Anomalous Size Dependence of Optical Properties in Black

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Anomalous Size Dependence of Optical Properties in Black Phosphorus Quantum Dots XiangHong Niu, Yunhai Li, Huabing Shu, and Jinlan Wang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02457 • Publication Date (Web): 10 Jan 2016 Downloaded from http://pubs.acs.org on January 11, 2016

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The Journal of Physical Chemistry Letters

Anomalous Size Dependence of Optical Properties in Black Phosphorus Quantum Dots Xianghong Niu, 1 Yunhai Li,1 Huabing Shu1 and Jinlan Wang*,1,2 1

Department of Physics, Southeast University, Nanjing 211189, China

2

Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha 410081,China

AUTHOR INFORMATION Corresponding Author

E-mail: [email protected]. Tel.: +86-25-52090600-8210

ABSTRACT Understanding electron transitions in black phosphorus nanostructures plays a crucial role for applications in electronics and optoelectronics. In this work, by employing time-dependent density functional theory calculations, we systematically study the size-dependent electronic, optical absorption and emission properties of black phosphorus quantum dots (BPQDs). Both the electronic gap and the absorption gap follow an inversely proportional law to the diameter of BPQDs in conformity to the quantum confinement effect. In contrast, the emission gap exhibits anomalous size dependence in the range of 0.8-1.8 nm which is blue-shift with the increase of size. The anomaly, in fact, arises from the structure distortion induced by the excited state relaxation and it leads to huge Stokes shift in small BPQDs.

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TOC GRAPHICS

Black phosphorus (BP), as a new two-dimensional (2D) layered material, has triggered a surge of research interest very recently. The single- and few-layer BP can be produced by mechanical or liquid exfoliation of bulk BP,1,2 which each phosphorus atom is covalently bonded to three neighboring atoms inside the phosphorene layer, forming a puckered honeycomb network. The unique structure induces highly anisotropic thermal and electrical conductivities, and optical responses.1,3-7 Meanwhile, different from zero bandgap graphene (without on/off ratio) and large bandgap transition metal dichalcogenides (1.1-2.5eV, 200 cm2V-1s-1),8-10 BP owns a tunable direct and thickness-dependent bandgap (0.3-1.5 eV)

1,11

with a moderate

on/off ratio (104-105) and a sufficiently high carrier mobility (up to 104 cm2V-1s-1) simultaneously,1,3,12 which are vital for semiconductor devices. Besides the 2D layered structure, 1D phosphorene nanoribbons have also been explored and their electronic properties are highly sensitive to the edge structures, edge types and width.13-16 These intriguing electronic and optical features make BP nanostructures promising candidates for field-effect transistors,2,17 solar-cells,18,19 gas sensing20 and


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photodetectors.21,22 Most recently, BP quantum dots (BPQDs), as another form of phosphorus nanostructures, have been successfully synthesized through chemical methods.23,24 These BPQDs exhibit good UV/Vis absorption spectroscopy and excellent memory performance.23 They also show great near-infrared photothermal performance with a large extinction coefficient of 14.8 Lg-1cm-1 at 808 nm, high conversion efficiency (28.4%) and good photostability.24 However, the underlying mechanism is still unclear and the size-dependent electronic and optical properties, the most important feature in finite sized QDs, are also absent. To fill in the gaps, we perform a systematic study on the absorption and emission of BPQDs ranged from 0.8 to 3.8 nm in diameter r within the framework of time-dependent density functional theory (TDDFT). Our study reveals that both the electronic gap and the absorption gap of BPQDs satisfy an inversely proportional law of A +B/r2 + C/r while the emission gap shows anomalous size-dependent behavior in small sizes. The anomaly is actually a consequence of the competition between the structure rearrangement during the excited state relaxation and the quantum confinement effect and it causes huge Stokes shift in small BPQDs. Since the as-synthesized BPQDs are rectangular-like23 and 2D BP monolayer is an orthorhombic lattice, we construct ten different rectangular monolayer BPQDs with armchair or zigzag edges, close edge lengths and similar corners. The dangling phosphorus bonds are passivated by hydrogen atoms. The diameter r is defined as the average length of two edges and it varies from 0.8 to 3.8 nm. As displayed in Figure



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S1 in Supporting Information (SI), BPQDs maintain the unique structural arrangement feature resembling a network of connected hinges as the layered BP. They have a puckered structure along the armchair direction (parallel to the X-axis), but a bilayer configuration along the zigzag direction (parallel to the Y-axis). The calculated optical absorption and emission spectra of BPQDs of various sizes are presented in Figure 1. As clearly seen from the figure, these BPQDs absorb light from 300 to 700 nm depending on the size and cover the major visible light range. All BPQDs have two prominent absorption peaks, and the intensity of the lower energy peak is stronger than that of the higher one. The main absorption peak is monotonously red-shifted as the increase of the BPQD size. Notably, the absorption spectra of BPQDs in low energy singlet transitions are quite different from those of graphene QDs (GQDs) which generally have “dark” excitation (shoulders peak) and poor luminescence efficiency.25,26 While the low-lying triplet states of BPQDs are always below the lowest excited singlet state by several hundreds of meV (see SI Table S1), which is similar to the case of GQDs.25 Regarding of the emission spectra, the results are more complicated. As depicted in Figure 1(d), the emission peaks are red-shifted with the increase of the size in the range of 1.8-3.8 nm. But for BPQDs with smaller sizes (0.8-1.8nm), the trend is inverse and the peaks are blue-shifted (see Figure 1(b)). This anomalous size-dependent emission behavior of BPQDs is completely different from those widely reported QDs, such as ZnO,27,28 CdSe,29 PbSe,30 CdSeTe,31 and graphene,32,33 whose emission spectra are always red-shifted with increasing size due to the


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quantum confinement effect. This kind of anomaly in luminescence has also been observed in small silicon clusters with the critical size is about 1.5nm.34-36

Figure 1. Absorption (a, c) and emission (b, d) spectra of BPQDs at various sizes. The absorption and emission energies were obtained based on the optimized ground state and the optimized first excited singlet state, respectively. All spectra were broadened with Lorentzian-type broadening of 0.25 eV.

The size-dependent electronic and optical properties of BPQDs are further illustrated in Figure 2. The electronic gap (defined as the energy difference between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, i.e., the HOMO-LUMO gap) and the optical absorption gap both drop rapidly from P16H10 to P84H24, and then gradually converge to the values of the monolayer BP. By contrast, the optical emission gap first rises abruptly in the range of 0.8-1.8 nm and reaches the maximum value of 2.18 eV, then declines slowly to approach the monolayer limit of 1.37eV.



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Figure 2. HOMO-LUMO energy gap (EHOMO-LUMO), absorption gap (Eabs), emission gap (Eemi), and Stokes shift of BPQDs ranging from P16H10 to P374H54 as a function of the diameter r.

The size-dependent HOMO-LUMO gap, absorption gap and emission gap can be further fitted to the following formula, EHOMO-LUMO (eV)= 1.67 +0.21/r2 + 1.78/r Eabs (eV)= 1.46 +0.30/r2 + 1.31/r Eemi (eV)= 1.37 -2.53/r2 + 2.69/r

(1) (2) (3)

where the first constant term represents the corresponding gap of monolayer BP, the second term (proportional to 1/r2) is the kinetic energy determined by quantum confinement effect and the last term stands for the Coulomb interaction energy with a 1/r dependence.37,38 It is well-known that the quantum confinement effect enlarges the gap and the Coulomb interaction is strengthened with decreasing size of QDs. Therefore, the HOMO-LUMO gap and the absorption gap show an inversely


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proportional law with the BPQD size and approach the values of the monolayer when r is large enough. However, for the emission gap, although the Coulomb term enlarges the gap as the decrease of size, the large negative coefficient of r-2 term remarkably lowers the gap for small r. The negative coefficient of r-2 term may arise from the geometric rearrangement induced by the electronic relaxation in excited states. It is known that the quantum confinement effect tends to blue-shift the emission gaps as less electrons fill in the energy levels when reducing the size. However, the structure in small BPQDs would become less rigid and easier to rearrange in the de-excitation emission process as well. As a result, it may even prevail over the quantum confinement effect and lead to the red-shifted anomalous emission behavior in small BPQDs. When BPQD is large enough (herein, the critical size is about 1.8 nm), the structure of BPQDs becomes rigid enough and restricts the relaxation of the excited state structures. The influence from the excited state relaxation is thus negligible and the quantum confinement effect plays the decisive role and makes the emission gap decrease as a function of size. The structure distortion induced by the excited state relaxation in BPQDs is clearly shown in SI Table S2 and Figure S2, which the lattice constants, bond lengths and bond angles of the ground and excite state structures are very different for P16H10 and P38H16, but they become rather close for large BPQDs, such as P84H24 and P126H30. Therefore, we conclude the anomalous emission in small BPQDs is actually a result of the competition between the quantum confinement effect and the structure rearrangement induced by the electronic excitation and



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relaxation in the excited states. It is noteworthy that the fitted monolayer emission gap, 1.37 eV, agrees well with the experimental value of ~1.3 eV.39

Figure 3. (a) Energy levels of the occupied and unoccupied frontier orbitals of BPQDs in the ground and excited state structures of representative BPQDs; (b, c, e, f) The iso-surfaces of wave functions of HOMO and LUMO in the ground and excited state structures of P38H16 and P84H24. (d, g) Vectors proportional to the displacements of each atom during the excited state relaxation. The displacements were magnified by seven times for clarity.

The size-dependent absorption and emission behavior can be further understood in light of the change of frontier orbital energy levels and wave function iso-surfaces. As shown in Figure 3a, for P16H10, the LUMO of the excited state structure shifts down toward lower energy while the HOMO shifts up to higher energy significantly with respect to the ground state structure, leading to the large reduction in the HOMO-LUMO gap. For P38H16, the LUMO still shifts down apparently, but the shift


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of HOMO is rather small. When the size is larger than P84H24, the shifts of frontier energy levels between the ground and excited state structures are all very small. This is also clearly reflected in the change of the density of states as presented in SI Figure S3. Generally speaking, the closer the frontier orbital energies of the ground and excited states, the more similarity the corresponding spatial distribution of wave functions. As a result, the HOMOs of the ground and excited states are both quite similar for P38H16 and P84H24, whereas the LUMO of the excited state is greatly different from that of the ground state structure in P38H16, as shown in Figure 3b, c, e, f, suggesting significant relaxation of the excited state. This can be further reflected by the vector displacements of the atoms during the relaxation process from positions ES(RGS) to ES(RES) (denoted in SI Figure S4). As clearly seen in Figure 3d, evident displacements are distributed throughout P38H16 and cause more energy loss via the non-radiative transition which has remarkably effect on the emission process. In contrast, for the case of P84H24, the displacements are mainly located on the edge atoms (see Figure 3g). Careful molecular orbital transition analysis shows that no matter for the adsorption or emission, the transitions between the LUMO and the HOMO account for more than 90% in the main absorption/emission peaks. Meanwhile, the HOMO and LUMO of the ground and excited state structures are mainly concentrated in the center position (see Figure 3b, c, e, f) in P84H24 and larger BPQDs. Thereby, the slight excited state relaxation in the center position in large BPQDs would have negligible influence on the emission gaps. Therefore, we conclude that when the size is small, the structure distortion arising from the



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electronic relaxation in the de-excitation process is a decisive factor to the emission gap while the quantum confinement effect is crucial for BPQDs larger than P84H24. Stokes shift, one of the most important quantities to evaluate the efficiency of luminescence, is determined by the difference between absorption and emission energies. When an electron-hole pair is created by optical excitation, the final state has approximately the same atomic configuration as the initial state according to the Franck-Condon principle.34 Prior to emission, however, the system can relax to a new configuration with lower energy. The electron-hole pair recombination will occur at the new configuration, leading to a red-shift of the emission gap with respect to the absorption gap, e.g., Franck-Condon shift, EStokes= Eabs - Eemi= (ES(RGS) - EGS(RGS) - (ES(RES) - EGS(RES))

(4)

Obviously, the large absorption gap and small emission gap in small BPQDs give rise to huge Stokes shift (less than 1.8nm). As BPQD is large enough, the emission gap follows the normal size-dependence and the Stokes shift becomes very small which is in favor of maximizing its quantum yield and efficiency in photoluminescence applications. The size-dependent Stokes shift can be further fitted as, EStokes (eV) = 0.08 +2.49/r2 -1.03/r

(5)

where the first term refers to the Stokes shift of monolayer BP, the second and third terms are associated with the quantum confinement effect and Coulomb effect, respectively. To further elucidate the underlying absorption and emission mechanism of BPQDs, we plot the vertical absorption excitation and emission de-excitation processes in


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Figure 4. As displayed in the figure, the energies of the first, second and nth high-lying singlet excited states S1, S2 and Sn with respect to the ground state minimum S0 are all decreased as the increase of the BPQD size, leading to the reduction of the absorption gap. On the contrary, the emission energies show totally opposite trend from P16H10 to P84H24, that is, it increases with the increase of the size. This is because the structural distortion of the excited state structure significantly narrows the emission gap. The greater the distortion of the excited state structure (see SI Table S2), the lower the emission energy. The P84H24 is the critical size with the largest emission gap. After that, the emission energy follows the normal quantum size effect, i.e., it decreases with increasing the BPQD size, similar to the case of the absorption energy. The Stokes shift, marked as the Wavy line in the figure, is huge (2.67 eV) in P16H10 and decreases with the increase of the BPQD size because of the opposite size-dependent absorption and emission gaps. Moreover, the number of bright lines increases as the increase of size and there is no evident dark state in low-energy transitions in P126H30 (see details in SI Table S3-12). This is in accord with the results that the intensities of the absorption and emission spectra are greatly strengthened as a function of size presented in Figure 1. The lowest singlet excited state is bright state for large BPQDs which is different from GQDs40 (having two lowest excited singlet dark states). The bright nature of the lowest excited-singlet states is expected to remarkably improve the luminescence efficiency of BPQDs.



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Figure 4. Illustration of the vertical absorption excitation and emission de-excitation processes for representative BPQDs. S0, S1 and Sn denote the ground state, the first singlet excited state and the nth high-lying singlet excited state, respectively. Eemi is the emission energy. The ground state energy S0 is set as zero, therefore S1 is in fact the absorption gap, Eemi is the emission gap and the wavy line stands for the Stokes shift. Black and red lines represent dark and bright transitions, respectively.

Besides the intriguing size-dependent behaviors, BPQDs also show highly anisotropic features in absorption and emission. The transition dipole moments are profoundly distinct in x, y and z directions (see SI Table S3-12). The highest absorption and emission intensities occur when the excitation or detection polarizations are aligned with the x direction, consistent with that of layered BP.39 This anisotropic characteristics originates from the selection rules associated with the symmetry of the anisotropic structure material.5,41 In summary, using state-of-the-art time-dependent density functional theory calculations, we elucidate the size-dependent absorption and emission of BPQDs and their underlying mechanism. The reduction of the electronic gap and the absorption


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gap with increasing size arises from the quantum confinement effect, while the anomalous size-dependence in the luminescence in small BPQDs is a result of the competition between the quantum confinement effect and the structure distortion of excited state relaxation. Moreover, this anomaly induces significant Stokes shift in small BPQDs, but the Stokes shift ultimately decays nearly to zero, suggesting that large BPQDs should still be good optical materials. The insights unveiled here would offer useful guidance to the maximal utilization of BPQDs in optical applications.

Computational Methods The DFT and TDDFT computations were carried out using the Becke three-parameter Lee-Yang-Parr hybrid (B3LYP)42 exchange-correlation functional with the double-zata plus polarization (DZP) basis set43 implemented in the Amsterdam Density Functional program package (ADF2013).44-45 To determine the absorption energy, we first fully optimized the structure of BPQDs at DFT level, yielding the optimal structure RGS and the ground state minimum energy EGS(RGS). Starting from this DFT computed RGS structure, the electronic excitation energies were then calculated using TDDFT with first ten singlet excited states and first ten triplet excited states taken into consideration. Since the electron-hole pair generation mainly occurs in the singlet state, the optical absorption gap Eabs was computed as the energy difference between the ground state minimum EGS(RGS) and the first singlet excited state ES(RGS). To determine the emission energy, following Kasha’s rule, we further relaxed the structure of the first singlet excited state using TDDFT taking RGS as the initial geometry and obtained the lowest singlet excited structure RES and the



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corresponding excited state minimum ES(RES). The electron-hole pair recombination was evaluated at fixing RES and this would give the corresponding ground state energy EGS(RES), and ultimately the vertical electronic transition from ES(RES) to EGS(RES), namely, the optical emission gap Eemi can be calculated. All optimizations were done without any symmetry constraint. This procedure has been widely used to calculate the absorption and emission properties of nanoparticles and quantum dots.33,35,36 The schematic diagrams of absorption and emission processes can be found in SI Figure S4.

ASSOCIATED CONTENT

Supporting Information Available:

The BPQDs model (Figure S1, S2), density of states, displacement scale, absorption and emission energies of the ground and excited states structure (Figure S3, Table S1-12) and Schematic representation of absorption and emission processes (Figure S4). (PDF)

AUTHOR INFORMATION Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENT


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This work is supported by the NSFC (21525311, 21173040, 21373045, 11404056) and NSF of Jiangsu (BK20130016) and SRFDP (20130092110029, 20130092120042) in China, and the Fundamental Research Funds for the Central Universities of China. The authors thank the computational resources at the SEU and National Supercomputing Center in Tianjin.

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Method. Theor. Chem. Acc.1998, 99, 391-403.


Anomalous Size Dependence of Optical Properties in Black

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