Atomic structures of graphene-like nanomaterials including SiC and BP

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ScienceDirect Materials Today: Proceedings 5 (2018) 11004–11010

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NanoThailand2016

Atomic structures of graphene-like nanomaterials including SiC and BP Taweesin Rerkhajornnamkula,b* and Tanakorn Osotchana,b a

Materials Science and Engineering Program, Faculty of Science, Mahidol University, Rama VI Road, Phyathai, Bangkok 10400 b Nanoscience and Nanotechnology Center, Faculty of Science, Mahidol University, Rama VI Road, Phyathai, Bangkok 10400

Abstract Honeycomb sheet, graphene like, structure has been interested and the planar structures of silicon carbide (h-SiC), boron phosphide (h-BP) and mixed of both materials h-(SiC)1-x(BP)x were investigated with x values of 0.00, 0.25, 0.50, 0.75 and 1.00. The 2 atoms per unit cell of hexagonal and 4, 8 and 16 atoms per unit cell of orthorhombic configurations were used in atomic structure calculation with 1.5 nm space distance between layers of graphene like structure. The calculation is set for 500 eV energy cutoff, using local density approximation (LDA) exchange-correlation functional, 200 Ry mesh cutoff. The lattice constant was varied to evaluate the stable atomic structures together with the average bond length. Then, the band structures including energy band gap, used to determine electronic property, was calculated to guide the utilization of novel electronic device for new millennium. © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of The 5th Thailand International Nanotechnology Conference (NanoThailand2016). Keywords: Band structure; graphene like; planar structure of SiC and BP

1. Introduction New materials for compensated resource and energy, electronic devices and comfortable applicants have been developed and graphene and its like structures have been discovered. They are two-dimensional (2D) structural materials which have many unique electronic properties for each compound. In our work, the graphene like structure h-(SiC)1-x(BP)x compounds are investigated theoretically especially on their lattice constants and energy band

* Corresponding author. Tel.: +66-44-217040 ext 1480; fax: +66-44-217047. E-mail address: [email protected] 2214-7853 © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of The 5th Thailand International Nanotechnology Conference (NanoThailand2016).

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structures including energy band gaps. The result will be useful to develop the fundamental knowledge of nanoscience and nanoelectronics of graphene like structures. 2. Simulation Method The quantum simulation program as SIESTA was used to evaluate the optimum graphene like structure. The calculation was set for 500 eV energy cutoff, using local density approximation (LDA) for exchange-correlation functional, and 200 Ry mesh cutoff. The two-atom unit cell of hexagonal configuration was employed for h-SiC and h-BP. The 4-, 8- and 16-atom unit cell of orthorhombic configurations were also used for h-SiC and h-BP structures for comparison. Two symmetries of h-SiC-BP were classified depending on the carbon bonded to either B or P, as called α or β-form, respectively. With increasing to 16 atom unit cell, the SiC-BP structure can be formed into two types according to the order of arrangement like SBSB (type I) or SSBB (type II). Thus the 16-atom unit cell of orthorhombic configuration can include all possible structures as h-SiC, h-BP, α-h-SiC-BP(I), β-h-SiC-BP(I), α-h-SiC-BP(II), β-hSiC-BP(II), α-h-(SiC)3-BP, β-h-(SiC)3-BP, and α-h-SiC-(BP)3 and β-h-SiC-(BP)3, as shown in Fig. 1. The optimized lattice constant was determined from calculated lattice constant-total energy graph by estimating minimum point with 3-degree polynomial function. Then, the band structures including energy band gap was determined from the structure with lattice constant at minimum point and then plotted in Brillouin zone.

graphene

h-SiC

h-BP

β-h-SiC-BP(I)

α-h-SiC-BP(I)

α-h-SiC-BP(II)

β-h-SiC-BP(II)

α-h-(SiC)3-BP

β-h-(SiC)3-BP

.

.

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α-h-SiC-(BP)3

β-h-SiC-(BP)3 – C,

– Si,

– B,

–P

Figure 1. Unit cell of graphene like structures used in the calculation.

Figure 2. Calculated total energy as a function of lattice constant to determine optimum lattice constant (182.67 pm) at minimum energy of α-hSiC-BP(I) by fitting with 3-degree polynomial.

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Table 1. Average bond length in angstrom of each structures.

Structure

Hexagonal

Orthorhombic

2

4

8

16

Graphene

1.4229

1.4233

1.4233

1.4233

h-SiC

1.7801

1.7804

1.7804

1.7804

h-BP

1.8609

1.8609

1.8609

1.8609

α-h-SiC-BP(I)

-

-

1.8268

1.8268

β-h-SiC-BP(I)

-

-

1.8227

1.8227

α-h-SiC-BP(II)

-

-

-

1.8231

β-h-SiC-BP(II)

-

-

-

1.8218

α-h-(SiC)3-BP

-

-

-

1.8034

β-h-(SiC)3-BP

-

-

-

1.8016

α-h-SiC-(BP)3

-

-

-

1.8434

β-h-SiC-(BP)3

-

-

-

1.8418

The lattice constant at minimum energy was used to represent average bond length. The lattice constant at minimum energy was used to determine average bond length and for α-h-SiC-BP(I) with 8-atom unit cell structure, the average bond length is 1.8267 Å, as shown in Fig. 2. The average bond length of the other structures were evaluated and listed in Table 1. 3. Energy Band Structure

Figure 3. Energy band structure of α-h-SiC-BP(I) indicating 1.46 eV energy band gap.

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For 8-atom unit cell α-h-SiC-BP(I) structure, the energy band gap locates at about -5 eV with energy band gap of 1.46eV at between Γ and Y point as shown in Fig. 3. The energy gap for others structure were calculated and listed in Table 2 and Fig. 4. It should be noticed that for hexagonal configuration, the energy band gap occurs at K point. The calculated band gap values of graphene like binary compound become close to the reported band gap values of 2.52 and 0.82 eV for h-SiC and h-BP, respectively[1].It can be observed that the band gap of α-form structures is higher than those in β-form. It also showed that the band gap of type I structure is higher than that of type II structure. Table 2. Energy band gap in eV of each structures between Γ and Y point or K point. Structure

Hexagonal

Orthorhombic

2

4

8

16

Graphene

0.00

0.02

0.02

0.02

h-SiC

2.40

2.40

2.40

2.40

h-BP

0.89

0.89

0.89

0.89

α-h-SiC-BP(I)

-

-

1.46

1.46

β-h-SiC-BP(I)

-

-

0.47

0.47

α-h-SiC-BP(II)

-

-

-

0.98

β-h-SiC-BP(II)

-

-

-

0.10

α-h-(SiC)3-BP

-

-

-

1.51

β-h-(SiC)3-BP

-

-

-

0.36

α-h-SiC-(BP)3

-

-

-

0.88

β-h-SiC-(BP)3

-

-

-

0.11

Figure 4. Energy band gap in eV of each structures between Γ and Y point or K point.

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Figure 5. Energy band structure of α-h-SiC-BP(II) with 0.98 eV energy band gap.

For calculated energy band structure of α-h-SiC-BP(II) as shown in Fig. 5., the energy levels are almost constant along the k direction between Y and S points, since electron can freely move parallel to y-axis. This electron freely move parallel to y-axis can also be found in β-h-SiC-BP(II), α-h-(SiC)3-BP, β-h-(SiC)3-BP, α-h-SiC(BP)3 and β-h-SiC-(BP)3 structures. In some β-form structures, the energy separation along S to X points is less than that along Γ to Y points. For example, the minimum energy difference between top of valence band and bottom of conduction band of 8 atom unit cell β-h-SiC-BP(I) between Γ and Y points is 0.47 eV while that between S and X points is 0.44 eV, as shown in Fig. 6. The values of evaluated band gap of the other structures were conducted and showed in Table 3.

Figure 6. Energy band structure of β-h-SiC-BP(I).

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Table 3. Minimum energy difference between bottom of conduction band and top of valence band (in eV) for β-form structures along S to X and Γ to Y points. atoms per

minimum energy between Ec and Ev along

Structure unit cell

S to Xs (eV)

Γ to Y (eV)

β-h-SiC-BP(I)

8

0.44

0.47

β-h-SiC-BP(I)

16

0.51

0.47

β-h-SiC-BP(II)

16

0.06

0.10

β-h-(SiC)3-BP

16

0.36

0.36

β-h-SiC-(BP)3

16

0.13

0.11

Considering β-h-SiC-BP(I) for 8- and 16-atom unit cell, the evaluated minimum energy along Γ to Y obtains the equal value of 0.47 eV while those along S to X are 0.44 and 0.51 eV, respectively. So the difference feature on the energy band along S to X is needed for further investigation. Conclusion: The band gap of graphene was verified to be 0.00 eV as that for semimetal material, while the band gap of β-form of calculated structures is much small than that of α-forms. The band gap of type II structures is slightly smaller than that of type I structures. The band gap of all evaluated h-(SiC)1-x(BP)x structures is greater than zero energy so that it becomes semiconductor. References: [1] H. Şahin1, S. Cahangirov, M. Topsakal, E. Bekaroglu, E. Akturk, R. T. Senger, and S. Ciraci1, Phys. Rev. B (2009) 80, 155453 [2] D. Sánchez-Portal, P. Ordejón, E. Artacho and J.M. Int. J. Quantum Chem (1997) 65, 453. [3] W. Kohn and L. J. Sham, Phys. Rev (1965) 140, 1133.