Molecular Dynamics Study on Ductile Behavior of SiC during Nanoindentation

Transcription

1 Tribology Online, 11, 2 (2016) ISSN DOI /trol Article Molecular Dynamics Study on Ductile Behavior of SiC during Nanoindentation Takuya Hanashiro 1), Ken-ichi Saitoh 2)*, Tomohiro Sato 2), Kenji Nishimura 3), Masanori Takuma 2) and Yoshimasa Takahashi 2) 1) Graduate School of Science and Engineering, Kansai University Yamate-cho, Suita-shi, Osaka , Japan 2) Department of Mechanical Engineering, Kansai University Yamate-cho, Suita-shi, Osaka , Japan 3) National Institute of Advanced Industrial Science and Technology (AIST) Namiki, Tsukuba-shi, Ibaraki , Japan * Corresponding author: saitou@kansai-u.ac.jp ( Manuscript received 31 August 2015; accepted 03 January 2016; published 30 April 2016 ) ( Presented at the International Tribology Conference Tokyo 2015, September, 2015 ) In order to clarify the plastic deformation mechanism of silicon carbide in cubic phase (3C-SiC), molecular dynamics (MD) simulations are performed on the nanoindentation using a spherical indenter. Transition from elastic deformation to plastic deformation has been confirmed by the phenomenon called pop-in in the load-displacement curves during nanoindentation. Dislocations on {1 1 1} slip planes are found during indentation. In order to analyze internal defects, common neighbor analysis (CNA) is slightly modified so that it is suitable for the analysis of slips of zinc-blend structure. In our method, the CNA is applied separately to sub-lattice of Si or C in the same SiC. By this method, structural changes are confirmed in a region with the shape of square pyramid when the pop-in behavior occurs. By measuring the atomic distances along the region of misalignment, it was confirmed that there is certainly atomic sliding by crystalline slip. Furthermore, it is found that, with increase of loading, dislocation loops spread along {1 1 1} slip planes. Keywords: molecular dynamics, silicon carbide, nanoindentation, plastic deformation 1. Introduction Today, electric devices such as power converter are required to improve their performance. For the purpose of energy-saving and high efficiency, downsizing and enhancement in reliability are pursued. Silicon carbide (SiC) has attracted much interest of many researchers because of its high performance compared to simple silicon (Si) which has been widely used as a semiconductor. However, in manufacturing process (forming, cutting or polishing etc.), it is difficult to control the deformation of SiC. It is because SiC is very hard material and is chemically and electrically stable. Besides, as the material used for the electronic devices, it is necessary to process with precision in order to increase the reliability. Therefore, it is essentially important to understand its mechanical properties from the atomic level. Such knowledge is sure to lead to the development of micro- and nano-sized electronic devices. Basically, SiC consists of a covalent bond between Si and C, so it has a variety of crystal structures. In particular, cubic-structured SiC (i. e. 3C-SiC) which is cubic as to the unit cell has isotropy and symmetry in mechanical properties. In addition, the change of performance due to temperature variation is small, so it has an advantage as a material for the electronic device. Therefore, a lot of experiments of crystal growth and simulation of defects of 3C-SiC have been studied well [1,2]. But, the mechanical properties of SiC in the geometry of thin film as usually used in electronic device is unclear. From a standpoint of experimental approach, nanoindentation is known as an excellent technique to obtain elastic-plastic (ductile) properties of thin films. In this field, as theoretical approach in advance, molecular dynamics (MD) simulation has been applied to the nanoindentation of 3C-SiC surface. A pyramidal-shaped Vickers indenter and Vashishta s interatomic potential were used there, and it was confirmed that there occur dislocation loops inside SiC specimen [3]. In the present study, we also investigate behavior of SiC in nanoindentation using more realistic spherical indenter by MD simulation. Compared to Si crystal, atomic mechanism of plasticity (ductile behavior) of SiC is unclear [4]. We focus on the onset of slip deformation in SiC and its expanding Copyright 2016 Japanese Society of Tribologists 183

2 Takuya Hanashiro, Ken-ichi Saitoh, Tomohiro Sato, Kenji Nishimura, Masanori Takuma and Yoshimasa Takahashi process by means of MD analysis. Additionally, an effective and original method based on common neighbor analysis (CNA) to detect defected atoms is proposed here. 2. Theory and simulation method 2.1. Calculation conditions and simulation model The present study is utilizing a parallel MD open-source software package called LAMMPS [5]. As visualization software, we use OVITO [6]. The MD model of nanoindentation specimen made up of SiC is shown in Fig. 1. Details of the simulation conditions are shown in Table 1. The crystal structure of SiC is zinc-blende whose atomic positions are the same as those in diamond structure. The bottom layer of the specimen in the pushing direction is constrained to be zero velocity. Since the Berkovich indenter tip often used in nanoindentation has a certain radius of curvature in nanoscale, it is always calibrated so as to calculate the load and contact area in experiment [7]. Therefore, since the MD analyses in the atomic scale requires an actual shapes with a radius of curvature, a spherical indenter is used in this study. The indentation is performed on to (0 0 1) surface as shown in Fig. 1. Load acting on surface atoms is calculated so as to be in proportion to the distance between coordinates of atoms and the center of spherical indenter. In practice, the equation of the force is expressed by F r k r R 2 (1) where r is the distance from the center of the indenter to Fig. 1 Table 1 Simulation model Simulation condition Cell size (x, y, z) [nm] (26.1, 26.1, 17.2) The number of atoms Indenter radius R [nm] 8.72 Lattice constant [nm] The plane of surface {1 0 0} Temperature [K] 300 Pushing speed [m/s] 1.0 Force constant k [GPa] 2.1 an atom and R is radius of the indenter. The constant k is a force constant which was estimated from a contact theory such as Hertz theory. Both in two directions parallel to the surface, periodic boundary condition is applied. Therefore, cell sizes of the specimen in two periodic directions do not change when it is pushed by the indenter. The lattice constant of SiC crystal is adjusted in accordance with thermal expansion at the simulated temperature (300 K). In this study, as a reliable interatomic potential, Tersoff type [8] is employed. The function form of the interatomic potential is expressed by bij bji E fc rij VR rij VA rij i j 2 (2) where, V R and V A two-body terms representing the repulsive and attractive forces respectively. The function b in Eq.(2) is called bond-order function, and it is a function of bonding angle. So, it is possible for this potential to consider the angular dependency of SiC provided by covalent bonds. Tersoff potential is one of empirical potentials. So, the parameters have been developed by various researches. Parameter sets used in this study are supposed to be better than other ones about reproducibility of elastic deformation and defects, as well as thermal properties [8]. Thereby we observe atomic behavior at the contact region between the indenter and the SiC material surface Common neighbor analysis by sublattice As a method of structural analysis, CNA [9,10] would be able to capture internal structural change as the indenter goes in. To assign a local crystal structure to an atom, three characteristic numbers n cn, n b and n lcn of the central atom are computed for its nearest neighbor bonds (only in the case of BCC it contains the 2nd nearest neighbor bonds) [10]. n cn is the number of neighbor atoms to which the central atom and its bonded neighbor have in common. n b is the total number of bonds between these common neighbors. n lcn is the number of bonds in the longest chain of bonds connecting the common neighbors. This yields each triplets (n cn, n b, n lcn ) for the N neighbors. These triplets are compared to a set of reference structures to assign a structural type to the central atom, as in Table 2. But, CNA has been only applied to simple crystal forms such as face-centered cubic (FCC) or body-centered cubic structures so far. In the present study, diamond or zinc-blende structure has to be detected. Zinc-blend structure is composed of superposition of two FCC sublattices, where the origin of atomic positions for each sublattice are (0, 0, 0) and (1/4, 1/4, 1/4) (that is, another lattice is obtained by the translation of the referenced lattice by 1/4 of lattice constant, in all directions). Therefore, slip plane in perfect crystal of zincblende is {1 1 1} plane which is just the same as that of FCC. Si layer and C layer are stacked on parallel to this slip plane in zinc-blende, and then theoretical point of view, slip deformation theoretically occurs between Si and C layers [4]. Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 184

3 Molecular Dynamics Study on Ductile Behavior of SiC During Nanoindentation Table 2 FCC (N = 12) HCP (N = 12) BCC (N = 14) 12 (4, 2, 1) Assignment of common crystal structure to triplets (n cn, n b, n lcn ) in common neighbor analysis (N is the number of the neighbors) Thus, in analyzing crystalline structure of SiC, we will consider separately FCC-structured sublattice of Si and that of C and apply the CNA to them respectively. 3. Results and discussion 6 (4, 2, 1) 6 (4, 2, 2) 8 (6, 6, 6) 6 (4, 4, 4) 3.1. Relationship between load indenter depth curve and change of atomic arrangement Figure 2 shows a load-indenter depth curve obtained in our nanoindentation simulation of 3C-SiC. Rapid drop of load is found in the area A of Fig. 2. This behavior is well known in nanoindentation, which is called pop-in. It indicates a change from elastic deformation to plastic deformation. Since, in this study, increase of indenter depth per time (i. e. indenter speed) is constant, the load always changes and a rapid drop of load naturally occurs. Figure 3 shows the atomic behavior on {1 1 0} plane which is obtained by the cut at the center of the model. Atomic arrangement in Fig. 3(a) shows no dislocation though all the atoms are remarkably distorted by compressive loading. However, just after that picture, as shown in Fig. 3(b), there occurs a V-shaped defect structure which is clearly specified by a gap of atomic displacement. This phenomenon in the material also occurs in the experiment of nanoindentation which is conducted on {1 0 0} surface by a spherical indenter [11,12]. The gap of atomic displacement found in Fig. 3(b) is distributed along the {1 1 1} plane of initial crystalline structure which is a slip plane of SiC crystal. Figure 4 also shows the measurement of the interatomic distance between the gap (between central region (A) and outside region (B)). The difference of interatomic distance is estimated to be nm, before and after the pop-in event. This is exactly equal to the distance between atoms adjacent to the slip plane when the SiC crystal contains perfect dislocation (it corresponds to the Burgers vector of SiC crystal, nm). So, it is understood that the initial plastic deformation of SiC crystal at temperature of 300 K takes place due to dislocation motion just like other metallic materials. Perfect dislocation of SiC are known to experience two distinct stages of partial dislocations [4]. In this study, however, partial dislocation was not observed from the measurement of interatomic distance around the initial dislocation. It is because atoms could hardly move in the direction of partial dislocation (< > or < 2 1 1>) under the indenter due to high compressive stress there. As a result, four perfect dislocations occurs suddenly and directly under the indenter at the same time and they go in <1 1 0 > directions which expand along the square pyramid. Fig. 2 Load-indenter depth curve Fig. 4 Interatomic distance Fig. 3 View of atomic arrangement in the cross-section at {1 1 0} plane (dark blue is Si and light blue is C) Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 185

4 Takuya Hanashiro, Ken-ichi Saitoh, Tomohiro Sato, Kenji Nishimura, Masanori Takuma and Yoshimasa Takahashi Fig. 5 Result of common neighbor analysis (CNA) on the cross-section of {1 1 0} plane Fig. 6 Result of CNA applied to each sub-lattices (at d = 3.06 [nm], where d is an indenter depth. Color indicates the magnitude of hydrostatic stress (or pressure) of atom) 3.2. Structure analysis by CNA The CNA is used to analyze crystalline structure and defects inside the material. However, as described in section 2, the original method of CNA is not suitable for analyzing the diamond-type crystalline structure. Therefore, we consider separately the FCC-structured sublattice of Si and that of C and apply the CNA to them respectively. The results of new CNA are shown in Fig. 5, for example. The characteristic structure recognized by the new CNA method shows the same transition for both sublattices. In addition, atoms in BCC structure are found immediately under the indenter just after the pop-in event. This behavior was also identified in the indentation experiment of Si single crystal [11]. Figure 6 shows only atoms which have changed their structure from initial one. In addition, the color of atoms indicates the magnitude of hydrostatic stress estimated at each atom. Figure 7 shows the relationship between the indenter depth d and the number of defect atoms detected on both sub-lattices by our new CNA. Increase of defect atoms occurs almost at the same time in each sub-lattice, but, after the pop-in (d > 3.06 nm), the number of defects atom of C is more than the number of defects atom of Si. This difference is caused by the fact that the dislocation core is different in Si and C [13]. Nevertheless, both distribution of defect atoms (those shown in Fig. 6) and the graphs in Fig. 7 have a very similar shape for Si and C lattices. So, the present CNA method which is applied to Fig. 7 Change of the number of defect atoms with the increase of indenter depth Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 186

5 Molecular Dynamics Study on Ductile Behavior of SiC During Nanoindentation sub-lattice is able to show effectively the characteristic of SiC. Therefore, in this study, we employ this analysis method. Figure 8 shows the result of CNA applied to Si sub-lattice at some times after the pop-in event (d = 3.06, 3.20, 3.32 [nm]) and at the time just before pop-in (d = 2.5 [nm]). From Fig. 8(b), it is recognized that the dislocation is generated by starting from the collection of defect atoms at directly under the indenter. The time of occurrence of dislocation core is consistent with the indenter depth which is at maximum stress and is estimated at directly under the indenter from a contact theory. As a result, slip planes there take the triangular form as outlined by dashed lines in Fig. 8(b), and they altogether constitute a region of structural change with a square pyramid shape. It can be observed that plastic deformation area spreads widely as the dislocation loop is extending as shown in Fig. 8(c) and (d). Figure 9 shows cross sectional view parallel to {1 1 1} plane including the triangularly deformed area of Fig. 8(b), which are obtained at d = 3.1 and 3.2 nm. Finally, a Fig. 8 Time-sequenced results of CNA by Si sub-lattice at around the time of pop-in event (Color indicates the magnitude of hydrostatic stress (or pressure)) Fig. 9 Dislocation loop observed on a {1 1 1} plane (arrow indicates the direction of spreading of the dislocation loop) Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 187

6 Takuya Hanashiro, Ken-ichi Saitoh, Tomohiro Sato, Kenji Nishimura, Masanori Takuma and Yoshimasa Takahashi hexagonal dislocation loop is generated from the triangular area on slip plane at d = 3.1 nm. After that, the dislocation loop is spreading toward the direction of arrow in Fig. 9(a). This direction is consistent with one of slip directions of the 90-degrees partial dislocation which is predicted by theory in the loop of the hexagons in zinc-blend or wurtzite structure such as SiC or diamond [4]. Thus, in the present study, temperature condition is not so high (300 K), but a certain amount of ductile deformation in SiC crystal is confirmed. Besides, atomistic mechanism of the ductile deformation is suggested. In the further study, it is needed to clarify the temperature dependence of ductile (dislocation) behavior, and we think that such extension will be possible and interesting, based on the present study. 4. Conclusions The mechanism of generation and expansion of ductile behavior in SiC crystal is studied by performing atomistic simulation of nanoindentation. Pop-in event as the initiation of plastic deformation is detected during the process of nanoindentation using spherical indenter. It is found that sudden gap of atomic displacement along {1 1 1} plane occurs at in the directly under the indenter. Interatomic distance between Si and C atom along the gap is equal to the Burgers vector of SiC crystal (0.288 nm). So, dislocation structure found in this study is a perfect one. Then, we analyze crystalline structure by CNA method for sublattice. Number of defect atoms of C are more than defect atoms of Si because the core energy of the dislocation is different between elements. So, the new CNA for sublattice proposed here is capable of analyzing zinc-blend structure. Region with structural changes in the pyramid shape is generated with each four-sides along different slip planes. In continuing applied load, the region of structural of change spreads. Dislocation loops are generated along initial slip plane in the direction of 90-degree partial dislocations. Acknowledgments This study is partly supported by research fund from Nippon Steel & Sumitomo Metal Corporation (2014, 2015). The authors also acknowledge AIST and Kansai University for collaboratively using computation facilities. References [1] Diani, M., Simon, L., Kubler, L., Aubel, D., Matko, I., Chenevier, B., Madar, R. and Audier, M., Crystal Growth of 3C-SiC Polytype on 6H-SiC(0001) Substrate, Journal of Crystal Growth, 235, 1-4, 2002, [2] Umeno, Y., Yagi, K. and Nagasawa, H., Ab Initio Density Functional Theory Calculation of Stacking Fault Energy and Stress in 3C-SiC, Physica Status Solidi B, 249, 6, 2012, [3] Chen, H. P., Kalia, R. K., Nakano, A., Vashishta, P. and Szlufarska, I., Multimillion-Atom Nanoindentation Simulation of Crystalline Silicon Carbide: Orientation Dependence and Anisotropic Pileup, Journal of Applied Physics, 102, 6, 2007, [4] Nabarro, F. R. N. and Hirth, J. P., Dislocation in Solids, 12, Elsevier, North Holland, 2005, [5] Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics, Journal of Computational Physics, 117, 1, 1995, [6] Stukowski, A., Visualization and Analysis of Atomistic Simulation Data with OVITO-The Open Visualization Tool, Modelling and Simulation in Materials Science and Engineering, 18, 1, 2010, [7] Suganuma, M. and Swain, M. V., Simple Method and Critical Comparison of Frame Compliance and Indenter Area Function for Nanoindentation, Journal of Materials Research, 19, 12, 2004, [8] Erhart, P. and Albe, K., Analytical Potential for Atomistic Simulations of Silicon, Carbon, and Silicon Carbide, Physical Review B, 71, 3, 2005, [9] Honeycutt, J. D. and Andersen, H. C., Molecular Dynamics Study of Melting and Freezing of Small Lennard-Jones Clusters, Journal of Physical Chemistry, 91, 19, 1987, [10] Stukowski, A., Structure Identification Methods for Atomistic Simulations of Crystalline Materials Modelling and Simulation in Materials Science and Engineering, 20, 4, 2012, [11] Zarudi, I. and Zhang, L. C., Structure Change in Mono-Crystalline Silicon Subjected to Indentation- Experimental Findings Tribology International, 32, 12, 1999, [12] Bradby, J. E., Williams, J. S., Wong-Leung, J., Swain, M. V. and Munroe, P., Transmission Electron Microscopy Observation of Deformation Microstructure under Spherical Indentaion in Silicon Applied Physics Letters, 77, 23, 2000, [13] Sun, Y., Izumi, S., Sakai, S., Yagi, K. and Nagasawa, H., Core Element Effects on Dislocation Nucleation in 3C-SiC: Reaction Pathway Analysis, Computational Materials Science, 79, 2013, Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 188