Influence of sulphur vacancies on ultrafast charge separation in WS$_2$-graphene heterostructures

This study demonstrates that deliberately introducing sulphur vacancies in WS$_2$-graphene heterostructures alters band alignment and doping, which prolongs electron lifetimes in WS$_2$ but shortens the overall charge-separated state lifetime by facilitating ultrafast electron tunneling (~4 ps) from vacancy states into graphene's Dirac cone.

The Gist

Imagine you have a high-tech factory made of two ultra-thin layers stacked on top of each other. The bottom layer is Graphene (a super-fast highway for electricity), and the top layer is WS2 (a solar panel that catches light).

When light hits the WS2 layer, it creates a pair of workers: an electron (a negative charge) and a hole (a positive charge). For this factory to work efficiently as a solar cell or a light detector, these two workers need to separate quickly and run in opposite directions. The electron wants to jump down to the Graphene highway to zoom away, while the hole stays behind.

The big mystery scientists have been trying to solve is: How long do these workers stay separated before they get tired, meet back up, and cancel each other out?

Some previous studies said they stay apart for a split second (1 picosecond), while others claimed they stay apart for a long time (1 nanosecond). That's a huge difference! The researchers in this paper decided to find out why. They suspected the culprit was Sulphur Vacancies.

What are Sulphur Vacancies?

Think of the WS2 layer like a perfectly tiled floor. A "Sulphur vacancy" is simply a missing tile. It's a tiny hole in the structure.

Usually, missing tiles are bad. But in this specific factory, the researchers wanted to see what happens if they deliberately knock out more tiles. They did this by heating the factory in a vacuum oven, essentially baking out the sulphur atoms to create more missing spots.

The Experiment: Baking the Factory

The team took their WS2-Graphene sandwich and baked it at increasingly high temperatures.

1. First, they checked the blueprint (Band Structure): Using a super-advanced camera (ARPES), they saw that as they created more missing tiles (vacancies), the "floor plan" of the factory changed. The energy gap between the WS2 layer and the Graphene highway got smaller. It was like lowering the height of a hurdle the electrons had to jump over.
2. Then, they watched the workers (Time-Resolved ARPES): They flashed a laser to create the electron-hole pairs and watched how long the electrons stayed in the WS2 layer before jumping to Graphene.

The Surprising Results

Here is where it gets interesting. The researchers found two opposite effects happening at the same time:

1. The "Longer Wait" in the Solar Panel (WS2)

• What happened: As they added more missing tiles (vacancies), the electrons stayed inside the WS2 layer for a longer time before they even tried to leave.
• The Analogy: Imagine the missing tiles act like a "trap" or a "waiting room." The electrons get stuck in these vacancies for a moment. It's like a runner getting their shoelace tied; they have to pause before they can sprint. This explains why the electrons lingered longer in the top layer.

2. The "Faster Crash" of the Separated State

• What happened: Even though the electrons waited longer in the top layer, the moment they did separate from the holes, the whole system collapsed much faster. The "separated state" didn't last as long.
• The Analogy: Think of the missing tiles as a shortcut or a tunnel connecting the WS2 waiting room directly to the Graphene highway.
  • When the tiles are missing, the energy levels shift. It becomes easier for the trapped electrons to tunnel through the "missing tile" directly into the Graphene.
  • Once they hit the Graphene highway, they are so close to the holes that they quickly recombine (meet back up and disappear).
  • The Result: The "separation" is short-lived because the vacancies provide a fast track for the electrons to rush back and cancel out the holes.

Solving the Mystery

The paper also solved the debate about the "1 nanosecond" vs. "1 picosecond" lifetimes.

• The researchers calculated that electrons tunneling through these vacancies take about 4 picoseconds to move. This matches their new, fast measurements.
• They concluded that the studies claiming "1 nanosecond" lifetimes were likely looking at samples that were either too thick (more than one layer of WS2) or had different types of defects. In a perfect, single-layer factory with these specific missing tiles, the separation is actually very short-lived.

The Big Picture

This study is like a mechanic figuring out exactly how a specific type of rust (the vacancy) affects a car's engine.

• Bad news: If you want to harvest light for a long time, these missing tiles are actually counter-productive because they make the separated charges crash back together too quickly.
• Good news: Now we know exactly why this happens. By understanding that missing tiles change the energy levels and create "tunnels," engineers can design better materials. They can either patch the holes to stop the crash or use this knowledge to control how fast electricity moves in future super-fast computers and solar cells.

In short: Creating holes in the material makes the electrons wait longer in the top layer, but once they move, they rush back to cancel out the holes much faster, shortening the time the device can actually harvest energy.

Technical Summary

1. Problem Statement

WS2-graphene heterostructures are promising candidates for light harvesting and photodetection due to their efficient ultrafast charge separation following photoexcitation of the A-exciton in monolayer WS2. However, the lifetime of the resulting charge-separated state has been a subject of significant controversy in the literature. Reported values range drastically from ~1 picosecond (ps) to ~1 nanosecond (ns).

While previous studies attributed these lifetimes to electron trapping at sulphur (S) vacancies within the WS2 layer, the precise mechanism and the specific impact of these defects on charge separation and recombination dynamics remained unclear. Resolving this discrepancy is critical for optimizing the efficiency of future optoelectronic devices.

2. Methodology

The authors employed a combination of controlled defect engineering, spectroscopic characterization, and theoretical modeling:

• Sample Preparation: WS2-graphene heterostructures were grown on SiC(0001) substrates. To deliberately introduce sulphur vacancies, the samples were annealed in an ultrahigh vacuum (UHV) environment.
  • Initial annealing at 600°C (4 steps) showed no significant changes.
  • Subsequent annealing at 650°C (3 steps) successfully generated sulphur vacancies, confirmed by the desorption of sulphur atoms.
• Spectroscopy:
  • Angle-Resolved Photoemission Spectroscopy (ARPES): Used to map the equilibrium band structure, specifically monitoring changes in band alignment and doping levels induced by annealing.
  • Time-Resolved ARPES (trARPES): Utilized a 1 kHz Ti:Sapphire amplifier system. The pump pulse (2 eV, resonant with the WS2 A-exciton) excited the sample, while a high-harmonic probe (21.7 eV) measured the relaxation dynamics of photoexcited electron-hole pairs with ~160 fs temporal resolution.
• Theoretical Modeling:
  • Density Functional Theory (DFT): Parametrized the model for electron density evolution.
  • Second-Order Born-Markov Approach: Used to calculate the electron transfer time from sulphur vacancy states to the graphene Dirac cone.
  • GW-BSE Calculations: Referenced to understand the impact of vacancies on excitonic absorption.

3. Key Results

A. Equilibrium Band Structure Changes (ARPES)

Annealing at 650°C to create sulphur vacancies resulted in two major changes to the electronic structure:

1. n-Doping: The heterostructure became n-doped, evidenced by the Dirac point of graphene dropping below the Fermi level ($E_D \sim -210$ meV).
2. Band Alignment Shift: The energy separation ($\Delta E$) between the maximum of the WS2 valence band (VB) and the graphene Dirac point decreased from ~1.43 eV to ~1.24 eV.

B. Non-Equilibrium Carrier Dynamics (trARPES)

The study revealed a counter-intuitive relationship between sulphur vacancy concentration ($n_v$) and carrier lifetimes:

1. WS2 Conduction Band (CB) Lifetime: The lifetime of photoexcited electrons inside the WS2 CB increased with higher $n_v$.
2. Charge-Separated State Lifetime: The lifetime of the charge-separated state (defined by the transient charging shift of the bands) decreased significantly with higher $n_v$.
   • The charge-separated state lifetime dropped from 3 ps to **0.6 ps** as annealing progressed.

C. Theoretical Transfer Time

Using the Born-Markov approximation and DFT parameters, the authors calculated the tunneling time for electrons moving from sulphur vacancy states to the graphene Dirac cone.

• Calculated Transfer Time: $\sim 4$ ps.
• This value aligns with the picosecond-scale lifetimes observed in this study and previous works by the same group, but contradicts the nanosecond-scale lifetimes reported in other literature.

4. Discussion and Mechanism

The authors propose a dual-mechanism model to explain the observed dynamics:

1. Enhanced Recombination via Vacancy States:

   • Sulphur vacancies create mid-gap states that hybridize with the graphene Dirac cone.
   • The annealing-induced band alignment shift increased the energy offset ($E_0$) between the lower sulphur vacancy level and the Dirac point.
   • According to the model, a larger $E_0$ increases the tunneling rate from vacancies to graphene, thereby shortening the charge-separated state lifetime. This explains the picosecond-scale recombination.

2. Reduced Excitonic Absorption:

   • Referencing recent GW-BSE calculations, the authors suggest that sulphur vacancies reduce the excitonic absorption cross-section at the A-exciton resonance.
   • At a constant pump fluence, reduced absorption leads to a lower density of photoexcited electron-hole pairs and lower carrier temperatures.
   • Lower carrier density reduces the screening of the Coulomb interaction, which prolongs the lifetime of electrons within the WS2 conduction band (explaining the increase in $\tau_{CB}$).

Resolution of the Controversy:
The authors argue that the ~1 ns lifetimes reported in other studies (e.g., Fu et al.) are likely not due to monolayer WS2 sulphur vacancies. They speculate those samples may contain thicker WS2 layers or different defect/impurity types that inhibit the fast recombination channel observed here.

5. Significance and Conclusion

• Clarification of Defect Roles: The study definitively links sulphur vacancies in monolayer WS2 to a shortening of the charge-separated state lifetime (to the picosecond scale) via a defect-mediated tunneling channel.
• Microscopic Understanding: It provides a quantitative model for electron transfer times ($\sim 4$ ps) through defect states, reconciling experimental data with quantum master equation predictions.
• Implications for Applications: For optoelectronic applications requiring long-lived charge separation (e.g., photodetectors), the presence of sulphur vacancies in monolayer WS2-graphene heterostructures is detrimental. Conversely, the ability to tune these lifetimes via defect engineering offers a pathway for optimizing device performance.
• Future Directions: The authors suggest that future work must account for layer thickness and specific defect types to fully understand charge dynamics in these heterostructures.