Polymorphic germanium films forming in slit nanopore

Computational Materials Science 127 (2017) 187–193

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Polymorphic germanium films forming in slit nanopore Yezeng He a,b, Hui Li b,⇑, Yanwei Sui a, Fuxiang Wei a, Qingkun Meng a, Jiqiu Qi a,⇑ a b

School of Materials Science and Engineering, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 4 July 2016 Received in revised form 24 October 2016 Accepted 28 October 2016 Available online 15 November 2016 Keywords: Two-dimensional Germanium film Solidification Graphene

a b s t r a c t The solidification of two-dimensional liquid germanium confined to slit nanopores with different sizes has been studied using molecular dynamics simulations. The results clearly show that the system undergoes an obvious liquid-solid phase transition to polymorphic ordered germanium films with the decrease of temperature, accompanied by dramatic change in potential energy and coordination number. Moreover, it is found that the slit size is of vital importance to the transition point and the structure of the germanium films. The results of radial distribution functions, density distribution functions and angular distribution functions suggest the obtained germanium films have various novel structures different from the graphene. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Graphene, a monolayer of carbon atoms packed into a dense honeycomb crystal structure, has arose intense research interest due to its distinctive properties such as quantum electronic transport, superior electronic structure, extremely high elasticity, and large thermal conductivity and its nearly infinite potential applications in electronics, biological engineering, filtration, lightweight/ strong composite materials, and energy storage [1–7]. However, the zero band gap poses a severe drawback for an electric field modulation suitable to graphene based logic devices, like field effect transistor (FET) basing on the opening and controlling of the band gap. Therefore, much effort has been made to investigate the graphene’s cousin, silicene, which was first pointed out by Takeda and Shiraishi and was named silicene by Guzmán-Verri et al. in 2007 [8,9]. Although many theoretical studies had predicted the existence of silicene, it was not until 2010 that the silicene with graphene-like electronic signature was first prepared experimentally on Ag(1 1 0) [10,11]. Thereafter, Ag(1 1 1) and diboride substrates have also been used to grow silicene composed of hexagonal unit cells [12,13]. Currently, silicene has been used in FET operating at room temperature with a Dirac charge mobility of
100 cm2 V1 s1 [14]. Developing new kinds of atomically thin materials and exploring their physical-chemical properties are retaining a booming interest, which is expected to have a tremendous impact on the development of future nanoelectronic devices. Recently, inspired ⇑ Corresponding authors. E-mail addresses: [email protected] (H. Li), [email protected] (J. Qi). http://dx.doi.org/10.1016/j.commatsci.2016.10.041 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.

by the fruitful results based on graphene and silicene, a lot of interest has been drawn to another group IV elemental honeycomb materials, germanene. The experimental fabrication of germanene, a 2D honeycomb lattice analogous to graphene, was first reported by Li et al. in 2014 [15]. Their results clearly show graphene growing on a Pt(1 1 1) surface exhibits a buckled configuration with a pffiffiffiffiffiffi pffiffiffiffiffiffi (3  3) superlattice coinciding with the substrate’s ( 19  19) superstructure. Soon afterwards, Dávila et al. [16] present compelling evidence of the synthesis of the germanium-based cousin of graphene on gold. Recently, continuous germanene layer has been synthesized on Al(1 1 1), covering uniformly the substrate with a large coherence [17]. The structural and electronic properties of germanene have also been determined from first principle calculations, confirming that germanene can be used in highperformance FET and other electronic devices [18–20]. In this paper, we perform molecular dynamics (MD) simulations to study the distinctive liquid and solid structure of quasi-2D germanium confined in a slit nanopore and provide evidence for the formation of germanene-like polymorph. This work may propose a possible way to fabricate the 2D germanium materials.

2. Methods In this study, MD simulations are used to investigate the structure of quasi-2D germanium films confined between two isolated and parallel walls which interacts with the atoms by generating a force on the atom in a direction perpendicular to the wall. The SW empirical potential is employed to describe the interaction between germanium atoms [21], possessing good accuracy of the

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lattice parameters and of the cohesive energy [22]. The 12-6 Lennard-Jones (LJ) potential, with a well depth e = 0.01 eV and size parameter r = 4.0 Å, is utilized to describe the atom-wall interaction. In this study, the software package LAMMPS is used to perform the simulations [23]. All simulations are carried out at zero lateral pressure, using the constant number, lateral pressure, temperature (NPT) ensemble. The Nosé-Hoover thermostat and barostat are used to control the temperature and pressure, respectively, and the velocity-verlet algorithm is used to integrate the equations of motion with a time step of 1 fs. The periodic boundary conditions are applied in the plane directions parallel to the wall. The slit size D, the vertical distance between two walls, is ranging from 7.9 to 13.4 Å. The system (liquid state) is firstly equilibrated at 3000 K, followed by a cooling process to 300 K, at a quenching rate of 0.1 K/ps. Then, the final structures are obtained after a relaxation process for 200 ps at 300 K.

3. Results and discussion To explore the structural transition of germanium film during the cooling process, we investigate the microscopic configuration at different snapshots as displayed in Fig. 1, which suggests that the structure has been dramatically transformed during the cooling process. It can be found that some ordered germanium islands randomly emerge in the disordered liquid germanium before solidification. The Ge islands in this stage can persist only for a short time and are easy to break into disordered structure inversely. With the decreasing temperature, the atom islands become increasingly stable and the size becomes increasing large. Subsequently, the islands begin to grow outwards by incorporating the disordered structure. Then, the Ge islands will encounter each other and combine to form a complete film. Fig. 2(a) shows the potential energy (PE) of germanium films confined to different slit nanopores during the cooling process. It could be found that the PE strongly dependent on the temperature and the slit size. As plotted in Fig. 2(a), the tendency of PE versus temperature for different slit sizes is similar, where the PE first drops slowly with the decrease of temperature at the beginning of cooling process and then drops sharply when the phase of system transfers from liquid to solid. For instance, at D = 7.9 Å, the PE declines by about 0.063 eV/atom from 2.617 eV/Atom to 2.680 eV/Atom. At D = 8.6 Å, the PE declines by about 0.134 eV/ atom from 2.696 eV/Atom to 2.830 eV/Atom. At D = 9.4 Å, the PE declines by about 0.345 eV/atom from 2.834 eV/Atom to 3.179 eV/Atom. At D = 13.4 Å, the PE declines by about 0.134 eV/atom from 3.178 eV/Atom to 3.321 eV/Atom. It can be easily found that the solidification temperature with the slit size firstly, but then decreases again for the largest slit size. To clarify the cause of this phenomenon, we plot the pressure along the confined direction as a function of temperature in Fig. 2(b). At D = 8.6 Å and 9.4 Å, the pressure increase steeply in the solidification stage, while at D = 7.9 Å and 11.4 Å, the pressure decreases. The changing of pressure is induced by the formation of ordered atomic islands and in turn affects the stability of the ordered structure. The increasing pressure resist the motion of atoms and further prevent the island structure breaking into disordered structure inversely, which induces the increase of solidification temperature. Therefore, the solidification temperature with the slit size firstly, but then decreases again for the largest slit size. To further clarify the structural details of germanium films, we investigate the coordination fraction as a function of temperature. In this study, the coordination number of each atom counts neighbors within a cutoff radius. To determine the cutoff value, we have investigated the structure of bulk germanium containing 8000 atoms under the periodic boundary conditions. The bulk

germanium is firstly heated to 3000 K, followed by a cooling process to 300 K, at a quenching rate of 0.1 K/ps. The structure evolution in the simulation process is shown in Fig. 3(a). It could be found that the bulk germanium undergoes an phase transition from the crystal to the liquid state during the heating process and further transforms into an amorphous state during the cooling process due to the fast cooling rate. The average coordination of liquid germanium at 1273 K is calculated as 5.62 if the cutoff radius is set to be 3.2 Å, consistent with previous experimental results [24]. For the amorphous germanium at 300 K, we also calculate the coordination number of the atoms. It is found that the average coordination is approximately 4.04 if the cutoff radius is set to be 2.8 Å, consistent with previous ab initio MD [25]. Then, we use the cutoff radii of 3.2 Å and 2.8 Å to calculate the coordination number of the confined Ge, respectively. As shown in Fig. 3(b), the cutoff radius of 3.2 Å could yield correct results for the both the liquid and solid phases of confined Ge in this study, while the cutoff radius of 2.8 Å would underestimate the coordination number of liquid germanium. Therefore, we select the cutoff radius of 3.2 Å to counting the coordination number in this study. As shown in Fig. 4, it can be found that the coordination fractions are closely related to the temperature and the slit size. At D = 7.9 Å, the liquid germanium is mainly composed of 3-fold coordinated atoms and 4-fold coordinated atoms before solidification. The average coordination first increases and then decrease slowly with the decreasing temperature. In the stage of liquid-solid phase transition (LSPT), the average coordination varies dramatically from 3.69 to 3.07. The fraction of 3-fold coordinated atoms increases sharply while the fraction of 4-fold coordinated atoms decreases steeply at the same time. At T = 300 K, nearly all atoms become 3-fold coordinated, similar to the graphene atoms. At D = 8.6 Å, in the stage of LSPT, the 4-fold coordinated atoms increase sharply and the 3-fold coordinated atoms decrease simultaneously. At T = 300 K, nearly all atoms become 4-fold coordinated. As shown in Fig. 4(c), the average coordination at D = 9.4 Å firstly increases to 4.58 before solidification and then dramatically drops to 4.11 in the stage of LSPT, due to the transition between 4fold coordinated atoms and 5-fold coordinated atoms. At D = 13.4 Å, the final structure is composed of 4-fold coordinated atoms (64%) and 5-fold coordinated atoms (34%). The microscopic structures of germanium film at 300 K are displayed in Fig. 5. It can be easily observed that the solidification structure is very different for different slit sizes. Unlike planar graphene, although the atoms is also 3-fold coordinated, the germanium film at D = 7.9 Å prefers a low-buckled (LB) hexagonal structure. The atoms in the hexagonal structure arrange alternatively in the two layers, which induces the bucked configuration as shown in Fig. 5(a). At D = 8.6 Å, another kind of bucked configuration is formed, where the atoms arrange in rows alternatively distributed in the two planes. The atoms, bonding with two atoms in the same row and two atoms in the neighbouring row, are 4-fold coordinated. The germanium films for D = 9.4 Å and 13.4 Å are composed of two and three atomic layers with hexagonal lattice, respectively. At D = 9.4 Å, the atoms in the two layers are mainly 4-fold coordinated. Previous study has reported that germanium should exhibit the crystalline b-Sn structure at such high pressure [26–28]. However, in this study, no evidence of this 6-fold coordinated tetragonal phase is seen in the model, which is in large part due to the use of the SW potential preferring to build tetrahedral structure. At D = 13.4 Å, the atoms in the outer layers are mainly 4-fold coordinated, while the atoms in the inner layers are mainly 5-fold coordinated, so that the whole film is a 4-5-4 coordinated sandwich structure. That is why the 4-fold coordinated atoms is about double of 5-fold coordinated atoms (Fig. 4(d)). Rather different from the 3-fold coordination dominated graphite, the hexagonal germanium films have few atoms with the coordination

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Fig. 1. Structural evolution of germanium film in cooling process. (a–c) D = 7.9 Å; (d–f) D = 8.6 Å; (g–i) D = 9.4 Å; (j–l) D = 13.4 Å.

number of 3. This is because the germanium atoms between two layers are combined by r bonds rather than the weaker p bonds. To further distinct the structural difference of germanium films at different slits, we have plotted the radial distribution functions g (r) at 300 K in Fig. 6(a). At D = 7.9 Å, the abscissa values of the first three peak are r1 = 2.45 Å, r2 = 4.15 Å and r3 = 4.75 Å. The ratios r2/ r1 and r3/r1 are 1.694 and 1.939 respectively, slightly smaller than the values (1.732 and 2.0) in perfectly flat graphene. This is because the monolayer germanium film has a low-buckled (LB) hexagonal structure. At D = 8.6 Å, it is worth noting that there is a new peak emerging between the first two peaks at D = 7.9 Å. The abscissa values of the first three peak are r1 = 2.55 Å, r2 = 3.65 Å, r3 = 4.25 Å and r4 = 5.05 Å. The ratios r2/r1, r3/r1 and r4/r1 are 1.431, 1.667 and 1.980, respectively. The value of r2/r1 approximates 1.414, suggesting the abscissa value of the second peak represents the diagonal distance in a four-atom square in Fig. 5(b). At D = 9.4 Å, the abscissa values of the first three peak are r1 = 2.55 Å, r2 = 3.55 Å, r3 = 4.35 Å and r4 = 5.05 Å. The ratios r2/r1, r3/r1 and r4/r1 are 1.392, 1.706 and 1.980, respectively.

Here, the abscissa value of the second peak represents the diagonal distance in a four-atom square between two layers. The ratios r2/r1 and r3/r1 are both larger than those at D = 7.9 Å, indicating the buckled degree of bilayer germanium is quite smaller than the monolayer germanium, as well as the trilayer germanium at D = 13.4 Å. Fig. 6(b) shows the density profile qz at different silts, which is measured by calculating the atomic number density within a thin slice with the thickness of 0.01 Å in the z direction. The results clearly suggest a structural correlation between the liquid and solid germanium. At D = 7.9 Å, 8.6 Å and 9.4 Å, the density distribution functions of the liquid and solid germanium both have two peaks, indicating the two phases are both composed of two atomic layers, although the density peaks of liquid germanium are rather smooth than that of the solid one. At 300 K, the spacing between two layers is about 0.6 Å, 1.4 Å and 2.4 Å at D = 7.9 Å, 8.6 Å and 9.4 Å, respectively. At D = 13.4 Å, the density distribution functions have three peaks, indicating the germanium film is both composed of three atomic layers with the spacing of 2.6 Å. Based on the above, one can draw a conclusion that the structural

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Fig. 2. (a) Potential energy per atom and (b) pressure along the confined direction as a function of temperature for the liquid germanium films confined to slit nanopores with different sizes.

Fig. 3. (a) Structural evolution of bulk germanium containing 8000 atoms. (b) Average coordination of liquid (1800 K) and solid (300 K) confined germanium using the cutoff radius of 2.8 Å and 3.2 Å, respectively.

difference of germanium film has already appeared before solidification and the layer number is determined by the slit size. Fig. 7 represents the calculated angular distribution functions within a radius of 3 Å. It is found that the bond angle distribution varies with the slit size. At D = 7.9 Å, the distribution of bond angle ranges from 100° to 130° and there is an obvious spike around 113°. It is worth noting that the band angle 114° locates at

between the 120° in the planar graphene-like structure and the 109.5° in the diamond-like structure. According to the previous DFT calculations [20,29], the germanium film has a larger interatomic distance than graphene, which weakens the p-p overlaps. However, the stability of LB structures is maintained by puckering induced dehybridization. As a result, the germanium atoms here are more likely to maintain orbit between sp3-like hybrid orbit

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Fig. 4. Fractions of atoms with different coordination number and average coordination as a function of temperature. (a) D = 7.9 Å; (b) D = 8.6 Å; (c) D = 9.4 Å; (d) D = 13.4 Å.

Fig. 5. Solidification structure for different slit sizes. (a) D = 7.9 Å; (b) D = 8.6 Å; (c) D = 9.4 Å; (d) D = 13.4 Å. The atoms in (a) and (b) are colored green and yellow to distinguish atoms in different planes. The blue atoms in (d) indicate the 5-fold coordinated atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 6. (a) Radial distribution functions g(r) and (b) Density distribution functions along the confined direction of germanium films.

germanium film has a graphene-like structure and the two layers connect each other by vertical bonds. At D = 13.4 Å, the bond angel distribution is quite similar with the case at D = 9.4 Å, except a peak at approximately 170° indicating the bonds connecting three layers. 4. Conclusion In conclusion, MD simulation has predicted an observable structural transition of germanium film confined in different slit nanopores from disordered liquid to polymorphic ordered germanium films by reducing the temperature. The results of the potential energy, coordination number, radial distribution functions, density distribution functions and angular distribution functions clearly show that the slit size not only affects the transition point, but also influences the structure of the germanium films. Both the liquid and solid germanium films may have various phases at slit nanopores with different sizes. These findings predict various 2D germanium materials quite different from the graphene. Acknowledgements The authors would like to acknowledge the support by the Fundamental Research Funds for the Central Universities (No. 2015QNA03), the National Natural Science Foundation of China (Grant Nos. 51271100 and 51501221), and the China Postdoctoral Science Foundation (No. 2016M591945). References

Fig. 7. Angular distribution functions of germanium films at 300 K.

and sp2-like hybrid orbit. The LB structure may makes the germanium film possible to open a band gap when a vertical electric field is applied, which can be used to fabricate an FET at room temperature, like silicene [14]. At D = 8.6 Å, there are three obvious peaks at approximately 90°, 117° and 173°, corresponding to the square, buckled and line structure, respectively. At D = 9.4 Å, the two peaks at approximately 90° and 120° indicates that each layer of the

[1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science 306 (2004) 666–669. [2] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438 (2005) 197–200. [3] J.S. Bunch, A.M. van der Zande, S.S. Verbridge, I.W. Frank, D.M. Tanenbaum, J.M. Parpia, H.G. Craighead, P.L. McEuen, Electromechanical resonators from graphene sheets, Science 315 (2007) 490–493. [4] S.V. Morozov, K.S. Novoselov, M.I. Katsnelson, F. Schedin, D.C. Elias, J.A. Jaszczak, A.K. Geim, Giant intrinsic carrier mobilities in graphene and its bilayer, Phys. Rev. Lett. 100 (2008) 016602. [5] K.S. Kim, Y. Zhao, H. Jang, S.Y. Lee, J.M. Kim, K.S. Kim, J.-H. Ahn, P. Kim, J.C. Choi, B.H. Hong, Large-scale pattern growth of graphene films for stretchable transparent electrodes, Nature 457 (2009) 706–710.

Y. He et al. / Computational Materials Science 127 (2017) 187–193 [6] J.H. Seol, I. Jo, A.L. Moore, L. Lindsay, Z.H. Aitken, M.T. Pettes, X. Li, Z. Yao, R. Huang, D. Broido, N. Mingo, R.S. Ruoff, L. Shi, Two-dimensional phonon transport in supported graphene, Science 328 (2010) 213–216. [7] E. Muñoz, J. Lu, B.I. Yakobson, Ballistic thermal conductance of graphene ribbons, Nano Lett. 10 (2010) 1652–1656. [8] K. Takeda, K. Shiraishi, Theoretical possibility of stage corrugation in Si and Ge analogs of graphite, Phys. Rev. B 50 (1994) 14916–14922. [9] G.G. Guzmán-Verri, L.C. Lew Yan Voon, Electronic structure of silicon-based nanostructures, Phys. Rev. B 76 (2007) 075131. [10] B. Aufray, A. Kara, S. Vizzini, H. Oughaddou, C. Léandri, B. Ealet, G. Le Lay, Graphene-like silicon nanoribbons on Ag(1 1 0): a possible formation of silicene, Appl. Phys. Lett. 96 (2010) 183102. [11] P. De Padova, C. Quaresima, C. Ottaviani, P.M. Sheverdyaeva, P. Moras, C. Carbone, D. Topwal, B. Olivieri, A. Kara, H. Oughaddou, B. Aufray, G. Le Lay, Evidence of graphene-like electronic signature in silicene nanoribbons, Appl. Phys. Lett. 96 (2010) 261905. [12] D. Chiappe, C. Grazianetti, G. Tallarida, M. Fanciulli, A. Molle, Local electronic properties of corrugated silicene phases, Adv. Mater. 24 (2012) 5088–5093. [13] A. Fleurence, R. Friedlein, T. Ozaki, H. Kawai, Y. Wang, Y. Yamada-Takamura, Experimental evidence for epitaxial silicene on diboride thin films, Phys. Rev. Lett. 108 (2012) 245501. [14] L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle, D. Akinwande, Silicene field-effect transistors operating at room temperature, Nat. Nanotech. 10 (2015) 227–231. [15] L.F. Li, S.Z. Lu, J.B. Pan, Z.H. Qin, Y.Q. Wang, Y.L. Wang, G.Y. Cao, S.X. Du, H.J. Gao, Buckled germanene formation on Pt(1 1 1), Adv. Mater. 26 (2014) 4820– 4824. [16] M.E. Dávila, L. Xian, S. Cahangirov, A. Rubio, G. Le Lay, Germanene: a novel two-dimensional germanium allotrope akin to graphene and silicene, New J. Phys. 16 (2014) 095002.

193

[17] M. Derivaz, D. Dentel, R. Stephan, M.C. Hanf, A. Mehdaoui, P. Sonnet, C. Pirri, Continuous germanene layer on Al(1 1 1), Nano Lett. 15 (2015) 2510–2516. [18] Z.Y. Ni, Q.H. Liu, K.C. Tang, J.X. Zheng, J. Zhou, R. Qin, Z.X. Gao, D.P. Yu, J. Lu, Tunable bandgap in silicene and germanene, Nano Lett. 12 (2012) 113–118. [19] N.J. Roome, J.D. Carey, Beyond graphene: stable elemental monolayers of silicene and germanene, ACS Appl. Mater. Interfaces 6 (2014) 7743–7750. [20] C.-C. Liu, W. Feng, Y. Yao, Quantum spin Hall effect in silicene and twodimensional germanium, Phys. Rev. Lett. 107 (2011) 076802. [21] Z.Q. Wang, D. Stroud, Monte Carlo studies of liquid semiconductor surfaces: Si and Ge, Phys. Rev. B 38 (1988) 1384. [22] P. S´piewak, M. Muzyk, K.J. Kurzydłowski, J. Vanhellemont, K. Młynarczyk, P. Wabin´ski, I. Romandic, Molecular dynamics simulation of intrinsic point defects in germanium, J. Cryst. Growth 303 (2007) 12–17. [23] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995) 1–19. [24] P.S. Salmon, A neutron diffraction study on the structure of liquid germanium, J. Phys. F: Met. Phys. 18 (1988) 2345–2352. [25] G. Kresse, J. Hafner, Ab initio molecular-dynamics simulation of the liquidmetal - amorphous-semiconductor transition in germanium, Phys. Rev. B 49 (1994) 14251. [26] S.D. Crockett, G. De Lorenzi-Venneri, J.D. Kress, S.P. Rudin, Germanium multiphase equation of state, J. Phys.: Conf. Ser. 500 (2014) 032006. [27] E.D. Chisolm, S.D. Crockett, D.C. Wallace, Test of a theoretical equation of state for elemental solids and liquids, Phys. Rev. B 68 (2003) 104103. [28] V.B. Prakapenka, A. Kubo, A. Kuznetsov, A. Laskin, O. Shkurikhin, P. Dera, M.L. Rivers, S.R. Sutton, Advanced flat top laser heating system for high pressure research at GSECARS: application to the melting behavior of germanium, High Press. Res. 28 (2008) 225–235. [29] S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, S. Ciraci, Two- and onedimensional honeycomb structures of silicon and germanium, Phys. Rev. Lett. 102 (2009) 236804.