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High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus.

Qiao J, Kong X, Hu ZX, Yang F, Ji W - Nat Commun (2014)

Bottom Line: The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy.Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties.These results make few-layer BP a promising candidate for future electronics.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Physics, Renmin University of China, Beijing 100872, China [2] Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China [3].

ABSTRACT
Two-dimensional crystals are emerging materials for nanoelectronics. Development of the field requires candidate systems with both a high carrier mobility and, in contrast to graphene, a sufficiently large electronic bandgap. Here we present a detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) to predict its electrical and optical properties. This system has a direct bandgap, tunable from 1.51 eV for a monolayer to 0.59 eV for a five-layer sample. We predict that the mobilities are hole-dominated, rather high and highly anisotropic. The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy. Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties. These results make few-layer BP a promising candidate for future electronics.

No MeSH data available.


Related in: MedlinePlus

Lattice and electronic structures of bulk black phosphorus.(a) Crystal structure of bulk BP marked with coordinate axes (x, y, z), lattice vectors (a, b, c) and structural parameters (R1, R2, θ1 and θ2). (b) Brillouin zone path of BP primitive cell. (c) Electronic bandstructures for bulk BP calculated with the HSE06 functional (red solid line) and the mBJ potential (blue dashed line), together with fitted effective masses along the Z–T′–A′, Z–Q and Z–G directions. At the right of the image, a zoomed-in plot shows the direct bandgap at Z. EVBM is the energy of valence-band maximum.
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f1: Lattice and electronic structures of bulk black phosphorus.(a) Crystal structure of bulk BP marked with coordinate axes (x, y, z), lattice vectors (a, b, c) and structural parameters (R1, R2, θ1 and θ2). (b) Brillouin zone path of BP primitive cell. (c) Electronic bandstructures for bulk BP calculated with the HSE06 functional (red solid line) and the mBJ potential (blue dashed line), together with fitted effective masses along the Z–T′–A′, Z–Q and Z–G directions. At the right of the image, a zoomed-in plot shows the direct bandgap at Z. EVBM is the energy of valence-band maximum.

Mentions: Because no experimental data are available for the atomic structure and electronic properties of few-layer BP, we begin by considering bulk BP to refine the accuracy of our theoretical predictions. We have performed DFT calculations using a number of different functionals to gauge which provide the best fit to experiment; a full list may be found in Supplementary Table 1 and we summarize our findings here. If one considers only the lattice geometry then the PBE-G06 (refs 20, 21) and optB86b-vdW22 methods produce the best results. However, neither local density approximation-modified Becke–Johnson (LDA-mBJ)2324 nor HSE06 (refs 25, 26) calculations based on these ‘best’ geometries can provide a satisfactory value for the bulk bandgap, as shown in Supplementary Fig. 1. To optimize both sets of properties simultaneously, we found that the optB88-vdW functional2227, combined with either the LDA-mBJ or HSE06 method to predict the electronic bandstructure, gave the best fits. Details of choosing the best-fit functional are available in Supplementary Methods. Figure 1a shows the fully relaxed atomic structure of bulk BP, where the equilibrium lattice constants obtained from optB88-vdW are only 1–2% larger than the experiment282930. The accompanying Brillouin zone (BZ) and electronic bandstructures, labelled mBJ (optB88-vdW) and HSE06 (optB88-vdW) are shown in Fig. 1b,c. Both combinations of methods predict that bulk BP is a semiconductor with a direct bandgap at the Z point of 0.31 eV (mBJ) or 0.36 eV (HSE06), both values being fully consistent with the experimental value of 0.31–0.35 eV (refs 31, 32, 33, 34).


High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus.

Qiao J, Kong X, Hu ZX, Yang F, Ji W - Nat Commun (2014)

Lattice and electronic structures of bulk black phosphorus.(a) Crystal structure of bulk BP marked with coordinate axes (x, y, z), lattice vectors (a, b, c) and structural parameters (R1, R2, θ1 and θ2). (b) Brillouin zone path of BP primitive cell. (c) Electronic bandstructures for bulk BP calculated with the HSE06 functional (red solid line) and the mBJ potential (blue dashed line), together with fitted effective masses along the Z–T′–A′, Z–Q and Z–G directions. At the right of the image, a zoomed-in plot shows the direct bandgap at Z. EVBM is the energy of valence-band maximum.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4109013&req=5

f1: Lattice and electronic structures of bulk black phosphorus.(a) Crystal structure of bulk BP marked with coordinate axes (x, y, z), lattice vectors (a, b, c) and structural parameters (R1, R2, θ1 and θ2). (b) Brillouin zone path of BP primitive cell. (c) Electronic bandstructures for bulk BP calculated with the HSE06 functional (red solid line) and the mBJ potential (blue dashed line), together with fitted effective masses along the Z–T′–A′, Z–Q and Z–G directions. At the right of the image, a zoomed-in plot shows the direct bandgap at Z. EVBM is the energy of valence-band maximum.
Mentions: Because no experimental data are available for the atomic structure and electronic properties of few-layer BP, we begin by considering bulk BP to refine the accuracy of our theoretical predictions. We have performed DFT calculations using a number of different functionals to gauge which provide the best fit to experiment; a full list may be found in Supplementary Table 1 and we summarize our findings here. If one considers only the lattice geometry then the PBE-G06 (refs 20, 21) and optB86b-vdW22 methods produce the best results. However, neither local density approximation-modified Becke–Johnson (LDA-mBJ)2324 nor HSE06 (refs 25, 26) calculations based on these ‘best’ geometries can provide a satisfactory value for the bulk bandgap, as shown in Supplementary Fig. 1. To optimize both sets of properties simultaneously, we found that the optB88-vdW functional2227, combined with either the LDA-mBJ or HSE06 method to predict the electronic bandstructure, gave the best fits. Details of choosing the best-fit functional are available in Supplementary Methods. Figure 1a shows the fully relaxed atomic structure of bulk BP, where the equilibrium lattice constants obtained from optB88-vdW are only 1–2% larger than the experiment282930. The accompanying Brillouin zone (BZ) and electronic bandstructures, labelled mBJ (optB88-vdW) and HSE06 (optB88-vdW) are shown in Fig. 1b,c. Both combinations of methods predict that bulk BP is a semiconductor with a direct bandgap at the Z point of 0.31 eV (mBJ) or 0.36 eV (HSE06), both values being fully consistent with the experimental value of 0.31–0.35 eV (refs 31, 32, 33, 34).

Bottom Line: The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy.Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties.These results make few-layer BP a promising candidate for future electronics.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Physics, Renmin University of China, Beijing 100872, China [2] Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China [3].

ABSTRACT
Two-dimensional crystals are emerging materials for nanoelectronics. Development of the field requires candidate systems with both a high carrier mobility and, in contrast to graphene, a sufficiently large electronic bandgap. Here we present a detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) to predict its electrical and optical properties. This system has a direct bandgap, tunable from 1.51 eV for a monolayer to 0.59 eV for a five-layer sample. We predict that the mobilities are hole-dominated, rather high and highly anisotropic. The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy. Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties. These results make few-layer BP a promising candidate for future electronics.

No MeSH data available.


Related in: MedlinePlus