Silicene and Germanene: A First Principle Study of ...

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Journal of Computational and Theoretical Nanoscience Vol. 11, 1–8, 2014

Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation Shyam Trivedi1 2 ∗ , Anurag Srivastava1 , and Rajnish Kurchania2 1

Advanced Materials Research Group, Computational Nanoscience and Technology Lab ABV-IIITM, Gwalior 474010, India 2 Department of Physics, Maulana Azad National Institute of Technology (MANIT), Bhopal 462051, India Using first principle calculations we have explored the structural and electronic properties of silicene (silicon analogue of graphene) and germanene (germanium analogue of graphene). The structural optimization reveals that buckled silicene and germanene are more stable than their planar counterparts by about 0.1 and 0.35 eV respectively. In comparison to planar graphene (buckling parameter = 0 Å) the germanium sheet is buckled by 0.737 Å and silicene by 0.537 Å but both have similar electronic structure with zero band gap at K point as that of graphene. Further we investigated the effects of complete hydrogenation on these materials by considering different geometrical configurations (chair, boat, table and stirrup) and found that chair-like structure has the highest binding energy per atom in comparison to other structures. Hydrogenated silicene (silicane) shows an indirect band gap of 2.23 eV while hydrogenated germanene (germanane) possess a direct band gap of 1.8 eV. Energy.

1. INTRODUCTION Graphene, a two dimensional honeycomb structure of carbon atoms has been extensively studied in the last few years because of its novel electronic properties. Since it is difficult to incorporate graphene in today’s silicon based electronic industry, much interest has been generated by other group IV elements like silicon and germanium in theoretical study.1 2 Germanene still remains a hypothetical material although ultrathin Ge nanobelts bonded with nanotubes have been fabricated and characterized by Han et al.3 Silicene stripes have been experimentally grown over Ag (110)4 5 and on zirconium diboride substrate.6 Earlier density functional theory (DFT) studies have shown that buckled hexagonal sheets of silicon and germanium are more stable than their planar arrangements.7 This indicates that barring carbon all group IV elements have a tendency to avoid sp2 hybridization. Corrugated structures of Si and Ge are promising materials in the design of field effect transistors as application of vertical electric fields can open and control the band gaps.8 9 Because of low buckled structure and greater spin orbit coupling, silicene can ∗

Author to whom correspondence should be addressed.

J. Comput. Theor. Nanosci. 2014, Vol. 11, No. 3

also be an important material for spintronics as Quantum spin Hall Effect in silicene has been reported by Liu et al.10 Hydrogen-passivated graphene (graphane) has attracted much attention in theoretical studies because of drastic changes in band gaps that occur upon hydrogenation.11 It has been synthesized in laboratory and the hydrogenation process is shown to be reversible thereby making it a potential candidate for hydrogen storage.12 Safe and efficient storage of hydrogen is a concern and various nanomaterials have been explored computationally so that hydrogen storage with high gravimetric and volumetric density becomes a reality.13 Hydrogenation of carbon and SiC nanotubes and their subsequent use in hydrogen storage have also been extensively studied in theory.14–16 The structure and electronic properties of different geometrical configurations of graphane (chair, table and boat) have been theoretically investigated by AlZahrani et al.17 finding a direct band gap of 3.9 eV and a buckling parameter of 0.46 Å. A new isomer of graphane having stirruplike structure is also explored by Bhattacharya et al.18 Osborn et al.19 have studied the geometry and energetics of partially hydrogenated silicene and found that adsorption energy of hydrogen on silicene increases with the hydrogenation ratio. Zhang et al.20 have investigated the

1546-1955/2014/11/001/008

doi:10.1166/jctn.2014.3428

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Keywords: Silicene, Germanene, Hydrogenation, First Principle, Electronic Structure, Binding

Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation

properties of half and fully hydrogenated chair-like structures of silicene and reported that the former acts like a ferromagnetic semiconductor. Houssa et al.21 have explored the electronic properties of hydrogenated silicene and germanene using many body perturbation methods and found that germanane has a direct average energy gap of 3.2 eV. In view of above, we thought it pertinent to explore the understanding of structural and electronic behaviour of silicon/germanium sheets and calculate the binding energies of different hydrogenated crystal geometries in order to investigate the change in bandstructure and density of states due to hydrogenation.

2. COMPUTATIONAL DETAILS

exchange correlation functionals along with double zeta single polarized basis sets. Self-consistent force optimizations were performed till Hellmann-Feynman force between the atoms and the associated stress of the lattice became less than 0.0025 eV/Å and 0.005 eV/Å3 respectively. The hexagonal ‘c’ parameter was kept very large (42.32 Å) so that inter layer periodic interactions can be treated as negligible. For Brillouin zone integration a mesh of 21×21×1k-points were used. A mesh cut off of 600 eV was found to be sufficient for the convergence of the plane wave function for both silicene and germanene crystals. Monkhorst-Pack scheme25 using a k-point grid of 11 × 11 × 1 was chosen for calculation of density of states of both silicene and germanene.

3. RESULTS AND DISCUSSION 3.1. Silicene and Germanene To perform the structural analysis of planar silicene, hexagonal graphene crystal structure was taken into consideration and in-plane atomic bond length of Si Si

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Structural optimization and calculations were performed using DFT based ab-initio approach implemented in Atomistix Toolkit-Virtual Nanolab (ATK-VNL) provided by Quantumwise.22 Local Density approximation (LDA) with Perdew and Zunger23 type parameterization and generalized-gradient approximation (GGA) with Perdew– Burke–Ernzerhof (PBE) parameterization24 were used as

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Fig. 1. (a) Energy variation with bond length for planar silicene for fixed lattice a = 3910 Å. (b) Energy variation with lattice for buckled silicene ( kept at 0.537 Å). (c) Energy variation with bond length for planar germanene for fixed lattice a = 4130 Å (d) Energy variation with lattice for buckled germanene ( kept at 0.737 Å).

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was varied from 2.10 Å to 2.35 Å for each of the lattice parameter ranging from 3.75 Å to 4.0 Å. The total energy was calculated for each configuration using both LDA-PZ and GGA-PBE exchange correlation methods. The lattice parameter at which minimum energy and stable bond length for planar silicene is obtained was selected. At this fixed value of lattice, energy variation as a function of bond length is plotted for planar silicene as shown in Figure 1(a). Here we have shown energy curves corresponding to GGA-PBE method only. To investigate the buckled structure of silicene one of the atom was made out of plane initially by 0.5 Å and optimization routine was run till minimum force and lattice stress condition is met. Corresponding to the minimum obtained energy, the bond length and buckling parameter of the crystal ( = 0537 Å) was calculated. In Figure 1(b) we have shown the energy variation with lattice for buckled silicene crystal. A similar procedure was used for analysis of planar and buckled germanene and the corresponding energy curves are shown in

Figures 1(c)–(d). Looking at the total energy values (for GGA-PBE) listed in Table I and energy curves of Figure 1 we note that the buckled structure of both silicene and germanene is more stable than its planar arrangement by 0.1 eV and 0.35 eV respectively, this is in agreement with earlier predictions.7 The phonon dispersion calculations performed by Cahangirov et al.26 also shows that planar structure is not stable. For comparative understanding the structure, band diagram and Fermi velocities of silicene, germanene and graphene are shown in Figure 2. Since they all are metallic in nature having zero band gap with linear dispersion at the K point, their Fermi velocities can be calculated through the E–k curve by using the following relationship: vf =

1 dE dk

(1)

where h is the reduced Planck’s constant. The calculated Fermi velocity of graphene and silicene is of the order of

Table I. Lattice parameter, bond length, total energy, band gap and buckling parameter for different arrangements of silicene and germanene. Properties SILICENE Planar LDA-PZ

Buckled LDA-PZ

GGA-PBE

Hydrogenated (chair-like) LDA-PZ GGA-PBE GERMANENE Planar LDA-PZ GGA-PBE Buckled LDA-PZ

GGA-PBE Hydrogenated (chair-like) LDA-PZ GGA-PBE

Bond length (Å)

Total energy (eV)

Band gap (eV)

Buckling parameter (Å)

387 384532 383033

224 22133

−355941

0

0

391

2252

−358213

0

0

3804 38557 383126 380832 382031

2265 22477 22477

−356039

0

0554 04426 05330 04431 04432

385 388120

2287 229819

−3583

0 2132

3826 382031 3876

2327

−388422

2353

2031 1233 2227

0733 07231 0727

388420

235919

−391262

23620

073619

401 413

231 2383

−559351 −561735

0 0

0 0

3938 38907 4031 394234 396835 4034

2376 23317

−559652

0

2443

−562085

0

0691 07131 063534 064535 0737

3876

237

−591463

3908

2401

−594308

1875 1531 1812

0782 06931 0821


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GGA-PBE

a (Å)

0537 054019

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Fig. 2.

Structure, bandstructure with Fermi velocities of silicene germanene and graphene.

106 and 105 m/s respectively while velocity in germanene lies somewhere in the middle. This result is in confirmation with Refs. [26 and 27]. At low values of energy, electrons in these structures behave like massless Dirac-fermions. Fermi velocity in silicene is less than half of the value reported for graphene.28 Theoretical calculations on effective electron mass in quantum wells, wires and superlattices have been performed by Bose et al.29 The higher the Fermi velocity the lower is the effective mass of electrons moving through the periodic structure. Since graphene is sp2 hybridized, the coupling between the nearest neighbour atoms is very strong and electrons can easily tunnel from one atom to another which may explain the larger velocities of electrons in graphene compared to silicene and germanene. The band structure of graphene, buckled germanene, planar and buckled silicene are quite similar but for planar germanene the Dirac point is slightly raised above the Fermi level (shown in Fig. 3) making it poorly metallic in character. This kind of ‘raised’ K-point band structure for planar germanene was also reported in Refs. [2, 26].

Fig. 3.

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Bandstucture of planar germanene.

However on structural transformation from planar to buckled, this crossing point shifts down to Fermi level. Germanene structure is more buckled than silicene. The buckling parameter for silicene was calculated to be 0.537 Å and for germanene it was 0.737 Å (GGA results). Our results of buckling parameter of silicene are in agreement with Ding and Ni30 but slightly higher than the values reported in Refs. [26, 31, and 32]. This may be due to the difference in the underlying methods of the tool used for performing simulation. The bond lengths, buckling parameter and band gaps are listed in Table I along with values obtained in previous works. The bond lengths in silicene and germanene are longer in comparison to graphene because of large size of Si and Ge atoms. Silicon has a preference towards sp3 hybridization than 2 sp . Figure 4(a) shows sp2 hybridized silicon in a planar

Fig. 4. (a) sp2 hybridized planar silicene (b) buckled silicene having sp3 hybridization.


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Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation Table II. Binding energy and bond lengths of different hydrogenated geometries of silicene and germanene. SILICANE configurations Table Chair Boat Stirrup GERMANANE configurations Table Chair Boat Stirrup

B.E (eV/atom)

Si

Si bond length (Å)

4426 471 4639 4528

2.333 2.353 2.346, 2.416 2.331, 2.364

B.E (eV/atom)

Ge Ge Bond length (Å) 2.524 2.401 2.4, 2.489 2.419, 2.429

3768 4069 4019 3904

3.2. Effect of Hydrogen-Passivation To analyse the role of hydrogenation we considered four different geometries of full-hydrogenated structures of silicene and germanene as shown in Figure 5. The band gap is calculated for the arrangement which has highest binding energy. The table structure has all the hydrogen atoms attached on one side of the sheet. The chair and the boat conformer has H atoms alternating in (1up-1down) and (2up-2down) fashion on either side of Si-plane (or Geplane) respectively. The stirrup-like model has three consecutive H atoms of each hexagon alternating on both sides of sheet (3up-3down). The binding energy in eV/atom for each of these configurations has been calculated (using

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Fig. 5. Various geometrical silicene/germanene.

configurations

for

hydrogenated

structure similar to graphene. The lobes of each atom are perpendicular to the plane of the silicon sheet and this results in formation of bonds with the nearest neighbours leading to conducting nature of the sheet. However in a buckled sp3 hybridized structure shown in Figure 4(b) the lobes of neighbouring atoms point in opposite directions so the bonds can only be formed with the second nearest neighbour rather than the first nearest neighbour. The sp2 hybridized orbitals get slightly dehybridized into sp3 -like orbital which causes weakening of bonds leading to buckled structure of silicene. The same reason could be accounted for buckled structure of germanene as well. J. Comput. Theor. Nanosci. 11, 1–8, 2014

Fig. 6. Optimized structure of chair like configuration for (a) silicane (b) germanane.

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Fig. 7.

Bandstructure of (a) silicane and (b) germanane.

GGA) by the following relation:

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BE =

Econfig − nEC − mEH n + m

(2)

where E(config) is the total energy of the geometry under consideration. EC and EH are the total energies of single carbon and hydrogen atom respectively, while n and m are the number of carbon and hydrogen atoms respectively in a unit cell under consideration. The binding energies and bond lengths for all four configurations are listed in Table II which clearly indicates that the chair conformer is the most stable of them followed by the boat arrangement. Two different Si Si bond

Fig. 8.

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lengths exist in the stirrup structure. The bond between silicon atoms which have hydrogen atoms lying over the plane of hexagon (3-up) has a length of 2.364 Å and those which contain hydrogen atom lying below the plane of hexagon (3-down) has a length of 2.331 Å. In the same way the boat arrangement also has two bond lengths. The optimized structure (with GGA values) of chair-like arrangement of silicane and germanane is shown in Figure 6. Hydrogenation of the silicene and germanene sheets causes the Si Si and Ge Ge bond lengths to increase in comparison to the normal sheet structure. The bond angles are very much close to tetrahedral angle 109.5 showing that sp3 -like arrangement is preferred for

(a) DOS for germanene (b) projected DOS for hydrogenated germanene (c) DOS for silicene (d) projected DOS for hydrogenated silicene.


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4. SUMMARY AND CONCLUSION We have performed a step by step structural and band gap analysis of sheets of silicon and germanium finding that buckled structure is energetically more favourable than the planar one. The band structure of buckled silicene and germanene is similar to that of graphene. The chair-like hydrogenated arrangement has the highest binding energy in comparison to boat, table and stirrup structures. Silicene and germanene show a metal to semiconductor transformation upon hydrogenation which is evident from band gap opening and change in density of states. DFT calculations generally underestimate the bandgap by 30–50%36 but it can be safely estimated that the correct band gap in silicane is less than that of graphane lying in 3.5–4 eV range and for germanane it is close to 3 eV making it a suitable material to be used in optoelectronic devices operating in blue-violet range of electromagenetic spectrum. In future these Quantum-Confined Optoelectronic Materials37 J. Comput. Theor. Nanosci. 11, 1–8, 2014

may prove to be useful for the emerging nanoelectronic industry. Acknowledgments: Shyam Trivedi is thankful to the Ministry of Human Resource Development (MHRD), Government of India for GATE scholarship and also to the Advanced Materials Research Group, ABV-IIITM Gwalior for providing infrastructural support.

References 1. G. G. Guzmán-Verri and L. C. L. Y. Voon, Phys. Rev. B 76, 075131 (2007). 2. S. Lebègue and O. Eriksson, Phys. Rev. B 79, 115409 (2009). 3. W. Q. Han, L. Wu, Y. Zhu, and M. Strongin, Nano Lett. 5, 1419 (2005). 4. P. De Padova, C. Quaresima, C. Ottaviani, P. M. Sheverdyaeva, P. Moras, C. Carbone, D. Topwal, B. Olivieri, A. Kara, H. Oughaddou, B. Aufray, and G. L. Lay, Appl. Phys. Lett. 96, 261905 (2010). 5. P. De Padova, C. Quaresima, B. Olivieri, P. Perfetti, and G. L. Lay, Appl. Phys. Lett. 98, 081909 (2011). 6. A. Fleurence, R. Friedlein, Y. Wang, and Y. Yamada-Takamura, Symposium on Surface and Nano Science (SSNS), Shizukuishi, Japan (2011). 7. K. Takeda and K. Shiraishi, Phys. Rev. B 50, 14916 (1994). 8. Z. Ni, Q. Liu, K. Tang, J. Zheng, J. Zhou, R. Qin, Z. Gao, D. Yu, and J. Lu, Nano Lett. 12, 113 (2012). 9. N. D. Drummond, V. Zólyomi, and V. I. Fal’ko, Phys. Rev. B 85, 075423 (2012). 10. C.-C. Liu, W. Feng, and Y. Yao, Phys. Rev. Lett. 107, 076802 (2011). 11. J. O. Sofo, A. Chaudhari, and G. D. Barber, Phys. Rev. B 75, 153401 (2007). 12. D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, and K. S. Novoselov, Science 323, 610 (2009). 13. M. Li, Q. Tang, and Z. Zhou, J. Comput. Theor. Nanosci. 8, 2398 (2011). 14. K. Xue and Z. Xu, J. Comput. Theor. Nanosci. 8, 853 (2011). 15. Souptik Mukherjee and Asok K. Ray, J. Comput. Theor. Nanosci. 5, 1210 (2008). 16. V. J. Surya, K. Iyakutti, M. Rajarajeswari, and Y. Kawazoe, J. Comput. Theor. Nanosci. 7, 552 (2010). 17. A. Z. AlZahrani and G. P. Srivastava, Appl. Surf. Sci. 256, 5783 (2010). 18. A. Bhattacharya, S. Bhattacharya, C. Majumder, and G. P. Das, Phys. Rev. B 83, 033404 (2011). 19. T. H. Osborn, A. A. Farajian, O. V. Pupysheva, R. S. Aga, and L. C. L. Y. Voon, Chem. Phys. Lett. 511, 101 (2011). 20. P. Zhang, X. D. Li, C. H. Hu, S. Q. Wu, and Z. Z. Zhu, Phys. Lett. A 376, 12301233 (2012). 21. M. Houssa, E. Scalise, K. Sankaran, G. Pourtois, V. V. Afanas’ev, and A. Stesmans, Appl. Phys. Lett. 98, 223107 (2011). 22. www.quantumwise.com. 23. J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). 24. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 25. H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976). 26. S. Cahangirov, M. Topsakal, E. Aktürk, H. Sahin, ¸ and S. Ciraci, Phys. Rev. Letters 102, 236804 (2009). 27. H. Behera and G. Mukhopadhyay, arXiv:1201.1164v1[condmat.mes-hall].

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these hydrogenated structures. The calculated Si Si and Si H bond lengths in silicane are 2.353 Å and 1.51 Å respectively along with a vertical buckling of 0.727 Å, a good agreement with Ref. [19]. Germanane gets buckled by 0.821 Å and as expected its bond length, buckling parameter are greater in magnitude in comparison to that of silicane. In general the buckling parameter for silicene and germanene increase due to hydrogenation and the structure becomes more stable. Hydrogen passivation leads to a remarkable change in the band structure as compared to ideal silicene and germanene (Fig. 7). A band gap opens up considerably turning them into semiconductor materials. Silicane has an indirect band gap of 2.23 eV between and M point while germanane has direct band gap of 1.8 eV at point. The opening of band gap due to hydrogenation is also reflected in density of states shown in Figures 8(a)–(d). For germanene the density of states starts to rise beyond the Fermi level and it has distinct features both in occupied and unoccupied energy regions. In the occupied region germanene has a sharp peak at Ef − 2 eV while in the unoccupied region large states are available particularly at Ef + 394 eV, Ef + 278 eV and Ef + 071 eV. Upon hydrogen passivation of germanene the and ∗ states are removed and a finite band gap opens. Figure 8(b) shows the projected density of states for germanane. A strong peak is present at Ef − 39 eV and Ef − 409 eV in the occupied region contributed mainly by H s and Ge p states. In the unoccupied range large density of states are available at Ef + 328 eV and Ef + 391 eV largely because of the contribution from Ge p, Ge d and H s states. Similarly, silicane also shows an opening of band gap in Figure 8(d) along with peak DOS at Ef + 387 eV and Ef − 398 eV in the unoccupied and occupied region respectively, contributed by Si p and H s states.

Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation 28. A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007). 29. P. K. Bose, N. Paitya, S. Bhattacharya, D. De, S. Saha, K. M. Chatterjee, S. Pahari, and K. P. Ghatak, Quantum Matter 1, 89 (2012). 30. Y. Ding and J. Ni, Appl. Phys. Lett. 95, 083115 (2009). 31. L. C. L. Y. Voon, E. Sandberg, R. S. Aga, and A. A. Farajian, Appl. Phys. Lett. 97, 163114 (2010). 32. H. Behera and G. Mukhopadhyay, AIP Conf. Proc. (2010), Vol. 1313, pp. 152–155.

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33. M. Houssa, G. Pourtois, M. M. Heyns, V. V. Afanas’ev, and A. Stesmans, J. Electrochem. Soc. 158, H107 (2011). 34. H. Behera and G. Mukhopadhyay, AIP Conf. Proc. (2010), Vol. 1349, pp. 823–824. 35. Q. Pang, Y. Zhang, J.-M. Zhang, V. Ji, and K.-W. Xu, Mater. Chem. Phys. 130, 140 (2011). 36. R. M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, Cambridge (2004). 37. K. P. Ghatak, S. Bhattacharya, A. Mondal, S. Debbarma, P. Ghorai, and A. Bhattacharjee, Quantum Matter 2, 25 (2013).

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Received: 25 January 2013. Accepted: 20 February 2013.

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