Ideal strength and phonon instability in single-layer MoS2

Abstract

Ideal tensile stress strain relations for single-layer MoS${}_{2}$ are investigated based on first-principle calculation, for biaxial tension and uniaxial tension along zigzag and armchair directions. The predicted ideal tensile strengths and elastic moduli are in excellent agreement with the very recent experimental measurements of Bertolazzi et al. [ACS Nano 5, 9703 (2011)] and Castellanos-Gomez et al. [Adv. Mater. 24, 772 (2012)]. It is identified that the tensile strength of single-layer MoS${}_{2}$ are dictated by out-of-plane soft-mode phonon instability under biaxial tension and uniaxial tension along the armchair direction. This failure mechanism, different from that of the truly two-dimensional material graphene, is attributed to the out-of-plane atomic relaxation upon tensile strain. Investigation of the electronic structures of single-layer MoS${}_{2}$ under tensile strain shows the material becomes an indirect semiconductor at small tensile strain ($<2$$%$) and turns into metallic before reaching the ideal tensile strength.