[Paper Review] Strain engineered direct-indirect band gap transition and its mechanism in 2D phosphorene

Xihong Peng, Andrew Copple+1 more|arXiv (Cornell University)|Mar 15, 2014

2D Materials and Applications4 citations

TL;DR

This study investigates strain-induced direct-to-indirect band gap transitions in 2D phosphorene using first-principles calculations. It reveals that axial strain—particularly −2% compressive strain in the zigzag direction—triggers a direct-indirect transition, with five distinct strain zones identified; the mechanism is linked to orbital hybridization changes, and effective masses show sharp variations at transition boundaries, enabling tunable carrier transport properties.

ABSTRACT

Recently fabricated two dimensional (2D) phosphorene crystal structures have demonstrated great potential in applications of electronics. In this work, strain effect on the electronic band structure of phosphorene was studied using first principles methods. It was found that phosphorene can withstand a surface tension and tensile strain up to 10 N/m and 30%, respectively. The band gap of phosphorene experiences a direct-indirect-direct transition when axial strain is applied. A moderate -2% compression in the zigzag direction can trigger this gap transition. With sufficient expansion (+11.3%) or compression (-10.2% strains), the gap can be tuned from indirect to direct again. Five strain zones with distinct electronic band structure were identified and the critical strains for the zone boundaries were determined. The origin of the gap transition was revealed and a general mechanism was developed to explain energy shifts with strain according to the bond nature of near-band-edge electronic orbitals. Effective masses of carriers in the armchair direction are an order of magnitude smaller than that of the zigzag axis indicating the armchair direction is favored for carrier transport. In addition, the effective masses can be dramatically tuned by strain, in which its sharp jump/drop occurs at the zone boundaries of the direct-indirect gap transition.

Motivation & Objective

• To understand the electronic response of phosphorene under mechanical strain.
• To identify critical strain thresholds that induce direct-to-indirect band gap transitions.
• To elucidate the underlying mechanism of band gap evolution based on orbital hybridization.
• To quantify strain-dependent effective masses and their implications for carrier transport.

Proposed method

• First-principles density functional theory (DFT) calculations were employed to model the electronic band structure of phosphorene under uniaxial strain.
• Strain was applied along the zigzag and armchair directions to probe anisotropic mechanical and electronic responses.
• The band gap evolution was analyzed by tracking the energy difference between the conduction band minimum and valence band maximum.
• Orbital hybridization analysis was used to explain the origin of energy shifts and band gap transitions under strain.
• Effective mass tensors were calculated along both zigzag and armchair directions to evaluate carrier mobility trends.
• Five distinct strain zones with unique band structures were identified based on critical strain values.

Experimental results

Research questions

• RQ1 What strain conditions induce a direct-to-indirect band gap transition in phosphorene?
• RQ2 How does uniaxial strain alter the electronic band structure and orbital character in phosphorene?
• RQ3 What is the physical mechanism behind the observed band gap transition under strain?
• RQ4 How does strain affect the effective mass of charge carriers in different crystallographic directions?
• RQ5 Can strain engineering be used to reversibly tune the band gap from indirect to direct and back?

Key findings

• Phosphorene can sustain up to 30% tensile strain and 10 N/m surface tension before structural failure.
• A −2% compressive strain in the zigzag direction triggers a direct-to-indirect band gap transition.
• At +11.3% or −10.2% strain, the band gap reverts from indirect to direct, indicating reversible tuning.
• Five distinct strain zones with unique electronic structures were identified, bounded by critical strain thresholds.
• Effective masses in the armchair direction are an order of magnitude smaller than in the zigzag direction, favoring higher carrier mobility along armchair.
• Sharp jumps or drops in effective mass occur precisely at the boundaries of direct-indirect transition zones.