Role of surface states and band modulations in ultrathin ruthenium interconnects

Using density functional theory, this study demonstrates that surface states fundamentally dictate the thickness-dependent resistivity of ultrathin ruthenium interconnects, where vacuum-terminated surfaces exhibit decreasing resistivity with reduced thickness while oxygen-terminated surfaces show the opposite trend, underscoring the critical role of surface engineering in optimizing next-generation device performance.

The Gist

The Big Problem: The "Traffic Jam" in Tiny Wires

Imagine the inside of your smartphone or computer as a massive, bustling city. The transistors (the brain cells) are the houses and offices, and the interconnects (the wires) are the roads connecting them.

For decades, engineers have been shrinking these houses to fit more of them into the city. But there's a catch: as the houses get smaller, the roads between them get incredibly narrow.

In the old days, we used Copper (Cu) roads. But when these roads get too narrow (thinner than a human hair), they start to clog up. Why? Because the electrons (the cars) start hitting the walls of the road and the potholes (grain boundaries) more often. This creates resistance, which is like a traffic jam. The more the cars slow down, the slower your phone works and the more battery it drains.

The New Candidate: Ruthenium (Ru)

Scientists are looking for a better material to replace copper. One promising candidate is Ruthenium (Ru). It's a shiny, noble metal that doesn't rust easily and can handle being very thin better than copper.

However, there's a mystery. When Ruthenium gets extremely thin, its electrical performance changes in weird ways. Sometimes it gets better as it gets thinner, and sometimes it gets worse. The researchers wanted to figure out why.

The Experiment: The "Naked" vs. The "Coated"

To solve the mystery, the researchers used a super-powerful computer simulation (like a digital wind tunnel) to build two types of ultra-thin Ruthenium films:

1. The "Naked" Ruthenium (Vacuum-terminated): Imagine a strip of Ruthenium floating in a vacuum, with nothing touching its top or bottom surfaces. It's completely exposed.
2. The "Coated" Ruthenium (Oxygen-terminated): Imagine the same strip, but this time, we spray a layer of oxygen atoms all over the top and bottom. It's like putting a protective coat of paint on the metal.

The Discovery: The "Superhighway" on the Surface

Here is where the magic happens. The researchers found that the surface of the metal acts like a secret superhighway for electricity.

• The "Naked" Strip (Good News):
  When the Ruthenium is naked, the surface creates special electronic "states." Think of these as magic lanes that appear right on the edge of the road.

  • The Analogy: Imagine a highway where, as the road gets narrower, a special "express lane" magically appears on the shoulder. Even though the main road is getting tight, the cars can zoom through this express lane.
  • The Result: As the Ruthenium film gets thinner, these magic lanes become more dominant. The electricity flows better as the film gets thinner. The resistivity (traffic jam) actually decreases.

• The "Coated" Strip (Bad News):
  When the Ruthenium is covered in oxygen, those magic lanes disappear. The oxygen atoms stick to the surface and "glue" the electrons down, blocking the special surface states.

  • The Analogy: Now, imagine we put a fence along that magic express lane. The cars are forced back onto the main road. As the road gets narrower, there are fewer lanes for the cars, and they hit the walls more often.
  • The Result: As the film gets thinner, the traffic gets worse. The resistivity increases, just like we expected with normal copper.

The "Why" Behind the Magic

Why do these magic lanes exist?
In quantum physics (the rules that govern tiny particles), when you cut a material very thin, the electrons behave differently at the edges. They form a "surface electron gas" that conducts electricity very well.

• Naked Ruthenium: Keeps these surface electrons free and happy.
• Oxygen-Coated Ruthenium: The oxygen bonds with the Ruthenium atoms, changing the rules so the surface electrons can't form that special highway.

The Takeaway: Engineering the Surface

This study teaches us a vital lesson for the future of technology: It's not just about the material; it's about the surface.

If we want to build faster, smaller chips in the future, we can't just pick a good metal like Ruthenium. We have to be very careful about what touches that metal.

• If we let the Ruthenium get oxidized (rusted) or covered by a bad barrier layer, we kill the "magic lanes," and the chip slows down.
• If we can engineer the surface to stay "naked" or protected in a way that keeps those magic lanes open, we can make interconnects that get more efficient as they get smaller.

In short: The researchers found that the "skin" of the metal determines how fast the electricity runs. Keeping the skin clean and special is the key to the next generation of super-fast computers.

Technical Summary

1. Problem Statement

As semiconductor technology advances into the sub-nanometer regime, the physical dimensions of interconnects are shrinking, leading to a critical performance bottleneck known as RC delay.

• Current Limitations: Copper (Cu), the industry standard, suffers from a sharp increase in resistivity at nanometer scales due to enhanced surface and grain boundary scattering. Additionally, the non-scalable barrier and liner layers required for Cu diffusion prevention further degrade performance.
• The Challenge: Identifying alternative materials that maintain low resistivity at ultrathin dimensions. Ruthenium (Ru) is a promising candidate due to its lower resistivity than Cu at thin thicknesses and its ability to form barrierless interconnects.
• The Gap: While semi-classical models (e.g., Fuchs-Sondheimer) account for scattering, they fail to capture how surface termination and quantum confinement alter the intrinsic electronic band structure. Specifically, the role of surface states (electronic states distinct from the bulk) in nanoscale transport remains poorly understood for Ru.

2. Methodology

The authors employed Density Functional Theory (DFT) combined with semi-classical transport theory to investigate the thickness-dependent resistivity of Ru thin films.

• Computational Framework:
  • Software: Quantum ESPRESSO (v.7.2).
  • Functional: Generalized Gradient Approximation (GGA) with the PBE functional.
  • Pseudopotentials: Scalar-relativistic Projector Augmented-Wave (PAW).
  • Structural Models:
    • Bulk Ru: Hexagonal Close-Packed (HCP) structure optimized to $a=2.718$ Å, $c=4.290$ Å.
    • Slab Models: 10-layer Ru slabs cleaved along the (0001) plane with a 15 Å vacuum layer.
    • Two Configurations:
      1. Vacuum-terminated Ru slab: Represents intrinsic surface states.
      2. Oxygen-terminated Ru-O slab: 1 monolayer of oxygen adsorbed on both surfaces (HCP-hollow sites) to passivate and suppress surface states.
• Transport Calculations:
  • BoltzTraP2: Used to interpolate band structures and calculate conductivity tensors based on the Boltzmann transport equation.
  • Approximation: Constant relaxation time approximation ($\tau$). The bulk $\tau$ was derived by matching calculated bulk resistivity to experimental values ($7.80 \, \mu\Omega \cdot \text{cm}$), yielding $\tau = 8.30$ fs at 300 K.
  • Normalization: Resistivity was calculated by normalizing conductivity against the physical thickness of the slab (excluding vacuum) to correct for volume effects.

3. Key Contributions

• Isolation of Surface State Effects: The study decouples intrinsic electronic structure effects (surface states and band modulation) from extrinsic scattering mechanisms (grain boundaries, surface roughness) to reveal the fundamental physics governing nanoscale Ru transport.
• Comparative Analysis of Termination: By comparing vacuum-terminated vs. oxygen-passivated slabs, the authors demonstrate that surface chemistry dictates whether resistivity increases or decreases as thickness shrinks.
• Quantification of Surface Conductance: The research quantifies the specific contribution of surface states to total conductance, identifying them as a distinct conduction channel that can counteract size effects.

4. Key Results

• Opposing Resistivity Trends:
  • Vacuum-terminated Ru: As thickness decreases, resistivity decreases. This counter-intuitive behavior is attributed to the presence of conductive surface states (Shockley-like states) that provide an additional conduction channel. As the film thins, the relative contribution of these surface states increases, dominating the transport.
  • Oxygen-terminated Ru-O: As thickness decreases, resistivity increases monotonically. Oxygen adsorption causes strong hybridization between Ru $d$-orbitals and O $p$-orbitals, which suppresses the surface states. Without these states, the film is dominated by quantum confinement effects (band modulation and energy level quantization), which reduce the number of available conducting states, leading to higher resistivity.
• Electronic Structure Analysis:
  • Fermi Surfaces: Projected Fermi surfaces show significantly higher surface contributions near the Fermi level for the bare Ru slab compared to the Ru-O slab.
  • Band Structure & PDOS: The bare Ru slab exhibits strong dispersive bands and high Density of States (DOS) at the Fermi level ($E_F$) localized at the surface. In contrast, the Ru-O slab shows a suppression of these states near $E_F$ due to orbital hybridization, while the bulk-like states remain largely unchanged.
• Quantitative Contribution: For films thicker than 1.5 nm, the conductance difference between the two models is a constant offset of approximately $4.4 \times 10^{-3}$ S, representing the intrinsic contribution of surface states. In the ultrathin regime (<1.5 nm), surface-surface coupling modifies these states.

5. Significance and Implications

• Surface Engineering Strategy: The findings suggest that the performance of ultrathin Ru interconnects is not solely determined by geometric scaling but is critically dependent on surface engineering.
• Design Guidelines: To minimize resistance in next-generation interconnects:
  • Interfaces must be engineered to preserve conductive surface states (e.g., by preventing oxidation or using capping layers that do not hybridize strongly with Ru $d$-orbitals).
  • Oxidation or strong chemical passivation that eliminates surface states will lead to the detrimental resistivity increase typically seen in scaled Cu interconnects.
• Theoretical Insight: This work provides a fundamental explanation for why Ru can outperform Cu at small scales if surface states are preserved, offering a new paradigm for designing low-resistivity nanoscale conductors beyond simple scattering models.

In conclusion, the paper establishes that surface states act as a "superhighway" for electron transport in ultrathin Ru films. Preserving these states through careful interface control is the key to overcoming the RC delay limitations in future semiconductor nodes.