Suppression of auxetic behavior in black phosphorus with sulfur substitution

TL;DR

This study reveals that sulfur substitution in black phosphorus distorts the bow-tie motif responsible for the intrinsic auxeticity, effectively suppressing both in-plane and out-of-plane negative Poisson's ratio. Using first-principles DFT with $C_{ij}$ analyses, the work shows concurrent increases in bulk modulus and Poisson's ratio, and decreases in Young's and shear moduli, along with a transition from semiconducting to metallic electronic structure as sulfur content rises. Mechanical stability persists up to about 25% S, after which significant distortions and instability occur, highlighting a practical dopant limit. The findings provide fundamental insights for the design of sulfur-stabilized, nanoscale electronic devices based on black phosphorus, balancing environmental robustness with elastic and electronic performance.

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 (that is, 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 bow-tie 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.

Figures (8)

• Figure 1: Crystal structures of bulk black P$_{1-x}$S$_{x}$. Phosphorus atoms are shown in blue, and sulfur atoms are shown in orange.
• Figure 2: Elastic properties of P$_{1-x}$S$_{x}$: (a) bulk modulus K (GPa), (b) shear modulus E (GPa), (c) Young's modulus G (GPa), and (d) average Poisson’s ratio $\nu$. Experimental values for K and G are reported from Ref. Ponaga_PhysRevB_2022, while E and $\nu$ are calculated using standard relationships with K and G. Experimental values are shown as red stars.
• Figure 3: Spatial dependence of Poisson's ratio for pure black phosphorus, P$_{7}$S$_{1}$-I, and P$_{6}$S$_{2}$-I, respectively. All plots were generated using the ELATE software Gaillac_2016. Blue lines represent the positive Poisson's ratio, and red lines represent the negative Poisson's ratio.
• Figure 4: Electron localization function (ELF) distribution (gray) for (a) b-P and (b) P$_7$S$_1$-I. (c)–(d) Top view of the ELF for the upper P–P (P–S) plane [highlighted in pink in (a) and (b)] in a single monolayer of pristine b-P and P$_7$S$_1$-I, respectively, illustrating the characteristic bow-shaped structural configuration responsible for the in-plane auxeticity in the xz-plane of b-P. (e)–(f) Corresponding P–P–P and P–S–P bond angles, along with P–P and P–S bond lengths, showing how S substitution distorts the bow-type configuration. Yellow circles represent bonding interactions, while red stars denote antibonding behavior.
• Figure 5: Elastic wave velocities and Debye temperature of P$_{1-x}$S$_{x}$ configurations with varying sulfur concentration.