Structure, electronic and optical properties of Al, Si, P doped penta-graphene: A first-principles study

Journal Pre-proof Structure, electronic and optical properties of Al, Si, P doped penta-graphene: A firstprinciples study X.S. Dai, T. Shen, Y. Feng, H.C. Liu PII:

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DOI:

https://doi.org/10.1016/j.physb.2019.411660

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PHYSB 411660

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Physica B: Physics of Condensed Matter

Received Date: 17 January 2019 Revised Date:

17 August 2019

Accepted Date: 20 August 2019

Please cite this article as: X.S. Dai, T. Shen, Y. Feng, H.C. Liu, Structure, electronic and optical properties of Al, Si, P doped penta-graphene: A first-principles study, Physica B: Physics of Condensed Matter (2019), doi: https://doi.org/10.1016/j.physb.2019.411660. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Structure, electronic and optical properties of Al, Si, P doped penta-graphene: A first-principles study X. S. Dai1,2,3, T. Shen1,2,3,∗, Y. Feng1,2,3 and H.C. Liu4 1

Key Laboratory of Engineering Dielectrics and Its Application, Ministry of Education, Harbin University of

Science and Technology, Harbin, 150080, China; 2

Heilongjiang Provincial Key Laboratory of Quantum Manipulation & Control, Harbin University of Science and

Technology, Harbin, 150080, China; 3

4

College of Science, Harbin University of Science and Technology, Harbin, 150080, China;

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China.

Abstract: Penta-graphene, an irregular pentagon two-dimensional structure, has an intrinsic quasi-direct band gap. In the paper, first-principles calculations have been performed to study the geometrical structures, electronic and optical properties of pure and Al, Si, P doped penta-graphene. The doping of Al, Si or P atoms significantly reduce the band gap of penta-graphene. The gap value of Al-doped penta-graphene at C1 is the largest, 1.693eV, and P-doped penta-graphene at C2 is the smallest, 0.314eV. For doped penta-graphene, the fluctuations of the partial density of states in the full energy range are similar, indicating that the orbitals of C and other impurity atoms are hybridized into bonds. Furthermore, it is found that the change of the static dielectric constant will be affected by the different doping atoms and the different positions of doping atoms. The effective width of absorption spectrum becomes narrower than that of pure penta-graphene after the doping. Our findings indicate the possibility of tuning the bandgap and the optical properties of the material to make it suitable for optoelectronic and photovoltaic applications.

Keywords: penta-graphene; geometrical structures; electronic properties; optical properties; first-principles

* Corresponding author. Tel.: +86 451 86390867; fax: +86 451 86390867. E-mail address: [email protected] (Shen Tao). 1

1. Introduction Graphene has received a lot of attention for its excellent electronic and mechanical properties since it was discovered in 2004 [1]. Due to excellent physical properties and potential applications in both nanoelectronics and nanophotonics, graphene has attracted much attention in recent years [2-7]. However, the pristine graphene is a zero bandgap material, which limits its application in semiconductor devices [8]. Therefore, more two-dimensional materials similar to graphene have been proposed and studied. Zhang et al. [9] demonstrated the stability and electronic properties of a new wide-gap semiconductor carbon allotrope composed of pentagonal graphene in February 2015, known as penta-graphene, which was the first reported case of penta-graphene. Since then, there has been some exploration of its structure, electronics and other properties [10-12]. Unlike graphene, penta-graphene are composed of sp^3 hybridized carbons and sp^2 hybridized carbon atoms as the new allotrope of graphene [13]. In appearance, the pentagonal pattern similar to the Cairo pentagonal tile. In addition, penta-graphene was found to be a kind of intrinsic quasi-direct semiconductor. It has been reported that penta-graphene exhibits interesting mechanical properties, ultrahigh ideal strength, relatively higher stability, and unusual negative Poisson's ratio. These unique properties make penta-graphene promising for potential applications in optoelectronics, photovoltaics, and electronics. In addition to the intrinsic properties of penta-graphene, the doped penta-graphene exhibits fascinating electronic properties. The substitutional doping is an effective way to tune the electronic and optical properties of penta-graphene. The doping can reduce the band gap of penta-graphene, which facilitates the transformation of penta-graphene from a wide-band gap semiconductor to a narrow-band gap semiconductor. In the semiconductor industry, band control is a common and mature way to modify some materials. The common methods to control the energy band of materials include doping, forming defects or constructing special structures. Wang et al. [14] elaborately investigated the electronic and optical properties of novel carbon allotropes including penta-graphene. Therefore, it has an important application prospect in the field of optoelectronics [15]. Besides, Bravo et al. [16] presented a tight-binding parametrization for penta-graphene that describes its electronic band structure and linear optical response. By the research of Sun et al. [17], the mechanical properties of penta-graphene have been studied. Quijano-Briones et al. [10] studied Si, Ge and Sn atoms doped penta-graphene and related hydrogenated penta-graphene structures by the density functional theory (DFT). The objective of this paper is to explore the structure, electronic and optical properties of Al, Si and P atoms doped penta-graphene. The lattice parameters, bond length, formation energy, predicted band gap value, density of states and various optical properties of these materials were studied systematically. As far as we know, the related optical properties of doped penta-graphene have not been elaborately investigated. Furthermore, the application of these new materials in the field of optics is predicted by calculating their optical properties. We believe that our theoretical studies will inspire experimental studies on the doped penta-graphene, which can then be used as a potential candidate for the future generation nanoelectronics and optical devices. In this study, considering the limitation of experimental methods, first-principles calculations are carried out to explore the structures, electronic and optical properties of pure penta-graphene and its related doped systems. In the next section, the details of the model and computational methods applied to optimize the geometry structures have been presented. Section 3 reveals the 2

results associated with the structures, electronic and optical properties of pure and doped penta-graphene. In the last section, we summarize the article and present the key conclusions. The study will provide valuable theoretical basis for developing new doping system of penta-graphene with excellent performances, which would increase the range of applicability of penta-graphene.

2. Computational details and models 2.1 Computational details In the computation, we used Cambridge Sequential Total Energy Package (CASTEP) Code, this code is an ab initio quantum mechanics program based on density functional method [18, 19]. All calculations in the paper were performed using the code to study pure penta-graphene and doped penta-graphene. By using the screened hybrid Heyd-Scuseria-Ernzerhof (HSE06) function [20] in the relaxation of the unit cell of pure penta-graphene and doped penta-graphene, the bandgap of semiconductors and insulators were improved. The type of pseudopotential were applied in the computational method by the ultrasoft pseudopotential method. In order to ensure better convergence of the calculation results, the cut-off energy and k-point convergence test were first performed. Monkhorst-pack scheme with 12x12xl k-point mesh was adopted to carry out special point sampling integral for Brillouin zone [21]. Moreover, the cut-off energy of plane wave expansion was set to 500eV. The most stable state was reached at this time. BFGS algorithm [22] was adopted in the process of geometric optimization. The convergence tolerances were set to the maximum values of displacement 0.002 Å, energy change 2.0x10-5 eV/atom, max force 0.05 eV/Å, max stress 0.1 GPa. Besides, the Self-consistent field (SCF) was 2.0x10-6 eV/atom.

2.2 Computational models We used the Materials Visualizer to build the penta-graphene model. The models of pure and Al, Si, P doped penta-graphene are shown in Fig. 1. A 2x2x1 penta-graphene supercell was built based on the penta-graphene unit cell composed of two sp^3 hybridized carbon atoms (Cl sites) and four sp^2 hybridized carbon atoms (C2 sites). There are two types of C-C bond: C2-C2, called the intralayer bond, is 1.34 Å, and C1-C2, called interlayer bond, is 1.55 Å, which are consist with previous literature [23]. In addition, in order to eliminate interactions between penta-graphene layers, a vacuum space of 15 Å was constructed. After structure optimization, lattice parameters of pure penta-graphene were obtained: a=b=3.639 Å. The results of the paper are in agreement with the description of the literature [9].

3

– – (a)–

(b)–

(c)

(d)

(e)

(f)

Fig. 1. The physical structures and side views of pure and Al doped penta-graphene at C1 (sp^3 hybridized) or C2 (sp^2 hybridized). Substituting Al for Si and P in the same position can result in Si doped penta-graphene and P doped penta-graphene.

3. Results and discussion 3.1 Geometrical structures of doped penta-graphene The optimized bond length, lattice parameters and formation energy (Eformation) are obtained in Table 1. The bond length between C2 and the impurity atom increased more than that between C1 and the impurity atom. This is obviously reasonable. In addition, C-Al bond length is the largest, followed by C-Si bond length, and C-P bond length is the shortest. It may be that the covalent radius of Al atom (1.18 Å) is the largest, and the covalent radius of P atom (1.06 Å) is the smallest, resulting in the variation of bond length. Obviously, the covalent radius of doping atoms are greater than that of C atom (0.77 Å). Furthermore, the bond length between C and the impurity 4

atom is greater than the C-C bond length of penta-graphene. The relevant information of lattice parameters about doped penta-graphene can be obtained from Table 1. As we can see, both the type of atom and the doping position will cause different changes of lattice parameters. To further verify the stability of doped penta-graphene, the formation energy was calculated for each system using the following equation:

E formation = Esystem − E penta − graphene + mµcarbon − nµdopant where Esystem, Epenta-graphene, µcarbon and µdopant stand for, respectively, the total energy of doped penta-graphene, pure penta-graphene, the chemical potentials of carbon and impurity atom. It can be concluded from Table 1 that it is possible to synthesize doped penta-graphene by the experimental methods. These changes in the structure of penta-graphene lead to corresponding changes in its electronic and optical properties. Table 1 The structural parameters and formation energy for penta-graphene. Structure

Bond types and length (Å)

Lattice parameters (Å)

Eformation (eV)

Al-doped at C1

C2-Al

2.241

5.046

-4.894

Al-doped at C2

C1-Al

2.092

5.364

-4.711

Si-doped at C1

C2-Si

2.022

4.506

-4.302

Si-doped at C2

C1-Si

1.854

4.801

-4.074

P-doped at C1

C2-P

2.013

4.527

-3.928

P-doped at C2

C1-P

1.803

4.992

-3.836

3.2 Electronic properties Fig. 2 shows the band structure and densities of states of pure penta-graphene based on GGA-PBE and HSE06 function, respectively. The Fermi level is chosen as the zero of the energy and the forbidden band width is the distance from the top of the valence band to the bottom of the conduction band. The calculated band gap is 2.419 eV based on GGA-PBE calculation, which is consistent with the previous studies [24]. The calculated band gap is 3.216 eV based on HSE06, which is also consistent with the reports calculated by Zhang et al [9]. It can be seen from the band structure that the penta-graphene is a kind of quasi-direct band gap semiconductor. The main energy of pure penta-graphene come from C1-s/p and C2-s/p in the range of -27eV to 10eV. The valence bands come mainly from the C1-p states, whereas the conduction bands originating from the C2-p states. In contrast, C1-s states and C2-s states provide less energy.

5

10

Energy(eV)

5

0

-5

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-15

-20

G

X

M

G

– (a)–

(b)–

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Energy(eV)

5

0

-5

-10

-15

-20

G

X

M

G

(c)

(d)

Fig. 2. Band structure (a) and densities of states (b) of pure penta-graphene based on GGA-PBE, band structure (c) and densities of states (d) of pure penta-graphene based on HSE06 function.

10

10

5

5

0

0

Energy(eV)

Energy(eV)

The band structures of Al, Si and P doped penta-graphene are shown in Fig. 3. Obviously, impurity atoms doped penta-graphene at C1 or C2 will cause different variation of band structure. The band gap of Al-doped penta-graphene at C1 or C2 is 1.693 eV, 0.620 eV, respectively. When Si atom is doped at C1 or C2 of penta-graphene, the band gap value become 1.204 eV, 0.329 eV, respectively. In addition, the band gap of P-doped penta-graphene at C1 or C2 is 0.751 eV, 0.314 eV, respectively, indicating that the doping of Al, Si or P atoms remarkably reduces the band gap of penta-graphene. Still, doped penta-graphene systems are intrinsic semiconductors. Since some of the impurity levels are connected to the conduction band, the semiconductor level is degenerate, resulting in the tailing effect and exhibiting metallic properties. Moreover, it can be observed from the Fig. 3 that the impurity atom doped penta-graphene at C2 reduces the band gap to a greater extent. In combination with Fig. 4, the main reason for the narrowing of band gap is the different energy contribution of different atoms.

-5

-5

-10

-10

-15

-15

-20

-20

G

X

M

G

G

–

X

M

G

–

(a)–

(b)–

6

10

5

5

0

0

Energy(eV)

Energy(eV)

10

-5

-5

-10

-10

-15

-15

-20

-20

G

X

M

G

G

–

X

G

–

(d)–

10

10

5

5

0

0

Energy(eV)

Energy(eV)

(c)–

M

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-5

-10

-10

-15

-15

-20

-20

G

X

M

G

G

(e)–

X

M

G

–

(f)–

Fig. 3. Band structure of Al-doped penta-graphene at C1 (a), Al-doped penta-graphene at C2 (b), Si-doped penta-graphene at C1 (c), Si-doped penta-graphene at C2 (d), P-doped penta-graphene at C1 (e) and P-doped penta-graphene at C2 (f).

The total density of states (TDOS) and partial density of states (PDOS) are shown in Fig. 4. From Fig. 4 (a) to Fig. 4 (f), the fluctuations of the partial densities of states in the full energy range are similar, indicating that the orbitals of C and doping atoms are hybridized into bonds. It is worth noting that C1/C2-p states are higher than that of other states in valance band. Moreover, the C1/C2-p states decreased slightly with Al, Si or P incorporation in penta-graphene. With the doping of impurity atoms, the conduction band minimum (CBM) determined by Al/Si/P-2p states shifts to low energy range obviously. This is the main reason for the decrease of the band gap in the doped penta-graphene.

– (a)–

(b)–

7

–

– (c)–

(d)–

– (e)–

(f)–

Fig. 4. Densities of states (TDOS and PDOS) of Al-doped penta-graphene at C1 (a), Al-doped penta-graphene at C2 (b), Si-doped penta-graphene at C1 (c), Si-doped penta-graphene at C2 (d), P-doped penta-graphene at C1 (e) and P-doped penta-graphene at C2 (f).

3.3. Optical properties Generally speaking, the optical properties of solids come from the electronic transitions. They are closely related to their electronic structures and are of great importance to their application. Besides, the optical properties of penta-graphene are calculated for incident radiations with the electric field vector E polarized along the Y direction. The dielectric function describes the linear response of medium to electromagnetic radiation and determines the characteristics of electromagnetic waves as they travel through medium [25]. The optical properties of penta-graphene can be obtained from the complex dielectric function:

ε (ω ) = ε1 (ω ) + iε 2 (ω ) where ω is the photon frequency, ε1(ω) and ε2(ω) are the real and imaginary parts of the complex dielectric function, respectively. The real part represents the polarization degree of the medium under the action of external electric field, while the imaginary part reflects the loss of the medium. Fig. 5 shows the real parts (a) and imaginary parts (b) of dielectric function for pure and Al, Si, P doped penta-graphene at C1 or C2, respectively. It can be seen from Fig. 5 (a) that the real part of the dielectric function of pure penta-graphene is all greater than zero, after the doping of Al or Si, the real part of the dielectric function shows an energy interval less than zero, indicating that light within this energy range cannot propagate in it. The peak in the real part of dielectric function for Al-doped penta-graphene at C1 is the strongest, 6.8, and Si-doped penta-graphene at C2 has the lowest value, -2.5. This is due to the fact that some C atoms were replaced by Al after

8

doping, and the electrons contributed by the p-orbital of the donor atom Al resulted in the existence of excess electrons near the Fermi level. The Al atoms bind the nearby excess electrons in the doped penta-graphene. Under the action of the applied electric field, the electrons trapped around Al are constantly reciprocating against a certain barrier to cause relaxation polarization and loss. In the low frequency region, the curve changes of the real part of the dielectric function of penta-graphene and penta-graphene doped system both reach a peak and then attenuate with the increase of energy. The real part of the dielectric function corresponds to the static dielectric constant at frequency of 0 eV. It is found that the change of the static dielectric constant will be affected by the different doping atoms and the different positions of doping atoms. The largest static dielectric function is the Al-doped penta-graphene at C1, 5.4; and the smallest is P-doped penta-graphene at C2, 1.5. Therefore, Al-doped penta-graphene has the strongest polarization ability and the highest photogenic electric field intensity. As a result, the photoexcited carrier migrates the fastest and the charge binding ability of the system is the strongest. For the imaginary part of the dielectric function, as shown in Fig. 5 (b), the peak values of doped penta-graphene all produce redshift to the low energy direction. Due to the introduction of impurity atoms, the band gap is reduced and the photon energy required to excite the electron transition is also reduced. The imaginary part of the dielectric function for Al-doped penta-graphene at C1 or C2, Si-doped penta-graphene at C1 or C2 has a significant peak value, which is higher than that of pure penta-graphene. On the contrary, the peak value of P-doped penta-graphene at C1 or C2 is lower than that of pure penta-graphene. Besides, pure penta-graphene approaches zero at 25 eV. After impurity atoms doping, the corresponding energy decreases when the value of dielectric function is zero. The dielectric function of Al-doped penta-graphene at C1 is close to zero at 22.5 eV, while other doped penta-graphene systems are close to zero at about 15 eV. The results show that the introduction of impurity atoms reduces the dielectric absorption bandwidth and the electromagnetic absorption capacity of penta-graphene.

(a)–

(b)–

Fig. 5. Real parts (a) and imaginary parts (b) of dielectric function for pure, Al-doped, Si-doped and P-doped penta-graphene at C1 or C2, respectively.

Fig. 6 shows the optical absorption for pure and Al, Si, P doped penta-graphene at C1 or C2, respectively. The absorption spectrum reflects the relationship between the absorption coefficient of light and the photon energy [26]. The absorption coefficient is not only related to the wavelength of light but also to the properties of the material itself. The adsorption spectrum for pure penta-graphene calculated are consistent with previous results in Wang [14]. Al-doped 9

penta-graphene at C1 has the absorption spectrum in the range of 0-25 eV, while other doping systems have the absorption spectrum in the range of 0-17.5 eV. However, it can be seen that the effective width of absorption spectra all become narrower than that of pure penta-graphene after doping with other atoms. In the range of 1.2 eV to 4 eV, the absorption spectra of Al-doped penta-graphene at C1 or C2 and Si-doped penta-graphene at C1 or C2 are significantly stronger than that of pure penta-graphene. Therefore, the absorption intensity of infrared light and near-infrared light is higher than that of pure penta-graphene, it may have some application value in this energy range. However, within the range of 5 eV to 14 eV, the absorption intensity of pure penta-graphene is generally higher than that of other doped penta-graphene, indicating that pure penta-graphene has stronger absorption intensity to visible light with smaller wavelength and near ultraviolet light.

Fig. 6. Calculated the optical absorption for pure, Al-doped, Si-doped and P-doped penta-graphene at C1 or C2, respectively.

The other optical properties are also calculated in our work, such as the reflection (shown in Fig. 7). In the reflection spectrum, the reflection peak is the macroscopic expression of the transition between energy bands caused by the perturbation of the solid electron in the light electromagnetic wave [27]. The reflection spectrum for pure penta-graphene calculated are consistent with previous results in Wang [14]. By comparing the peaks in Fig. 6 and Fig. 7, it can be observed that if penta-graphene strongly absorbs light at a certain energy segment, it can effectively reflect light at that energy segment. The reflection spectrum of pure penta-graphene reaches a peak value of 0.12 at about 15 eV in the far ultraviolet region, that is, the reflectivity of light is 12%. The addition of other atoms alters the reflectivity of penta-graphene. The peaks of other doped systems are higher than that of pure penta-graphene except that P-doped penta-graphene at C2. The largest peak is Si-doped penta-graphene at C2, 0.66, which greatly improves its reflectivity. It has certain application value in the field of light reflecting materials. In addition, when the reflectivity drops to zero, the corresponding energy is reduced compared with that of pure penta-graphene after doping with other atoms.

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Fig. 7. Calculated the reflectivity for pure, Al-doped, Si-doped and P-doped penta-graphene at C1 and C2, respectively.

The energy loss function describes the energy loss of electrons as they pass through a uniform dielectric [28]. The peak value of the function represents plasma turbulence, and the corresponding oscillation frequency is known as the plasma frequency. The energy loss function curve is shown in Fig. 8. The loss function for pure penta-graphene calculated are consistent with previous results in Wang [14]. However, the energy range that we calculated is much larger. Penta-graphene has two energy loss peaks at 11.2 eV and 15.8 eV, respectively. It is shown that when electrons with different energies are incident on the surface of penta-graphene, the C atom is prone to inelastic collisions with electrons with energies of 11.2 eV and 15.8 eV, resulting in energy loss. Therefore, the pure penta-graphene has two plasma oscillation peaks with corresponding oscillation frequencies of 11.2 eV and 15.8 eV. ;When the doping atom is Al or Si, the peak of loss function is significantly higher than that of pure penta-graphene. Among them, Si-doped penta-graphene at C2 reaches the maximum peak around 10.3 eV, 8.5. In addition, P-doped penta-graphene at C2 has the lowest peak energy loss function. The value of pure penta-graphene is reduced to zero at around 25 eV, but the corresponding energy decreased when the loss function is zero after doping with other atoms. The lowest energy is P-doped penta-graphene at C2 with a value of 12.5 eV. In summary, P-doped penta-graphene at C2 has the best loss function performance.

Fig. 8. Calculated the loss function for pure, Al-doped, Si-doped and P-doped penta-graphene at C1 and C2, respectively.

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4. Conclusions By first-principles calculations, the geometrical structures, electronic properties and optical properties for pure and doped penta-graphene have been elaborately investigated within the screened hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional approximation. Penta-graphene is a kind of quasi-direct band gap semiconductor material. According to our calculations, the band gap decreases with the doping of Al, Si and P atoms at C1 or C2. The semiconductor properties of doped penta-graphene have also changed. The C atoms of penta-graphene are hybridized with other impurity atomic orbitals to form a bond. In addition, doped penta-graphene systems are mainly powered by the p orbital of the impurity atom and C atom, while the s orbital of that provide less energy. Penta-graphene has stronger absorption to visible light with small wavelength and near ultraviolet light. After doping with other atoms, the peak of absorption spectrum shows redshift phenomenon. Besides, P-doped penta-graphene at C2 has the best energy loss function performance. In summary, our research provides a feasible research direction for penta-graphene in the field of photoelectricity.

Acknowledgements The authors acknowledge financial support from National Natural Science Foundation of China (Grant 51677044), Natural Science Foundation of Heilongjiang (Grant E2018047) and the Outstanding Youth Innovation Foundation of Harbin [grant number 2017RAYXJ022].

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AUTHOR DECLARATION We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. We understand that the Corresponding Author is the sole contact for the Editorial process (including Editorial Manager and direct communications with the office). He/she is responsible for communicating with the other authors about progress, submissions of revisions and final approval of proofs. We confirm that we have provided a current, correct email address which is accessible by the Corresponding Author and which has been configured to accept email from ([email protected]) Signed by all authors as follows: Xiaoshuang Dai, Tao Shen, Yue Feng, Hongchen Liu