional Fermi surface. Like the delafossites, CoSn has strongly anisotropic transport properties — its in-plane conductivity is substantially higher than the c-axis value. My work involves growing epitaxial CoSn thin films and single-crystal microstructures, then fabricating nano-scale wires using FIB-SEM and electron-beam lithography (EBL) to directly measure the resistivity size effect in confined geometries.

Preliminary results indicate a product of bulk resistivity and effective wire resistivity (r_wire) of approximately 2.6 × 10⁻¹⁶ Ω·m², which provides a quantitative benchmark for CoSn's suitability for sub-10nm interconnect applications.

Key Findings

Methodology

The experimental approach combines UHV magnetron sputtering for thin film deposition, cryogenic resistivity measurements (10–300 K) for Fuchs-Sondheimer analysis, AFM for surface roughness quantification, XRD/XRR for crystallographic and thickness characterization, and FIB-SEM fabrication for nano-wire transport measurements. For the delafossite single crystals, focused ion beam (FIB) microstructuring is used to define precise geometries for directional resistivity measurements.

The FS model fit uses a modified version that accounts for asymmetric scattering at the film-substrate versus film-vacuum interfaces, parameterized by specularity values p_top and p_bottom. This dual-specularity approach is critical for epitaxial films where the atomically registered film-substrate interface may scatter electrons very differently from the free surface.

Impact and Applications

This research directly informs the semiconductor industry's roadmap for replacing Cu in the most critical interconnect layers at the 3nm node and beyond. The identification of conductor materials with intrinsically favorable scattering properties could enable continued interconnect scaling without prohibitive RC delay penalties. Results from this work are disseminated through SRC-funded channels and directly inform interconnect material selection at member companies including Intel, Samsung, TSMC, and GlobalFoundries.

Collaborators & Funding

This research is supported by the Semiconductor Research Corporation (SRC) through tasks 2875.001 and 3174.001, with additional support from Tokyo Electron Limited (TEL) and the Center for Materials, Devices, and Integrated Systems (cMDIS) at RPI. Key collaborators include Prof. Daniel Gall (advisor, RPI), groups at the University of Notre Dame, Cornell University, and the National Institute for Materials Science (NIMS, Japan).