Raman Activity of Multilayer Phosphorene under Strain

Abstract

Using computational tools, we study the behavior of activities of lattice vibrational Raman modes in few-layered phosphorene of up to four layers subjected to a uniaxial strain of −2 to +6% applied in the armchair and zigzag directions. We study both high- and low-frequency modes and find very appreciable frequency shifts in response to the applied strain of up to ≈20 cm–1. The Raman activities are characterized by Ag2/Ag1 activity ratios, which provide very meaningful characteristics of functionalization via layer- and strain-engineering. The ratios exhibit a pronounced vibrational anisotropy, namely a linear increase with the applied armchair strain and a highly nonlinear behavior with a strong drop of the ratio with the strain applied along the zigzag direction. For the low-frequency modes, which are Raman active exclusively in few-layered systems, we find the breathing interlayer modes of primary importance due to their strong activities. For few-layered structures with a thickness ≥4, a splitting of the breathing modes into a pair of modes with complementary activities is found, with the lower frequency mode being strain activated. Our calculated database of results contains full angular information on activities of both low- and high-frequency Raman modes. These results, free of experimental complexities, such as dielectric embedding, defects, and size and orientation of the flakes, provide a convenient benchmark for experiments. Combined with high-spatial-resolution Raman scattering experiments, our calculated results will aid in the understanding of the complicated inhomogeneous strain distributions in few-layered phosphorene or the manufacture of materials with desired electronic properties via strain- or layer-engineering.

Strain-induced vibrational properties of few layer black phosphorus and MoTe2 via Raman spectroscopy

“…they had different sensitivities, ∆ω/∆σ, where ω is the Raman shift and σ is the strain. Our observation on the different shifting rates, ∆ω/∆σ of A 2 g , B 2g compared to A 1 g is consistent with previously reported results on the comparison of polarization Raman spectroscopy between near armchair and near zigzag strain-red shift calculations [19,40]. For any intermediate direction, it is also reported to have a red shift even though the in-plane modes are insensitive to near armchair strain while the zigzag strain has more prominent effect on these in plane modes.…”

Strain Modulation of Optoelectronic Properties in Nanolayered Black Phosphorus: Implications for Strain-Engineered 2D Material Systems

“…Although there are negligible shifts in the A g 1 phonon mode of BP, a blue-shift of 0.15 and 0.07 cm –1 /% strain was observed in the B 2g and A g 2 vibrational modes, respectively, as compressive strain increases (Figure c,d). This is indicative of compressive strain on the bonds within BP’s crystal lattice along the zigzag direction, resulting in an enhancement in phonon modes and thus a blue-shift in Raman peaks. , It is also important to note that while many existing theoretical studies show that compressive strain on BP results in a large blue-shift of ∼9 cm –1 /% strain in the B 2g phonon mode (zigzag direction), − the blue-shift in the B 2g peak, which we had observed, has ∼60× lesser shift in Raman peaks. Due to the anisotropic response to bond compression of BP to compressive strain, it has a tendency to induce ripple formation along the zigzag direction (Figure a), which enables the release of strain energy in the out-of-plane direction and therefore creates a relaxation in bond compression and a smaller shift in Raman peaks .…”

Anisotropic Behavior of Optical Properties in Edge-Modified Phosphorene Quantum Dots

“…These characteristic high-frequency Raman modes for bulk BP are known to be around 365, 440, and 470 cm –1 . Previous reports indicate that the high-frequency modes are affected by the number of layers of pristine phosphorene. − The A g 1 mode is the most sensitive to the layer thickness out of the high-frequency modes, resulting in a significant increase in activity in comparison to the A g 2 mode with an increasing number of layers . The heightened sensitivity of the A g 1 mode to layer thickness is not relevant here, as this study pertains to the planar growth of PQDs (i.e., an increase along armchair or zigzag directions).…”

“…78−80 The A g 1 mode is the most sensitive to the layer thickness out of the high-frequency modes, resulting in a significant increase in activity in comparison to the A g 2 mode with an increasing number of layers. 79 The heightened sensitivity of the A g 1 mode to layer thickness is not relevant here, as this study pertains to the planar growth of PQDs (i.e., an increase along armchair or zigzag directions). Increasing system size along the armchair direction (i.e., systems within a single panel of Figure 5) induces a significant increase in activities for both the A g modes, which can be attributed to the enhanced polarizabilities.…”