Abstract

Black phosphorus is a newly rising layered material with tremendous and intriguing physical, chemical, and electronic properties. Recently, it was reintroduced into the community from the perspective of two-dimensional (2D) materials, showing excellent carrier mobility, strong light–matter interactions in the mid-infrared (mid-IR) range, and unique anisotropic physical properties. These features are beyond the existing 2D materials in terms of bandgap range and mobility/bandgap trade-off, making it possible to bridge the application gaps ranging from mid-IR photonics to high-performance field-effect devices. In this paper, we review the status and perspectives of the optical properties of black phosphorus, with a particular emphasis on their broadband tunable bandgap and anisotropic optical properties. We began with a brief introduction on the history, synthesis, crystal/band structures, and basic physical properties of black phosphorus. In Section 3, we discuss the optical properties of black phosphorus, including comparison of the electronic-excitation-induced versus phonon-excitation-induced optical properties, linear versus nonlinear absorption, and static versus dynamic photoresponse, as well as the quasi-particle effect versus the effect. After that, we exemplify typical black phosphorus photonic devices in Section 4. We highlight recent progress in photodetectors covering mid-IR and terahertz wavelength, ultrafast Q-switching and mode-locking pulse lasers and nanophotonic devices. Finally, we present a summary and outlook of black phosphorus regarding current challenges and future application opportunities in Section 5.

© 2016 Optical Society of America

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Figures (21)

Figure 1
Figure 1 Crystal structure of black BP. Left panel: side view of BP crystal lattice. Right panel: top view of the lattice of single-layer BP. The structural parameters shown in the figures are defined in Table 1.
Figure 2
Figure 2 Band structure of bulk BP mapped out by ARPES measurements. A bandgap is clearly observed. Superimposed on top are calculated bands of the bulk crystal. Blue solid and red dashed lines denote empty and filled bands, respectively. The directions of the ARPES mapping are along U (L–Z) and T, as indicated in the first Brillouin zone shown in the inset. Ef is the Fermi energy. Reprinted by permission from Macmillan Publishers Ltd.: Li et al., Nat. Nano 9, 372–377 (2014) [4]. Copyright (2014).
Figure 3
Figure 3 (a) Polarization-resolved IR relative extinction spectra when light is polarized along the six directions as shown in the inset. Inset: an optical micrograph of a BP flake with a thickness of around 30 nm. Scale bar: 20 μm. The crystalline orientation can be determined by polarization-resolved IR measurements. φ is the angle between the x direction and the 0° reference. Reprinted by permission from Macmillan Publishers Ltd.: Xia et al., Nat. Commun. 5, 4458 (2014) [5]. Copyright (2014). (b) Polarization-dependent transmission spectra for a BP flake. The polarization direction of the incident light for each curve is shown in the inset by an arrow of the same color. Light interacts more strongly with the material along the x direction. Reprinted with permission from Lan et al., ACS Photon. 3, 1176–1181 (2016) [42]. Copyright (2016) American Chemical Society.
Figure 4
Figure 4 (a) Complex index of refraction of BP along the x and y directions. The refractive index (na and nb) is retrieved from the transmission and reflection at normal incidence with the known sample thickness [42]. The imaginary part, which corresponds to optical absorption, has a difference of 0.5 between the two optical axes (dashed blue and red lines). (b) Relative permittivity (a.k.a. dielectric constant, ε=ε+iε) of layered BP. The permittivity is related to the refractive index by ε=(n)2(n)2 and ε=2nn, where n (n) corresponds to the real (imaginary) part of the refractive index in (a).
Figure 5
Figure 5 Imaging and spectroscopy of phase anisotropy in black phosphorus. (a) Optical setup for the phase anisotropy measurement. The relative phase retardance between the principle axes of the BP is calibrated against a voltage-controlled liquid crystal retarder. The BP sample rotates around the optical path to locate the crystal axes and quantify the phase anisotropy. Destructive interference for light through the BP flake occurs when the principal axes (a and b) are aligned along the ±45° directions along with an induced total phase anisotropy ΔΦc(V)=ΔΦab+π. (b) Transmission images for a representative BP sample (45 nm thick) when destructive interference occurs at the substrate and the BP flake. The light source is monochromatic at 635 nm. (c) Transmission contrast at λ=635  nm for different thicknesses of the BP samples. Transmittance is lower when the incident light is polarized along the slow axis, a, of the BP structure. (d) Phase anisotropy, ΔΦab=ΦbfastΦaslow, of layered black phosphorus for various sample thicknesses determined using polarization interferometry. The retardation Φ is defined as the absolute phase delay of light through the sample with respect to that through a substrate region. Reprinted with permission from Lan et al., ACS Photon. 3, 1176–1181 (2016) [42]. Copyright (2016) American Chemical Society.
Figure 6
Figure 6 Orbital component analysis of bulk BP band dispersion. In the Z–L direction, only light polarized in the x  direction can be absorbed. “+” and “−” represent the parity of the bands. Red, blue, and green represent band dispersion from the pz, px, and py orbitals. Reprinted by permission from Macmillan Publishers Ltd.: Yuan et al., Nat. Nano 10, 707–713 (2015) [41]. Copyright (2015).
Figure 7
Figure 7 Layer-dependent transmission anisotropy in bulk-like black phosphorus. (a) Microscopic images of the BP samples with a series of thicknesses, ranging from 20 to 70 nm. (b) Transmission contrast between the principle axes, ΔTab=TbfastTaslow, of the BP flakes with varied thicknesses. The slow and fast axes of the sample are identified in the phase measurement. A dashed red line represents a fixed wavelength of light used in Fig. 5. The inset plots the resonant wavelengths as a function of thickness.
Figure 8
Figure 8 (a) Real part of optical conductivities Re(σxx) and Re(σyy) for 10-nm-thick intrinsic BP, i.e., the Fermi level is located at midgap. See main text for parameters used in the calculations. Intersubband contributions to the σxx are plotted, where the respective optical transition processes are illustrated in the inset. Conductivities are normalized with respect to σ0=e2/4h. (b) Re(σxx) for intrinsic BP of different thicknesses as indicated. (c) Re(σxx) for BP with different chemical potential μ as indicated, calculated for 4- and 20-nm-thick films. Figures 2(a), 2(b), and 3(c) reprinted with permission from Low et al., Phys. Rev. B 90, 075434 (2014) [43]. Copyright (2014) by the American Physical Society.
Figure 9
Figure 9 (a) Schematic diagram of polarization-resolved transient reflection experiment. (b) Representative transient reflection spectrum with pump polarization along the x direction and probe polarization at the y direction. (c) Probe polarization dependence of transient reflection spectrum with pump polarization fixed along the x and y directions. (d) Probe polarization dependent dynamical evolution of Re(σ) at different delays. Inset: enlarged plot of area marked by red rectangle. Reprinted with permission from Ge et al., Nano Lett. 15, 4650–4656 (2015) [46]. Copyright (2015) American Chemical Society.
Figure 10
Figure 10 (a) Fluence-dependent transmittance of the 1100 nm thick BP film measured with ultrafast pulses at two orthogonal polarized light directions. (b) Relative transmittance change measured from 25-, 350-, and 1100-nm-thick BP films as a function of input pulse fluence. The input polarization direction is along the armchair direction of the BP films. Reproduced from [49] under the terms of the Creative Commons Attribution 4.0 License.
Figure 11
Figure 11 Evolution of bandgap calculated by different methods and optical absorption peak according to the stacking layer number of few-layer phosphorene. The power-law fitting curves are presented by dashed lines. Figure 2 reprinted with permission from Tran et al., Phys. Rev. B 89, 235319 (2014) [26]. Copyright (2014) by the American Physical Society.
Figure 12
Figure 12 (a) Optical absorption spectra of monolayer, bilayer, trilayer, and bulk phosphorene for the incident light polarized along the x direction. In particular, bulk absorbance is the optical absorbance per layer in bulk phosphorus. The single-particle optical absorption spectra are presented by dashed lines, while those spectra with electron–hole interaction included are presented by solid lines. A 0.1 eV Gaussian smearing was employed in these plots. (b) Optical absorption spectra of monolayer, bilayer, trilayer, and bulk phosphorene for the incident light polarized along the y direction. Figures 4 and 5 reprinted with permission from Tran et al., Phys. Rev. B 89, 235319 (2014) [26]. Copyright (2014) by the American Physical Society.
Figure 13
Figure 13 (a) Polarization-resolved PL spectra, revealing the excitonic nature of the emission from monolayer black phosphorus. The excitation 532 nm laser is linearly polarized along either the x (gray curves) or y (blue curves) direction. On the detection side, a half-wave plate and linear polarizer selects x- or y-polarized components of the emitted light, leading to a total of four different combinations as shown. (b) PL peak intensity as a function of polarization detection angle for an excitation laser polarized along the x- (gray), 45° (magenta), and y (blue) directions. The excitation laser power remains constant. The PL emission along the y direction is always less than 3% of that in the x direction, regardless of the excitation light polarization angle. Solid lines are guides to the eye. Reprinted by permission from Macmillan Publishers Ltd.: Wang et al., Nat. Nano 10, 517–521 (2015) [55]. Copyright (2015).
Figure 14
Figure 14 (a) PL excitation intensity map as a function of both excitation and emission photon energies. (b) Selected PL spectra along the three horizontal lines shown in (a), showing that the PL is the strongest when excitation photon energy is about 2.45 eV (505 nm). Inset: PL intensity at the emission peak of 1.32 eV as a function of excitation photon energy. The estimated quasi-particle band edge (before interference correction) is indicated by the shaded region. The data are taken along the vertical white dashed line in (a). Reprinted by permission from Macmillan Publishers Ltd.: Wang et al., Nat. Nano 10, 517–521 (2015) [55]. Copyright (2015).
Figure 15
Figure 15 Polarization dependence of Raman modes for different excitation wavelengths. Each row shows polarization dependence of the three main modes, taken with excitation wavelengths of 441.6, 488, 514.5, 532, and 632.8 nm as indicated. The curves represent best fits to the Raman intensities using the expressions in main text. The polarization behaviors of the Ag modes exhibit strong dependence on the excitation wavelength, whereas the B2g mode does not show such dependence. Reproduced from [64] under the terms of the Creative Commons Attribution 3.0 License.
Figure 16
Figure 16 Polarization dependence of Raman modes for different sample thickness. (a)–(d) are the atomic-force microscopy images of 5-, 65-, 70-, and 90-nm-thick samples. Each row shows the polarization dependence of the three main Raman modes, taken with excitation wavelengths of 441.6 and 514.5 nm, as indicated. The curves represent best fits to the Raman intensities using the expressions in the main text. The polarization behaviors of the Ag modes exhibit strong thickness dependence for the 514.5 nm excitation wavelength, whereas no such dependence is seen for 441.6 nm. Reproduced from [64] under the terms of the Creative Commons Attribution 3.0 License.
Figure 17
Figure 17 Anisotropic Raman spectra of an 18 layer BP. (a) Both HF and LF modes are shown. The shear mode (C) and layer breathing modes (LB) are marked. (b) Raman intensities of C and Ag modes as functions of incident light polarization.
Figure 18
Figure 18 (a) Energy band diagram of the device at zero (top) and finite (bottom) source–drain bias. The polarities of the various photocurrents, i.e., thermoelectric, bolometric, and photovoltaic, are indicated. (b) and (c) Photocurrent cross sections extracted from photocurrent maps taken along the direction of maximum amplitude measured as a function of optical power density. The photocurrent is laser excited at a visible wavelength of 532 nm at different (b) incident power and (c) applied source–drain bias. Figures 2(a), 3(a), and 3(b) reprinted with permission from Low et al., Phys. Rev. B 90, 081408 (2014) [75]. Copyright (2014) by the American Physical Society.
Figure 19
Figure 19 Photovoltaic effect in BP phototransistors. (a) The splitting gates device after fabrication. The schematic is shown in the upper panel. (b) False-color map of the short-circuit current (Isc, Vds=0  V) as the voltages on the two local gates are changed independently. (c) False-color map of the open-circuit voltage (Voc, Ids=0  A) as the voltages on the two local gates are changed independently. (d) Band diagrams illustrating the photovoltaic mechanism in PN and NP configurations: an impinging photon (red arrow) generates an electron–hole pair that is swept away from the junction region by the built-in electric field. (e) 3D illustration of the configuration of a waveguide-integrated BP photodetector, featuring a few-layer graphene top gate. (f) The response of the BP photodetector is measured when the BP is gated to low and high doping. At low doping, the response is broadband with a cut-off frequency of 3 GHz, which is limited by the RC bandwidth of the contact pads and the input impedance of the preamplifier. At high doping, the response rolls off at 0.2 MHz, indicating that the photoresponse is of thermal origin as expected from the bolometric effect. Inset: receiver eye diagram at 3  Gbit/s data rate measured with the BP photodetector. (a)–(d) Reprinted by permission from Macmillan Publishers Ltd.: Buscema et al., Nat. Commun. 5, 4651 (2014) [79]. Copyright (2014). (e) and (f) Reprinted by permission from Macmillan Publishers Ltd: Youngblood et al., Nat. Photonics 9, 247–252 (2015) [81]. Copyright (2015).
Figure 20
Figure 20 (a) Schematic of the laser setup. PC, polarization controller; LD, laser diode; WDM, wavelength division multiplexer; EDF, erbium-doped fiber; ISO, isolator. The inset shows the transferred BP on the optical fiber end. The scale bar: 60 μm. The red point in the center indicates the 10  μm diameter optical fiber core, with the outside concentric gray circle of the 125 μm fiber cladding. The area marked by the pink dotted line specifies the transferred BP. BP Q-switching fiber laser results: (b) output pulse train and (c) output polarization property. BP mode-locked fiber laser results: (d) output spectrum and (e) output autocorrelation trace, giving a pulse duration of 786  fs. (f) Radio-frequency spectrum at the cavity fundamental repetition rate f0(f0=14.7  MHz). The resolution bandwidth is 100 Hz. Inset: output pulse train. Reproduced from [49] under the terms of the Creative Commons Attribution 4.0 License.
Figure 21
Figure 21 Energy loss and plasmon dispersion. (a) Loss function, L(q,ω)=I[1/ε(q,ω)], calculated for monolayer BP for electron doping of 1×1013  cm2, for q along the two crystal axes x (right) and y (left). Shaded regions are the Landau damping regions. (b) Plasmon scaling with carrier concentration. Plasmon energies ωpl, as functions of density n, calculated for the monolayer and for a 20 nm BP thick film at a specified q along x. Graphene plasmons are shown for comparison. Figures 2(a) and 3 reprinted with permission from Low et al., Phys. Rev. Lett. 113, 106802 (2014) [94]. Copyright (2014) by the American Physical Society.

Tables (2)

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Table 1. Crystal Structural Parameters of Black Phosphorus under Normal Conditions

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Table 2. Linear and Nonlinear Optical Coefficients of BP Dispersions from the Fitting of Open-Aperture z-Scan Traces

Equations (2)

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2Ag+B1g+B2g+2B3g+Au+2B1u+2B2u+B3u.
I(Ag)(|a|cos2θ+|c|cosφcasin2θ)2+|c|2sin2φcacos4θ,I(B2g)4|e|2sin2θcos2θ,

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