🔬 mesoscale physics

Measurements of absolute bandgap deformation-potentials of optically-bright bilayer WSe $_2$

This study experimentally determines the absolute bandgap deformation potentials for the indirect and direct bandgaps of bilayer WSe $_2$ using nanoparticle-induced strain and photoluminescence measurements, revealing that minimal localized strain can significantly enhance its optical brightness and enable direct bandgap conversion.

Original authors: Indrajeet Dhananjay Prasad, Sumitra Shit, Yunus Waheed, Jithin Thoppil Surendran, Kenji Watanabe, Takashi Taniguchi, Santosh Kumar

Published 2026-06-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Indrajeet Dhananjay Prasad, Sumitra Shit, Yunus Waheed, Jithin Thoppil Surendran, Kenji Watanabe, Takashi Taniguchi, Santosh Kumar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Stretching a Material to Change Its Personality

Imagine you have a piece of rubber. When you stretch it, it changes shape. Now, imagine a material so sensitive that when you stretch it, it doesn’t just change shape—it changes its personality. Specifically, it changes how it handles light and electricity.

This paper is about a very thin material called Bilayer WSe2 (pronounced "double-layer Tungsten Diselenide"). Think of this material as a sandwich made of two atomic layers.

Normally, this "sandwich" is a bit shy with light. It’s an indirect bandgap semiconductor. In simple terms, this means that when electricity flows through it, it doesn’t easily release that energy as light (like a lightbulb does). It’s more like a person who keeps their thoughts to themselves rather than shouting them out.

However, the researchers discovered that if you gently stretch this material, you can force it to become "loud" and bright, acting like a direct bandgap semiconductor (like a standard LED light).

The Experiment: Using Tiny Bumps as Stretchers

How do you stretch something as thin as two atoms? You can’t just pull it with your hands.

The team used a clever trick involving nanoparticles (tiny spheres of silica, smaller than a virus). They placed these tiny spheres underneath the WSe2 sandwich.

The Analogy: Imagine laying a thin sheet of plastic wrap over a bowl of marbles. The plastic wrap will stretch and curve over the tops of the marbles. The marbles act as "stressors," creating localized tension in the plastic.

In this experiment:

They put tiny silica nanoparticles on a substrate.
They placed the WSe2 sandwich on top.
The WSe2 stretched slightly over the tops of the nanoparticles.

The Measurement: Listening to the Light

To see what was happening inside the material, the scientists used a technique called Photoluminescence (PL). They shone a laser on the material and measured the color (energy) of the light that came back out.

Unstretched Material: The light emitted had a specific color (energy level).
Stretched Material: As the material stretched over the nanoparticles, the color of the light shifted.

The key finding was that both types of light emissions from the material shifted to lower energies (a "redshift") when stretched. This shift tells the scientists exactly how much the material’s internal energy structure changed due to the strain.

The Key Numbers: The "Deformation Potential"

The main goal of the paper was to calculate a specific number called the Absolute Bandgap Deformation Potential.

The Analogy: Think of this number as a "sensitivity rating." It tells you: For every 1% you stretch this material, how much does its energy gap change?

The researchers calculated two different sensitivity ratings for the Bilayer WSe2:

For the "Direct" transition (Kc-Kv): The sensitivity is -8.50 eV. This is a strong reaction to stretching.
For the "Indirect" transition (Qc-Kv): The sensitivity is -5.10 eV. This is a moderate reaction.

(Note: "eV" stands for electron-volt, a unit of energy. The negative sign means the energy gap gets smaller as you stretch it.)

The Surprising Discoveries

Based on these calculations, the team made two major claims:

1. The "Switch" Point (0.9% Stretch)
Normally, Bilayer WSe2 is "indirect" (shy/dim). But the math shows that if you stretch it by just 0.9% (biaxial tensile strain), the energy levels flip. The material becomes "direct" (loud/bright).

Why this matters: 0.9% is a very small amount of stretch. It’s easy to achieve in a lab or a device. This means we can easily turn this material into an efficient light emitter just by stretching it slightly.

2. The "Brightness" Match (0.4% Stretch)
Even before it fully switches to a "direct" material, the stretching makes it much brighter. The researchers found that with just 0.4% stretch, the Bilayer WSe2 became just as bright as a Monolayer (single-layer) WSe2 that wasn't stretched at all.

The Analogy: Imagine a quiet library (unstretched bilayer). If you whisper (apply 0.4% strain), it becomes as loud as a normal conversation (unstretched monolayer). If you shout (apply 0.9% strain), it becomes a rock concert (direct bandgap).

Why This Matters (According to the Paper)

The paper states that knowing these exact numbers (the deformation potentials) is crucial for engineers. It allows them to:

Design flexible electronics that change properties when bent.
Create sensors that detect tiny amounts of strain.
Build optoelectronic devices (devices that use light and electricity) and quantum photonic devices with precise control.

Summary in a Nutshell

Material: A two-layer sandwich of WSe2.
Action: Stretching it slightly using tiny nanoparticles underneath.
Result: The material’s energy structure changes predictably.
Key Finding 1: You only need 0.9% stretch to turn it from a dim material into a bright, efficient light emitter.
Key Finding 2: You only need 0.4% stretch to make it as bright as a single-layer version of the material.
Takeaway: We now have the exact "recipe" (the deformation potential numbers) to engineer this material for future flexible and light-based technologies.

Technical Summary: Measurements of Absolute Bandgap Deformation-Potentials of Optically-Bright Bilayer WSe2

Problem Statement
Transition-metal dichalcogenide (TMD) bilayers, particularly bilayer tungsten diselenide (BL-WSe2), exhibit unique properties such as long-lived interlayer excitons and wide bandgap tunability via strain. While the indirect-to-direct bandgap transition is well-documented in monolayer (ML) TMDs, the experimental determination of deformation potentials (DPs) for BL-WSe2 remains largely unexplored in the literature. DPs are critical parameters that quantify the energetic changes in conduction and valence band extrema per unit strain at high-symmetry points in the Brillouin zone. Understanding these values is essential for strain engineering in flexible electronics, sensors, and optoelectronic devices. Specifically, there is a lack of experimental data regarding the absolute bandgap DPs for the indirect $Q_c-K_v$ and direct $K_c-K_v$ transitions in BL-WSe2.

Methodology
The authors employed a combination of local biaxial strain engineering and spatially- and spectrally-resolved micro-photoluminescence ( $\mu$ -PL) spectroscopy.

Sample Preparation: Exfoliated WSe2 flakes containing both ML and BL regions were transferred onto a substrate stack consisting of SiO2 nanoparticles (NPs) spin-coated on hexagonal boron nitride (h-BN), which itself was placed on few-layer graphene (FLG) and a SiO2/Si substrate. The WSe2 was encapsulated with a thin top h-BN layer. The NPs acted as stressors, inducing local biaxial tensile strain in the WSe2 flakes.
Strain Quantification: The authors developed a theoretical model relating the change in exciton emission energy ( $\Delta E_{X^0}$ ) to the absolute/hydrostatic bandgap deformation potential ( $a_{gap}$ ). For biaxial strain ( $\varepsilon_{||}$ ), the relationship is defined as $a_{gap} = \Delta E_{X^0} / [(2-\rho)\varepsilon_{||}]$ , where $\rho$ is the Poisson’s ratio.
Spectral Analysis: To resolve the overlapping direct ( $K_c-K_v$ , denoted $X^0_{KK}$ ) and indirect ( $Q_c-K_v$ , denoted $X^0_{QK}$ ) excitonic peaks under strain, the authors utilized a Dose-Response function fitting method on integrated-normalized PL spectra. This allowed for the extraction of emission energies even when peaks were energetically close.
Reference Calibration: The absolute DP for the $K_c-K_v$ transition ( $a^{gap}_{KK}$ ) was determined using literature data from ML-WSe2 (Roy et al.), based on the hypothesis that the $K_c-K_v$ DP is independent of layer number (ML vs. BL) and strain type (uniaxial vs. biaxial). This value was then used to calibrate the local strain distribution induced by the NPs in the BL regions.

Key Contributions and Results

Determination of Absolute Deformation Potentials:
- The absolute bandgap deformation potential for the direct $K_c-K_v$ transition in BL-WSe2 was determined to be $-8.50 \pm 0.92$ eV.
- The absolute bandgap deformation potential for the indirect $Q_c-K_v$ transition in BL-WSe2 was experimentally determined to be $-5.10 \pm 0.24$ eV.
Strain-Induced Bandgap Crossover:
- The study demonstrates that the $K_c-K_v$ bandgap decreases faster with strain than the $Q_c-K_v$ bandgap due to its larger deformation potential.
- The authors calculated that approximately 0.9% biaxial tensile strain is required to convert BL-WSe2 from an indirect to a direct bandgap semiconductor. This is significantly lower than the $\approx 2.63\%$ uniaxial tensile strain required for the same transition.
Optical Brightness Enhancement:
- The authors observed that a relatively small localized biaxial tensile strain of $\approx 0.4\%$ is sufficient to make the PL emission intensity of indirect BL-WSe2 comparable to that of unstrained direct ML-WSe2.
- This enhancement is attributed to strain-induced funneling effects and potentially reduced electron-phonon scattering in the strained BL regions compared to ML regions.
Gauge Factor:
- The gauge factor for the $Q_c-K_v$ exciton emission in BL-WSe2 was determined to be $-102.6 \pm 2.5$ meV/% biaxial tensile strain.

Significance
The paper claims that these experimentally determined bandgap deformation potentials provide a quantitative basis for precise strain engineering in BL-WSe2. The findings highlight that BL-WSe2 can be efficiently tuned from an indirect to a direct bandgap semiconductor with minimal biaxial strain ( $\approx 0.9\%$ ) and can achieve optical brightness comparable to ML-WSe2 with even less strain ( $\approx 0.4\%$ ). These results are presented as foundational for advancing the development of strain sensors, flexible devices, and optoelectronic and quantum photonic devices based on TMD bilayers.