COMPUTATIONAL ANALYSIS AND CHEMICAL MECHANICAL POLISHING FOR MANUFACTURING OF OPTICAL COMPONENTS NGUYEN NHU Y SCHOOL OF MECHANICAL & AEROSPACE ENGINEERING 2016 COMPUTATIONAL ANALYSIS AND CHEMICAL MECHANICAL POLISHING FOR MANUFACTURING OF OPTICAL COMPONENTS NGUYEN NHU Y SCHOOL OF MECHANICAL & AEROSPACE ENGINEERING A thesis submitted to the Nanyang Technological University in partial fulfilment of the requirement for the degree of Doctor of Philosophy 2016 ABSTRACT High precision optical components are required for modern life and future. To achieve component’s surfaces with high quality, chemical mechanical polishing (CMP) is required. It is a unique method to obtain the global uniformity planarization across the surface without scratches. In the polishing of optical components, a new approach has been applied, including two phases: phase one is using the fixed abrasive pad with abrasive-free slurry and phase two is using the soft pad (the fabric cloth pad) with colloidal silica slurry.
This process has created a better uniformity surface with lower surface roughness. The non-uniformity of substrates after polishing is one of the most interesting things in current trends in research. One of the reasons for the non-uniformity is a pad wear profile. Researching on the pad wear profile by improving the pad conditioning process creates a better pad surface, and through that the substrates is polished with better uniformity.
Another reason for the non-uniformity is the distribution of abrasive particles in the interface between the wafer and pad surfaces under effects of the pad and wafer rotations. In this research, an analytical model was established by combining of the kinematic motions and the contact time to investigate the pad wear non-uniformity. The results have indicated that the cutting path density and the contact time at positions near the pad center are more than that near the pad edge. It is a good agreement with experiments.
New shapes of the pad and the conditioner have been developed to create a better pad wear profile. The pad after conditioning is convex and more uniform. Page | i In addition, a new computational fluid dynamic model was built. It was a combination of multiphase and discrete phase modelling to investigate the abrasive particles behaviour and the slurry distribution in the interface.
The total numbers of particles in the gap were quantified to characterize their mechanical effects under different operating parameters. The simulation results have shown that the particles are non-uniformly distributed below the wafer and provided a deeper insight understanding of the material removal of the CMP mechanism. From the understanding above, a new idea has been developed to explain the mechanism of the CMP processes. Page | ii ACKNOWLEDGEMENT First of all, I would like to express my gratitude to my supervisor, Associate Professor Zhong Zhaowei, for his supports, encouragements and insightful advice throughout my candidature.
I had learned a lot and grow a lot under his tutelage. I would like to thank my co-supervisor, Doctor Tian Yebing, from SIMTech, for his support, training and discussion in the research, also for supplements for experiments. I would also like to thank Nanyang Technological University and SIMTech for providing an excellent environment for my Ph. I wish to thank my husband and my daughter for their strong supports, encouragements.
I also thank my dear parents, my sister, and my brother for encouraging in all my endeavours. Special thanks to my dear friends who has discussed and helped me in my work and my life. Page | iii LIST OF PUBLICATIONS [1] N. Tian, "Analysis and improvement of the pad wear profile in fixed abrasive polishing," The International Journal of Advanced Manufacturing Technology, vol.
Tian, "An analytical investigation of pad wear caused by the conditioner in fixed abrasive chemical-mechanical polishing," International Journal of Advanced Manufacturing Technology, vol. Zhong, "Modeling and simulation for the distribution of slurry particles in chemical mechanical polishing," International Journal of Advanced Manufacturing Technology, vol. Zhong, "Improvement of the pad wear shape in fixed abrasive chemical-mechanical polishing for manufacturing optical components," presented at the International Conference on Optical and Photonic Engineering, Singapore, 2015. Page | iv TABLE OF CONTENTS ABSTRACT.
iii LIST OF PUBLICATIONS. iv TABLE OF CONTENTS. v LIST OF SYMBOLS. ix LIST OF FIGURES.
xiii LIST OF TABLES. xvii CHAPTER 1 INTRODUCTION.5 Organization of the thesis. 7 CHAPTER 2 LITERATURE REVIEW.2 Fixed abrasive polishing (FAP) .3 Non-uniformity in CMP processes .1 Effects of the head load (or polishing pressure) .6 Pad wear profile .8 Improvement of the non-uniformity .4 Material removal rate. 28 CHAPTER 3 ANALYSIS AND DEVELOPMENT OF THE FIXED ABRASIVE CHEMICAL MECHANICAL POLISHING PROCESS .2 Motion of one abrasive grain of the conditioner .5 Effects of operation speeds on the pad wear profile .6 Effects of sizes, patterns, and positions of the conditioners on the pad wear profile .7 Developing a new model to improve the pad wear profile.
54 Page | vi CHAPTER 4 COMPUTATIONAL FLUID DYNAMIC SIMULATION OF DISTRIBUTION OF ABRASIVE PARTICLES IN TRADITIONAL CMP .1 Volume of fluid (VOF) model .2 Discrete phase model (DPM) .3 Multiple moving frame .4 Motion of particles .5 Observation of the slurry flows in CMP process. 81 CHAPTER 5 INVESTIGATING THE WAFER NON-UNIFORMITY IN FIXED ABRASIVE POLISHING & CHEMICAL MECHANICAL POLISHING .2 The non-uniformity of surfaces in FAP and conventional CMP .1 Non-uniformity of wafer surfaces in FAP .2 Non-uniformity in conventional CMP. 100 CHAPTER 6 CONCLUSION AND FUTURE WORK.1 Review of objectives and conclusions .2 Major contributions and limitations. 107 Page | viii LIST OF SYMBOLS p Angular velocity of a pad c Angular velocity of a conditioner o Oscillating velocity of a conditioner no Frequency of the conditioner np The pad’s speed nc The conditioner’s speed rM Distance from a point M to the conditioner center Lt Distance between the conditioner and pad centers f Feed rate of a grain on the conditioner t Time A A matrix expressing the rotation around a origin D A matrix expressing the rotation around the conditioner center and the translation from the conditioner center to the pad center M An initial angle of the point M p An initial angle of the pad Page | ix rmin The smallest distance between grains and the center on the conditioner rmax The largest distance between grains and the center on the conditioner D p , Dc , Dw Diameter of the pad, the conditioner, the wafer, and the carrier, respectively Dca L Distance between the pad center and the wafer center V, H Distance between the pad center and a inlet (x and y direction, respectively) hc Distance between the pad and carrier surfaces h Distance between the pad and wafer surfaces m aw Mass transfer from phase air to phase water m wa Mass transfer from phase water to phase air w Water density w Water volume fraction in a cell a Air density mw Water viscosity ma Air viscosity Page | x Water velocity vw F Force/unit particle mass u Fluid phase velocity up Particle velocity m Molecular viscosity of a fluid Fluid density p Particle density dp Particle diameter C Cunningham correction to Stokes drag law Molecular mean free path v A frame’s absolute velocity A frame’s relative velocity vr A frame’s angular velocity r A frame’s position vector x, y, z A particle position Fu Shearing force Page | xi u Shearing stress Fn Head load P Pressure Ls Length of surface roughness ws Width of surface roughness E Young modulus k Particle concentration Rs Surface roughness Page | xii LIST OF FIGURES Figure 1.
Chemical mechanical polishing model. 3M fixed abrasive pad construction [44]. Schematic of a) a conventional nozzle, b) a new nozzle with a height of 10 mm, c) a new nozzle with a height of 30 mm, and d) a new nozzle with a height of 50 mm [9]. The new developed CMP in comparing with the traditional CMP [59].
Model of motions of the pad and the conditioner. Trajectories of four grain points of the conditioner M1, M2, M3, and M4 on the pad surface when the oscillation frequency is at 0 strokes/min, 2 strokes/min, 7.5 strokes/min, and 15 strokes/min. Trajectories of four grain points M1, M2, M3, and M4 with different ratios of the conditioner speed and the pad speed: 1/2, 2/3, 3/4, 4/3, 3/2, and 2. The conditioner geometry and the divided pad.
Distances that the grain moves in one time step in the X and Y directions. Flowchart of the program for calculating the Z coordinate of the pad surface. Measured positions for the pad height on the pad in experiments. Standardization values of the Z coordinates of the pad surface of the model; a) comparing to the experiment data, and b) comparing to the non-contact time model.
41 Page | xiii Figure 3. Effects of the oscillation speeds on the pad wear profile. Effects of the conditioner rotation speeds on the pad wear profile. Effects of the pad rotation speeds on the pad wear profile.
Effects of conditioner’s patterns on the pad wear shape when the conditioner placed static (only rotation, not oscillation). Effects of the conditioner size on the pad wear shape. Effects of conditioner’s position on the pad wear shape. A new model of the pad and conditioner shapes to improve the pad wear profile.
The improved result of the pad wear shape of the new model compared to the old model. Comparing effects of the new model, design 1 and design 2. Modeling of the CMP machine. Boundary condition model for ANSYS Fluent simulation: a) full model, and b) cross sectional view.
(a) Mesh schematic of the whole model and (b) sectional view and detailed mesh of the gap between the wafer, carrier and pad surfaces. Distribution of the fluid velocity in the gap with the simulation conditions: a pad speed of 20rpm, a wafer speed of 40rpm, slurry flow rate of 100ml/min, 10%v/v. 67 Page | xiv Figure 4. Static pressure below the wafer versus time at the pad speed of 20 rpm, the wafer speed of 40 rpm, the slurry flow rate of 100ml/min and the film thickness of 40 µm.
Static pressure of the fluid below the wafer and the carrier surfaces after 25 sec at the pad speed of 20 rpm, the wafer speed of 40 rpm, the slurry flow rate of 100ml/min and the film thickness of 40 µm. Dynamic pressure below the wafer and the carrier surfaces after 25 sec at the pad speed of 20 rpm, the wafer speed of 40 rpm, the slurry flow rate of 100ml/min and the film thickness of 40 µm. Number of particles in the gap between the wafer and pad surfaces at the slurry flow rate of 200 ml/min, the pad speed of 40 rpm, and the wafer speed of 40 rpm. Number of particles in the gap versus time at the same pad speed of 20 rpm, the wafer speed of 20 rpm and the slurry flow rate of 100 ml/min (10%v/v).
Number of particles in the gap between the wafer and pad surfaces at the same thickness of 40 µm, the pad speed of 40 rpm, and the wafer speed of 40 rpm. Total number of particles in the gap at 22 sec with the same slurry flow rate of 100 ml (10%v/v) and (a) the pad speed of 20 rpm, (b) the wafer speed of 20 rpm. Average number of particles per m2 on the interface between the wafer and the pad at the same pad speed of 20 rpm, slurry flow rate of 100 ml/min (10%v/v). Slurry distribution on pad surface with a pad speed of 20 rpm, a wafer speed of 40 rpm, slurry flow rate of 100 ml/min, (a) particle flow at the first second Page | xv from the inlet in the simulation, (b) water distribution after 15 sec and (c) particle distribution on the pad surface after 15 sec.
