Vacancy-defect effect on the electronic and optical properties of Pmm2 BC2N: A first-principles study

Physics Letters A 383 (2019) 125933

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Discussion

Vacancy-defect effect on the electronic and optical properties of Pmm2 BC2 N: A first-principles study Xiong Li a , Yan Zhu b,∗ , Can Huang b a b

School of Artificial Intelligence and Information Technology, Nanjing University of Chinese Medicine, Nanjing 210023, China College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

a r t i c l e

i n f o

Article history: Received 22 July 2019 Received in revised form 22 August 2019 Accepted 2 September 2019 Available online 5 September 2019 Communicated by R. Wu Keywords: BC2 N DFT Electronic properties Optical properties

a b s t r a c t Orthorhombic-Pmm2-BC2 N as a superhard photocatalyst simulates great interests in the researches of materials-design and application. To promote the studies of Pmm2 BC2 N as a multifunctional material with both great hardness and good optical properties, we investigated the electronic and optical properties of Pmm2 BC2 N with various vacancy-defects by the systematic first-principles density functional theory (DFT) calculations in this work. The absorption, refractivity, reflectivity, and photoconductivity of considered structures were calculated and explored. The various characteristics of the optical properties were analyzed based on relative computed density of states (DOS). © 2019 Elsevier B.V. All rights reserved.

1. Introduction Since the photocatalytic activity of TiO2 was firstly observed by Fujishima and Honda in 1972, semiconductor-based photocatalysts have simulated great interests in environmental protection and energy conversion [1,2]. Within the photocatalysts, superhard material due to its extremely high hardness and great thermo-chemical stability has attracted extensive attention since superhard β -C3 N4 was discovered [3,4]. So far, considerable efforts have been devoted to searching the new superhard photocatalysts in boron–carbon– nitrogen (B–C–N) compounds. However, exact atomic arrangement and lattice constant of some B–C–N compounds (for example BC6 N and B2 CN) are difficult to be accurately determined compared with BC2 N [4–6]. On the other hand, various BC2 N-structures have been investigated by first-principles calculations. Among all, the orthorhombic-Pmm2-BC2 N is one of the most stable compounds [4,7–16]. Moreover, Li et al. calculated the electronic and optical properties of Pmm2 BC2 N, and showed that Pmm2 BC2 N has barely absorption in visible-light region though it has an indirect energy bandgap of ∼1.7 eV [12]. More studies confirmed its super-high hardness, but its optical properties remained unknown [4,10–12, 15]. The application potential of superhard Pmm2-BC2 N can be certainly improved if it simultaneously offers great optical properties.

*

Corresponding author. E-mail address: [email protected] (Y. Zhu).

https://doi.org/10.1016/j.physleta.2019.125933 0375-9601/© 2019 Elsevier B.V. All rights reserved.

For instance, great absorption of visible-light is needed for lightharvesting materials. Low reflectivity and high transmittance can enable use as lens coatings. On the contrary, high reflectivity in the ultraviolet strongly indicates the application of being employed as protective coatings in some extreme environments (i.e., in outer space) [17]. More recently, Zhao et al. investigated the influence of the O dopant on the optical properties of Pmm2 BC2 N [4]. In order to promote the study/application of Pmm2 BC2 N as a multifunctional material with both great hardness and good optical properties, we investigated the electronic and optical properties of Pmm2 BC2 N with various vacancy-defects by the systematic firstprinciples density functional theory (DFT) calculations in this paper. 2. Computational detail First-principles DFT calculations were used to optimize the structures, and to calculate the electronic and optical properties. In geometrical optimizations, all forces on the atoms converged to 0.05 eV/Å, and the convergent threshold of the total energy was set to 10−5 eV. The exchange-correlation function was general gradient approximations (GGA) with the Perdew–Burke–Ernzerhof parameterization (known as GGA-PBE) [18]. The potentials for B, C, and N took the 2s2p valence electrons into account [4,18, 19]. The plane-wave cutoff energy was 430 eV for all the calculations. A 2×2×2 supercell (32 atoms) was considered in our work as presented in Fig. 1 [4]. Four sites including two for C atoms, and one for B and N atoms were deleted to induce cor-

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responding vacancy-defects, which were respectively referred as C1-vacancy, C2-vacancy, B-vacancy, and N-vacancy structures (the deleted sites are marked in the Fig. 1). The k-point meshes of 3×3×3 (Monkhorst-Pack scheme) and 7×7×7 (Monkhorst-Pack scheme) were respectively used for the calculations of geometrical optimizations, and optical properties and density of states (DOS). All calculations were performed in the Vienna Ab initio Simulation Package (VASP).

Fig. 1. (Color online.) The 2 × 2 × 2 supercell of orthorhombic-Pmm2-BC2 N. The blue, brown, and green balls represent B, C, and N atoms, respectively, and the deleted sites are marked.

3. Results and discussions The optimized structure parameters for all considered Pmm2 BC2 N supercells are listed in Table 1. The formation energy (E form ) was calculated and illuminated in Table 1. Similar to the literature, the energy of the deleted atoms (B, C and N) are −6.02 eV, −8.72 eV, and −8.32 eV, where energy-N is the energy per atom of one nitrogen molecule in 1.5 nm × 1.5 nm × 1.5 nm cell and energies-B and -C are the average energy per atom of the elemental crystal of boron (carbon). Compared with pristine BC2 N, all vacancy-defect structures have higher total energies (E total ) due to the inducing of vacancy-defects. Compared with the previous results, all vacancy-defect structures hold small formation-energy confirming the possibility of inducing these vacancies. The DFTcalculated structure parameters and E total of pristine BC2 N is very close to the literature, which confirms the reliability of our computations here [4]. Within the linear response range, the optical properties of material can be determined by its calculated dielectric function, ε (ω) = ε 1 (ω) + iε 2 (ω) [20–23]. The imaginary-part, ε2 (ω), can be calculated from the momentum matrix elements between unoccupied and occupied states based on GGA-PBE calculations [20–23]. The real-part ε 1 (ω) is derived from ε 2 (ω) by the Kramers–Kronig transformation [20–23]. The corresponding formulas are as follows:

ε 2 (ω ) =

 4π 2  m2

ω

2



C ,V B Z

2

(2π )

3

   M C , V (k)2

 × δ E kC − E kV − hω d3k, Table 1 The DFT-calculated optimized total energy E total (eV), lattice parameters (nm), formation energy E form (eV), and energy bandgap (E g ) of all structures (the energy of the deleted atoms was calculated based on the report of the literature to compare our results with the reported ones).

Eg a b c E total E form

Pristine

C1-vacancy

C2-vacancy

B-vacancy

N-vacancy

1.68 0.5117 0.5065 0.7270 −270.525 –

2.68 0.5019 0.5062 0.7413 −256.528 5.277

0.83 0.5072 0.5057 0.7444 −257.455 4.350

2.05 0.5011 0.5063 0.7435 −258.495 6.010

– 0.5164 5.040 7.235 −257.8219 4.383

ε 1 (ω ) = 1 +

2

π

∞

ρ0 0

ω  ε 2 (ω ) dω . ω 2 − ω2

All optical parameters, such as the absorption coefficient, reflectivity, photoconduction, and energy loss spectrum, can be derived from the ε (ω) [20–25]. Fig. 2 presents the calculated real- and imaginary-parts of the dielectric function for the orthorhombicPmm2-BC2 N with various vacancy-defects. For the orthorhombic crystal, its dielectric tensor is nondiagonal, i.e., ε 1xx (ω) = ε1yy (ω) = ε1zz (ω) , ε2xx (ω) = ε2yy (ω) = ε2zz (ω). However, the

Fig. 2. (Color online.) The calculated real- and imaginary-parts of the dielectric function for C1- and B-vacancy BC2 N. The results of pristine BC2 N are also plotted for comparison.

X. Li et al. / Physics Letters A 383 (2019) 125933

difference between the lattices a and b of BC2 N is slight, which may indicate the optical absorption coefficient (α ) for the light polarization along a and b axes (α xx and α yy ) is nearly isotropic. The pristine BC2 N was also computed for comparison. Near 10 eV, a significant peak was observed in ε 2xx,yy,zz (ω ) results for all BC2 N, which result from the excitation of inner electrons (in the deep valence bands) to the deep conduction bands. A smaller peak from ε 2(ω) below 5 eV was observed for BC2 N with various vacancies but absent for pristine BC2 N, and could be attributed to the enhanced electrons excitation from higher level of valence bands to the to lower level of conduction bands [4,17]. This obvious change from pristine to vacancy-defect BC2 N strongly suggests an effective vacancy-defect effect in electronic density of state which will be discussed below. The α (ω) deciding the absorption capacity  of materials was √ calculated from the ε (ω), α (ω) = 2 ωc [ ε 12 (ω) + ε 22 (ω) −

Fig. 3. (Color online.) The calculated photon-energy dependency of absorption coefficient of the C1- and B-vacancy BC2 N. The results of pristine BC2 N are also included for comparison.

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ε1(ω)]1/2 [20–25]. Photon energy dependent ε2 (ω) for all BC2 N obtained from the first-principles calculations is presented in Fig. 2. In the case of intrinsic absorption caused by interband transitions, the energy must be greater than or equal to energy bandgap (E g ) [4,17]. The calculated α (ω ) of the considered structures is illustrated in Fig. 3. As presented in Table 1, the E g results for BC2 N with C2 and N vacancies are smaller than 1.23 V which is the minimum potential for splitting water [26]. For BC2 N with C1 and B vacancies, their E g s are over the lower limit of 1.23 V, and is within the range of about 1.6 ∼ 3.2 eV for the absorption of visible-light. These indicate that the BC2 N with C1 and B vacancies has great absorption in the visible-light range. Hence, we focused on the optical properties of BC2 N with C1 and B vacancies. Also, the result of pristine BC2 N is provided for comparison. In spite of the E g of the pristine BC2 N is suitable for visiblelight absorption, only one obvious absorption peak for the light polarization along three axes near 10 eV was gotten for its energy dependent absorption, implying that it could hardly be employed as a material to harvest visible-light energy. This absorption peak was also easily observed for the C1- and B-vacancy BC2 N. The obvious absorption peaks near 10 eV for pristine and C1-/Bvacancy BC2 N strongly indicate significant absorption in the ultraviolet range and correspond to the obvious dielectric peak near 10 eV shown in Fig. 3. The isotropy of the α xx and α yy is found for all considered materials and is accordance with the above discussion about the structure characteristic. However, after inducing the C1 and B vacancies in pristine BC2 N, absorption outset redshift to the range of visible-light, suggesting that these two structures are benefit for harvesting visible-light energy and implying that C1 and B vacancies can effectively help promote the photocatalytic use of BC2 N in visible-light range. In the range of visible-light energy and energy >2.2 eV, the absorption of vacancy-defect BC2 N was improved compared with the pristine BC2 N, implying that they have more potential to be light-harvesting materials. Furthermore, several absorption peaks were found in the range of 4 ∼ 6 eV for the BC2 N with C1 and B vacancies, strongly indicating enhanced photocatalytic performances can be expected in this energy range. The improved absorption of C1-vacancy and B-vacancy BC2 N mentioned above indicates that the considered vacancy-defect BC2 N structures are more promising in photocatalytic performances [27]. We further studied the complex refractive index, expressed as n + ik, where the real-part n is the refractive index that determines the propagation speed of light while the imaginary-part k connects

Fig. 4. (Color online.) The complex refractive index for the pristine BC2 N, and C1- and B-vacancy BC2 N.

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Fig. 5. (Color online.) The reflectivity (R) of the pristine BC2 N, and C1- and Bvacancy BC2 N.

with attenuation [17,20–25]. The complex refractive index was calculated by the computed dielectric functions [20–25]. We plotted the extinction coefficient k and refractive index n in Fig. 4. As can be seen, k shows a tendency similar to the α (ω ), which is accordance with the linear relationship of α (ω ) ≡ 2ωk/c [20–25]. The refractive index for these three structures is very similar even almost isotropic. However, the n(ω) for the light polarization along a axis of C1- and B-vacancy BC2 N exhibits an additional peak near 4 eV, which is similar to the cases of α (ω ) and results from the induced vacancy-defect in their structures. Moreover, the refractive index for pristine and vacancy-defect BC2 N is very high in the infrared and visible-light range, and comparable to the value of 2.0 for various C-N materials [17]. Also, their refractive index shows relatively stable in the range of infrared and visible-light, which will be benefit for the usages of high-refractivity devices. The highest static refractive index reaches up to 3.25 and is observed for C1-vacancy BC2 N. Especially, this n is much higher than the one of 2.42 for diamond [17]. According to the discussion above, these are therefore high-n material because a value of 1.70 is considered to be the n-threshold. Hence, these three structures could be employed to make wearresistant lenses. For the infrared device of optical thin films, the thinner the coated layer, the less the stress between the layers leading to a better usage. In addition, more membrane-layers result in more infrared absorption as well. Thus, high-n material is often employed to reduce the stress and the membrane-layers. Besides, these structures themselves have high-temperature resistance, high-pressure resistance, and good thermal and chemical stability, thus they are promising to be cladding/coated materials for applications of infrared optical thin-film devices in extreme environment [17,28]. When light directly perpendicularly incident into the medium with a complex refractive index, reflectivity has a relationship with the refractive index [20–25]. Fig. 5 shows the reflectivity calculated from refractive index of the pristine, C1-vacancy, and B-vacancy BC2 N. As can be seen, the energy dependency of reflectivity for these three structures is nearly the same, except for a peak located near 4 eV. Significant peaks near 4 eV are present in the reflectivity for the light polarization along a axis for C1-vacancy

Fig. 6. (Color online.) The real-parts of photoconductivity (C ) of the pristine BC2 N, and C1- and B-vacancy BC2 N.

and B-vacancy BC2 N, but absent for the pristine, which predicts an enhanced reflection near this energy. Similar peaks were also observed in α (ω) and n(ω) (mentioned above), and can be contributed to the vacancy-defects in respective structures. According to these results, the interband transition for reflection increases with increasing the photon energy up to 22 eV, which means an enhanced metal-like reflection. The highest value of reflectivity reaches 85%. Below 22 eV, a monotonous decrease of reflectivity with increasing energy was observed. The photoconductivity of a semiconductor refers to a phenomenon in which the conductivity of a semiconductor changes due to illumination, and the change may be an increase in electrical conductivity or a decrease in electrical conductivity. Photoconductivity effect is the physical basis of optoelectronic applications, such as radiation detection/measurement, solar photovoltaic energy conversion and light-controlled switch. The realparts of photoconductivity of these three structures were also calculated and are plotted in Fig. 6 [20–25]. No photoconductivity was found for all structures below 2 eV (the infrared range and partial visible-light range). Obvious increase of the photoconductivity was gotten for all structures with increasing the energy to ∼10 eV. From 10 to 15 eV, the average of the photoconductivity is about 15 fs−1 , they can therefore be promising in being employed as high-photoconductivity materials within this energy-region. Furthermore, peaks near 4 eV for the light polarization along a axis can be also observed here, which is very similar to the cases of other optical-constants discussed above and further confirms the existence of the vacancy-defect effects. To analyze the absorption mechanism and investigate the electronic properties, the computed partial density of states (PDOS) and total density of states (TDOS) of all structures were plotted in Fig. 7. All structures except for N-vacancy BC2 N show obvious E g in TDOS, implying that all structures except for N-vacancy BC2 N are semiconductors. Due to just a few densities could be observed at/near Fermi level, the N-vacancy BC2 N is predicted to be a bad metal. The detailed values of E g s were listed in Table 1. Also, the data of the pristine BC2 N was also plotted and shown for comparison. The computed E g of pristine BC2 N was about 1.68 eV, which is consistence with the one of about 1.70 eV from the literature and then confirm the reliability of our computations here [4,12]. It can

X. Li et al. / Physics Letters A 383 (2019) 125933

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Fig. 7. (Color online.) The partial density of states (PDOS) and total density of states (TDOS) of (a) pristine, (b) B-vacancy, (c) C1-vacancy, (d) C2-vacancy, and (e) N-vacancy BC2 N.

be seen that the E g was enlarged from 1.68 to 2.05 eV and from 1.68 to 2.68 eV after inducing B-vacancy and C1-vacancy, respectively. Compared to the pristine BC2 N, almost no blueshift of the absorption for the vacancy-defect structures could be found though the enlargement of E g (will be discussed below). Besides, the E g was decreased to 0.8 eV by inducing C2-vacancy. Due to the values of E g s, there is no need to analyze the potential for splitting water by C2-vacancy and N-vacancy BC2 N as shown above [26]. The distributions of the DOS near both edges of the forbidden band determine the transition possibility for light-absorption [17,27]. Based on the DOS results in Fig. 7, we could try to understand the distinctive absorption characteristics of our considered structures: weak absorption in the visible-light range but a gradual increase in the ultraviolet (even though their E g -values are quite promising). For all considered structures, the top of valence bands (VB) is composed of 2p hybrid orbital of B, C, and N, and a significant hump starting at ∼5 eV. Also, obvious humps oc-

cupied by 2p shell of B, C, and N for conduction bands (CB) of all considered structures. The obvious absorption peak near 10 eV is related to the transition from the hump of VB to the one of CB: the average of density of states within the hump-regions of VB and CB is the highest. Below 3.2 eV (the upper limit of the visible-light) the density is small, so that just weak absorption is observed. In deeper of the valence and conduction bands, the density is increasing, the absorption therefore is enhanced. Compared with the DOS of the pristine, there is an additional peak near the top of the VB of the C1- and B-vacancy BC2 N coming from the inducing of vacancy-defect. The peaks near 4 eV in α (ω ) can be owing to the additional density-peak by vacancy-defect. Thus, inducing vacancy could be an effective and promising method for an enhanced absorption. Secondly, in spite of the E g s of the vacancydefect structures were enlarged compared with pristine BC2 N, the locations of the hump-regions of CB and VB are almost the same,

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so that almost no blueshift of the absorption for the vacancy-defect structures could be obtained. 4. Conclusion We investigated the electronic and optical properties of superhard Pmm2-BC2 N structures by using the first-principles DFT calculations. Compared with the pristine BC2 N, the absorption of C1- and B-vacancy BC2 N was improved, which implies that the considered vacancy-defect BC2 N structures have more potential to be light-harvesting materials and are more promising in enhancing the photocatalytic performances. The refractive index for pristine and C1-/B-vacancy BC2 N is very high and relatively stable in the infrared and visible-light range, and they therefore could be employed to make wear-resistant high-n lenses (especially in extreme environments). The reflectivity for the pristine and C1-/Bvacancy BC2 N is similar, except for peaks located near 4 eV were observed for the light polarization along a axis for C1-vacancy and B-vacancy BC2 N. These additional peaks predict an enhanced reflection near this energy and suggested applications as protective high-reflectivity coatings in some specific environment (i.e., in outer space). Weak photoconductivity in the infrared and visiblelight range was found for both the pristine and hold-defect BC2 N. However, obvious increase of the photoconductivity was gotten for all structures after 10 eV. The high average of the photoconductivity of ∼15 fs−1 strongly indicated that their potential in being employed as high-photoconductivity materials in the range of 10 to 15 eV. Furthermore, the various characteristics of the optical properties for pristine and vacancy-defect BC2 N were studied based on the computed DOS. Finally, our results can provide helpful/meaningful references for the design of advanced (multi)functional optical BC2 N-materials with characteristics such as anti-reflection, wear-resistance, high-reflectivity, transparency, or high-absorption, as well as high-refractivity. Acknowledgements This work was funded by the National Natural Science Foundation of China (NSFC) with Grant No. 11204131.

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