Characterization of interfacial mechanical properties using wedge indentation method 1

CHARACTERIZATION OF INTERFACIAL MECHANICAL PROPERTIES USING WEDGE INDENTATION METHOD YEAP KONG BOON NATIONAL UNIVERSITY OF SINGAPORE 2010 CHARACTERIZATION OF INTERFACIAL MECHANICAL PROPERTIES USING WEDGE INDENTATION METHOD YEAP KONG BOON (B. Eng. (Hons.), University Technology Malaysia) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 Preface This dissertation is submitted for the degree of Doctor of Philosophy in the Department of Mechanical Engineering, National University of Singapore (NUS) under the supervision of Associate Professor, Dr. Zeng Kaiyang. Part of the research works have been conducted at Institute of Materials Research and Engineering, Singapore (IMRE). To the best knowledge of the author, all of the results presented in this dissertation are original, and references are provided to the works by other researchers. The majority portions of this dissertation have been published or submitted to international journals or presented at various international conferences as listed below: Journal Papers: 1. K. B. Yeap, K. Zeng, H. Jiang, L. Shen and D. Chi, Determining Interfacial Properties of Submicron Low-k Films on Si Substrate by using Wedge Indentation Technique, Journal of Applied Physics, 101, 123531 (2007). 2. K.B. Yeap, K.Y. Zeng and D.Z. Chi, Determining the Interfacial Toughness of Low-k Films on Si Substrate by Wedge Indentation: Further Studies, Acta Materialia, 56, p.977-984 (2008). 3. K.B. Yeap, K.Y. Zeng and D.Z. Chi, Wedge Indentation Studies of Low-k Films at Inert, Water and Ambient Environments, Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing, 518, p.132-138 (2009). 4. L. Chen, K.B. Yeap, K.Y. Zeng and G.R. Liu, Finite Element Simulation and Experimental Determination of Interfacial Adhesion Properties by Wedge Indentation, 89, p. 1395-1413 (2009). Contributions: Providing nanoindentation experimental supports, involvement in discussions and making comparison of the experimental and simulation results. i 5. J. Zhu, K.B. Yeap, K.Y. Zeng and L. Lu, Mechanical and Interfacial Properties of Sputtered Ruo2 Thin Film on Si Substrate for Solid State Electronic Devices. Submitted to Thin Solid Film for review. Contributions: Providing nanoindentation experimental supports and involvement in discussions. Book Chapter: 1. K.Y. Zeng, K.B. Yeap, A. Kumar, L. Chen and H.Y. Jiang, Fracture Toughness and Interfacial Adhesion Strength of Thin Films: Indentation and Scratch Experiments and Analysis, to be published in CRC Handbook of Nano-structured Thin Films and Coatings (Three Volume Set), Vol. 1, Chapter 3, Ed. S.Zhang, CRC Press (2010). Conference Presentations: 1. K. B. Yeap, K. Zeng, L. Shen and D. Chi, Determining the Interfacial Properties of Low-k Film by Wedge Nanoindentation, Materials TriConference: Thin Film 2006, Singapore (Presented by Kong Boon Yeap). 2. K.B. Yeap, L. Chen, K.Y. Zeng, and D.Z. Chi, A Simple Method to Quantify Interfacial Mechanical Properties of Low-k /Si: Wedge Indentation Technique, MRS Spring 2009, California, USA (Presented by Kong Boon Yeap). 3. K.B. Yeap and K.Y. Zeng, A Simple Method to Quantify Interfacial Mechanical Properties of Low-k /Si: Wedge Indentation Technique, ICMAT 2009, Singapore (Presented by Kong Boon Yeap). 4. K. B. Yeap and K.Y. Zeng, Determination of Interfacial Mechanical and Timedependent Properties of Low-k Films by Wedge Indentation Method, Advanced Materials Workshop 2009, Cottbus, Germany (Presented by Kong Boon Yeap). 5. K.B. Yeap, K.Y. Zeng, R. Yvonne and E. Zschech, Determining Cohesive Toughness and Adhesion of Low-k Film by Nanoindentation, 11th Stress Workshop 2010, Dresden, Germany (Presented by Kong Boon Yeap). ii Acknowledgements First of all, I would like to express my sincere gratitude to my supervisors, Associate Prof. Dr. Zeng Kaiyang and Dr. Chi Dongzhi, for their guidance, supervision, encouragement and advice during the course of my Ph.D. study. The scientific methods and research skills imparted by them are the most valuable gift for my future research career in the field of “Nanomechanics of Materials”. Also, I would like to thank the research staffs in the Institute of Materials Research and Engineering (IMRE) and the National University of Singapore (NUS). I especially thank Ms. Shen Lu (IMRE) for the help on conducting the nanoindentation experiments and Madam Zhong Xiangli (NUS) for the help on operating the focusedion-beam system. In addition, I would like to thank my room mates, laboratory colleagues and friends for their support and help. Finally, I owed many thanks to my girl friend and my family for their love, patience, support and encouragement, without that I would not be able to complete this Ph.D. thesis. iii Table of Contents Preface i Acknowledgements iii Table of Contents iv Summary viii List of Tables x List of Figures xii List of Symbols xix Chapter 1: Introduction 1.1 Overview of the Interfacial Toughness Characterization Methods 1.2 Background of Low-k Thin Films 1.3 Research Objectives and Significance 1.4 Thesis Outline 10 Reference 11 Chapter 2: Literature Review 14 2.1 Relationships between Interfacial Delaminations and Nanoindentation Load-Penetration Curves 15 2.2 Indentation Methods Developed to Determine the Interfacial Toughness of Thin Film/Substrate Structure 16 2.2.1 Conical Indentation 19 2.2.2 Microwedge Indentation of Line Structure 23 2.2.3 Wedge Indentation on the Systems with Strong Interfaces 27 iv 2.3 Area under Indentation Load-Penetration Curve and Work of Fracture 31 2.4 Mechanical Aspects and Reliability of Low-k Films 33 2.4.1 Interfacial Fracture of Low-k Films 36 2.4.2 Time-Dependent Fracture of Low-k Films 39 Reference 45 Chapter 3: Experiment Methodology 49 3.1 Sample Materials 49 3.2 Nanoindentation Experiments 51 3.2.1 Elastic Modulus and Hardness Characterization 53 3.2.2 Interfacial Toughness Characterization 55 3.2.3 Time-Dependent Fracture Properties Characterization 56 3.3 Crack Profile Characterization 57 3.3.1 Plane View Imaging of Indentation Impressions 58 3.3.2 Cross-Sectional Imaging of Indentation Impressions 59 3.3.3 Chemical Analysis of Fracture Surfaces 61 Reference 62 Chapter 4: Development of Wedge Indentation Method to Characterize the Interfacial Toughness of Sub-Micron Low-Dielectric (k) Thin Films 63 4.1 Correlations between the Nanoindentation P-h curves and the Fracture Processes 64 4.1.1 The Correlation Studies on the MSQ/Si System 65 4.1.2 The Correlation Studies on the BD/Si System 75 4.2 Mechanics of Interfacial Adhesion 78 4.3 Curvature of the Crack Front 88 v 4.4 Determination of Interfacial Adhesion 94 4.4.1 Elastic Modulus and Hardness 95 4.4.2 MSQ film on Si Substrate 97 4.4.3 BD films on Si Substrate 101 4.4.4 Chemical Analysis to Confirm the Delamination Crack Path 111 4.4.5 Work of Indentation and Fracture Energy 112 4.5 Conclusion Reference Chapter 5: Comparison of the Finite Element Simulation and Experiments of Wedge Indentation Test 118 120 123 5.1 Elastic-Plastic Properties of BD and MSQ films 124 5.2 Interfacial Adhesion Energy and Strength 128 5.2.1 BD films on Si Substrate 129 5.2.2 MSQ film on Si Substrate 131 5.3 Conclusion Reference Chapter 6: Wedge Indentation Studies of Low-k Films at Inert, Water and Ambient Environments 134 135 136 6.1 Time-Dependent Fracture during Wedge Indentation Tests 139 6.2 Lifetime and Loading-Rate Analysis 147 6.3 Influences of Test Environments on Fracture Processes 151 6.4 Crack Growth at Inert Environment 155 6.5 Conclusion 156 Reference 158 vi Chapter 7: Wedge Indentations on Hard-Film-Soft-Substrate System 160 7.1 Correlation Study on RuO2/Si System 161 7.2 Interfacial Toughness of RuO2/Si System 164 7.3 Conclusion 168 Reference Chapter 8: Summary, Conclusions and Recommendations 170 171 8.1 Interfacial Toughness 171 8.2 Time-dependent Fracture 173 8.3 Wedge Indentation on Multilayer 175 8.4 Hard-Film-on-Soft-Substrate 178 8.5 Other Avenues for Future Works 179 Appendix A: Schematic Diagram of a FIB Cutting on Wedge Indentation Impression 183 Appendix B: Generalization of Indentation Induced Stress 184 Appendix C: EDX results 186 Appendix D: FEM simulation and model for Wedge Indentation Induced Delamination 195 vii Summary Shrinkage of device dimensions in microprocessors and micro-electromechanical systems to nanometer scale has brought major concerns on the device reliability and the material compatibility with existing fabrication processes. A vast amount of work has been dedicated to understand and enhance the mechanical properties of this nanometer structure, e.g. elastic modulus, cohesive toughness and interfacial adhesion. However, the mechanics of interfacial adhesion is a rather complicated subject. This thesis develops a simple way to measure the interfacial adhesion of thin film/substrate structure using the wedge indentation method. We intend to simplify the existing indentation experimental procedures and analytical solutions, so that the measurement of interfacial adhesion is simple enough for scientists and engineers who may have little experience in this area. The development of a new wedge indentation experiment to characterize interfacial adhesion can be divided into three parts. In the first part, the correlation between the cracking sequence and indentation load-penetration curve (indentationfracture correlation) is established. In the second part, based on the indentationfracture correlation, a simple experiment and analysis procedure is developed to measure the interfacial adhesion of thin film/substrate structures. In the third part, the experiment is conducted on low-k/Si systems (e.g. BlackDiamond™ (BD/Si) and methyl-silsesquioxane (MSQ/Si)) and RuO2/Si system to verify the accuracy of the interfacial adhesion measured using the simple analysis procedure. viii Chapter 3.2 Nanoindentation Experiments: Nanoindentation is a mechanical characterization tool commonly used to measure elastic modulus and hardness. The main objective of this thesis is to develop the nanoindentation experiments and analysis to characterize the interfacial toughness of thin films. Comparing to other methods, such as the micro-tensile test, the wafer curvature test, and the beam bending technique [1-3], nanoindentation has several advantages. In a nanoindentation test, a very small load can be applied and the penetration of the indenter tip can be accurately measured at nanometer scale. In addition, the sample preparation for nanoindentation test is relatively simple, and a large amount of information can be extracted from a small sample. Two nanoindentation systems (Nanoindenter XP®, MTS Nano-instruments, MTS Corp., USA and UMIS-2000H®, CSIRO, Australia) were used during the course of this study to determine different mechanical properties. The MTS Nanoindenter XP was used to measure elastic modulus and hardness, while the UMIS-2000H nanoindenter was used to measure interfacial toughness and time-dependent fracture properties of thin films. Tables 3.2 and 3.3 show the specifications of the two nanoindentation systems. There are two range-settings for UMIS-2000H® (Table 3.3). Range A of the load and displacement was used, when the test was conducted on lowk films. But for stiffer film systems, such as RuO2 films, both range A and B were needed. 51 Chapter Table 3.2: MTS Nanoindenter XP® system specifications Parameters Specifications Displacement resolution 500 µm Maximum load 500 mN Load resolution 50 nN Contact force < µN Table 3.3: UMIS-2000H® system specifications Range of penetration Displacement resolution Range of maximum force Force resolution Range A Range B – µm – 40 µm 0.05 nm – 50 mN – 500 mN 0.75 µN The UMIS-2000H® nanoindenter system was used together with two types of indenter tips, wedge and axisymmetric tips. The contact between the indenter tips and sample surface is assumed to be frictionless. To measure the interfacial toughness and the time-dependent fracture properties of the thin film/substrate systems, the primary indenter tips used in this study were the diamond wedge tips with two inclination 52 Chapter angles* (90° and 120°). Axisymmetric indentations (a standard Berkovich indenter and a conical indenter with inclination angle 90° and tip radius µm) were performed on the same samples, so that the crack profiles generated by wedge and axisymmetric indentations can be compared (Section 4.1). Using field-emission-scanning-electronmicroscope (FESEM), the length of the wedge tips, l was measured as 4.06 μm and 7.24 μm for the 90° wedge-tips, and 4.21 μm for the 120° wedge-tip, respectively. Despite the differences in the wedge indenter geometry, the interfacial toughness of a thin film/substrate system measured from 90° and 120° wedge indentations should be consistent. Based on this concept, a self-assessment of the accuracy of the interfacial toughness results was achieved by comparing the results obtained from 90° and 120° wedge indentations (Section 4.4.2). 3.2.1 Elastic Modulus and Hardness Characterization: The Continuous Stiffness Measurement (CSM) option in the MTS Nanoindenter XP was used to determine the elastic modulus and the hardness of the thin films. In a typical CSM test, a high frequency sinusoidal signal is imposed on top of the DC signal that drives the motion of the indenter. Subsequently, the contact stiffness, S is calculated at every point along the loading curve based on (a) the amplitude of the displacement signal and (b) the phase difference between the force and displacement signals [4,5]. The relation between reduced elastic modulus, Er and contact stiffness is given as * Inclination angle of a wedge indenter refers to the angle in between the two wedge indenter surfaces. 53 Chapter S = β 24.56 Er hc , (3.1) where hc is the contact depth and β is a numerical factor. Hardness is given as indentation load divided by the contact area. In this work, CSM tests were conducted with a standard Berkovich indenter tip under strain-rate (defined as dh/dt/h) controlled mode (0.05/s). For thin film sample with thickness, t, the maximum indentation depth was set at 0.5t and 0.8t. When an indentation is made on a thin film/substrate structure, elastic and plastic responses may be detected from both the film and the substrate; this phenomenon is commonly known as the substrate effects. CSM test enables the continuous measurement of elastic modulus and hardness along the loading curve; therefore, the substrate effects can be separated, and the film-only elastic modulus and hardness can be determined (Section 4.4.1). 54 Chapter 3.2.2 Interfacial Toughness Characterization: Fig. 3.1: Single loading/unloading curve of the BD film (500nm) by 90° wedge indentation. The interfacial toughness values of low-k/Si and RuO2/Si systems were determined from the single loading/unloading indentation tests with wedge indenter tips. The indentation process consists of three main segments: (a) Loading in 20s to the maximum load; (b) Holding at the maximum load for 20s; and (c) Unloading with the same rate as the loading segment. Fig.3.1 shows a load - penetration (P-h) curve obtained from the wedge indentation test on a BD film. To determine the critical load for interfacial crack initiation, Pcritical, wedge indenters were allowed to penetrate as deep as 50% to 120% of the film thickness by applying various maximum loads, Pmaximum (Fig.3.1). At least 10 indents were made at each predefined Pmaximum. In addition, for test samples that may be susceptible to time-dependent fracture, it is 55 Chapter important to keep the time spent in the loading segment less than 8s, so that the critical strain energy release rate or interfacial toughness can be characterized. 3.2.3 Time-Dependent Fracture Properties Characterization: A non-porous BD film with a thickness of 500 nm was used to study the timedependent fracture behavior. Three test environments with different levels of exposure to water molecules were used: (a) inert environment: the BD film samples were annealed at 100°C for 72h and the surface was immediately covered with a layer of silicone oil as the samples were removed from the oven; (b) watered environment: the sample surface was covered by droplets of distilled water; and (c) ambient environment: as-received samples tested at normal 60–70% of humidity. The temperatures of these three environments were maintained at room temperature (25°C). With certain modifications to the sample holder, it is possible to completely immerse the sample in water environment. However, before the water droplet could completely evaporate, the effects of water exposure level should be the same for complete immersion or covered by water droplets. In this study, all of the indentation tests were completed before the water droplet evaporated, thus the sample holder modification was not done in this study. Using a diamond wedge tip (90° inclination angle and 4.055 µm wedge length) mounted on the UMIS-2000H nanoindenter, wedge indentations were conducted on all of the samples treated with above environments. Two types of wedge indentation tests were conducted: (a) load-holding test; and (b) varying-loading-rates test. Both 56 Chapter indentation tests consisted of three main segments: (a) loading to a pre-defined maximum load, Pmaximum; (b) holding at Pmaximum for a period of time; and (c) unloading to and holding at 30% of Pmaximum for thermal draft correction and followed by complete unloading. In the load-holding tests, the Pmaximum were set in a range of to 7mN and the holding times were set in a range of 10 to 10,000s. Furthermore, to complete the entire time-dependent fracture processes in the holding segments and to avoid possible timedependent crack growth during the loading segment, the time spent during loading (before reaching to the value of Pmaximum) was controlled at less than 8s. On the other hand, in the varying-loading rates test, Pmaximum was set at 10mN to ensure that the time-dependent fracture process was completed within the loading segment, and the loading rates between µN/s and 250 µN/s were obtained by adjusting the time to reach 10 mN from s to 1000 s. At least 20 data sets were collected for each of the wedge indentation tests, and the average values were calculated with the errors represented by the standard deviations of the data. In addition, these two tests were repeated on a 400nm thick porous MSQ film on Si substrate; and the results were compared with those obtained from BD/Si system. 3.3 Crack Profile Characterization: This section and the following sub-sections (Sections 3.3.1-3.3.3) present the characterization methods used to determine the crack profile of low-k/Si and RuO2/Si systems. After completed a series of indentation tests at a wide range of Pmaximum, the 57 Chapter indentation impressions were observed from cross-sectional and plane views to determine the correlation between the fracture processes * and the indentation P-h curves. The plastic strain energy stored around the indentation impression may lead to interfacial crack propagation along the interfacial path or the cohesive path several nanometers above or below the interface. Therefore the failure path is analyzed by conducting qualitative chemical analyses on the fracture surfaces using energy dispersive X-ray (EDX) analysis in SEM. 3.3.1 Plane View Imaging of Indentation Impressions: A field-emission-scanning-electron-microscope (FESEM) (Hitachi S-4300, Hitachi High Technologies America Inc., USA) was used to obtain the plane view images of (a) indentation impressions, (b) film cracking features and (c) fracture surfaces. The area of an interfacial fracture surface was measured on the region of a plane view image, where the film material has been spall-off, using an image analyzing software (Scion Image, Scion Corp., USA). To obtain high resolution images in FESEM, the FESEM parameters are set as following: working distance of mm, accelerating voltage of 15 kV and current of 11 µA. * Fracture processes refer to the formation of film or interfacial cracks as indentation load is gradually increased. 58 Chapter 3.3.2 Cross-Sectional Imaging of Indentation Impressions: The FEI focused-ion-beam (FIB) system (Quanta 200 3D DualBeamTM, FEI Company, USA) with Ga liquid metal ion source was used to cut the indentation impressions on the thin film samples and to observe the cross-sections of thin film/substrate structures. The acquisition of a good cross-sectional image required removal of unwanted defects produced from the FIB cutting process (e.g. materials redeposition and damage) as much as possible by tuning the ion beam voltage and current (Table 3.4). The single-step cutting technique with the low-energy ion-beam with voltage (20 kV) and current (37 pA) was applied on the low-k/Si samples, because high-energy ion-beam can easily burn and deteriorate the low-k materials. For RuO2 film, a double-step cutting technique was used: (a) Step 1: the high-energy ionbeam setting with voltage (20 kV) and current (0.21 nA); and (b) Step 2: the lowenergy ion-beam setting with voltage (20 kV) and current (37 pA). This double-step process was utilized, because the low-energy ion-beam was too slow to remove a high density material (e.g. RuO2), but was needed to produce a clean final-cut. Table 3.4: FIB cutting parameters for the MSQ, BD and RuO2 films RuO2 Low-k materials FIB parameters (MSQ and BD) Step Step Voltage (kV) 20 20 20 Current (pA) 37 210 37 59 Chapter Besides the ion beam voltage and current adjustments, a proper patterningmode selection can also improve the cross-sectional image quality. The rectangularpatterning mode (cuboid) and the regular-cross-section-patterning mode (right triangular prism) in the dual beam FIB system were used to cut the thin film samples. Using the high-energy ion-beam setting, the rectangular-patterning mode will take approximately 40 mins to mill away 30 μm3 of low-k materials. However, the regularcross-section-patterning mode will only require one quarter of the time spent by the rectangular-patterning mode to obtain a similar cross-sectional image of the low-k/Si interface. For optimum FIB cutting quality and time, the rectangular-patterning-mode was used for thin films with thickness less than 300 nm, whereas the regular-crosssection-patterning-mode was used for thin films with thickness more than 300 nm. To observe the crack profile from different cross-sectional directions, the FIBcutting was arranged in a number of different orientations with respect to the indentation impression: (a) perpendicular to and at the middle of a wedge indentation impression; (b) perpendicular to and at 500 nm away from the end of a wedge indentation impression; (c) parallel to a wedge indentation impression; and (d) at the center-point of an axisymmetric indentation. These FIB-cutting orientations were repeated at least times for every indentation test parameters reported in Sections 3.2.2 - 3.2.3. After the cutting process was completed, the cross-sectional images of the low-k/Si and the RuO2/Si interfaces were rapidly captured, using extremely-lowenergy ion-beam with voltage (30 kV) and current (10 pA) to minimize the damage created by the ion beam. The cross-sectional images of interfaces were captured at working distance (15 mm) and tilt angle (52°). Based on these images, the interfacial 60 Chapter crack lengths and area can be measured and used for the calculation of the critical strain energy release rate (Section 4.4 and 7.2). 3.3.3 Chemical Analysis of Fracture Surfaces: The fracture surfaces created by wedge indentation were qualitatively analyzed to determine the failure path: (a) interfacial path or (b) cohesive path near the interface. The energy-dispersive X-ray spectroscopy (EDX) associated with Hitachi S-4300 FESEM was used for the chemical analysis on: (a) the film surface, (b) the delaminated area around indentation impressions and (c) the bare Si substrate surface. Due to the fact that the low-k film’s remnants at the fracture surface might be as thin as a few nanometers thick, a small accelerating voltage (5 kV) and current (11 µA) were used for the chemical analysis. This analysis was repeated in many different spots, especially within the delaminated crack areas (Section 4.4.4). 61 Chapter References: 1. M. Morgen, E.T. Ryan, J.H. Zhao, C. Hu, T.H. Cho and P.S. Ho, Annu. Rev. Mater. Sci., 30, p.645-680, (2000). 2. J.H. Zhao, I. Malik, T. Ryan, E.T. Ogawa, P.S. Ho, W.Y. Shih, A.J. McKerrow and K.J. Taylor, Appl. Phys. Lett, 74, p.944-946, (1999). 3. J.H. Zhao, T. Ryan, P.S. Ho, A.J. McKerrow and W.Y. Shih, J. Appl. Phys., 85, p.6421-6424, (1999). 4. X.D. Li and B. Bhushan, Mater. Charact., 48, p.11-36, (2002). 5. W.C. Oliver and G.M. Pharr, J. Mater. Res., 7, p.1564-1585, (1992). 62 Chapter 4: Development of Wedge Indentation Method to Characterize the Interfacial Toughness of Sub-Micron Low-Dielectric (k) Thin Films The research methodologies to develop the wedge indentation method for interfacial toughness characterization follow these sequences: (a) development of a fundamental understanding of the fracture processes during the wedge indentation; (b) development of the corresponding quantitative mechanics analysis; (c) applications of the experimental and analytical methodologies onto some technologically important thin film systems (low-k films used in microelectronic devices – MSQ and BD films); and (d) confirmations of the consistency and precision of the characterization method. Before developing any kind of analytical or empirical solution for interfacial toughness, a solid understanding of the correlation between the indentation P-h curves and fracture processes must be obtained (Section 4.1). The analytical or empirical solution must be able to generate accurate results when the wedge indentation method is applied on different thin film materials with different film thicknesses, as well as when different wedge indenter geometries are used (Section 4.2 – 4.4). In addition, the interfacial toughness values determined from the wedge indentation experiments must be consistent with the numerical results obtained from the simulation studies such as FEM simulations (Section 5.2). 63 Chapter 4.1 Correlations between the Nanoindentation P-h Curves and the Fracture Processes Two types of silica based low-k thin films, MSQ and BD films, are used for correlation studies, so that clear relationships between the nanoindentation P-h curves and the crack initiation and propagation processes (indentation-fracture correlation) can be established. The investigations on the indentation-fracture correlations are first performed on the MSQ/Si system to determine the most suitable indenter geometry (Wedge tips with 90° and 120° inclination angle, or Berkovich tip) for interfacial toughness characterization, and to obtain the crack-configuration required to develop the analytical solution for wedge-indentation induced delamination (Section 4.1.1). Further studies are then conducted to determine the similarities and the differences of the indentation-fracture correlations of the MSQ/Si and the BD/Si systems. Because the material structure of the BD and the MSQ films are different at macroscopic and molecular levels, there may be certain differences in the P-h curves, and the crack initiation and propagation processes (Section 4.1.2). In these correlation studies, indentation impressions are made at different maximum loads, Pmax (below and above the pop-in load, Ppop-in, Fig.3.1). The P-h curves obtained from the tests are examined for any distinctive pop-in* events, as they might be indicating a sudden loss of the contact stiffness due to the formation of cracks either within the film or at the interface. The unloading segments of the P-h curves for the MSQ/Si and the BD/Si systems are found to be almost linear. Therefore, * When an indenter is loaded on a material, it may elastically or/and plastically deform the material. Pop-in refers to an abrupt increase of penetration depth, which cannot be related to the elastic or plastic properties of that material. 64 Chapter all the film and interfacial cracks can be assumed to occur within the loading segment, and can be associated to a certain Pmax. Based on these assumptions, the indentationfracture correlation is developed. This correlation will be used as a platform for the development of an analytical solution to quantify the interfacial toughness (Section 4.2). 4.1.1 The Correlation Studies on the MSQ/Si System Fig.4.1 shows the P-h curves obtained from the indentations on the MSQ/Si system using three types of indenters (90° wedge, 120° wedge, and Berkovich). As can be seen in Figs.4.1(a-b), the P-h curves for wedge indentations with both 90° and 120° inclination angles show pop-in events at a similar indentation depth of approximately 0.2 µm. This depth corresponds to about 50% of the thickness of the film. On the other hand, indentations with a standard Berkovich indenter exhibit smooth P-h curves without pop-ins (Fig.4.1(c)). The indentations using the 90° wedge tip have shown much pronounced pop-ins on the P-h curves as compared to that of indentations using the 120° wedge tip. This observation indicates that a wedge indenter with a sharper inclination angle may better facilitate the initiation of a central crack, because the popin event is only related to the central crack of the MSQ film (as shown below). 65 Chapter Fig. 4.1: Load vs. penetration depth (P-h) curves for the MSQ/Si system: (a) the 90° wedge indentation, (b) the 120° wedge indentation, and (c) the standard Berkovich indentation [1]. 66 [...]... p .17 53 -17 55, (19 94) 12 M.D Drory and J.W Hutchinson, Proc R Soc London, Ser A, 452, p.2 319 23 41, (19 96) 13 M.R Elizalde, J.M Sanchez, J.M Martinez-Esnaola, D Pantuso, T Scherban, B Sun and G Xu, Acta Mater., 51, p.4295-4305, (2003) 14 M.D Kriese, W.W Gerberich and N.R Moody, J Mater Res., 14 , p.30073 018 , (19 99) 11 Chapter 1 15 M.D Kriese, W.W Gerberich and N.R Moody, J Mater Res., 14 , p.3 019 3026, (19 99)... p.2639-2644, (19 84) 6 M.P DeBoer and W.W Gerberich, Acta Mater., 44, p. 316 9- 317 5, (19 96) 7 M.P DeBoer and W.W Gerberich, Acta Mater., 44, p. 317 7- 318 7, (19 96) 8 M.R Begley, D.R Mumm, A.G Evans and J.W Hutchinson, Acta Mater., 48, p.3 211 -3220, (2000) 9 M Schulze and W.D Nix, Int J Sol Struc., 37, p .10 45 -10 63, (2000) 10 J.J Vlassak, M.D Drory and W.D Nix, J Mater Res., 12 , p .19 00 -19 10, (19 97) 11 M.D Drory... wedge indentation, and (c) the standard Berkovich indentation Fig 4.2 Cross-sectional views of 90° wedge indentations on the MSQ/Si system using FIB: (a) no interfacial crack; (b) - (d) interfacial crack propagation Fig 4.3 Cross-sectional views of 12 0° wedge indentations on the MSQ/Si system using FIB: (a) no interfacial crack; (b) - (d) interfacial crack propagation Fig 4.4 Plane views of 90° wedge indentations... and 6. 61 µm, for 90° and 12 0° wedge indentations, respectively (2) Maximum Loads, Pmax for 90° and 12 0° wedge tip indentations are 9 mN and 15 mN, respectively Table 4.5 The calculation of interfacial toughness for the BD/Si system Note: (1) Data are averaged from 15 indentation impressions (2) The indentation plastic depth is determined from an indentation loadpenetration curve averaged from 15 indentations... [18 ] Year of Production 2007 2008 2009 2 010 2 015 Interconnect Metal -1 HalfPitch (nm) 68 59 52 45 25 Transistor Physical GateLength (nm) 25 22 20 18 10 Interlevel-Metal-Insulator’s Bulk Dielectric Constant (k) 2.5 - 2.9 2.5 - 2.9 2.3 - 2.7 2.3 - 2.7 1. 9 - 2.3 Interconnect RC-delay (ps) for a 1 mm Cu Metal -1 wire* 558 717 848 11 32 312 8 Fig .1. 3: Scanning electron microscopy (SEM) image of the low-k interfacial. .. indentation, (b) 12 0° wedge tip indentation, and (c) crosssectional view at 500 nm away from the end of the wedge indent for the 90° wedge tip indentation Fig 4.20 Plane view of the interfacial crack pattern by SEM: (a) BD film with thickness of 200 nm; (b) BD film with thickness of 500 nm Fig 4. 21 Interfacial toughness for the BD films with thickness ranging from 10 0 nm to 10 00 nm The interfacial toughness... the end of the wedge indentation impression Fig 7.2 (a) Cross-sectional image of 12 0° wedge indentation on the RuO2 film (thickness, t = 15 0 nm), showing the formation of interfacial crack at the pop-in load (b) Plane-view image of 12 0° wedge indentation on the RuO2 film, showing no observable film crack Fig 7.3 Load versus penetration depth (P-h) curves for the RuO2/Si system: (a) the 90° wedge indentation, ... depth hp Indentation plastic depth H Hardness k Dielectric constant l The length of wedge indenter tip N The strain hardening exponential P Indentation load xix Pc Critical indentation load for interfacial crack initiation P90c Critical indentation load for interfacial crack initiation for 90° wedge indentation P120c Critical indentation load for interfacial crack initiation for 12 0° wedge indentation. .. represent the simulation and experiment curves of 12 0° wedge indentation, respectively, open and closed square boxes represent the simulation and experiment curves of 90° wedge indentation, respectively Fig 5.3 The BD/Si system’s interfacial energy-strength contour for 90° and 12 0° wedge indentation showing the intersections of Pc90/(σyf Δo) = 5 .16 – 5 .18 µm and Pc120/(σyf Δo) = 6.58 – 6.92µm Full lines represent... (LKD- 610 3 JSR Corp., Japan) in NaOH solutions and water Fig 2 .11 The interfacial toughness degradation of an OSG/SiNx system as a function of the water-exposure time (water temperature at 95°C and 25°C) Fig 3 .1 Single loading/unloading curve of the BD film (500nm) by 90° wedge indentation Fig 4 .1 Load vs penetration depth (P-h) curves for the MSQ/Si system: (a) the 90° wedge indentation, (b) the 12 0° wedge . Crack Path 11 1 4.4.5 Work of Indentation and Fracture Energy 11 2 4.5 Conclusion 11 8 Reference 12 0 Chapter 5: Comparison of the Finite Element Simulation and Experiments of Wedge Indentation. Recommendations 17 1 8 .1 Interfacial Toughness 17 1 8.2 Time-dependent Fracture 17 3 8.3 Wedge Indentation on Multilayer 17 5 8.4 Hard-Film-on-Soft-Substrate 17 8 8.5 Other Avenues for Future Works 17 9. and D. Chi, Determining Interfacial Properties of Submicron Low-k Films on Si Substrate by using Wedge Indentation Technique, Journal of Applied Physics, 10 1, 12 35 31 (2007). 2. K.B. Yeap,