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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.


Electronic structures of few-layer BP.(a,b) Top view of the atomic structure of the monolayer and the associated Brillouin zone. (d,e) Side views of the atomic structure of the bilayer. (c,f) Bandstructures of monolayer and bilayer BP calculated with the HSE06 functional (red solid lines) and the mBJ potential (blue dashed lines), respectively. Two valence (VB1 and VB2) and two conduction states (CB1 and CB2) are marked in panel f. (g) Spatial structure of wavefunctions for the four marked states illustrated in the xz and yz planes using an isosurface of 0.0025 e Å−3. (h) Evolution of the direct bandgaps as a function of the sample thickness. Functionals used for structural optimization are shown in parentheses. Bandgap values are marked for the monolayer system, for the extrapolation of our results and for real bulk BP.
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f2: Electronic structures of few-layer BP.(a,b) Top view of the atomic structure of the monolayer and the associated Brillouin zone. (d,e) Side views of the atomic structure of the bilayer. (c,f) Bandstructures of monolayer and bilayer BP calculated with the HSE06 functional (red solid lines) and the mBJ potential (blue dashed lines), respectively. Two valence (VB1 and VB2) and two conduction states (CB1 and CB2) are marked in panel f. (g) Spatial structure of wavefunctions for the four marked states illustrated in the xz and yz planes using an isosurface of 0.0025 e Å−3. (h) Evolution of the direct bandgaps as a function of the sample thickness. Functionals used for structural optimization are shown in parentheses. Bandgap values are marked for the monolayer system, for the extrapolation of our results and for real bulk BP.

Mentions: Results from our bandstructure calculations for the five few-layer BP systems are shown in Fig. 2. In the monolayer, the original Z point of the bulk BZ folds back to the Gamma (G) point, so that the original Z–Q and Z–T′–A′ directions of the bulk BZ project onto the G–X and G–Y directions of the monolayer, which correspond respectively to the a and b directions in real space (Fig. 2a,b). Results obtained from the mBJ method are quantitatively the same as those obtained from HSE06. Supplementary Figure 2 and Supplementary Table 2 show that the predicted bandgap is rather less sensitive than the unit-cell dimensions to the functional used for optimizing the atomic structures, with similar values emerging for all few-layer BP systems from the best-performing functionals. However, other physical quantities, notably the location of band maximum (minimum) and the carrier effective mass (and hence the mobility) are in fact very sensitive to the choice of the functional, and hence we have focused primarily on our optB88-vdW results for the discussion of these. Monolayer BP is indeed a direct-bandgap semiconductor, as shown in Fig. 2c, with the gap value of 1.51 eV obtained at the G point. Phosphorus is a heavier element than carbon and therefore should have stronger spin-orbit coupling (SOC) in its 2D forms than graphene. We have considered full SOC effects in calculating the electronic bandstructure of bulk BP. Supplementary Figure 3 shows that inclusion of SOC terms has no appreciable effect on the primary features of the bandstructure, indicating that phosphorus is ‘not sufficiently heavy’ to cause any qualitative changes. Only a very small separation of the formerly fourfold degenerate bands, into two band pairs, can be found from X along N (or M for few-layer BP) to Y, which reaches a maximum of 23 meV around the N (M) point. Along G–X and G–Y, these bands are already separated by bandstructure effects and SOC causes no further splitting. That the spin-orbit splitting energy is so small is a consequence of the small effective nuclear charge (Zeff) of the P atom and the weak variation of the charge gradient in an elemental system such as BP.


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)

Electronic structures of few-layer BP.(a,b) Top view of the atomic structure of the monolayer and the associated Brillouin zone. (d,e) Side views of the atomic structure of the bilayer. (c,f) Bandstructures of monolayer and bilayer BP calculated with the HSE06 functional (red solid lines) and the mBJ potential (blue dashed lines), respectively. Two valence (VB1 and VB2) and two conduction states (CB1 and CB2) are marked in panel f. (g) Spatial structure of wavefunctions for the four marked states illustrated in the xz and yz planes using an isosurface of 0.0025 e Å−3. (h) Evolution of the direct bandgaps as a function of the sample thickness. Functionals used for structural optimization are shown in parentheses. Bandgap values are marked for the monolayer system, for the extrapolation of our results and for real bulk BP.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
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f2: Electronic structures of few-layer BP.(a,b) Top view of the atomic structure of the monolayer and the associated Brillouin zone. (d,e) Side views of the atomic structure of the bilayer. (c,f) Bandstructures of monolayer and bilayer BP calculated with the HSE06 functional (red solid lines) and the mBJ potential (blue dashed lines), respectively. Two valence (VB1 and VB2) and two conduction states (CB1 and CB2) are marked in panel f. (g) Spatial structure of wavefunctions for the four marked states illustrated in the xz and yz planes using an isosurface of 0.0025 e Å−3. (h) Evolution of the direct bandgaps as a function of the sample thickness. Functionals used for structural optimization are shown in parentheses. Bandgap values are marked for the monolayer system, for the extrapolation of our results and for real bulk BP.
Mentions: Results from our bandstructure calculations for the five few-layer BP systems are shown in Fig. 2. In the monolayer, the original Z point of the bulk BZ folds back to the Gamma (G) point, so that the original Z–Q and Z–T′–A′ directions of the bulk BZ project onto the G–X and G–Y directions of the monolayer, which correspond respectively to the a and b directions in real space (Fig. 2a,b). Results obtained from the mBJ method are quantitatively the same as those obtained from HSE06. Supplementary Figure 2 and Supplementary Table 2 show that the predicted bandgap is rather less sensitive than the unit-cell dimensions to the functional used for optimizing the atomic structures, with similar values emerging for all few-layer BP systems from the best-performing functionals. However, other physical quantities, notably the location of band maximum (minimum) and the carrier effective mass (and hence the mobility) are in fact very sensitive to the choice of the functional, and hence we have focused primarily on our optB88-vdW results for the discussion of these. Monolayer BP is indeed a direct-bandgap semiconductor, as shown in Fig. 2c, with the gap value of 1.51 eV obtained at the G point. Phosphorus is a heavier element than carbon and therefore should have stronger spin-orbit coupling (SOC) in its 2D forms than graphene. We have considered full SOC effects in calculating the electronic bandstructure of bulk BP. Supplementary Figure 3 shows that inclusion of SOC terms has no appreciable effect on the primary features of the bandstructure, indicating that phosphorus is ‘not sufficiently heavy’ to cause any qualitative changes. Only a very small separation of the formerly fourfold degenerate bands, into two band pairs, can be found from X along N (or M for few-layer BP) to Y, which reaches a maximum of 23 meV around the N (M) point. Along G–X and G–Y, these bands are already separated by bandstructure effects and SOC causes no further splitting. That the spin-orbit splitting energy is so small is a consequence of the small effective nuclear charge (Zeff) of the P atom and the weak variation of the charge gradient in an elemental system such as BP.

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.