Advanced numerical characterization of silicon with defect by nanoindentation

Queensland University of Technology Brisbane Australia Advanced Numerical Characterization of Silicon with Defect by Nanoindentation Qiang Fu Principal Supervisor: Associate Professor Yuantong Gu Associate Supervisor: Associate Professor Cheng Yan A thesis submitted in fulfilment of the requirements for the degree of master of engineering Faculty of Science and Engineering Queensland University of Technology Jan 2012 Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Acknowledgement I The author of this thesis would like to take this opportunity to acknowledge those who have offered their assistance and support during the research Firstly, the author would sincerely express his gratitude to his principal and associate supervisor, Professors Yuantong Gu and Cheng Yan, for the guidance, advice, patience and encouragement Without their knowledge, vision and support, this work would not have been possible Secondly, the author would express his appreciation to the QUT High Performance Computing & Research Support Team With their help, the massive computational simulations have been completed efficiently Special thanks extended to Mr Haifei Zhan, for the knowledge of the MD simulation field At last but not least, the author would thanks to his beloved family for their always support and encouragement throughout the completion of this work and his life Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Publication II During the course of this project, one journal paper has been accepted It is listed below for reference Fu Q, Zhan HF and Gu YT Atomistic investigations of single-crystal silicon with preexisting defect Accepted by Advanced Science Letters in 2011 Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Abstract III Nano silicon is widely used as the essential element of complementary metal oxide semiconductor (CMOS) and solar cells It is recognized that today, large portion of world economy is built on electronics products and related services Due to the accessible fossil fuel running out quickly, there are increasing numbers of researches on the nano silicon solar cells The further improvement of higher performance nano silicon components requires characterizing the material properties of nano silicon Specially, when the manufacturing process scales down to the nano level, the advanced components become more and more sensitive to the various defects induced by the manufacturing process It is known that defects in mono-crystalline silicon have significant influence on its properties under nanoindentation However, the cost involved in the practical nanoindentation as well as the complexity of preparing the specimen with controlled defects slow down the further research on mechanical characterization of defected silicon by experiment Therefore, in current study, the molecular dynamics (MD) simulations are employed to investigate the mono-crystalline silicon properties with different pre-existing defects, especially cavities, under nanoindentation Parametric studies including specimen size and loading rate, are firstly conducted to optimize computational efficiency The optimized testing parameters are utilized for all simulation in defects study Based on the validated model, different pre-existing defects are introduced to the silicon substrate, and then a group of nanoindentation simulations of these defected substrates are carried out The simulation results are carefully investigated and compared with the perfect Silicon substrate which used as benchmark Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation It is found that pre-existing cavities in the silicon substrate obviously influence the mechanical properties Furthermore, pre-existing cavities can absorb part of the strain energy during loading, and then release during unloading, which possibly causes less plastic deformation to the substrate However, when the pre-existing cavities is close enough to the deformation zone or big enough to exceed the bearable stress of the crystal structure around the spherical cavity, the larger plastic deformation occurs which leads the collapse of the structure Meanwhile, the influence exerted on the mechanical properties of silicon substrate depends on the location and size of the cavity Substrate with larger cavity size or closer cavity position to the top surface, usually exhibits larger reduction on Y Queensland University of Technology IV Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Certification of Thesis V I hereby declare that no part of this work has previously been accepted for the award of any other person in any university or institute This thesis was completed during my enrolment for degree of master by research at Queensland University of Technology, and to the best of my knowledge the material presented is original except where due reference is made in the text of this thesis Qiang Fu Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Table of Contents 1 Chapter Introduction 1.1 Background 1.2 Current Research of Nano Silicon 1.3 Objective 10 1.4 Scope 12 1.5 Structure of Thesis 13 Chapter Literature Review 14 2.1 Nanoindentation 14 2.1.1 Y 2.1.2 Hardness 16 2.1.3 Other Mechanical Properties 17 2.2 M 16 2.1.3.1 Strain-Rate Sensitivity 17 2.1.3.2 Activation Volume 18 Contact Mechanics 18 2.2.1 Hertz Contact Theory 18 2.2.2 Oliver and Pharr method 21 2.2.3 Comments 23 2.3 Methodology Review 23 2.3.1 FEM Models 24 Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 2.3.2 Molecular Dynamics 24 2.3.3 Multi-scale Method 26 2.3.4 Discussion 27 2.4 Review of Molecular Dynamic 27 2.4.1 Initial Condition 28 2.4.2 Interatomic Potentials 29 2.4.2.1 Pair Potential 29 2.4.2.1.1 Lennard-Jones potential (L-J) 29 2.4.2.1.2 Born Lande potential 30 2.4.2.1.3 Morse potential and Johnson potential 30 2.4.2.1.4 Tersoff potential 31 2.4.2.2 Multi-body Potential 31 2.4.2.2.1 Embedded Atom Method (EAM) 32 2.4.2.2.2 Stillinger-Weber (SW) Multiple-Body Potential 33 2.4.3 Integration Algorithms 33 2.4.4 Molecular Dynamics in Different Ensembles / Temperature conversion 34 2.5 Phase Transformation of Silicon 34 Chapter Characterization of Mono-crystalline silicon and Parametric Study 36 3.1 Numerical Implementation 36 3.2 Interatomic potentials 37 3.3 Loading-Displacement Curve 40 Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 3.4 Results of indentation of the perfect substrate 43 3.5 Parametric Studies of Specimen Size and Loading Rate 44 3.5.1 The influence of substrate lateral size 45 3.5.2 The influence of Substrate Thickness 49 3.5.3 The Influence of Loading Rate 52 3.6 Conclusion 54 Chapter Characterization of Mono-crystalline Silicon with Defects 57 4.1 Computational Model and Defects Description 58 4.2 Effect of the Cavity Size 59 4.2.1 Description of Defect Cases 59 4.2.2 Load-Displacement Curve and Test Results 59 4.2.3 Phase Transformation and Atomic Configuration 62 4.2.4 Discussion 65 4.3 E 70 4.3.1 Description of Defect Cases 70 4.3.2 Load-Displacement Curve and Test Results 71 4.3.3 Phase Transformation and Atomic Configuration 74 4.3.4 Discussion 77 4.4 Effect of multiple cavities 80 4.4.1 Description of Defect Cases 80 4.4.2 Load-Displacement Curve and Test Results 81 Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 4.4.3 Phase Transformation and Atomic Configuration 82 4.4.4 Discussion 83 Chapter Conclusion and Future Work 86 5.1 Conclusions 86 5.2 Recommended Future Work 89 Bibliography 90 Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 81 4.4.2 Load-Displacement Curve and Test Results From the load-displacement curves of cases e1-e4, as illustrated in Figure 24, during the loading process all load-displacements curves are very close to each other However, the detailed analysis reveals that the unloading curves become steeper while the size of the cavity becomes smaller Interestingly, when the cavity is excluded in the model, the curve becomes less steep than those cases with cavities in this group This trend can also be observed in the calculated Y presented in Table 15 Y s increases from 122.79 GPa at case e4 to 130.85 GPa in case e1 then jump back to 123.17 GPa for the perfect substrate Figure 24 Load-displacement curves of Group e, cavities with the radii of 0.5a, 1a, 1.5a and 2a, respectively Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 82 Table 15 E Y G e Case d0 e1 e2 e3 e4 Cavity Radius 0.5a 1a 1.5a 2a Young’s modulus 123.17 130.85 126.53 125.21 122.79 Hardness 33.36 32.41 33.64 32.85 32.70 *Young’s modulus and hardness unit in GPa 4.4.3 Phase Transformation and Atomic Configuration Similar to the single cavity cases discussed in previous section, the deformation of spherical structured cavity absorbs energy Figure 25 shows the atomic configuration for the cases e1 and e4 The location of the cavity is relatively far away from the deformation zone, and in both cases, the atomic structures around cavities are elastically compressed during loading After unloading, the strain energy that stored in the deformed cavity is released, and the atomic structure around the cavity recovers back to Si-I phase Although there is some plastic deformation can be observed on the surface of the silicon substrate, there is nothing other than Si-I structure is found around the cavities Therefore, it can be postulated that the cavities are not directly involved in the effect to the phase transformation, the increase of the Y modulus and hardness is the result of the energy absorption due to cavity structural elastic deformation Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 83 (a1) Case e1; 1.857nm (b1) Case e1; Unloaded (a2) Case e2; 1.857nm (b2) Case e2; Unloaded (a3) Case e3; 1.857nm (b3) Case e3; Unloaded (a4) Case e4; 1.857nm (b4) Case e4; Unloaded Figure 25 Atomic configurations of cases e1 and e4 at two different stages: (a1)-(a4) at the indentation depth of 1.857 nm; (b1)-(b4) full unloaded; Atoms with the CN value between and 13 are visualised 4.4.4 Discussion Figure 26 and Figure 27 show the number of atoms with CNs of six, seven, and eight for cases e1 and e4 In case e1, after the relaxation process, the number of atoms with the CN of six is 712 After being fully unloaded, this number becomes 380, with a reduction of 332 Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation The number of atoms with CN of six for case e4 decreases more, i.e., 731 at the end of relaxation and then the number of atoms with CN of six reduces from 397 to 334 after being fully unloaded For the prefect case d0 the number of atoms with CN of six recovered during the unloading process is 325 Comparing to case e1, the effect of elastic deformation is obvious Figure 26 Number of atoms with specified CNs (6,7 and 8) versus time for case e1 Queensland University of Technology 84 Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 85 Figure 27 Number of atoms with specified CNs (6, and 8) versus time for case e4 It is observed that in group e, the existence of some small cavities can enhance the mechanical performance of silicon substrates From the results of simulations, it is found that the Young s moduli of cases e1, e2, and e3 are larger than the prefect case d0 The investigation of the atomic configurations for cases e1 and e4 shows that atomic structures around the cavities not transform permanently Those atomic structures recover back to Si-I phase during unloading The recovery of those atomic structures has contributions to the Young s modulus of silicon substrate When the cavities are small enough, the mechanical properties are enhanced because the recovery of those atomic structures around the cavities overcomes the weakening effect brought by the cavities, so the Young s moduli of those cases with small cavities exceed that of the perfect case It is interesting to conclude that the existing small cavity does not lead to the weakness of the atomic structure, such as the substrate contains the cavities with a radius of 0.5a Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Chapter Conclusion and Future Work 5.1 Conclusions The MD simulation is performed to reproduce the nanoindentation on the monocrystalline silicon By comparing the simulation results with other successful simulation cases, the MD model is validated at first Utilizing this simulation model, influences from some key simulation parameters are investigated Those parameters, including the lateral size and thickness of silicon substrate and the loading rate applied on the indenter, have significant influences to the results According to MD results, the following conclusions can be made:  The smaller lateral size of the silicon substrate leads to higher corresponding force at the maximum indentation depth For the silicon substrate with smaller lateral size, more strain energy is expected to be relieved, during relaxation, larger force reduction is induced Both loading and unloading curves for the substrate with smaller lateral size are steeper Thus, the Young s modulus calculated from the unloading curve is greater than those substrates with larger lateral size The Young s modulus converges to the value of substrate with infinity lateral size The hardness calculated from the unloading force and indentation depth shows opposite trend to the Young s modulus  The influence from substrate thickness is observed and analysed Young s modulus is larger for the thinner substrates, but the hardness does not increase monotonically along with the increase of the thickness The hardness under the influence of rigid atoms layer rises up at thinner thickness The similar phenomena Queensland University of Technology 86 Advanced Numerical Characterization of Silicon with Defects by Nanoindentation is also reported by A.V.Bolesta and V.M.Fomin[83], who investigated mechanical 87 properties of Cu thin film  The loading rate has significant influence on the estimated mechanical properties of silicon substrate The higher loading speed leads to steeper loading curve and higher loading value at maximum indentation depth During the relaxation process, the corresponding force with higher loading speed has larger reduction Higher indentation speed of the indenter results in the higher Young s modulus, and Young s modulus quickly converges with the decrease of the speed This conclusion consist with Liu s [79] finding It is also noted that when the loading speed reduces down to 0.01 nm/Ps, there is no reduction of loading due to the relaxation effect Based on the parametric study preformed, the optimized parameters are adopted to ensure the accuracy and computational efficiency The validated MD model is employed to investigate the mono-crystalline silicon properties with different pre-existing cavities under nanoindentation Cavities with different radii and positions are considered The factors Y M numbers of six, seven and eight have been obtained conclusions can be drawn as follows:  Pre-existing cavities in the silicon substrate have obvious influences on the mechanical properties of silicon under nanoindentation;  Pre-existing cavities can absorb part of the strain energy during loading and then release during unloading It possibly causes less plastic deformation to the substrate Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation  The larger offset of the cavity in the lateral direction, the less influence we found, and the higher Y moves s and hardness has been found When the cavity , the larger influence is induced In our cases, we found that, for a cavity with a radius of 2.5a, when it is located at a deep of 9a beneath the surface, or at a depth of 8a and a distance of 3a from the lateral centre It will eliminate the influence of cavity brought to the estimated mechanical results  The combination of the location closer to indenter and larger size of cavity may introduce more plastic deformation around the cavities When the pre-existing cavities are close enough to the deformation zone or big enough to exceed the bearable stress for the spherical cavity, larger deformation occurs, which results in the collapse of the cavity, and the transformation of the silicon due to stress will not able to recover Furthermore, some cavity cases not have visible plastic deformation, but silicon phase transformation  When or the cavity is small enough, even there is visible elastic deformation, the cavity is considered as no significant influence to the plastic deformation, minor increase of Y odulus and hardness is observed  When substrate contains multi-cavities with small radius, the mechanical properties of the substrate can be enhanced, because the elastic recovery of compressed Queensland University of Technology 88 Advanced Numerical Characterization of Silicon with Defects by Nanoindentation atomic structures around the cavities overcomes the weakening effect brought by 89 the cavities 5.2 Recommended Future Work Due to the limitations of available resource and timeframe, there is a couple of possible extended topics have not been included in this thesis Therefore, we list them in this section for recommended future work In this thesis, we only examined a simple multiple defect case The main parameters to define a multiple defects only include the location, size, and cavitations density In future study, the same MD simulation can be employed, and the different multiple cavities can further be designed by removing atoms out of the substrate The expected outcome is to have quantitative results of the influence on the mechanical properties with respect of location, size and cavitations density Another topic is to investigate different types of defects In this thesis, only cavity defect cases are considered In the future project, the more types of defects can be included, such as grain boundary (GB), impurity embed, dislocation or even different sharp of cavitations MD modeling is able to satisfy all the needs to investigate the existing defects in the silicon substrates More complex defects were not considered in the present project It is feasible to upgrade the MD model to multi-scale model, and extend this project to investigate the mechanism of crack propagation on the atomic level The benefit of multi-scale simulation is able to couple the continuum modeling and atomic modeling together, in order to unify the theory of atomic scale and macro scale Queensland University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Bibliography 90 Sinano, I., Advanced Nanoelectronics Technology 2009 Sinano, I., Sinano Institute Vision, 2009 Oda, S and D.K Ferry, Silicon nanoelectronics2006: CRC KAWAMOTO, H and K OKUWADA, Development Trend for High Purity Silicon Raw Material Technologies Pharr, G., W Oliver, and D Harding, New evidence for a pressure-induced phase transformation during the indentation of silicon Journal of Materials Research, 1991 6(06): p 1129-1130 Zarudi, I and L Zhang, Structure changes in mono-crystalline silicon subjected to indentation-yexperimental findings Tribology 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Defects... Queensland University of Technology IV Advanced Numerical Characterization of Silicon with Defects by Nanoindentation Certification of Thesis V I hereby declare that no part of this work has previously... University of Technology Advanced Numerical Characterization of Silicon with Defects by Nanoindentation 3.4 Results of indentation of the perfect substrate 43 3.5 Parametric Studies of Specimen