Key Takeaways & Executive Findings
- •• • Tensile strain along the zigzag direction increases the phosphorene bandgap, as governed by the negative hopping parameter t1 = -1.220 eV; this contrasts with MoS2, where tensile strain reduces the bandgap due to positive hopping parameters (t11, t22, t12 > 0), enabling opposite strain-tuning strategies for NIR versus visible emitters. • • The bandgap of phosphorene is dominated by the nearest-neighbor hopping terms: E_g^BP ≈ 4t1 + 2t2, with t1 = -1.220 eV and t2 = 3.665 eV; this simplification allows rapid prediction of strain effects, critical for designing NIR photodetectors and lasers with tailored emission wavelengths. • • For monolayer MoS2, the bandgap at K is given by E_g^MoS2 = ε1 - ε2 - 3t0 + (3/2)(t11 + t22) + 3√3 t12, where t0 is negative and t11, t22, t12 are positive; tensile strain reduces the bandgap, underscoring the material-specific strain response that must be accounted for in heterostructure integration. • • The anisotropic strain response in phosphorene enables selective tuning of NIR exciton emission, with potential for strain-tunable emitters operating in the 0.3–0.8 eV range (corresponding to 1.5–4 µm), essential for telecommunications and infrared sensing; this contrasts with TMDs, which typically operate in the visible range.
Abstract
Monolayer black phosphorus (phosphorene) exhibits a direct bandgap and strong in-plane anisotropy, making it a promising candidate for near-infrared (NIR) optoelectronic devices. However, the precise modulation of its excitonic emission via anisotropic strain remains insufficiently understood, particularly regarding the contrasting strain responses of phosphorene versus transition metal dichalcogenides (TMDs). Here, we combine experimental characterization with tight-binding (TB) modeling to elucidate the strain-dependent bandgap evolution in phosphorene. Using a four-band TB model, we derive the bandgap at the Γ point as E_g^BP = 4t1 + 2t2 + 4t3 + 2t5, with hopping parameters t1 = -1.220 eV, t2 = 3.665 eV, t3 = -0.205 eV, t4 = -0.105 eV, and t5 = -0.055 eV. Under tensile strain along the zigzag (ZZ) direction, the interatomic distance associated with t1 increases, reducing the magnitude of |t1|. Since t1 is negative, the bandgap increases, contrary to the behavior of monolayer MoS2, where tensile strain decreases the bandgap due to positive hopping parameters t11, t22, and t12. This anisotropic strain response enables selective tuning of NIR exciton emission. Our findings provide a quantitative framework for strain engineering in phosphorene-based NIR devices, highlighting the critical role of hopping parameter signs in determining bandgap modulation.
1. Introduction
Existing commercial near-infrared (NIR) optoelectronic devices, such as InGaAs photodetectors and quantum cascade lasers, rely on epitaxial III-V semiconductors, which incur high fabrication costs and necessitate cryogenic cooling for optimal performance. Two-dimensional (2D) materials offer a promising alternative due to their atomic-scale thickness and van der Waals integration; however, most TMDs possess bandgaps in the visible range, limiting their utility for NIR applications. Phosphorene, a monolayer of black phosphorus, features a direct bandgap that is tunable from 0.3 eV (bulk) to 2.0 eV (monolayer), covering the NIR spectrum. Despite this, the precise control of its excitonic emission via strain—a key knob for band structure engineering—remains poorly quantified, particularly regarding the anisotropic strain response that distinguishes phosphorene from TMDs.
This study addresses the bottleneck of strain-dependent bandgap modulation in phosphorene by combining experimental measurements with a four-band tight-binding model. We demonstrate that tensile strain along the zigzag direction increases the bandgap, contrary to the behavior of TMDs like MoS2, where tensile strain decreases the bandgap. This opposite trend arises from the sign of the dominant hopping parameter t1 = -1.220 eV in phosphorene, versus positive hopping parameters in MoS2. Our analytical expressions for the bandgap—E_g^BP ≈ 4t1 + 2t2 for phosphorene and E_g^MoS2 = ε1 - ε2 - 3t0 + (3/2)(t11 + t22) + 3√3 t12 for MoS2—provide a quantitative framework for strain engineering. These findings enable the rational design of phosphorene-based NIR emitters and detectors with strain-tunable emission wavelengths, overcoming the limitations of current III-V technologies.
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Yao Yun, Song Jiexi, Xuan Fengyuan, Zhang Shuo, Wang Dong, Zhang Quanlong, Wang Xiaoran, Wang Xiangyi, Xu Jing, Xu Junsheng, Zhang Junrong, Wang Junyong, Zhang Kai (2026). Anisotropic Strain Tunable Near-Infrared Exciton Emission in Phosphorene. SCIENCE CHINA Materials. https://doi.org/10.1007/s40843-026-4263-3
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Frequently Asked Questions
What is the fundamental mechanism behind the opposite strain response of phosphorene and MoS2?
The opposite strain response stems from the sign of the dominant hopping parameters. In phosphorene, the nearest-neighbor hopping parameter t1 = -1.220 eV is negative; tensile strain along the zigzag direction increases the interatomic distance, reducing |t1| and thus increasing the bandgap (E_g^BP ≈ 4t1 + 2t2). In contrast, MoS2 has positive hopping parameters t11, t22, t12 > 0, so tensile strain reduces the bandgap (E_g^MoS2 = ε1 - ε2 - 3t0 + (3/2)(t11 + t22) + 3√3 t12). This sign difference dictates the divergent strain-tuning strategies for NIR versus visible emitters.
How does the anisotropic strain affect the exciton emission wavelength in phosphorene?
Tensile strain along the zigzag direction increases the bandgap, leading to a blueshift in exciton emission. Given the monolayer phosphorene bandgap range of 0.3–2.0 eV, strain can tune the emission across the NIR spectrum (e.g., from 0.3 eV to higher energies). This enables selective tuning of emission wavelengths for applications such as telecommunications (1.55 µm, ~0.8 eV) and infrared sensing, with the exact shift determined by the strain magnitude and the hopping parameter changes.
What are the scalability and cost implications of strain-engineered phosphorene devices compared to III-V NIR technologies?
Phosphorene can be exfoliated or grown on large-area substrates, potentially reducing material costs compared to epitaxial III-V semiconductors. However, scalable strain engineering requires precise control of mechanical deformation, which may add processing complexity. The tight-binding model provides a predictive tool to optimize strain conditions, minimizing trial-and-error and enabling cost-effective design. Nevertheless, long-term stability under ambient conditions remains a challenge, as phosphorene degrades rapidly without encapsulation.
What are the failure mechanisms under sustained strain, and how do they impact device reliability?
Sustained tensile strain can induce crack formation or plastic deformation in phosphorene, particularly at grain boundaries or defects. The anisotropic nature means that strain along the zigzag direction may cause different failure modes than along the armchair direction. Additionally, phosphorene is prone to oxidation under ambient conditions, which is exacerbated by strain-induced defects. Encapsulation with inert layers (e.g., hBN) and limiting strain to elastic regimes (<5%) are critical for reliable operation.
How does the tight-binding model account for strain beyond the elastic limit, and what are the limitations?
The four-band tight-binding model assumes harmonic strain effects, where hopping parameters vary linearly with interatomic distance. Beyond the elastic limit (>5% strain), anharmonic effects and structural transformations (e.g., phase changes) occur, which the model does not capture. Experimental validation is required for large strains. The model's strength lies in predicting trends within the elastic regime, providing a foundation for more sophisticated simulations that include anharmonicity and defects.
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