Thickness-dependent Electronics Structure: Black Phosphorus

A novel two-dimensional anisotropic material, Black phosphorus that is to enunciate a single atomic layer of black phosphorus, has attracted a remarkable renaissance of interest for potential applications in the electronic and photonic application. Here we experimentally demonstrated that the electronic structure of multilayer layer Black phosphorus varies significantly with the thickness dependent, in good agreement with our theoretical calculations. The interband optical transitions spread over an extensive region from visible to mid-infrared which is a value technologically significant spectrum. Moreover, we observe strong photoluminescence in monolayer Black phosphorus at energy position that fit well with the theoretical absorption edge based on first-principles calculation. The experimental observation of strongly thickness-dependent electronic structure of Black phosphorus, in combination with its significantly small effective mass, not only opens avenues for the future investigations of many-electron physics in this unique material but also proposes its promising future in optoelectronic and nanoelctronics devices from the infrared to the visible spectral range.

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Introduction

The two-dimensional (2D) layered materials have developed as a new class material with possessing a unique property that promise for photonic and electronics application. Various 2D layered materials research has been demonstrated; the topic covers the semimetallic graphene, metallic TaSe₂, semiconducting TMDCs, topological insulator Bi₂Se₃ and superconducting NbSe₂. Recently, a new member-Black phosphorus, with a bandgap in the range from 2.0 eV to 0.3 eV, such bandgap range bridges a significant technological value in rich variety currently 2D materials library. With its strong in-plane anisotropy properties, thus, it holds promise for applications in near- and mid-infrared optoelectronics (i.e. solar energy, telecommunication), and for the development of conceptually novel devices that based on the anisotropic properties. In monolayer Black phosphorus, three adjacent phosphorus atoms are covalently bound to each phosphorus atom to procedure a puckered honeycomb structure, resulting in strong in-plane anisotropy behavior. Theoretical prediction monolayer Black phosphorus is a semiconductor with a direct optical bandgap of ~ 1.5 eV at the Γ point of the Brillouin zone. Owing to the interlayer interactions, the band gap in few-layer and multilayer phosphorus can be powerfully changed and therefore resulting in a bandgap that decreases with Black phosphorus film thickness, ultimately reaching to the bulk limit of 0.30 eV.

To date, experimental observations of thickness-dependent band structure in black phosphorus has yet to uncover the most fundamental and intriguing properties of such material in 2D limits. Meanwhile, photoluminescence (PL) spectroscopy act as a tool for probe the band gap of monolayer and few-layer phosphorus has their limitations, because the measured PL can be dominated by impurity and defect states instead of the bandgap emission and that monolayer and few-layer phosphorus is extremely subject to debasement. Definitely, the different research group has reported extensively different bandgap values from 1.75eV to 1.32 eV for monolayer Black phosphorus, meaning our understanding of the fundamental properties of Black phosphorus remains incomplete.

Here we report the study of the enhanced thickness-dependent reflection spectroscopy in high-quality Black phosphorus on Aluminum substrate. Thickness-dependent optical bandgap in the Infrared and sub-bands gap in visible were systematically investigations. The monolayer PL peaks are close to the theory calculated absorption bandgap, indicating the direct nature of the bandgaps. Interestingly, and on PL measurement, the thickness-dependent spectroscopy offers a reliable determination of the development of the optical band gap and sub-bands gap in multilayer Black phosphorus. We found that optical absorption above the bandgap indicates additional resonances in multilayer black phosphorus corresponding to optical transitions between higher sub-bands induced by quantum confinement along the thickness directions. The systematic evolution of both the optical bandgap in the infrared region and absorption peaks caused by higher sub- band transitions in the visible region matches well with our DFT-HSE06 calculations. The thickness-tunable electronic structure of black phosphorus can be further varied through mechanical strain and the external electrostatic field, creating an exciting possibility for both optoelectronic and nanoelectronic device applications from the infrared to the visible spectral range.

As schematically shown in Fig. 1a, each phosphorus atom in Black phosphorus is covalently bonded to three adjacent atoms to form a puckered honeycomb structure, thus resulting in a highly asymmetric band structure and remarkably strong in-plane anisotropy. Monolayer and multilayer Black phosphorus samples are prepared by mechanical exfoliation of bulk crystals. To reduce sample degradation in air, all samples are stored in the N₂ box and completed the measuring as soon as possible. Figure 1b displays an optical micrograph of a monolayer and few-layer flake on 300 nm silicon oxide. We identified the Black phosphorus monolayers by atomic force microscopy (AFM) in Figure 1 d. The thickness of the freshly exfoliated monolayer flakes was measured to be ∼0.69 nm (see Fig 1c). The thickness value is somewhat larger than the theoretical monolayer Black phosphorus thickness of 0.53 mm, but suggestively less than the bilayer thickness of 1.06 mm, signifying that the measured flake is certainly a monolayer.

We employed transmission electron microscopy (TEM) to characterize the crystallinity of the exfoliated Black phosphorus flakes. Figure 2a presents a low-resolution transmission electron microscopy (TEM) images of few-layer Black phosphorus flakes. The Black phosphorus flakeswere further characterized using high-resolution transmission electron microscopy (HRTEM). An HRTEM image of a few-layer area of the sample is shown in Figure 2b. The uniformity in this image specifies that the lattice contains no extended defects (i.e., single vacancies), and no amorphization of the thin sample was kept. Therefore, few-layer black phosphorus flakes are stable and crystalline.

Owing to the thin areas of the flake is sensitive to the beam, we use a low beam intensity and electron diffraction (ED) with a large illumination area of 300 nm in diameter to investigate their crystal structure. ED patterns were recorded with the 0° tilt angle at various locations of the flake.

Figures 2 (d) show the diffraction pattern corresponding to a thin region of the flake in Figure 2b,

The Black phosphorus exhibits a clearly periodic atomic arrangement with a rectangle-like structure. Furthermore, a clearly sixfold coordination symmetry is observed in Figure 2c via the Fast Fourier Transform (FFT) images of the solid orange areas highlighted in Figure2b.

Figure 3a presents thickness-dependent Raman spectra of Black phosphorus sample. The Raman spectra were measured at excitation wavelength 473 nm with a linearly polarized laser incident along the z direction and perpendicular to the x-y plane. As indicated in Fig 3a, three peaks can be observed near 365, 440 and 470 cm^−1 due to the selection rules; which corresponding to the Ag1, B_2g, and Ag2 Raman vibration modes, respectively. Raman spectroscopy characterizations also reveal the crystal orientations of Black phosphorus sample. We identify a detailed study of few-layer Black phosphorus using polarization-resolved Raman spectroscopic analysis. Figure 3b presents the polarization-resolved Raman vibration modes of few layer Black phosphorus. The spectra are in total agreement with the previous reports.

To better evolution of the bandgap transitions in monolayer black phosphorus, we investigated polarization-resolved photoluminescence(PL) spectra of monolayer samples with photoexcitation at 2.62 eV (~473 nm) and 1.96 eV (~633 nm). Detection and excitation polarization were selectively aligned along either the x or y-axis, indicating a total of four different spectra (see Fig 4a, 3b). Irrespective of the excitation or detection polarization, the emission spectra display a single peak with a full-width at half-maximum (FWHM) of ∼115 meV centered at ∼1.69 eV. For multiple measured monolayer black phosphorus samples, all the emission peaks located at a range of 1.69 ± 0.05 eV. It indicates that monolayer black phosphorus is a nature of direct bandgap, consistent with theoretical predictions. The optical bandgap value is good agreement with recent experimental results.   

We also found that the highest photoluminescence intensity appears when both excitation and detection polarizations are oriented with the x-direction. The emission intensity along the y direction is consistently less than that along the x direction, regardless of the excitation light polarization, as shown in Fig 4a and Fig 4b. Such strong anisotropy originates from the unique crystal structure of black phosphorus( see Fig 1a) and indicates the excitonic nature of the observed PL spectra. This intriguing observation of strongly polarized photoluminescence emission is consistent with that, optical transitions polarized at the Γ point only allowed for (x-axis) armchair-polarized light and along the (y-axis) zigzag direction is forbidden by symmetry due to the selection rule, resulting in excited states are dominated by anisotropic excitons.. Hence, we expect armchair-polarized light absorption at around the energy gap for monolayer BP. Our theoretical calculation further indicates the monolayer PL spectra show strong polarization dependence similar to that of the calculated absorption (see Fig 4d). One note that the PL peaks are relatively broad and occasionally include multiple resonant features.

To systematic evolution of the higher-energy resonances in multilayer black phosphorus. We investigate optical absorption of multilayer black phosphorus on Aluminum substrate through reflectance measurements at room temperature. The reflection spectrum ΔR/R is directly associated with the complex dielectric function of black phosphorus., where is imaginary part of the refractive index which is proportional to optical absorption and features evidently absorption peaks, while the real part of the dielectric function can bring about the relatively broad background. In this study, we will concentrate on the optical resonances and the position of optical absorption peaks can be consistently identified as resonances in the reflection spectra. We use a tungsten lamp acted as the light source for the visible reflection spectra and Fourier Transform Infrared Spectroscopy (FTIR) for the infrared region. The incident polarization light controlled by a broadband calcite polarizer and focused onto the black phosphorus samples in a microscopy setup, and the observed reflected light was collected and analyzed in a Horiba spectrometer equipped with silicon detector.

The higher-energy resonances in multilayer black phosphorus can be described phenomenologically by selection rule of optical transition. According to group theory analysis, BP crystal belongs to group, which includes 3 mirror planes, 3 rotation axes, and inversion symmetry. The superscript number x is a translational symmetry indicated the difference between BP family ( i.e. x=7, for an odd number of layer BP, x=11 for an even number of layer BP, and x=18 for bulk BP). Based on Fermi's Golden Rule, the optical absorption coefficient can be written as

where is electron-photon matrix element responsible for optical emission and absorption processes, which are related to the electron-photon interaction only, which corresponds to an optical transition between states i and m, respectively.is the laser photon energy; and are the energy of the initial electronic state i and intermediate states m and m′, respectively.

For a given incident light beam with polarization , when electron-photon interaction Hamiltonian can be treated as dipole approximation , the matrix element based on the optical selection rule between intermediate state can be writted as

where is the polarization vector of the incident light, and is a dipole vector.Based on Eq(3), we found that optical emission and absorption processes occur at when should have a nonzero component which is parallel to the light polarization vector . Since, the selection rule for the optical transition governs which two energy bands can be electron transition under a given incident excitation energy with a specific light polarization and in sequence various for different excitation photon energies and different incident light polarizations .

As shown in Figure 5a and 5b, the measured reflection spectra in visible and infrared region are in fairly good agreement with the calculated optical subband transition in bandstructure. For the polarization parallel to an armchair, the observed spectra have peaked at a position at 1.8eV,2.3eV and 2.62 eV, while he calculated one has peaked at 1.78eV(),2.3eV() and 2.69()eV. The selectivity of the optical absorption anisotropy to the flake thickness and laser polarization indicates that the subband optical transition in either zigzag or armchair direction, depending on the symmetries of the affected electronic states (Figure 5c). Therefore, our optical absorption measurements enable the understanding of the electron-photon interaction in anisotropic 2D materials.

For the parallel polarization zigzag, the observed spectra have similar peak positions but have a little shifting. Indicating that the peak position is rather sensitive to the details of the band structure. To get more quantitative agreement between experiment and theory regarding peak position, it maybe to do a more refined band structure calculation is required.

All the observed optical absorption spectra exhibit robust absorption peaks under Armchair ( red color), and Zigzag (black color) polarized illumination was shown in Figure 3a-3b. As to polarization P=90, we can observe that counterpart of those peaks in the reflection spectrum, which also appear in that for the polarization P=0. This fact suggests that reflection spectra for the polarization P=90 are not intrinsic, but trivial, and it comes from mixing of the P=0 component into the P=90, one caused probably by misalignments of angle in the x-y plane of the sample.

We can obtain the absorption and reflection for the BP/air interface sunder normal incidence, where and is the real and image parts of the complex refractive index of BP. Based on the reported paper, remarkably larger than , and then the reflection is simplifying as . Compared to , demonstrations much weaker dependence on the crystalline orientation. This result in the weaker anisotropy of reflection spectra than that of the theory calculation absorption spectra of BP (see Figure).s

Figure 1. Crystal structure and AFM image of Few-layer Black phosphorus samples. (a), Puckered honeycomb lattice structure of monolayer Black phosphorus. x and y present the armchair and zigzag crystal orientation, respectively. (b), Optical image of monolayer and few-layer Black phosphorus samples on Si/SiO₂(300nm) substrate. (c)Line profile across the AFM image in (d), which shows a clear value of around 0.69 nm for the monolayer thickness.(d)Atomic force microscopy (AFM) image of the monolayer and few-layer Black phosphorus.

Figure 2. Transmission electron microscopy (TEM) investigation of few-layer Black phosphorus flakes. (a) Optical image of a black phosphorus flake transferred onto a holey carbon copper grid. (b) High-resolution transmission electron microscopy(HRTESM) image of the few-layered region of the flake (~ 30 layers). The inset shows a zoom-in the regions. (c) Fast Fourier transforms (FFT) of the solid orange areas highlighted on images (b). (d) Electron diffraction patterns acquired with a 200 µm spot on the thick (~ 20 layers) region of the flake.

Figure 3. Layer-dependent and Polarization-resolved Raman spectra of black phosphorus flakes. (a). Thickness dependent Raman spectra of black phosphorus at room temperature from a monolayer to bulk. (b). Polarization dependence of Raman modes for few-layer black phosphorus.

Figure 4. Polarization-resolved photoluminescence spectra of monolayer black phosphorus. The spectra arerevealing the excitonic nature of emission from the monolayer black phosphorus. The excitation 633 nm(a) and 473 nm(b) laser is linearly polarized along either x (grey curves) or y (blue curves) directions. (c) DFT calculation band structure of monolayer Black phosphorus. (d) Absorption spectra of monolayer Black phosphorus based on the DFT calculation in Figure(c).

Figure 5. Reflection spectra of Black phosphorus at the visible and infrared region. (a) Visible reflection spectra of Black phosphorus on an Alumnin substrate with excitation polarization P=0(armchair) and P=90(zigzag). (b) Infraredreflection spectra of Black phosphorus on an Alumnin substrate with excitation polarization P=0 and P=90. (c) Band structure of bulk Black phosphorus based on the DFT calculation with HSE06 function. Calculated polarization dependence of the absorption in bulk BP for optical transitions allowed by symmetry. Green (red) labels of irreducible representation correspond to symmetric (anti-symmetric) states under inversion symmetry. The different possible optical transitions in bulk BP with the corresponding symmetry assignments are labeled with arrow. The absorption intensity is defined by the square of optical matrix elements.

Figure 6. Thickness-dependent visible reflection spectra of Black phosphorus. Thickness-dependent reflection on a gold substrate with excitation polarization P=0 (a) and P=90 (b), respectively. Thickness-dependent transmission on a glass substrate with excitation polarization P=0 (c) and P=90 (d), respectively.