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C: Physical Processes in Nanomaterials and Nanostructures

Size-Dependent Photocatalytic Activity of Cubic Boron Phosphide Nanocrystals in the Quantum Confinement Regime Hiroshi Sugimoto, Bálint Somogyi, Toshiyuki Nakamura, Hao Zhou, Yuichi Ichihashi, Satoru Nishiyama, Adam Gali, and Minoru Fujii J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b06487 • Publication Date (Web): 21 Aug 2019 Downloaded from pubs.acs.org on August 22, 2019

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The Journal of Physical Chemistry

Size-Dependent Photocatalytic Activity of Cubic Boron Phosphide Nanocrystals in the Quantum Confinement Regime Hiroshi Sugimoto,*,†Bálint Somogyi,‡ Toshiyuki Nakamura,† Hao Zhou,†　Yuichi Ichihashi,§ Satoru Nishiyama,§ Adam Gali‡,⊥ and Minoru Fujii*† † Department

of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe

University, Rokkodai, Nada, Kobe 657-8501, Japan ‡

Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian

Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary §Department

of Chemical Science and Engineering, Graduate School of Engineering, Kobe

University, Rokkodai, Nada, Kobe 657-8501, Japan ⊥ Department

of Atomic Physics, Budapest University of Technology and Economics, Budafoki

út 8, H-1111 Budapest, Hungary

ACS Paragon Plus Environment

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Cubic boron phosphide (BP) is an indirect band gap semiconductor with the band gap of 2.0 eV and promising for a highly stable photocatalyst to produce hydrogen from water under visible light irradiation. Here, we performed a comprehensive study on the energy level structure and photocatalytic activity of BP nanocrystals (NCs) in the quantum confinement regime (< 5 nm in diameter). First, we calculated the electronic structure of cubic BP NCs up to 2.8 nm in diameter, hexagonal BP nanoflakes and cubic/hexagonal BP nanostructures by the density functional theory and the time-dependent density functional theory. We then synthesized BP NCs with 2 to 13 nm in diameters and performed detailed structural analyses and optical measurements. The photocatalytic bleaching experiments for dye molecules under visible light irradiation revealed that the bleaching rate depends strongly on the size of BP NCs; the increase in the band gap of BP NCs by the quantum size effects (QSE) enhanced the photocatalytic activity. The band gap increase by the QSE also enhanced the rate of photocatalytic hydrogen evolution in water.

1. Introduction Cubic boron phosphide (BP) is III-V compound semiconductor with the zinc-blende structure having prominent mechanical, thermal and electronic properties.1–3 Due to the strong covalent bonding, cubic BP has very high decomposition and oxidation temperatures, and is chemically very stable; it is not attacked by concentrated mineral acids and aqueous alkali solutions.4–6 Due to these properties, cubic BP has been considered to be promising candidate materials for electronic devices operating in extreme conditions. Cubic BP is an indirect band gap semiconductor with the band gap of ~2.0 eV.6,7 Figure 1 shows the absolute energies of the conduction and valence band edges measured from the vacuum level.6,8 In the same figure, the redox potentials of H2O are also shown. The energy relation between the


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two materials and the relatively small band gap of cubic BP suggest that photocatalytic water splitting under visible light irradiation is possible.6,9 Shi et al. recently demonstrated that n-type cubic BP particles produced by solid state reaction can catalyze hydrogen (H2) evolution from water without loading metal cocatalysts.6 Demonstration of water splitting under visible light irradiation by metal-free stable photocatalytic materials composed of light-weight and abundant elements is a very important step for achieving low cost photoelectrochemical hydrogen generation.

Figure 1. Redox potential of H2O and conduction and valence band edge energies of bulk cubic BP crystal.

In the previous study on photocatalytic hydrogen evolution from water by cubic BP particles, the size of the particles was very large (hundreds of nanometres to a few micrometres), 6 and thus the energy band structure was in principle the same as that of the bulk crystal. If the size of cubic BP crystal is much smaller and in the quantum confinement regime, strong modification of the photocatalytic activity is expected due to the size-dependent shifts of the conduction band and valence band edges. However, to our best knowledge, such researches have never been performed. Furthermore, even simple consequences of the quantum size effects (QSE) such as the high energy


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shift of the band gap with decreasing the size have not been clearly observed. Since the effective Bohr radius of excitons in bulk cubic BP crystal is 2.6 and 4.6 nm for light and heavy holes, respectively,10 the QSE start to appear below ~10 nm. Difficulty in producing high-quality singlenanometer-scale cubic BP crystal has been an obstacle to conduct such researches. Recently, we found that cubic BP nanocrystals (NCs) with the diameters of 2 to 6 nm can be produced by the reduction of oxides of boron (B) and phosphorus (P) in silicon (Si)-rich borophosphosilicate glass (BPSG) into cubic BP crystal by excess Si.11 The development of the process to produce single-nanometer-size BP NCs makes detailed studies on the QSE possible, and opens up the possibility to explore the new functionalities. In this paper, we first perform comprehensive theoretical studies on the electronic structure and optical properties of cubic BP NCs up to 2.8 nm in diameter by the density functional theory (DFT) and the time-dependent density functional theory (TDDFT). We also study the energy level structure of hexagonal BP mono- and multilayer flakes and those of a cubic BP NC with a single hexagonal BP monolayer on its surface. We then prepare cubic BP NCs 2 to 13 nm in diameters by the method similar to that developed in our previous work11 and perform comprehensive characterization by Raman spectroscopy, transmission electron microscopy (TEM) and optical absorption spectroscopy. The photocatalytic bleaching of dye molecules under visible light irradiation demonstrates that the catalytic reaction rate depends strongly on the size of cubic BP NCs. Finally, we demonstrate that cubic BP NCs are capable of H2 evolution from water under visible light irradiation and the rate depends on the size.

2. Theoretical study on energy level structures of BP nanocrystals 2.1 Energy level structure of cubic BP nanocrystals


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We consider spherical, stoichiometric and hydrogen (H)-terminated cubic BP NCs with diameters in the range of 1.3-2.8 nm (Figure 2a). We deliberately chosen geometries with small dipole moments, because BP NCs with large dipole moments (resulting from large polarized surfaces) are energetically unfavorable (for more information, see the Supporting Information). The diameters (and chemical formulas) of the model BP NCs are 1.28 nm (B65P65H98), 1.62 nm (B119P119H158), 1.71 nm (B143P143H170), 1.83 nm (B171P171H198), 1.89 nm (B189P189H198), 2.07 nm (B240P240H246), 2.36 nm (B301P301H306) and 2.84 nm (B592P592H446). Figure 2b shows the calculated PBE0 Kohn-Sham energies for different sized BP NCs, including solvation effects. For the largest NC, calculating the Kohn-Sham energies with the PBE0 functional proved to be infeasible, thus the plotted electronic structure was obtained from a PBE calculation where the energies of the unoccupied Kohn-Sham states were shifted by a scissor operator of 1.4 eV. This value was derived from our results for the smaller BP NCs, where PBE0 and PBE results can be compared (see Supporting Information for details). Figure 2c and d show the first vertical excitation energies and radiative lifetimes, respectively (see Supporting Information for details). The Coulomb-interaction between the electron and hole lowers the excitation energy by 0.4-0.5 eV compared to the HOMO-LUMO gap. Both the vertical excitation energies and the radiative lifetimes exhibit the QSE, showing a decreasing and increasing trend with increasing NC diameter, respectively. However, neither the excitation energies nor the radiative lifetimes show monotonous size-dependence. This is once again related to the polarized nature of the BP NCs. B or P terminated {111} and {100} facets of the model NCs influence the shape and localization of the HOMO-LUMO orbitals, resulting in the nonmonotonous size dependence (see Supporting Information for more details). This is especially prominent for the radiative lifetimes, which are very sensitive to the shape of the HOMO and


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LUMO orbitals. According to these results, one should expect a quite broad distribution of lifetimes in a realistic ensemble of BP NCs, as the transition rate between the excited and ground state is very sensitive to the shape of the BP NCs. In addition, as the experimentally produced BP NCs are less symmetric than the models, the HOMO and LUMO might become even more localized resulting in decreased radiative rates. For hydrogen evolution, it is necessary for the semiconductor NCs to have proper band alignment relative to the water redox potentials. The position of the H2/H+ (-4.44 eV) and O2/H2O (-5.67 eV) redox potentials can be compared to the electronic structure of the BP NCs, where the vacuum energy was used as a reference to align the electronic structure of BP NCs with the redox potentials. It was demonstrated however, that using the vacuum level as reference is not reliable because the band realignment at a semiconductor-water interface is not captured properly by this approach.12,13 We follow the previously reported approach12 to calculate the alignment between the H2/H+ level and the conduction band minimum (CBM) of bulk cubic BP by creating an explicitly water solvated BP slab model. This approach predicted the alignment with an average error of 0.19 eV for six semiconductor materials.12 The details of our calculations can be found in the Supporting Information. Our simulation resulted -0.2 eV value for the CBM (referenced to the NHE), and +1.8 eV for the VBM using the experimental value of 2.0 eV for the band gap of BP. These values agree well with the experimental results.8 Unfortunately, both our results and the experimental data concern bulk BP, and might not be valid for small NCs. The band alignment between the BP NCs and the redox potentials is likely to be size-dependent. For small BP particles, the band gap opens wider due to the quantum confinement, while the flat-band potential is also expected to be different due to the increasing surface/volume ratio.


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Figure 2. (a) Model geometries with diameters of 1.28 nm, 1.89 nm and 2.84 nm. (b) Calculated PBE0 Kohn-Sham eigenenergies of the BP NC models within a continuum solvent with ε = 80. (c) Calculated vertical excitation energies and (d) radiative lifetimes of the BP NC models in vacuum.

Finally, we comment on the stability of the BP crystal against photo-induced oxidation/reduction. We consider the following reactions through which the generated holes/electrons can oxidize/reduce the BP crystal first instead of water: 2 BP + 3 H2O → B2O3 + P + 3H2 (oxidation) 2 BP + 3 H2 →B + 2 PH3 (reduction)


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Based on these reactions, we follow the previously reported approach14 to calculate the oxidation/reduction potentials of BP. The Gibbs free energy of formation is obtained from literature15 for BP and from Lange’s handbook16 for all the reactants except for BP. The calculated oxidation and reduction potentials of BP are -0.87 eV and -0.88 eV vs. NHE (pH = 7), respectively. These values tell that BP is resistant to electron reduction, but thermodynamically unstable to hole oxidation. The same result is found in various other non-oxide semiconductors.14 The experimentally observed apparent stability of BP crystal indicates that the oxidation is kinetically blocked. We also consider the effect of the surface chemistry on the electronic properties of the model BP NCs by substituting the surface terminating (B)-H atoms with hydroxy (-OH) groups. The results for the 1.28 nm and 1.71 nm NCs are shown in Figure 3 where the electronic structure of (B)H/(P)-H terminated BP NCs are compared with those that are terminated by (B)-OH/(P)-H. Upon substituting the (B)-H atoms by (B)-OH groups, the gap of the NC decreases due to new electronic states appearing above the HOMO of the (B)-H terminated NC. These levels are localized on the (B)-OH terminated surfaces on the NC (see Figure 3). Figure 3 also illustrates that the solvation effects are rather prominent for BP NCs as the dielectric screening of polarized facets by water opens up the gap by 0.3-0.5 eV (see Supporting Information for details). This holds for both surface terminations considered in this work.


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Figure 3. Left: The effect of B-OH termination on the electronic structure for two different-sized BP NCs. Black and red lines represent occupied and unoccupied Kohn-Sham levels (PBE0), respectively. White and light blue backgrounds represent calculations performed in vacuum and in a continuum solvent model with ε=80. The inset figures illustrate the surface termination (B-H, P-H or B-OH, P-H) of the model. Right: the HOMO of a B-OH terminated BP NC.

2.2 Energy level structure of hexagonal BP nanoflakes As will be shown later in the experimental study of BP NCs, graphite-like structures are observed on the surface of cubic BP NCs in the TEM images when the growth temperature is very high. The most probable candidate of the graphite-like structure is hexagonal phase BP. As the hexagonal BP is not very-well studied, we characterize the electronic structures of stoichiometric hexagonal BP flakes with diameters in the range of 1.3-3.6 nm in the same manner as for cubic BP NCs. The Kohn-Sham energies, vertical excitation energies and radiative lifetimes are shown in Figure 4a, b and c, respectively. Due to the direct gap of hexagonal BP, the flakes exhibit much shorter lifetimes compared to cubic BP NCs, and also show strong QSE. Interestingly, the calculated lifetimes does not change monotonously with the diameter, a local minimum appears around 2.3 nm. This can be explained by the nature of the HOMO and LUMO orbitals. For the larger


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hexagonal flakes, the HOMO and LUMO are essentially equivalent to the π bands of graphene, with an energy gap due to the broken symmetry between the sub-lattices. The HOMO is localized on the P atoms while the LUMO is localized on the B atoms. This is not the case for the smallest flakes, where both the HOMO and LUMO are sp2-like. Finally, we note that the largest investigated flake has significantly larger dipole moment (8.1 Debye) compared to the rest of the models (1-2 Debye). This polarization is the reason that the HOMO and LUMO are localized on the opposite halves of the flakes, resulting in very small transition dipole moment.

Figure 4. (a) The PBE0 Kohn-Sham energies of round flakes of a single hexagonal BP monolayer with different diameters. (b) The calculated vertical excitation energies and (c) radiative lifetimes of single hexagonal BP monolayers obtained by TDDFT (PBE0) calculations.

We also consider hexagonal BP flakes with multi-layers.17 The electronic structure of multilayered hexagonal BP can significantly differ from that of the monolayer. There are five possible stacking configurations for a bilayer. The most stable one is that B atoms of the two layers are stacked directly on top of each other, whereas the P atoms are located above (below) the center of the hexagonal rings of the neighboring layer. We consider the flakes with diameters of 1.6 nm


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and 2.3 nm, in which up to 6 identical copies are stacked on top of each other (Figure 5a). The smaller multilayer structures are characterized by both PBE and PBE0 functionals, while the larger one is characterized only by PBE due to increased computational costs. Figure 5b and c show the calculated PBE0 density of states (DOS) for the 1.6 nm multilayer structures as well as the HOMOLUMO gaps for both the 1.6 nm and 2.3 nm multilayers. For the 1.6 nm multilayers both the PBE and PBE0 results show the same trend with an approximately constant 1.2 eV difference between the PBE0 and PBE gaps. Comparing the PBE gaps of the 1.6 nm and 2.3 nm multilayer structures, we see an almost identical trend with an almost constant energy difference between the two sets of HOMO-LUMO gaps. The electronic structure for the stack number (n) of 5 and 6 is almost identical indicating convergence. Our results indicate ~0.4 eV reduction of the HOMO-LUMO gap for multilayer (n > 3) hexagonal flakes compared to a monolayer. This result is consistent with the PBE results of multilayer hexagonal BP layers.17

Figure 5. (a) Multilayer structure of hexagonal BP flakes. (b) Normalized DOS for multilayered BP flakes obtained by PBE0 for n=1...6. (c) HOMO-LUMO gaps of multilayered BP structures as a function of the number of flakes stacked on top of each other.


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Finally, we create a minimal model to investigate the electronic structure of cubic/hexagonal BP heterostructures (Figure 6a). The diameter of the cubic BP NC is 1.71 nm while the diameter of the hexagonal flake is 2.3 nm. Figure 6b shows the electronic structure of the system, where each Kohn-Sham state is categorized by its spatial localization. The HOMO and LUMO of the heterostructure belong to the cubic BP NC and to the hexagonal BP flake, respectively. This indicates that the excited electron can tunnel to the hexagonal BP layers from the cubic core. This picture also stands for larger BP NCs and hexagonal flakes: the CBM of the 2D hexagonal flakes falls below the CBM of the cubic BP NCs promoting the escape of electrons from the cubic phase to the hexagonal phase. The energy difference between the lowest energy state localized on the BP NC and the LUMO (which is localized on the monolayer) is 0.58 eV and 0.49 eV in vacuum obtained by PBE and PBE0 calculations, respectively. In aqueous solution, this value increases to 1.24 eV, leading to a significant decrease of the overall system’s HOMO-LUMO gap. Figure 6b shows the radiative lifetimes between the HOMO, LUMO and the lowest energy unoccupied state localized on the BP NC. Both transitions are in the 1 μs range, indicating that the trapped electrons can efficiently decay to their ground states by either photon emission or even faster by nonradiative processes.


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Figure 6. (a) Cubic BP NC in the presence of a single hexagonal BP monolayer. Pink, tan and white balls represent B, P and H, respectively. Blue and red clouds represent the HOMO (localized on the BP NC) and LUMO (localized on the monolayer). (b) Kohn-Sham energy levels of the BP NC+hexagonal monolayer. The energies are calculated at the PBE level which underestimates the gap. Blue and red lines represent occupied and unoccupied states, respectively. The horizontal position of the lines indicates where they are localized: lines on the left side of the diagram indicate states localized on the BP NC, lines on the right side indicate electronic states localized on the monolayer. Intermediate lines are delocalized between the two nanostructures. The radiative lifetimes were calculated in the temperature averaged independent particle approximation with PBE Kohn-Sham orbitals.

3. Experimental study on photocatalytic activities of BP nanocrystals 3.1 Structural characterization BP NCs in BPSG matrices are prepared by the procedure described in 6.2 Experimental methods. Figure 7a shows the Raman spectra of BP NCs in silicate matrices grown at different temperatures. The peak around 825 cm-1 with a long tail toward a lower wavenumber can be assigned to a LO phonon mode of cubic BP crystal (~828 cm-1).18,19 The broad band around 450 cm-1 may arise from silicate matrices. The 825 cm-1 peak becomes narrow and the low wavenumber tail becomes weak with increasing the growth temperature. Figure 7b shows Raman spectra after liberating BP NCs by etching in a mixture solution of hydrofluoric acid and nitric acid (HF/HNO3). Raman signals from silicate matrices disappear and the 825 cm-1 peak becomes narrow. A small peak around 800 cm-1 observed in higher-temperature-grown samples is the TO phonon mode of cubic BP. Figure 7c shows the full-width at half-maximum (FWHM) and peak wavenumber of the LO mode of BP


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NCs obtained from the spectra in Figure 7b. The FWHM decreases and the peak shifts to higher frequency as the growth temperature increases. We will discuss the relation between the Raman spectra and the particle size later.

Figure 7. Raman spectra of BP NCs (a) before and (b) after HF/HNO3 etching. The growth temperature is changed from 1050 to 1250oC. (c) Peak wavenumbers and FWHMs of Raman spectra as a function of growth temperature.


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Figure 8a-e shows TEM images of BP NCs grown at temperatures from 1050 to 1250oC, respectively. We can see that the particle size gradually increases with increasing the growth temperature. In Figure S6 in the Supporting Information, the electron diffraction pattern of BP NCs grown at 1150oC is shown. The observed diffraction rings agree well with the diffraction data of cubic BP crystal (JCPDS No. 11-0119). The high-resolution TEM images shown in the insets of Figure 8a-d demonstrate that the particles are single crystal. The lattice spacing estimated from the images are 0.26 nm which corresponds to {111} planes of cubic BP crystal. Different magnification TEM images and the fast Fourier transformation (FFT) images are shown in the Supporting Information (Figure S7). In the image of BP NCs grown at 1250oC (Figure 8f and Figure S8 in the Supporting Information), in addition to the lattice fringes corresponding to cubic BP crystal, graphite-like layers with the lattice spacing of 0.35 nm are observed on the surface of a cubic BP NC. A possible candidate of the surface graphite-like structure is hexagonal BP crystal.20–23 The layer-to-layer distances (d-spacing) of AA- and AB-stacking of hexagonal BP crystal are calculated to be 3.9 Å and 3.4 Å, respectively,24 which is very close to the lattice spacing in Figure 8f. In X-ray photoelectron spectroscopy (XPS) (Figure S9 in the Supporting Information), both B and P are predominantly in the metallic states and the composition (B : P) is nearly 1: 1 independent of the growth temperature. These results exclude the possibility that other materials such as oxides of B and/or P are formed on the surface. Figure 8g shows the size distribution obtained from TEM images. The average diameter is changed from 2.7 to 12.8 nm with increasing the growth temperature. With increasing the growth temperature, the distribution becomes broad and a tail extends to the larger size range.


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Figure 8. TEM images of BP NCs grown at different temperatures. (a) 1050oC (b) 1100oC (c) 1150oC (d) 1200oC and (e) 1250oC. Insets of (a-d) show the high-resolution TEM images. (f) High resolution image of a BP NC grown at 1250oC. (g) Size distributions obtained from TEM images.

3.2 Optical characterization Figure 9a-e shows the Tauc plots, (αhν)n  (hν – Eopt), where α, h and ν are an absorption coefficient, the Planck's constant and a photon frequency, respectively, of the absorption spectra of BP NC samples obtained by diffuse reflectance measurements. n is set to 1/2 to obtain the indirect band gap. Although the Tauc plot is not an accurate method to determine the optical band gap due mainly to the arbitrariness of fitting regions, it is convenient for the rough estimation. The estimated indirect band gap is plotted as a function of the growth temperature in Figure 9f. The indirect band gap first increases and then decreases with increasing the growth temperature. We will discuss the size dependence of the optical band gap later.


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Figure 9. (a-e) Tauc plots of BP NCs grown at different temperatures. (f) Indirect band gap energy as a function of growth temperature. Red dashed line is the band gap of bulk BP.

3.3 Photocatalytic activity of BP nanocrystals Figure 10a shows absorption spectra of mixture solutions containing BP NCs grown at 1100oC and Methyl Orange (MO). An absorption band of MO (400-600 nm) appears on the broad absorption tail of BP NCs. Irradiation of the solution with 405 nm light leads to significant bleaching of the MO band. After 13 min irradiation, the absorption by MO completely disappears and only a yellowish color due to absorption by BP NCs remains. The bleaching is caused by the reduction reaction of MO. As control experiments, we measured the absorption spectra of a MO


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solution without BP NCs under light irradiation and a mixture solution without light irradiation (Figure S10 in the Supporting Information). In all possible control experiments, bleaching was not observed. Therefore, the observed bleaching of MO is due to photocatalytic effect of BP NCs. It should be noted that, under 405 nm excitation, bleaching of MO is much faster in BP NCs than in TiO2 NCs (7 nm in diameter) (see Figure S11 in the Supporting Information). Several routes are considered for the photocatalytic reaction.25–27 One route is the direct reduction of MO by electron transfer from a LUMO of a BP NC to a MO molecule adsorbed on the surface. Another route is that a photo-generated electron in a BP NC reacts with a O2 molecule in a solution and forms a superoxide anion radical (*O2−),25–27 which degrades a MO molecule. Furthermore, a photogenerated hole in a HOMO of a BP NC reacts with surface hydroxyl groups and produces a highly reactive hydroxyl radical (*OH),25–27 which also degrade a MO molecule. At this stage of research, we do not know the relative contribution of each reaction route. Figure 10b and c compares XPS spectra (B 1s and P 2p, respectively) before and after the photocatalytic reaction in Figure 10a (405 nm (30 mW) irradiation for 13 min). The results of deconvolution of the peaks are shown in the Supporting Information (Figure S12). No signature of photo-oxidation is seen. Instead, the signal of P sub-oxide (~133.5 eV) decreases after the photocatalytic reaction. The HRTEM images (Figure S13 in the Supporting Information) demonstrate that the crystalline structure of BP NCs is perfectly preserved after the photocatalytic reaction. These results demonstrate photostability of BP NCs even when the size is very small. In order to discuss the dye bleaching rate quantitatively, we extracted the absorbance of MO at 500 nm by subtracting the absorbance of BP NCs and estimated the concentration (C). Figure 10d shows the concentration normalized with that before starting light irradiation (C0) in a logarithmic scale (-ln (C/C0)) as a function of irradiation time. We can see that the bleaching rate depends


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strongly on the growth temperature. The lines in Figure 10d are the results of the fitting of the data with a first-order reaction model (Langmuir-Hinshellwood model51), -ln (C/C0) = kt, where k is the apparent reaction rate. All the data could be well fitted by the model. Figure 10e shows k as a function of the growth temperature. With increasing the growth temperature, k increases and then decreases rapidly. The maximum reaction rate is obtained when the growth temperature is 1100oC. In the inset of Figure 10e, k normalized by the total surface area of BP NCs estimated from the average diameter is plotted. The growth temperature dependence does not change qualitatively by the normalization process. We will discuss the size dependence of the reaction rate later.

Figure 10. (a) Progression of absorption spectra of BP NCs-MO mixture solution under light irradiation (405 nm). Inset shows photos of solution before and after irradiation. (b) B 1s and (c) P 2p XPS spectra of BP NCs grown at 1100oC before (black solid lines) and after (red dash lines) laser irradiation for 15 min. (d) Normalized concentration of MO (-ln(C/C0)) as a function of irradiation time. Lines are the results of fittings with a first order kinetic model. (e) Apparent


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reaction rate (k) as a function of growth temperature. Inset shows the reaction rate normalized by total surface area. 3.4. Size dependence of photocatalytic property Up to now, we showed the optical and photocatalytic properties of BP NCs as a function of the growth temperature. In this section, we reexamine all the data as a function of the size. Figure 11a shows the Raman peak wavenumber and the FWHM as a function of the diameter. The Raman peak wavenumber and the FWHM of relatively large BP crystal (> 10 µm) in literatures are 829 cm-1 and 7-9 cm-1, respectively.2,19,28 In the Raman data of the largest size BP NCs in this work (Dave = 12.8 nm), the peak wavenumber is 827 cm-1, which is slightly lower than the literature value and the FWHM is 12.5 cm-1. With decreasing the size, the peak shifts to lower wavenumber and becomes broad. The clear size dependence of the Raman spectra suggests that the observed low energy shift and the broadening of the Raman peak are the manifestation of the phonon confinement effects.29,30 Figure 11b shows the optical band gap as a function of the diameter. With decreasing the size, the optical band gap increases significantly until around 3 nm and then decreases. Since the diameter of our BP NCs is close to the exciton Bohr radii of cubic BP, i.e., 2.6 and 4.6 nm for light and heavy holes, respectively,10 size dependent widening of the band gap is expected. Moreover, the DFT calculation in Figure 2 clearly demonstrates the strong size dependence of the HOMOLUMO gap for cubic BP NCs with diameters up to 2.8 nm. Therefore, the observed increase of the band gap with decreasing the size is considered to be the manifestation of the QSE. The decrease of the band gap in 2.8 nm BP NCs is probably due to the formation of band tails originating from the lattice distortion. This explanation is consistent with significant increase of the Raman FWHM below 3 nm. It should also be noted that the band gap of BP NCs above 6 nm


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in diameter is smaller than that of bulk BP (2.0 eV).7 A possible explanation is the reduction of effective band gap by heavily n or p type doping31–33 due to slight imbalance of B and P.6,34 Another more plausible explanation is the contribution of a hexagonal BP shell shown in the TEM image in Figure 8f to the optical transition. In section 2.3, the DFT results indicate that hexagonal BP on the surface of cubic BP NCs reduces the gap significantly. However, the theoretically predicted decrease of the gap is more significant than the experimental value. Possibly, DFT-related errors or the relatively small size of the model cubic-hexagonal system is behind the discrepancy. Figure 11c shows the photocatalytic reaction rate normalized by the surface area as a function of the size. We can see surprisingly similar size dependence between the optical band gap (Figure 11b) and the photocatalytic reaction rate. In the inset of Figure 11c, the reaction rate is plotted as a function of the optical band gap. We can see clear correlation between them. The correlation indicates that the reaction rate is predominantly determined by the energy of the LUMO and/or HOMO levels of a BP NC. This is consistent with the classical Marcus theory,35 where the charge transfer rate from a donor molecule to an acceptor molecule is proportional to exp(-(ΔG+λ)2/4λRT), where ΔG is the free activation energy, λ is the reorganization energy, R is the gas constant and T is the temperature. In the normal region (|ΔG|

Size-Dependent Photocatalytic Activity of Cubic ... - ACS Publications

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