First-principles study of optical aspects of Penta-graphene and T- Carbon nanostructures

doi:10.21203/rs.3.rs-3221946/v1

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First-principles study of optical aspects of Penta-graphene and T- Carbon nanostructures

https://doi.org/10.21203/rs.3.rs-3221946/v1

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In this study, after the introduction of two new carbon allotropes nanostructures named Penta-graphene and T- Carbon, based on the first-principles calculations using the Density Functional Theory (DFT), and using Wien2k computing codes, the optical properties of these nanostructures such as the joint density of states, the real and imaginary part of the complex dielectric function, absorption, and reflectivity spectrum under special conditions such as applying the hydrostatic pressure, and buckling effects, are studied and changing the behavior of the optical aspects of these nanostructures are analyzed. It can be concluded that these nanostructures are suitable for use in designing optoelectronic devices, especially as sensors under the proposed conditions.

Carbon allotropes nanostructures

First-principles calculations

Density Functional Theory (DFT)

Optical properties

Hydrostatic pressure

Buckling effect

Carbon as a unique element, due to the covalent bond of each atom with its type or with other types of atoms, has caused the creation of unlimited and very diverse carbon structures and nanostructures. Carbon allotropes such as nanofibers and nanostructures have an important contribution to nanotechnologies. The diverse and unique physicochemical allotropes of nanofibers and carbon structures have made these structures play a large role in modern and advanced technologies. Predicting new carbon compounds and structures with new electronic and optical aspects can play a significant role in constructing and producing new electronic and optical tools. The discovery of graphene has become a turning point for the beginning of extensive research on the physical properties of this carbon allotrope, such as dynamic, electronic, and optical properties for designing electronic and optoelectronic devices. Various types of two and three-dimensional carbon allotropes were discovered and predicted in different classifications. The physical aspects such as the dynamic, electronic, and optical properties of some of them were investigated [1–18]. In this study, optical properties such as the joint density of states, the real and imaginary part of the complex dielectric function, absorption, and reflectivity spectrum of two examples of new carbon allotropes that have been predicted recently, based on the method of first-principles calculations [7, 11]. The basis of density functional theory (DFT) using Wien2k calculation code based on full potential approximation under the influence of special application conditions such as applying hydrostatic pressure, stress, strain, and buckling, investigating and changing the behavior of the optical aspects of these nanostructures are analyzed [12, 14].

To calculate the optical properties of the carbon nano-allotropes in this study under applied conditions using first principles calculations in density functional theory, from the Wien2k computational code [19]. Wien2k is a computational code for processing crystalline and molecular structures and nanostructures with the full potential approximation and software based on the linear amplified flat wave method with the full potential, which is considered one of the most accurate methods for calculating the energy band structure. Using this software, it is possible to simulate crystal structures as well as nanostructures and predict many of their physical properties. Also, by solving the Cohen-Sham equations in a crystal lattice, the electronic and magnetic structure and other aspects such as charge and spin distribution in determined crystal structures. This calculation package determines the structural properties of crystals and molecules in the presence of impurity and under various approximations such as GGA, and LDA which can solve problems by the application of mean-field approximations, such as the Hubbard parameter.in this study to analyze the optical properties of two following carbon nano-allotropes using the Wien2k computational code with the GGA generalized gradient approximation by selecting 1x12x12 and 1x25x25 meshing. For inverted points in the first Brillion zone, the (PBE) method is used [20], and for the calculations of exchange-correlation interactions, the Monkhorst-Peck approximation is used [22]. Calculation input parameters RMTK_max = 7, G_max = 14 Ry^1/2, l_max = 10, separation energy of the nucleus from the valence electrons equal to 8 Ry is selected and the calculations are performed with non-polar settings. Also, Kramers-Kronig relations and the random phase approximation method (RPA) are used to obtain different components of the dielectric function [23].

A new two-dimensional allotrope of carbon, called penta-graphene, was predicted as an indirect bandgap semiconductor in 2015 [11]. Then, by using density functional theory (DFT) the energy structure and electronic properties of the two-dimensional penta-graphene nanostructure have been studied to understand the feasibility of synthesizing this nanostructure and its application in Nano-electronics. In this section, based on the principles of basic calculations related to the density functional theory, in line with new research, the optical properties of the optimized structure of the penta-graphene unit cell under buckling due to vertical compressive strain in the Z direction are investigated [12]. The final results show that according to the considered conditions, the desired nanostructure can be effective in the design of multi-purpose electro-optical devices.

The two-dimensional crystal nanostructure of penta-graphene shown in Fig. 1, has space group no. 113 and P-421m with a tetragonal lattice consisting of two types of carbon-carbon bond lengths (C1 & C2), where the atomic layer C2 with sp3 hybridization is located between two layers of C1 with sp2 hybridization. According to Fig. 1, the constants of the penta-graphene network have been optimized using the thermodynamic mode of Birch-Murganan equations [24]:

$$E\left(V\right)={E}_{0}+\frac{9{B}_{0}{V}_{0}}{16}\left\{{\left[{\left(\frac{{V}_{0}}{V}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-1\right]}^{3}{B}_{0}^{{\prime }}\right\}+\frac{9{B}_{0}{V}_{0}}{16}\left\{{\left[{\left(\frac{{V}_{0}}{V}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-1\right]}^{2}\left[6-4{\left(\frac{{V}_{0}}{V}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right]\right\}$$

(1)

In Eq. (1), the optimum volume energy is gotten with the lattice parameters (a, b) where${B}_{0}^{{\prime }}$concerns the bulk modulus under pressure, B₀ is the modulus in zero pressure, and V₀ is the primary volume. Figure 1 (a), shows the top and side views of the Penta-graphene 2D crystal supercell, and (b) indicates the volume vs energy curve for the penta-graphene. The curve's minimum point in Fig. 1(b) shows the optimized volume in the least energy of the unit cell. By the obtained equilibrium volume, the optimized lattice parameter is proposed as a = b = 3.649A°, and the thickness between each upper and lower layer of the C1 atom is called the buckling (δ), which is equal to 0.589A°. Consequently, the total thickness of the 2D Penta-graphene nanosheet is 1.178A°.

Table 1, demonstrates the calculated optimized structural data of Penta-graphene such as lattice parameter, buckling constant, Bond length, and optimize energy by using the PBE-GGA approximation method [12].

Table 1

optimized structural data of Penta-graphene by PBE-GGA method.
Method	Optimized lattice (A⁰)	Buckling (A⁰)	Bond length (A⁰)	E_opt (Ry)
PBE-GGA	a = b = 3.649	δ = 0.589	C1-C2 = 1.543 C1-C1 = 1.342	-456.735

Results of the investigation of the structural properties of this 2D carbon allotrope indicate that optimized penta-graphene nanostructure is known as an indirect band gap semiconductor, it has structural data in accordance with previous studies 27, 28. Also according to Fig. 2, the band gap and total energy are calculated under buckling reduction up to 12%. The results show that when the buckling constant is reduced, the total energy and consequently, stability of the system slightly decreases according to the blue curve in Fig. 2. The band gap shifts under the effect of buckling variation shown by the violet curve in Fig. 2, which illustrates by imposing vertical stress, the band gap of penta-graphene is reduced.

2.1 Penta-graphene optical properties

In this part, some significant optical properties such as joint density of states, real and imaginary parts of the complex dielectric function, absorption, reflectivity spectrum, and energy loss, of the penta-graphene, in optimal state and buckling variation condition up to 12 percent, are examined in the 0–30 eV energy range. Taking into account the fact that in order to make variations in the buckling, it is necessary to apply stress in the vertical direction on the nanosheet, the optical properties in the Z polarization direction are investigated and plotted.

The joint density of states (joint DOS) for the study of the optical inter-band transitions from the occupied states to the unoccupied states is investigated and shown in Fig. 3. This figure illustrates the joint DOS spectrum of the penta-graphene in the Z direction, without stress and under vertical stress conditions with 4, 8, and 12 percent to reduce buckling constant. Figure 3 shows that the joint DOS spectrum decreases with application stress in the nanomaterial. According to Fig. 3, due to the active stress, the buckling parameter decreases in the z-direction. In such a way that the sharp peak with the energy of about 11 eV in the non-stressed state, with stress, applied up to 12 percent on the penta-graphene, decreases the slope and moves towards the energy of about 14 eV.

Complex dielectric function, which consists of two parts, real and imaginary components as an operational factor to recognize all optical aspects such as absorption and reflectivity spectrum, is given by the following equation [25]:

$${\varvec{\epsilon }}_{\varvec{c}\varvec{o}\varvec{m}\varvec{p}\varvec{l}\varvec{e}\varvec{x}}= \mathfrak{R}+\mathfrak{ }\mathbf{i} \mathfrak{I}\varvec{\epsilon }$$

The real component of the dielectric function obtained using the krmaers-kroning relations is as follows:

$$\mathfrak{R}{\epsilon }^{\alpha \beta }\left(\omega \right)={\delta }_{\alpha \beta }+\frac{2}{\pi }Pr.{\int }_{0}^{\infty }\frac{\mathfrak{I}\mathfrak{ }{\epsilon }^{\alpha \beta }\left(\omega {\prime }\right)}{{\omega {\prime }}^{2}-{\omega }^{2}} \omega {\prime }d\omega {\prime }$$

Where $Pr.$ indicates the Cauchy principal value. Also, the effective factor in the inter-band optical transmissions between occupied (ik) and unoccupied electron states (fk) can be considered as the imaginary part of the complex dielectric function, the equation of which is:

$$\mathfrak{I}{\epsilon }^{\alpha \beta }\left(\omega \right)=\frac{4\pi {e}^{2}}{{m}^{2}{\omega }^{2}} \sum _{i,j}\int \frac{2{d}^{3}k}{{\left(2\pi \right)}^{3}}{\left|⟨ik|{P}_{\alpha }|fk⟩\right|}^{2}{f}_{i}^{k}(1-{f}_{f}^{k})\delta ({E}_{f}^{k}-{E}_{i}^{k}-\stackrel{-}{h}\omega )$$

The real and imaginary plots of the dielectric function related to the penta-graphene in the Z direction, without stress and under vertical stress conditions with 4, 8, and 12 percent to reduce buckling constant, are displayed in Figs. 4 and 5, respectively. As shown in Fig. 4, a sharp peak of transition occurred at about 6 eV in the non-stressed state, which decreases by increasing the stress up to 12%. Next sharp peaks are formed for modes affected by bucking for stresses of 8 and 12 percent, at higher energies in the range of 10 to 12 eV. Also According to Fig. 5, by applying stress in the imaginary part, in addition to reducing the peak of transition in the energy of about 10 eV, we see a rebound of transition peaks for stress states of 8 and 12 percent in energy of about 13 to14 eV. These indicate the matching of the optical and electronic behaviors of this semiconductor under these conditions.

Two important aspects for the exploration of optical properties are undoubtedly absorption and reflectivity. Figures 6 and 7 respectively, illustrate the 2D nanostructure of the penta-graphene absorption and reflectivity spectrums in the Z direction, which are affected by changes in buckling on this material by applying stresses with values of zero, 4, 8, and 12 percent. According to the figures, the absorption and reflectivity spectrums, from visible light energy to about 11 eV, are reduced by applying stresses up to 12%. This trend continues for a 4% stress state for higher optic energies up to 30 eV. But in energies between 13–15 eV for states of 8 and 12% stress, a rapid rise in the absorption and reflectivity amplitudes is observed by creating sharp peaks at 14 eV. These changes in optical behavior in these conditions are related to the electronic behaviors of this material, in the transformation of the indirect band into a direct band semiconductor, along with reducing the band gap.

At the end of this section, the energy loss spectrum (ELOSS) of penta-graphene has been examined under the conditions of this research. According to Fig. 8, the energy loss spectrum of this structure under compressive strain is relatively reduced by 8%. But at 12% buckling reduction, sudden and rapid changes occur in the sharp peak, which indicates the plasma frequency of the structure, which shifts from the energy of 21 to 22 electron volts to the energy of 15 electron volts.

T-Carbon structure as a 3D cubic crystalline nanostructure of carbon has lower density and the space group Fd3m similar to diamond which is shown in Fig. 9(a), is obtained by replacing each atom in the diamond with a carbon tetrahedron respectively shown in the [100], [110], and [111] directions in Fig. 9(b-d) [14].

In Table 2, the calculated structural properties of T-Carbon such as optimized lattice parameter, total energy, band gap, and cohesive energy by using the PBE-GGA approximation method [14], are compared with previously obtained values from other methods [7].

Table 2

Structural Data, lattice parameter, band gap and cohesive energy for T-Carbon
Method	l(A⁰)	E_G(eV)	E_cho(eV/atom)
(LDA)	7.446	2.22	7.577
(GGA)	7.52	2.25	6.573
(PBE-GGA)	7.52	2.257	6.545

The total energy and energy band gap variation of the T-Carbon unit cell under external hydrostatic pressure up to 9 GPa, are calculated and shown in Fig. 10. The obtained results show that when this nanostructure is subjected to pressure, the stability of the system decreases with increasing pressure up to 9 GPa limitedly according to the blue curve in the figure. While the bandgap decreases under the effect of pressure according to the red curve in Fig. 10.

3.1 T-Carbon optical properties

In this part to better understand the behavior of T-Carbon under hydrostatic pressure conditions, some important optical aspects of the structure are investigated under hydrostatic pressure in the energy range of 0–30 eV. To study the internal transition of the optical band from the occupied state to the unoccupied state, we study the joint DOS spectrum of the T-Carbon crystal in the Z direction, for the optimal state and under the conditions of applying pressure up to 9 GPa. Figure 11, shows the optical spectrum of the joint density of states of T-Carbon under the mentioned conditions. As can be seen in the figure, by applying pressure up to 9 GPa on the nanostructure, the spectrum of the density of states decreases slightly.

The real and imaginary spectrum of the complex dielectric function related to the T-Carbon in the Z direction, in the optimal state and under pressure up to 9 GPa, are shown in Figs. 12 and 13, respectively. According to the spectrum of the diagram in the following figures, in the real part, with an increase in pressure up to 9 GPa, a slight increase, and in the imaginary part of the dielectric function of this nanostructure, a slight decrease occurs under the conditions applied in this problem. In general, due to the application of pressure, slight changes are observed in the real and imaginary plots of the dielectric function of this structure.

Two important features to investigate optical aspects are definitely absorption and reflectivity. In the following, the optical properties under pressure up to 9 GPa on T-Carbon crystal have been studied. These optical properties are plotted in the Z-axis polarization direction in Figs. 14 and 15. The results show that due to the symmetry of the T-Carbon cubic crystal and the excitation of valence electron behaviors, it has almost the same results in both X and Z polarization directions. According to these figures, by increasing the pressure up to 9 GPa on the crystal, its absorption and reflection spectrum increases slowly.

Finally, the energy loss frequency spectrum (ELOSS) of the T-Carbon crystal was investigated under the applied conditions in this research and it is drawn in the direction of Z polarization in Fig. 16. Based on this figure, a slow change occurs in the energy loss spectrum of this 3D nanostructure under hydrostatic pressure up to 9 GPa. It should be noted that the plasma frequency in T-Carbon crystal is detected between 23 and 24 electron volts. According to the figure, the value of this frequency slowly shifts to higher values with the increase of hydrostatic pressure towards 9 GPa.

To summarize this study, as a new approach and research, the optical Aspects of two new carbon allotropes nanostructures called Penta-graphene and T-Carbon were investigated by first-principles calculation in the framework of density functional theory (DFT) using the Wien2k computational code. The optical properties investigation results such as joint density of states, real and imaginary part of the complex dielectric function, absorption, reflectivity, and energy loss (ELOSS) spectrum for T-Carbon as 3D carbon nanostructure under the effect of pressure, confirm small fluctuations in the optical properties spectra of the crystal. The optical properties of Penta-graphene as 2D carbon nanostructure under buckling strains conditions show a relative reduction in optical spectrums up to 4% strain, and also for 8 and 12 percent strains, the behavioral change is observed in optical properties, indicating well-matched properties with the electronic ones under these conditions Finally, it can be concluded that these nanostructures are suitable for use in designing optoelectronic devices, especially as sensors under the proposed conditions.

Acknowledgments

This study is supported by, Khatam Ol-Anbia University, Tehran, Iran. Hamidreza Alborznia would like to thank Fateme Afrashte, and Alireza Alborznia for their interest in this work

Funding: The authors did not receive support from any organization for the submitted work.

Availability of data and material: The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.

Code availability: Not applicable.

Authors' contributions: Not applicable.

Conflict of interest: The author declares that there is no conflict of interest in this study.

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No competing interests reported.

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First-principles study of optical aspects of Penta-graphene and T- Carbon nanostructures

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Abstract

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1. Introduction

2. Penta-graphene

2.1 Penta-graphene optical properties

3. T-Carbon

3.1 T-Carbon optical properties

Conclusions

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