SYSTEM IMPLEMENTATION, MODELING AND DEFECTS PATTERN RECOGNITION FOR FLIP CHIP SOLDER JOINT INSPECTION USING LASER TECHNIQUES

Transcription

1 SYSTEM IMPLEMENTATION, MODELING AND DEFECTS PATTERN RECOGNITION FOR FLIP CHIP SOLDER JOINT INSPECTION USING LASER TECHNIQUES A Thesis Presented to The Academic Faculty By Sheng Liu In Partial Fulfillment Of the Requirements for the Degree Doctor of Philosophy School of Mechanical Engineering Georgia Institute of Technology March 2001

2 ii SYSTEM IMPLEMENTATION, MODELING AND DEFECTS PATTERN RECOGNITION FOR FLIP CHIP SOLDER JOINT INSPECTION USING LASER TECHNIQUES Approved: I. Charles Ume, Chairman Suresh K. Sitaraman Achyuta Achari George Vachtsevanos Ye-Hwa Chen C. P. Wong Jerry H. Ginsberg Date Approved:

3 iii DEDICATION To my parents, my wife and my brother, for their support and sacrifices.

4 iv ACKNOWLEDGEMENT I would like to express my sincere appreciation to the many people who have helped me with this work. Special thanks go to my advisor, Dr. Charles Ume, for his guidance and support throughout this research, and for his assistance and friendship during these four years. I would like to thank my thesis reading committee: Drs. Achyuta Achari, Ye-Hwa Chen, Jerry Ginsberg, Suresh Sitaraman, George Vachtsevanos, and C. P. Wong, for their expertise and valuable suggestions. I would like to acknowledge the financial and technical supporters of this research: Visteon, Siemens, Atlanta Technology Development Center, and Department of Energy. I would also like to thank my colleagues for their assistance along the way: Sandra Hopkin, Dathan Erdahl, Bao Mi, Akio Kita, Hai Ding, Yu Qiu, Turner Howard, and Reinhard Powell. My wife, Bingqing Yang, has been supportive and compassionate beyond words. My parents, and my whole family have always been the source of support and courage. To them, I owe my humblest thanks.

5 v TABLE OF CONTENTS DEDICATION... III ACKNOWLEDGEMENT...IV TABLE OF CONTENTS... V LIST OF TABLES... X LIST OF FIGURES...XI SUMMARY... XV CHAPTER I... 1 INTRODUCTION... 1 CHAPTER II... 4 LITERATURES AND BACKGROUND... 4 FLIP CHIP TECHNOLOGY... 4 CONVENTIONAL FLIP CHIP SOLDER JOINT QUALITY INSPECTION TECHNIQUES... 7 ULTRASOUND GENERATION BY LASER IRRADIATION VIBRATION MODAL ANALYSIS OF PLATES Different Approaches for Vibration Modal Analysis of Plates... 13

6 vi Finite Element Vibration Analaysis DEFECTS PATTERN RECOGNITION Pattern Recognition Paradigm Supervised Learning and Unsupervised Learning Bayesian Decision Theory CHAPTER III SYSTEM DESIGN AND IMPLEMENTATION SYSTEM CONSTRUCTION Laser Optical Fibers X-Y Precision Positioning Stage Interferometer Filter/Amplifier Data Acquisition Power meter Computer SYSTEM CHARACTERIZATION Insonification Position Relative To Sensor Isolation of Environmental Vibration Laser Power SYSTEM RESOLUTION... 42

7 vii CHAPTER IV EXPERIMENTAL PROCEDURES AND DATA ANALYSIS DATA ACQUISITION SCANNING PATTERN SIGNALS FROM FLIP CHIP SAMPLES TIME DOMAIN ERROR RATIO ANALYSIS DETECTING ON TOP OF EACH SOLDER JOINT POWER SPECTRUM ANALYSIS IN FREQUENCY DOMAIN PERIODOGRAM AVERAGING ANALYSIS IN FREQUENCY DOMAIN CHAPTER V CAPABILITIES OF THE FLIP CHIP DEFECTS INSPECTION SYSTEM DETECTION OF MISSING SOLDER BALL/UNDERSIZED SOLDER BALL DETECTION OF FLIP CHIP SURFACE DEFECTS DETECTION OF MISALIGNED SOLDER BALL SYSTEM RESOLUTION TEST THROUGHPUT OF THE SYSTEM CHAPTER VI MODELING BASED ON VIBRATION MODAL ANALYSIS WHY USE VIBRATION ANALYSIS FOR MODELING THEORY BEHIND VIBRATION MODAL ANALYSIS MODELING BY USING FINITE ELEMENT METHOD... 91

8 viii Geometric Solid Modeling Materials Meshing Boundary Conditions Modal Analysis Results Experimental Verification CHAPTER VII PATTERN RECOGNITION OF DEFECTS PREPROCESSING FEATURE EXTRACTION Training Samples CLASSIFICATION Region of Interest Probabilistic Neural Network Classifier PNN Classifier Training PNN Classifier Testing FURTHER CLASSIFICATION CHAPTER VIII IMPACT AND CONTRIBUTION IMPACT

9 ix CONTRIBUTION CHAPTER IX CONCLUSION AND RECOMMENDATIONS APPENDIX MATLAB PROGRAMS MATLAB ROUTINE FOR ERROR RATIO ANALYSIS MATLAB ROUTINE FOR FFT AND PSD ESTIMATION BY USING BARTLETT (PERIODOGRAM AVERAGING) METHOD MATLAB ROUTINE FOR FEATURE EXTRACTION AND PNN CLASSIFICATION. 139 REFERENCES

10 x LIST OF TABLES TABLE 5-1: THROUGHPUT PARAMETERS OF CURRENT AND OPTIMIZED SYSTEM TABLE 6-1: VIBRATION FREQUENCIES (KHZ) OF DIFFERENT CHIPS (MODELING RESULTS) TABLE 6-2: VIBRATION FREQUENCIES (KHZ) OF DIFFERENT CHIPS (EXPERIMENTAL RESULTS) TABLE 6-3: MODELING RESULTS COMPARED WITH EXPERIMENTAL RESULTS

11 xi LIST OF FIGURES Figure 2-1: Various Flip Chip Technologies... 5 Figure 2-2: Laser Ultrasound Generation Figure 2-3: Pattern Recognition Paradigm Figure 2-4: Bayes Decision Theory Figure 3-1: System Construction Figure 3-2: Prototype of Solder Joint Quality Inspection System Figure 3-3: Nd:YAG Laser Used as Ultrasonic Source Figure 3-4: Optical Fiber Figure 3-5: Fiber Comes In With 45º Angle Figure 3-6: XY-Positioning Stage Figure 3-7: Heterodyne Interferometer Figure 3-8: Polytec Interferometer Figure 3-9: Filter/Amplifier Unit Figure 3-10: Power Meter Figure 3-11: Signals Detected at Different Chip Position Figure 3-12: Effects of Environmental Vibration Figure 3-13: Laser Power with Time Figure 4-1: Flip Chip on Ceramic Substrate Figure 4-2: Scanning Pattern of Flip Chip Sample... 45

12 xii Figure 4-3: Solder Joints of Flip Chip Samples Figure 4-4: Signals at Detection Point A Figure 4-5: Signal at Detection Point B Figure 4-6: Signal at Detection Point C Figure 4-7: Signal at Detection Point D Figure 4-8: Error Ratio of Good Chip Figure 4-9: Error Ratio of Bad Chip Figure 4-10: Error Ratio of Bad Chip Figure 4-11: Error Ratio of Good Chip 2 on Top of Each Solder Joint Figure 4-12: Error Ratio of Bad Chip 1 on Top of Each Solder Joint Figure 4-13: Signal Recorded for Frequency Analysis Figure 4-14: Power Spectrum Distribution of Signal Figure 4-15: Frequency Response of the Band Pass Filter Figure 4-16: Power Spectrum of Signals After Filtering Figure 4-17: Noisy Signal Recorded by Interferometer Figure 4-18: Power Spectrum Distribution of Noisy Signal Figure 4-19: Theoretical PSD of a Vibration Signal Figure 4-20: Time Domain Averaging Compared with Bartlett Method Figure 4-21: Power Spectrum of Flip Chip Samples Figure 5-1: Good Chips and Chips with Defects at Solder Bump Figure 5-2: Signals from Four Flip Chip Samples for Solder Joints Defects Inspection.. 71 Figure 5-3: Error Ratios for Solder Joints Defects Inspection... 72

13 xiii Figure 5-4: Good Chips and Chip with Surface Defects Figure 5-5: Signals from Four Flip Chip Samples for Surface Defects Inspection Figure 5-6: Error Ratios for Surface Defects Inspection Figure 5-7: Good Chips and Chips with Solder Joint Misaligned Figure 5-8: Signals from Four Testing Samples for Misalignment Inspection Figure 5-9: Error Ratios for Misaligned Solder Ball Inspection Figure 5-10: Solder Ball and Detection Point Distribution of Test Sample Figure 5-11: Error Ratio Distribution Along the Three Edges Figure 6-1: Standard Mass-Spring System Figure 6-2: A Bar Supported by Springs Undergoing Flexural Displacement Figure 6-3: Mode Functions For an Elastic Bar Supported by Springs Figure 6-4: Geometric Model of Flip Chip and Solder Ball Figure 6-5: Solid Model of a Good Chip Figure 6-6: Solid Model of Chip with One Missing Solder Ball Figure 6-7: Solid Model of Chip with Delamination on a Solder Joint Figure 6-8: Solid 187 3D 10-Node Tetrahedral Structural Solid Figure 6-9: A Flip Chip Model After Meshing Figure 6-10: Mode Shape of the 1 st Vibration Mode Figure 6-11: Mode Shape of the 2 nd Vibration Mode Figure 6-12: Mode Shape of the 3 rd Vibration Mode Figure 6-13: Mode Shape of the 4 th Vibration Mode Figure 6-14: Solder Joints of Flip Chip Samples

14 xiv Figure 6-15: Power Spectrum of Good Chip Figure 6-16: Power Spectrum of Good Chip Figure 6-17: Power Spectrum of Bad Chip Figure 7-1: Views of Training Samples (Chip 1 to Chip 10) Figure 7-2: Views of Training Samples (Chip 11 to Chip 20)Feature Vector Design Feature Vector Design Figure 7-3: Maximum Error Ratio of Each Training Sample Figure 7-4: Dominant Frequency of Each Chip Figure 7-5: Feature Vector Distribution of Sample Chips Figure 7-6: Training Feature Vectors and Region of Interest Figure 7-8: Architecture of Probabilistic Neural Network Figure 7-9: A Radial Basis Function On the Planar Feature Space Figure 7-10: An Example of Two Input Features and Two Output Classes Figure 7-11: Output of the PNN Classifier Figure 7-12: Training Vectors Distribution with Decision Surface Figure 7-13: Views of Test Samples Figure 7-14: Classification Results of Test Samples Figure 7-15: Output of PNN Classifier for Further Classification Figure 7-16: Further Classification Results

15 xv SUMMARY A trend in electronic packaging interconnection technology is the change from wire bonding chip attach technology to solder bump technology. Solder bump technology has been proven to be a reliable interconnection in many advanced packaging formats including flip chip, ball grid array (BGA), chip scale, multi-chip module (MCM), and other surface mount components. However, because of the physical configuration of these integrated circuit (IC) packages, traditional solder joints inspection methods, such as X-ray, acoustic microscopy or visual inspection, are either not suitable for solder bump inspection, or not efficient for automated on-line inspection. Therefore, new techniques for inspecting the solder bump defects of these new IC packages in a reliable, fast and non-destructive means are highly desired in today's electronic packaging industry. The objective of this research is to develop a non-contact, non-destructive, low cost, fast, accurate, high resolution, and automated system for monitoring the quality of solder bumps (balls) in flip chips and other surface mount components. This novel approach for solder bump quality inspection has been developed by using laser ultrasonic and interferometric techniques. It is the first application of laser ultrasound technology to solder bump inspection. In the developed system, a pulsed Nd: YAG laser is directed to a chip s surface through a fiber or fibers. The thermal expansion and contraction, caused by rapid laser pulses, generate ultrasound at the chip s surface, causing the chip to vibrate on its joints. An interferometer is used to measure the displacement at the chip s surface

16 xvi due to vibration. Changes of solder joint quality in areas close to the inspection points produce different vibration responses at that specific point. Signal-processing algorithms have been developed to increase the signal-to-noise ratio, and to quantitatively measure the difference between a good chip and chip with defects, both in time domain and frequency domain. Experimental results indicate that this system is capable of detecting solder joint defects such as missing solder balls, undersized solder balls, misaligned solder balls, and other surface defects on silicon die. Other solder defects such as cracks, voids, and etc have not been investigated. Although the resolution limit of this method has not been tested, with current setup, a missing solder ball with diameter of 120µm has been detected. A finite element model, based on vibration modal analysis, has been constructed to model the chip vibration phenomenon, to explain experimental results, and to improve the design of a defects pattern recognition algorithm. The modeling results match up with experimental results very well. Both results indicate that defects in a solder joint change chip s vibration transient response and its natural frequencies of vibration. Measurement of these properties can be used to detect solder joint defects. In order to automate this system, a defects pattern recognition method was also developed to automatically classify chips into different clusters, so that good chips can be distinguished from chips with defects. In this method, a feature vector was designed as a vector containing error ratio and dominant frequency as elements. The classifier was constructed by using probabilistic neural network. The defects pattern recognition

17 xvii method can find differences between good and bad chips, as well as classifying the type of defect. This laser ultrasound/interferometric system offers great promise for solder bump inspection in a fast and efficient manner. A fully developed system could be used in an assembly line for quality assurance, or off-line during process development for process optimization.

18 CHAPTER I INTRODUCTION Consumer demands are driving the microelectronic packaging industry to make products that are compact, high density, light and thin. These products must also be fast, reliable, robust and available at minimal cost. Chip interconnection methods are critical to achieving these design objectives because improved connection methods reduce IC package size while maintaining reliable connections. A trend in interconnection technology is the change from wire bonding chip attachment to solder bump technology. Solder bump technology has been proven to be a reliable interconnection in many advanced packaging formats including flip chip, ball grid array (BGA), chip scale and multi-chip module (MCM) packages, and other surface mount components. These packages use small solder bumps underneath chips for interconnection, making them superior in performance to all other interconnection technologies. Unfortunately, the physical configuration of these interconnects makes quality inspection impossible or inefficient using techniques practiced with previous interconnection technologies (e.g. wire bonding, TAB, etc.). Therefore, new techniques for detecting solder bump defects in a reliable, fast, and non-destructive means are highly desired in today s electronic packaging industry.

19 2 The overall purpose of this research is to develop a non-contact, non-destructive, low cost, fast, accurate, high resolution, and automated system for monitoring the quality of solder bumps (balls) in flip chips. It can also be extended to inspect solder bumps on BGAs, chip scales, MCMs, and other surface mount components in the future. This system has been used to measure the surface defects on flip chips, misaligned, undersized and missing solder balls on flip chip packages. It is expected that a fully developed system can be used to inspect solder bumps quality in production line, and off-line during process development for process optimization. The focus of my own research is in the following three areas: to contribute in the design and construction of a laboratory prototype of this solder bump quality inspection system, with specific focus on developing experimental procedures and data analysis methods; to develop an automated pattern recognition analysis method for detecting and classifying solder joint; to model chip vibration phenomenon by using finite element analysis technique. The measurement system developed comprises of a laser ultrasonic unit and a laser interferometric unit. In this system, a pulsed Nd:YAG laser excites a flip chip into vibration by a thermoelastic generated ultrasound, and a heterodyne laser interferometer measures the displacement of the chip s surface at several points. Presence of a bad solder joint, or a chip defect produces abnormal vibration responses at inspection points closest to the defect. Signal-processing algorithms have been developed to increase signal-to-noise ratio, and to measure differences between a good chip and a chip with defect(s). Error ratio and vibration frequencies are used to quantitatively measure the

20 3 differences, both in time domain and frequency domain. Since only a few brief laser pulses are needed to get a signal from one chip, this method is an efficient means of determining solder joint quality. A finite element model, based on vibration modal analysis, was developed to model chip vibration phenomenon, to explain experimental results, and to improve the design of a defects pattern recognition algorithm. Both experimental results and modeling results indicate that defects in solder joints not only change a chip s vibration transient response, but also its natural frequencies of vibration. Measurement of these properties can be used to detect solder joint defects. The defects pattern recognition method has been developed using probabilistic neural networks. Experimental results indicate that this defects pattern recognition method can distinguish good chips from bad chips. It can also classify defects into different types. The pattern recognition method makes complete automation of the solder bump monitoring system possible. In my research, flip chips are chosen as test vehicles, because flip chip is becoming widely used in the electronic packaging industry, and also the sponsors of this research provided us with flip chip test samples.

21 4 CHAPTER II LITERATURES AND BACKGROUND The objective of this research is to develop a non-contact, non-destructive, low cost, fast, accurate, high resolution and automated system for monitoring the quality of solder bumps (balls) in integrated circuits by using laser ultrasound and interferometric techniques. To achieve this objective, a wide range of knowledge and a multidisciplinary background are required, including flip chip technology, conventional solder joint inspection techniques, laser ultrasound and interferometric techniques, mechanicalelectrical system design and implementation, digital signal processing, vibration analysis and modeling, and defects pattern recognition. Flip Chip Technology Flip chip is the type of chip whose active side is facing the substrate, and chip is connected to the substrate through interconnects (see Figure 2-1). The solder-bumped flip chip was introduced by IBM in the early 1960s, as an alternative to the expensive, unreliable, low yield, low productivity, face-up wire-bonding technology (Lau, 1995).

22 5 Figure 2-1: Various Flip Chip Technologies A typical flip chip attachment process can be described as follows. The first step is to deposit solder balls on the chip. A solder paste is laid down using either a screenprinting process or a small syringe. The screen-printing process puts pastes of solders on the substrate through small holes drilled in a metal screen. In the next stage, a pick-andplace machine is used to accurately place the chips on top of the solder pastes. A camera is used to find the exact location through fiducial marks on the corners of the board. To clean all of the contacts, and to help hold the chip in place, a flux is often used between the chip and the board. The third step is to pass the board assembly through a soldering oven. The oven brings the entire assembly above the liquidus temperature for the solder in use, and the solder wets the surface of the chip and the surface of the substrate. Special care is taken to create under bump metallurgy (UBM) that keeps the solder in small cups made to be wet. The UBM helps prevent solder shorts and encourages good

23 6 bonds between the chip and substrate. After leaving the oven, the chips should be solidly attached to the circuit board (Blackwell, 2000). Compared to the more widely used face-up wire-bonding technologies, flip-chips provide the shortest possible leads, lower inductance, higher frequency, better noise control, higher density, greater input/output (I/O), smaller device footprint and lower profile. From an automation perspective, the two processes are substantially different. Wire bonding is best characterized as a single-point-unit operation. Each bond is individually produced. Flip chip is a wafer-scale operation. Bumps are formed on an entire wafer, and the wafer is diced; individual die are picked, fluxed and placed on the substrate (Elenius, et al, 2000). In summary, motivation to use flip chip attachment revolves around the following technological and economic variables (Bogdanski, 2000): 1) Highest performance in terms of speed, reduced inductance, superior power and ground distribution, improved signal propagation and noise isolation; 2) Higher I/O count per die; 3) Increased wafer utilization; 4) Retaining the same die pad footprint as the die shrinks, eliminating the need to relayout substrates or PWBs; 5) Wider pitches over the entire area of a die or multiple staggered rows on the die, which offer cost relief and routing relief in the substrates of BGA packages;

24 7 6) Enhanced thermal management of high speed high I/O IC s; 7) Machine utilization and throughput. Since flip chip technology is being used more widely, an important consideration in the design of a flip-chip system is interconnection quality and reliability. In a perfect assembly process, quality inspection or reliability testing would not be necessary. However, in reality, such a perfect process is not possible. Process characteristics shift with time, incoming materials vary, power gets interrupted, and human errors. These and other variations make inspection a necessity (Whitaker, 2000). Conventional Flip Chip Solder Joint Quality Inspection Techniques In the past few decades, many solder joint quality inspection techniques have been developed. Why must a new technique be developed? Traditional methods, such as x-ray, acoustic microscope and visual inspection techniques, were originally designed to detect wire bonding interconnection quality, and when they are applied to flip chip solder joint inspection, there are some drawbacks. There are two main types of x-ray detection methods: laminography and microfocus radiography. The difference is on cost, complexity and shadowing methods (Masi, 1991). Laminography can take images of layers within the part, and determine defect location based on planar scan. Although X-ray laminography can produce images of cross sections of a solder joint, it is too expensive and time consuming. The X-ray radiography approach provides a means of looking through the chips and substrates to see

25 8 the relative location and size of solder balls, but it is still unsuitable for this application. Because x-ray methods rely on the thickness of material the x-rays pass through, poor connections, delaminations, and cracks are very difficult to detect. In addition, images are produced, but they must be interpreted. Extracting solder joint quality information from these images is difficult, time-consuming, and subjective, making the process hard to automate (Edward, 1991). Acoustic microscopes utilize high frequency ultrasound to examine the internal features in materials and components (Adams, 1995). Defects such as pre-existing voids in the solder joints and non-wetting of the solder to the chip or to the substrate bond pads can be observed (Semmens, et al, 1997). The reason to choose high frequency ultrasound is that it has the penetrating power needed and has been shown to be sensitive to solder joints defects (Masi, 1991). However, the ultrasonic imaging systems currently in the market could be destructive to some test samples, because the printed wiring board (PWB) assembly must be immersed in water during the inspection process (Kubota, 1992). In addition, these techniques are difficult for on-line inspection. For off-line inspection it takes several minutes to image the solder beads under a single chip. Because many solder joints are located near the edge of the chip, edge effects distort the ultrasound, providing a poor image in the region of interest. Visual inspection techniques are not adequate for the evaluation of flip chip attach because the solder joints are hidden from view in this type of package. Currently, the widely used inspection techniques are functional testing methods. After assembling the entire printed circuit board (PCB), the testing fixture checks for

26 9 electrical continuity and proper operation by comparing the electrical response at specific nodes to previously determined values. However, unsoldered joints may still pass this test if any type of mechanical contact exists, although the part may fail after a short service life because of cracks or partial connections. The equipment necessary for these tests can be very expensive and time consuming, so other options need to be pursued. Some other solder joint inspection methods have also been tested in the past. The laser-thermal inspection technique uses an infrared laser beam to heat a spatially localized region (a solder joint) and infers joint characteristics from the way the joint heats up and cools down (Traub, 1985; Vanzetti, et al, 1989). The electro-optic probe technique detects the electric field intensity above two adjoining solder joints (Yojima, et al, 1998). The vibration detection method is used to detect surface-mount component leads for solder joint inspection. An impulse force, such as an air jet, is used to excite vibrations in the leads. Defects are detected by measuring the vibration frequency shifting of leads (Lau, 1989; Hiroi, 1993; Keely, 1989). The above methods are time consuming to use, and can t be used in IC solder bump(s) inspection. Because of the weaknesses of traditional solder joint inspection methods, it is highly desired to develop an on-line, fast, low cost, non-contact and non-destructive system for inspecting flip chip, BGA and other IC packages that use solder balls interconnections. It is the objective of this research to develop such an automated solder joint inspection system by using laser ultrasound and interferometric techniques.

27 10 Ultrasound Generation by Laser Irradiation In order to detect flip chip solder joint defects, some kind of signal source must be chosen to generate signals inside the chip. The signal generation method must be easy to control and implement, as well as be completely nondestructive. To fulfill the requirements, a technique called laser ultrasound was chosen. Laser Source Thermoelastic Expansion Figure 2-2: Laser Ultrasound Generation Irradiating a specimen surface with pulsed laser energy can generate broadband acoustic waves, mainly at ultrasonic frequencies. When laser light falls incident on a specimen, a portion of the energy is absorbed by the specimen and a portion is reflected. The absorbed energy serves to increase the temperature of the specimen in the vicinity of irradiation. The local thermal expansion and contraction generate stress waves in the sample, as shown in Figure 2-2 (Scruby, 1990; Hopko, 1999).

28 11 It is important to note that the characteristics of the laser source affect the type of elastic waves generated. When the energy absorbed is within the thermoelastic regime for the tested material, the stresses induced fall below the elastic limit for that material, so that no permanent deformation or damage occurs. Permanent damage begins to occur as the incident power density is increased beyond the thermoelastic limit. When the thermal flux is too high, the surface temperature rise is capable of exceeding the vaporization temperature. Atoms leave the surface at high velocities imparting a momentum to the sample surface, which is the source of ultrasound. This mode of generation is referred to as ablation. In this research, because electronic chips are delicate, only thermoelastic generation of ultrasound can be used to generate signals without damaging the chips. Vibration Modal Analysis of Plates As discussed above, it is well known that pulsed laser can generate acoustic waves because of the local thermal expansion and contraction (Scruby, 1990). In recent years, the dynamic excitation based on laser pulses has started to be used for modal analysis (Philp, 1995 and Castellini, 1999). In this research, a pulsed laser is directed to a flip chip s surface in order to cause it to vibrate. During the test process, the chip is vibrating on top of solder supports, and the effect is that of a plate supported by springs (Singal, et al, 1992). To model this vibration phenomenon caused by laser ultrasound, vibration modal analysis of plates can be used. The modeling result can be used to

29 12 explain the experimental results, and to improve the defects pattern recognition algorithm (Adams, 1967). It is well known that there exists a large number of discrete frequencies at which a structure will undergo large-amplitude of vibration by sustained time varying forces of matching frequencies. These are said to be resonant, natural, or free vibration frequencies of that structure. It is also known that associated with each natural frequency there is a distinct characteristic or mode shape which the structure acquires as it vibrates. In this research, because only the transverse vibration on chip s surface can be excited and detected, and the chip s length and width are usually much larger than it s thickness, a chip can be simply modeled as a rectangular plate with pin supports. The differential equation governing the pure bending of plates is well known. It is attributed to Lagrange and its development is presented in detail by Timoshenko (Timoshenko, 1959), where it is written W ( x, y) W ( x, y) W ( x, y) q( x, y) = x x y y D (Eq. 2.1) Here W ( x, y) is the surface displacement, q ( x, y) is the applied static loading and D is the plate flexural rigidity. In the free vibration of a plate there will be no surface loading. However, there will exist an inertial body force which must be taken into consideration. This inertial force is due to the oscillatory nature of the plate motion. We thus obtain the governing differential equation

30 13 0 ),, ( ), ( ), ( 2 ), ( = t t y x W D y y x W y x y x W x y x W ρ (Eq. 2.2) Note that in this equation, the surface displacement W must be expressed as a function of the coordinates x and y and time t. This displacement function ),, ( t y x W can be expressed as the product of two functions. This equality can be written as ) ( ), ( ),, ( t T y x W t y x W = (Eq. 2.3) For vibration modal analysis, we are only interested in the displacement function ), ( y x W. By using dimensionless space variables ξ and η, where a x / = ξ, and b y / = η, the free vibration governing differential equation can be written in the form 0 ), ( ), ( ), ( 2 ), ( = + + η ξ λ φ ξ η ξ φ ξ η η ξ φ η η ξ W W W W (Eq. 2.4) where, D a / 2 2 ρ ω λ = and the plate aspect ratio a = b / φ (Gorman, 1982). Theoretically, there are an infinite number of solutions to the governing differential equation shown above, and each solution corresponds to one natural frequency and vibration mode. Different Approaches for Vibration Modal Analysis of Plates The subject of vibration modal analysis of plates has a long history. It is widely used in mechanical engineering, civil engineering and other areas. There have been three

31 14 principal approaches taken toward resolving these plate vibration problems: Rayleigh- Ritz Method, Superposition Method and Finite Element Method (FEM). The most popular traditional approach is based on energy considerations and the method of analysis is known as the Rayleigh-Ritz Method. In order to use this method, one must choose an appropriate set of functions to represent the plate mode shape. These functions must also satisfy certain boundary conditions of the problem under study. Mode shapes are usually represented by an infinite series of functions, but only a finite number of functions can be employed in the analysis. It is found that frequencies obtained generally represent upper limits for the actual frequencies (Gorman, 1999). The Ritz series method is a powerful tool for evaluating the response of continuous systems, but it is difficult to implement when a system s configuration is irregular or intricate (Ginsberg, 1998). An alternate approach is the Superposition Method. The superposition technique takes its roots in the work of Timoshenko where it was exploited to obtain the response of plates to lateral static loading (Timoshenko, 1959). Its application to dynamic free and forced vibration problems was achieved essentially by replacing the static lateral loads with lateral inertial loads. It is the only one of the three methods which provides solutions satisfying the governing differential equation exactly throughout the entire domain of the plate (Gorman, 1999). Similar to the Ritz series method, the superposition method is also difficult to implement when a system s configuration is irregular or not symmetric.

32 15 In recent years, with the development of high-speed digital computers, use of the finite element method has become very popular. In this approach, numerical methods have been used to obtain solutions which satisfy, as closely as possible, the plate governing differential equation and the prescribed boundary conditions. In comparison to the Ritz series method, which fits one description to the entire system, the finite element method applies a different representation to each constituent part. Another difference is that the generalized coordinates in FEM are actual displacement variables for selected points, instead of the abstract amplitudes of basis functions covering the entire system. The finite element method can be used to solve vibration problems with irregular system configuration and complicated boundary conditions. For a flip chip, the distribution of solder balls is not always symmetric and the boundary condition is usually complicated. Therefore, finite element method is a good choice to model the vibration of flip chips. Finite Element Vibration Analaysis When applying the finite element method to vibration analysis, typically the following procedure is used (Petyt, 1990): 1) Geometry modeling The first step is to build a geometric model of the structure, by using 3D solid modeling. 2) Develop finite element mesh

33 16 The second step is to mesh the vibration structure into finite elements. There are different types of elements. The element type should be appropriately chosen according to the structure, the problem to be solved, and assumptions. For each element, interpolating functions need to be defined, which should satisfy all geometric continuity conditions. Interpolating functions are used to construct the displacement function. 3) Derive the energy expressions for each element in terms of nodal degrees of freedom relative to local coordinates. The next step is to construct the mechanical energies and power expressions associated with the element displacement. Elemental inertia matrix and stiffness matrix need to be derived. 4) Transform the energy expression for each element into expressions involving nodal degrees of freedom relative to global coordinates. The task now is to combine these elemental matrices and to form the global system matrices. 5) Assembly of the elements By assembling all elements, the energies of the elements are added together. The full equation can be solved by numerical methods. Although the finite element solution is just an approximate solution, with the ever increasing computer speed and memory, the finite element mesh can be further refined to give a solution that is closer to that of the closed form (Reddy, 1993).

34 17 Defects Pattern Recognition One major objective of this research is to automate solder joint inspection system, making it available for on-line inspection, because there is a dramatic need for quality assurance of packaged electronics. Traditionally, reliable automated inspection of solder joints is hampered by unclear rejection criteria, inadequate data acquisition technologies, and time consuming algorithms for classification of defects. In this research, we are trying to solve this problem by using defects pattern recognition technology. Pattern recognition is one of the key technologies for the automation of solder joint inspection, and some pattern recognition methods have already been used in some of the inspection systems. Sankaran developed a neural network approach to classify image data on visual and X-ray laminography devices (Sankaran, et al, 1998). Oyeleye and Lehtihet developed a classification algorithm and optimal feature selection methodology for implementation of an automated solder defect inspection system (Oyeleye, et al, 1998). In their system, computer generated three-dimensional geometric models of solder joint defect are used to train the system and simulate defect classification. Ko and Cho used neural network and fuzzy rule-based classification in solder joint inspection (Ko, et al, 1998). Pattern recognition methods currently used on solder joint inspection are all based on image processing or geometric model, which are time consuming and subjective (Vachtsevanos, et al, 1995). Sometimes, it is not necessary to create images during

35 18 inspection process. In our research, a waveform pattern recognition method will be used to recognize solder joint defects. There is a long history of waveform pattern recognition. The measured data in many applications are a set of waveforms, from which desired information must be extracted (Lee, 1993; Miao, et al, 1996; Kahl, 1997). In practice, waveforms contains far more information than can be fully extracted by human users (Chen, 1982). Waveform pattern recognition methods are widely used in the field of mechanical engineering, including condition monitoring of machines, production quality control, modal testing and others (Braun, 1986). But the waveform pattern recognition method has not been applied to solder joint inspection in package electronics. Generally, pattern recognition can be categorized into three groups: Syntactic Pattern Recognition, Conventional Statistical Pattern Recognition, and Neural Network Pattern Recognition. Syntactic Pattern Recognition deals with primitive selection, pattern grammar, syntactic classification, error correcting, parsing and syntactic clustering. It is often used on handwriting recognition. Therefore, it is not suitable for waveform processing. Statistical Pattern Recognition assumes a statistical basis for classification of algorithms. By considering the patterns as statistical in nature, the statistical pattern recognition deals with the statistical description of digital signals, the extraction of mathematical features, decision rules, clustering, and the estimation of parameters and densities (Schalkoff, 1992).

36 19 Neural Pattern Recognition emerged from attempts to draw on knowledge of how biological neural systems store and manipulate information. Neural Networks can be characterized by network topologies, adaptive training rules, and nonlinear node functions (Lippman, 1987; Morgan, 1991). The boundary between Neural Pattern Recognition and Statistical Pattern Recognition is fuzzy and fading. They share common features and common goals. But Neural Pattern Recognition is particularly well suited for pattern association applications and non-linear classification. In this project, a set of characteristic measurements, denoted features, are extracted from the input data and are used to assign each feature vector to one of several classes. Sometimes because of the characteristic of feature vector distribution, different classes are not linearly separable. Therefore, a type of neural pattern recognition method was used. Pattern Recognition Paradigm As described before, signals measured by this inspection system are all surface vibration waveforms. In order to automate this inspection system, a pattern recognition method needs to be used to classify those waveforms, and then identify the solder joint defects. A typical pattern recognition paradigm should consist of preprocessing, feature extraction and optimization, and selection of an appropriate classifier topology that provides the best mapping to the underlying good feature distribution (Kil, 1996). The

37 20 three components of the integrated pattern recognition paradigm mutually reinforce one another, as shown in Figure 2-3. transform FeatureExtraction Class separability Signal Physics Dimension reduction Preprocessing Energy compaction Noise suppression Low-dimensional signal characterization class discrimination optimized features performance metrics process sequence divide-andconquer Classifier Topology Feature pdf shapes Temporal variability Computational issues Figure 2-3: Pattern Recognition Paradigm Preprocessing accomplishes signal sorting or separation, energy compaction via noise suppression and filtering, and low-dimensional signal characterization via appropriate transform algorithms. The main objective here is to separate signals of interest from confusing elements, such as noise, interference, and environmental propagation. Feature extraction attempts to capture essential target attributes useful for class separation. Although it is possible that the raw time-domain data can be used as features, it is not recommended because the raw data may contain noise and interference that can

38 21 be suppressed or filtered by appropriate transform algorithms. Furthermore, the resulting feature dimension directly from raw data is too high, leading to the curse of dimensionality in classifier design. Besides, construction of initial features and subsequent feature optimization provides us with insight into signal physics. It is very important that the classification process does not remain as a black box, but as a physical entity that is logically explainable. After feature extraction, appropriate classifier architectures need to be developed to exploit the underlying feature distribution. Classifiers are nothing but projection operators that transform the optimized feature subset onto a classification decision dimension. Supervised Learning and Unsupervised Learning Pattern recognition methods can also be categorized into supervised (guided) pattern recognition and unsupervised (unguided) pattern recognition. In supervised pattern recognition, there exists a training set with labeled patterns. In unsupervised pattern recognition, patterns in the training set are not labeled. In our research, we used supervised pattern recognition, which means the inspection system must be trained before it can be used for automated defects inspection. The original perceptron and backpropagation are examples of supervised learning paradigms. In supervised learning, the network is trained on a training set consisting of vector pairs. One vector is applied to the input of the network; the other is used as a

39 22 target representing the desired output. Training is accomplished by adjusting the network weights so as to minimize the difference between the desired and actual network outputs. This process may be an iterative procedure, or weights may be calculated by closed-form equations. Paradigms using the latter form of training may seem to be so far from the biological method that they fail to qualify as an artificial neural network. Nevertheless, such methods are useful and satisfy a broad definition of artificial neural networks. Bayesian Decision Theory When using pattern recognition method, after signal preprocessing and feature extraction, a classifier needs to be designed to classify feature vectors into different groups. Bayesian decision rule is the fundamental theory for the design of many classifiers. Given a classification task of two classes, ω 1, ω 2, and an unknown pattern, which is represented by a feature vector x, we assume that the a priori probabilities p ( ω 1 ), p ω ) are known. This is a reasonable assumption, because even if they are not ( 2 known, they can easily be estimated from the available training feature vectors. The other statistical quantities assumed to be known are the class conditional probability density functions p x ω ), i = 1, 2, describing the distribution of feature vectors in each ( i of the classes. If these are not known, they can also be estimated from the available training data (Duda, 1973).

40 23 Recall that the Bayes rule can be expressed as p( x ωi ) p( ωi ) p( ω i x) = (Eq. 2.5) p( x) where p (x) is the pdf of x and for which we have p( x) = 2 i= 1 p( x ω ) p( ω ) (Eq. 2.6) i i The Bayes classification rule can now be stated as If p( ω 1 x) > p( ω 2 x), x is classified to ω 1 (Eq. 2.7) If p( ω 1 x) < p( ω 2 x), x is classified to ω 2 (Eq. 2.8) Figure 2-4 presents an example of two classes. The dotted line at x0 is a threshold partitioning the feature space into two regions, R 1 and R 2. According to the Bayes decision rule, for all values of x in R 1 the classifier decides ω 1 and for all values in R2 it decides ω 2. However, it is obvious from the figure that decision errors are unavoidable. The error is given by p e + = 0 p x 2 ) dx + p( x ω1) 0 ( ω dx (Eq. 2.9) Which is equal to the total shaded area under the curves in Figure 2-4.

41 24 p ( x ω ) p x ω ) ( 1 p x ω ) ( 2 x 0 R R 1 2 x Figure 2-4: Bayes Decision Theory

42 25 CHAPTER III SYSTEM DESIGN AND IMPLEMENTATION System Construction The solder joint inspection system has been designed to be flexible in configuration and to keep component simple. To perform testing, three components are necessary: a fixture to hold and move the sample, a source of ultrasound, and a sensor to record the sample s reaction. A computer controls the ultrasonic source, adjusts the sample position, and records and processes acquired signals. Figure 3-1 shows the system layout (Erdahl, 2000). Nd-Yag Laser Interferometer Chip Computer X-Y Positioning Stage Figure 3-1: System Construction

43 26 The fixture for holding the specimen allows the interferometer to be scanned over the chip s surface, so that data may be taken at multiple points on the surface. A rightangle platform is used to accurately position each sample, and the platform is mounted on top of an XY-positioning stage that is controlled by two stepper motors. Using the current stage, the position is accurate to about 12µm, as long as the position of the chip remains constant from board to board. All of the components are adjustable, allowing different types of tests necessary for optimizing the system s performance. A pulsed Nd:YAG infrared laser provides power for creating ultrasound. Instead of letting the laser pulses fire at the flip chip directly, an optical fiber transmits power from the laser to the testing fixture. Using a fiber to deliver the infrared energy provides control on the amount of power delivered and allows flexibility in positioning of the test fixture and the location of the chip. Currently, a single fiber with a core diameter of 1mm delivers the power to the center of the chip. The fiber end must be close to the chip because the laser pulse diverges rapidly when leaving the fiber. Because the fiber must be very close to the chip, the fiber approaches the chip at a 45 angle, leaving plenty of space for the interferometer head to see the surface. The angle also prevents reflected laser pulses from damaging the sensitive detector in the interferometer. After a flip chip has been properly positioned, a laser interferometer records the surface displacement of the chip at specific points. The interferometer uses a fibercoupled head for flexibility in positioning. The sensor has focusing optics on the end, allowing the sensor to remain at a distance from the specimen. The instrument records data on a very wide bandwidth, 20MHz, making the tool useful for a broad range of

44 27 applications. The signals recorded from the interferometer are noisy because the instrument is extremely sensitive, so signal averaging and filtering are necessary to produce clearer signals. The maximum resolution of the interferometer is 0.25nm, allowing detection of small differences in the vibration response. A picture of the entire inspection system is shown in Figure 3-2. The final system design includes direct recording of the signal through a high-speed data-acquisition card and immediate signal processing, providing a real-time tool for measuring solder joint quality. Figure 3-2: Prototype of Solder Joint Quality Inspection System Equipment and experimental methods used in this research are introduced individually below.

45 28 Laser A Surelite II model laser from Continuum, shown in Figure 3-3 was used for all the experiments presented in this dissertation. The laser is a Nd:Yag laser, operating in the infrared (1064 nm), at 10 Hz repetition rate. It has a maximum power output of about 650mJ/pulse, or 6.5W, at a wavelength of 1064 nm for a 7 mm diameter beam. However, the laser was never used to its full power in this project. Power was adjusted by altering the Q-switch delay setting. Note that higher Q-switch delays result in lower power. A power meter was used to measure the laser power. Usually, power less than 30mW is used to generate ultrasound on test chips. Note that this power value is not from the bare laser measurement, but from the optical fiber delivery system. Figure 3-3: Nd:YAG Laser Used as Ultrasonic Source Optical Fibers Fiber optic delivery systems have become a key component for optical systems used for inspection applications. Optical fibers serve as light guides in many industrial

46 29 applications, including laser welding and drilling (Jones, 1989; Doubrava et al., 1990; Kocher, 1985) and ultrasonics (Jarzynski, 1989; Yang et al., 1993; Yang and Ume, 1994; Graham et al., 1998). Laser ultrasonics applications require optical fibers capable of transmitting high power levels. These fibers are larger than types used in the telecommunications industry, and are usually made from highly pure materials, such as fused silica. A typical fiber is made up of three layers, as shown in Figure 3-4 (Hopko, 1998). The fiber core is made from the purest material, and is capable of transmitting high energy. The cladding creates a reflective surface, which results in total internal reflection of the light; the fiber bend radius must be larger than the recommended minimum. The fiber jacketing material is usually chosen based on the application. The polyimide-coated fibers are made to withstand high temperature and caustic environments. core cladding jacketing Figure 3-4: Optical Fiber The fiber end should be well prepared before being used. Fiber end preparation includes cleaving and polishing. The quality of end preparation has a large effect on the amount of energy transmitted. For example, an imperfect cleave (chip on the edge) results in loss of surface area for launching the light into the fiber.

47 30 The laser pulses are delivered to the chip through a fused silica optical fiber that has a core diameter of about 1 mm. Optical fibers increase the flexibility of the laser ultrasonic system by simplifying the alignment between source and specimen, permitting the laser to remain stationary while the fiber tool is positioned with the x-y stage. To keep this fiber out of the field-of-view of the interferometer, it comes in at an angle of 45º, as shown in Figure 3-5, allowing the fiber to be close to the surface to prevent the laser energy from diverging. The angle also keeps the reflected infrared energy from entering the interferometric sensor. An adjustable tilt stage allows the fiber to be aligned directly with a specific point on the chip s surface, usually the center of the chip. The interferometer head is positioned directly over the chip. Figure 3-5: Fiber Comes In With 45º Angle

48 31 The power transmitted through the fiber is about 30mW. Larger chips will require more energy to get a stronger signal. An array of fibers can be used to produce stronger ultrasound without exceeding the damage limit of the chip. X-Y Precision Positioning Stage A right-angle fixture is used to accurately position each sample. The circuit boards are aligned using two of their edges. The fixture is mounted on top of a xypositioning stage created using components purchased from Parker-Daedal (Figure 3-6). The stages shown are series BN Miniature Linear Positioning stages. Each stage has a maximum travel of 100 mm, using a 5 mm lead screw, with a standard NEMA 23 stepper motor mount on the ends. Figure 3-6: XY-Positioning Stage

49 32 To drive the stages, stepper motors and motor controllers were added. The motor controllers are DM-224i Intelligent Microstep Controller/Drivers from API Controls. All of the inputs and outputs are optically isolated for protection. It has a VDC input range and a 3A maximum output. Each controller is individually addressable through the RS-232 serial communications port on a computer and has the ability to store control programs in flash memory. By taking advantage of these features, the automation program was simplified. Control commands for the desired position were sent to the controllers, saving the effort of controlling the stepper motors directly through software. Stepper motors that matched the controllers were selected. The motors are model M from API Controls. These motors have the NEMA 23 connection to match the stages and are 3VDC, 2A microstepping motors. The motors plug directly into the controller and get both the stepping sequence and power from the controller. Using this stage assembly, the chip position is accurate to about 12µm, as long as the position of the chip remains constant from PCB to PCB. Leaving these components adjustable adds flexibility into the system, allowing for performance optimization. Interferometer To measure the surface displacement at specific points on a chip, an interferometer is used. Interferometers for the detection of ultrasonic movements of surfaces may be divided into two distinct types: homodyne interferometer and heterodyne interferometer. In a homodyne interferometer, light reflected from a surface is made to

50 33 interfere with a reference beam, thus giving a measure of optical phase and hence instantaneous surface displacement. The heterodyne interferometer is designed as a highresolution optical spectrometer to detect changes in the frequency of the reflected light. It thus gives an output which is dependent on the velocity of the surface. The homodyne type is the more widely used and the most practical at lower frequencies. The heterodyne type offers a higher sensitivity, particularly at high frequencies. The interferometer in this system is a heterodyne interferometer. The structure of a heterodyne interferometer is shown in Figure 3-7 (Bergh, 1999). Fixed Mirror CW Laser Reference Path Beam Splitter Frequency Shifter Measurement Path δ (t) Fixed Specimen Detector Figure 3-7: Heterodyne Interferometer The interferometer was purchased from Polytec Incorporated and is a model OFV-511 heterodyne fiber interferometer with an OFV-2700 Ultrasonics Vibrometer Controller, as shown in Figure 3-8. The interferometer measures the displacement of the

51 34 surface, and the vibrometer controller contains electronics to provide an analog signal for data acquisition. The controller has a high pass filter to reject low frequency noise below 25 khz and a maximum bandwidth of 20 MHz. The maximum range of displacement measurements is 75 nm while the minimum detectable displacement is on the order of 0.25 nm. Therefore, any change in the solder joints that causes a change in the surface vibration of a least 0.25 nm will be detected by the system, giving the system a high resolution. Figure 3-8: Polytec Interferometer Filter/Amplifier The KH3945 filter/amplifier (see Figure 3-9) between the interferometer and the data acquisition board conditioned the signal before sampling. This unit was purchased

52 35 from Krohn-Hite Corporation. The Krohn-Hite Model 3945 is multi-channel, Butterworth/Bessel filter, which is a combination of 2 channels of model 3944 and one channel of model It offers a programmable filter covering a cutoff range from 3Hz to 25.6MHz, with a frequency response characteristic of maximally flat (Butterworth) for clean filtering in the frequency domain, or linear phase (Bessel) to provide superior pulse or complex signal filtering. Figure 3-9: Filter/Amplifier Unit In this project, the filter was configured to have a passband between 100kHz to 2MHz. The amplifier was set to 6dB amplification. Data Acquisition The signals from the interferometer are recorded on a high-speed data acquisition board purchased from GaGe Incorporated. The board has model number 8012A/PCI, and came as a two-board set. The A/D converter plugs into an ISA slot in the computer and

53 36 the data transfer card plugs into a PCI slot. At the fastest acquisition rate, the card can take 100 million samples per second (MS/s) with a resolution of 12 bits on one channel. When two channels are used, then the maximum acquisition rate is 50 MS/s. The board comes with C drivers and API for Windows, allowing development of an automated program to control the entire system. The data capture, motor control, and analysis can all take place in one program. In order to control the system and tie all of the pieces together, a control program was needed. A Windows compatible program was written in Borland C ++ Builder V3.0 to control all aspects of data acquisition. All of the components used in this program, from the ultrasonic source to the data acquisition program are adjustable, making the system flexible. The extremely flexible nature of the system allows the adjustment needed in the laboratory. Power meter Laser power is critical in this system, because higher power generates higher magnitude ultrasound in the sample. The laser power must remain constant during data acquisition to provide a constant ultrasound for all samples. To monitor laser power during inspection process, a power meter was used. The power meter is a product of Scientech, model MD10, as shown in Figure It can be used to detect power and energy. The power meter measurements are given in terms of continuous power. Conversions are simple(hopko, 1999):

54 37 Energy per pulse = (Power meter measurement)/ (repetition rate) (Eq. 3.1) Power per pulse = (Energy per pulse)/ (pulse width) (Eq. 3.2) Power density = (Power per pulse)/ (spot size) (Eq. 3.3) Figure 3-10: Power Meter Computer A Dell computer, with Pentium III 450MHz CPU, 120MB RAM and 9GB hard disk space, is used in this inspection system. This computer is used as the central controller of the whole system, including data acquisition, X-Y stage movement control, and all signal processing and data analysis routines.

55 38 System Characterization Before any measurements with he inspection system can be trusted, the system must prove that the measurements are repeatable. System repeatability is important for this inspection technique because the basic assumption is that changes in solder joint quality will change the vibration response. If the difference between a good chip and a bad chip is very small, an inconsistent system could mask differences and produce faulty results. Only a system with good repeatability can guarantee that the signal contains useful information. Some factors that may affect system repeatability are chip position on the PCB, variations in laser power, and environmental vibration. After experimentations to isolate these potential sources of error, adjustments were made to minimize the effects of these factors. Some other factors are shown to have negligible effects and have been neglected (Liu, 2000). Insonification Position Relative To Sensor In this system, the ultrasonic signal is very sensitive to the chip position relative to the incident laser light. All of the chips must be in the same position, relative to the incident laser light and the interferometer, during measurement. Unfortunately, the chips positions on the circuit board are not consistent from sample to sample. Error is introduced because the sample position fixture uses edges of a circuit board for positioning instead of edges of a chip. Therefore, the position of each chip must be

56 39 adjusted during the data acquisition process to maintain alignment with the incident laser source and the interferometer. Using the stepper motors, the circuit board position is adjusted until the interferometer points to a fixed point on each chip. All of the data points taken on each chip are referenced from this fixed point. The following experiment shows how much the variations in chip position affect the final signal. To characterize the sensitivity of the system to chip position, one chip was put into the fixture and measurements were taken at an initial spot and distances of 0.08mm and 0.32mm away from the initial point. Figure 3-11 shows the ultrasonic signals detected after changing the chip s position. The change in the waveform is negligible when the error in position is only 0.08mm, but the waveform has a very large change for a position error of 0.32mm. The actual chip position variation on the board can be more than 0.32mm, therefore, causing a large error in the final analysis if left uncorrected. After adjustment, the possible error is estimated to be no more than 0.08mm, which is acceptable. In the future, machine vision methods can be used to more accurately locate the sensor position relative to the chips for on-line inspection during the manufacturing process.

57 Magnitude(V) mm 0.08 mm 0.32 mm 0.00E E E E-05 Time(s) Figure 3-11: Signals Detected at Different Chip Position Isolation of Environmental Vibration In the data acquisition process, a pulsed laser excites the sample chip into a vibration mode, and the signal detected is the vibration response of the chip s surface. If the environmental vibration is significant, the sensor and the sample could be moving relative to each other, causing error in the recorded vibration response. To evaluate the effect of environmental vibration, signals were acquired at the same point both with and without using an air compressive vibration isolation table. Figure 3-12 shows that the environmental vibration is small enough to be neglected. The vibration response hardly changed. The environmental vibration was rejected by the interferometer, which has a low frequency cutoff at 25 khz. In an industrial application, environmental vibration

58 41 noise may be much larger in magnitude than seen in the laboratory, but it usually occurs at low frequencies. Therefore, the vibration noise can be removed with filters, or the interferometer sensor may reject the noise automatically Magnitude(V) w ith vibration isolation w ithout vibration isolation Time(s) Figure 3-12: Effects of Environmental Vibration Laser Power Another potential source of error is the incident laser power on a sample. Because higher laser power generates higher magnitude ultrasound in a sample, laser power must remain constant during data acquisition to provide a constant source of ultrasound for all of the samples. Figure 3-13 shows a plot of the laser power with time. The plot shows the laser power remains steady during the data acquisition process,

59 42 dropping less than 5% over the course of one hour. Aligning the optics inside the laser to optimize the output will provide an even more consistent source over a longer time frame. Sets of data were all taken in much shorter amounts of time, so no compensation was made for the small decrease in laser power. All measurements were made after letting the laser warm up for 30 min Laser Power (mw) Tim e(m in) Figure 3-13: Laser Power with Time System Resolution The smallest defect that can be detected by this system is mainly determined by the sensitivity of the interferometer. In this prototype system, the minimum detectable displacement of the interferometer is on the order of 0.25 nm. Therefore, any change in

60 43 the solder joints that causes a change in the surface vibration of at least 0.25 nm can potentially be detected by the system, hence, giving the system a high resolution. Because of limited number of tests that have been performed, the resolution of this system has not been tested to its limit. However, for the samples we have been tested, the system is able to detect a missing solder ball in flip chip, which has a diameter of 120µm and a pitch of 457µm. More experimental results on resolution will be shown in Chapter V.

61 44 CHAPTER IV EXPERIMENTAL PROCEDURES AND DATA ANALYSIS The inspection system introduced in the last chapter has been used to test some flip chip samples. Data acquired using that system is simply ultrasound waveforms. The big research issue is how to extract solder joint quality information from these waveforms. In this chapter, experimental procedures and data analysis techniques will be discussed. Data Acquisition Scanning Pattern A flip chip on ceramic substrate was chosen as a test vehicle. The chip measures 3.023mm by 2.281mm, as shown in Figure 4-1. Figure 4-1: Flip Chip on Ceramic Substrate

62 45 There are 14 solder balls under each chip, labeled from 1 to 14, as shown in Figure 4-2. The diameter of solder ball is 330 microns and the pitch size is 670 microns. These samples have no underfill, making the solder balls the only constraint on vibration. Therefore as the stiffness of the supports change, the vibration response will change. The laser power irradiates the center of the chip s surface, generating ultrasound at that point. Signals are recorded from four points on each chip, labeled as detection points A, B, C, and D. The location of these points is symmetric about the center of the chip. For each chip, the system records signals from points A to D in sequence, and the signals at each point are most sensitive to the solder joints in the immediate vicinity. Incident Laser Light D C 9 8 Chip Surface 14 Solder Ball 1 A B Interferometer Detection Point Figure 4-2: Scanning Pattern of Flip Chip Sample Images of the solder joints of four sample chips are shown in Figure 4-3. The top pictures are side views taken by microscope, and the bottom pictures are x-ray images taken through the circuit board. As shown in the picture, there are two good chips, labeled as Good Chip 1 and Good Chip 2. The other two chips have defects. Solder ball

63 46 2 of Bad Chip 1 is missing, and Bad Chip 2 has a missing solder balls at position 9. Because of these defects, the vibration responses of the bad chips will be significantly different from those of the good chips. Missing Solder Ball 2 Missing Solder Ball 9 Good Chip 1 Good Chip 2 Bad Chip 1 Bad Chip2 Figure 4-3: Solder Joints of Flip Chip Samples Signals from Flip Chip Samples Data at all four points on the four chips were collected, and analyzed to determine the solder joint quality. The waveform shapes were correlated to physical deficiencies in the solder connections. Since the chip is vibrating on top of solder supports, the effect is that of a plate supported by springs and dampers. When a solder joint is missing, the amplitude of vibration increases and the damping ratio decreases due to a change in stiffness. The effect will be noticeable across the entire surface of the chip, but it will be

64 47 most noticeable at the detection point closest to the defect. Figure show signals recorded from testing these four chips. Figure 4-4 shows signals at detection point A. It is clear that Good Chip1 and Good Chip 2 have similar waveforms, since the amplitude and phase are nearly identical. The waveform of Bad Chip 1 differs a lot from the others because that chip has a missing solder joint near detection point A, as shown in Figure 4-3. The amplitude changes, and the waveform also shifts in phase, indicating a significant change in the solder joint quality near point A. Similarly, Figure 4-6 shows signals at detection point C. Because Bad Chip 2 has a missing solder ball near point C, the signal from Bad Chip 2 is significantly different from the other signals, showing larger phase shift and maintaining high amplitude vibration for many cycles. Figure 4-5 and Figure 4-7 show the vibration response for points B and D, respectively. The amplitude and phase changes are much less evident. This occurs because points B and D are farther away from the defects.

65 48 Figure 4-4: Signals at Detection Point A Figure 4-5: Signal at Detection Point B

66 49 Figure 4-6: Signal at Detection Point C Figure 4-7: Signal at Detection Point D

67 50 From above analysis, some estimates of chip quality can be determined, but it is very difficult to assess the total amount of damage. The signals from both bad chips look very similar, measuring the change in amplitude may not be good enough. Therefore, an automated comparison process was developed to provide a quantitative estimate of the solder joint quality at each detection point. This method uses a numerical algorithm to assign a value, called the Error Ratio, representing quality of each chip at each detection point, and it is described in detail below. Time Domain Error Ratio Analysis To automate the comparison process, a data analysis algorithm was developed. The algorithm compares a reference signal from a properly attached flip chip, and the signal recorded from any other chip of the same type, producing a value called the Error Ratio. The Error Ratio is a variable that measures the similarity of two waveforms, by measuring the distance of their waveform vectors. There are many different ways to define the distance between vectors. The Error Ratio defined here measures the Euclidean distance of vectors, then normalizes it using the reference value. The Error Ratio is defined as (Liu, 2000) Er = 2 ( f ( t) r( t)) dt r( t) 2 dt, (Eq. 4.1) where r (t) is the reference waveform and f (t) is another measured waveform.

68 51 Because the square value of the error is used, the Error Ratio value will be positive. Therefore, a signal that matches the reference signal closely will have a small value, while a signal that has large changes in amplitude and phase will have a large value. Since this is a completely numerical comparison, a threshold value must be set to determine whether the solder joints are acceptable or not. The system seems to have only a small effect on the Error Ratio, so the threshold value for determining acceptable and unacceptable solder joints can be set by using a comparison between the signals recorded from two good chips. The Error Ratio comparison method was used on the waveforms presented in Figure 4-4 to Figure 4-7, and since Good Chip 1 has no defects, it was chosen as a reference. To calculate the Error Ratio values for each of the other chips, the waveforms recorded at points A, B, C, and D from Good Chip 1 were compared with the waveforms recorded at the corresponding points on each of the other chips. The Error Ratio contains most of the useful information such as signal magnitude and phase delay, making it sensitive to changes in stiffness. For the reference Good Chip 1, the Error Ratio is equal to zero, but for every other chip the Error Ratio has a positive value. First, the Error Ratio values were calculated from the measured ultrasonic signals at each detection point of Good Chip 2, as shown in Figure 4-8. Since this chip is also a good chip, the Error Ratio values are small, less than 0.2. Therefore, the threshold value must be at least 0.2. The Error Ratio values for the bad chips should be greater than 0.2.

69 52 Error Ratio A B C D Detection Point Figure 4-8: Error Ratio of Good Chip 2 Since the Error Ratio values for Good Chip 2 are very low, the Error Ratio values for the two bad chips are calculated for comparison. Figure 4-9 shows the Error Ratio values calculated for Bad Chip Error Ratio A B C D Detection Point Figure 4-9: Error Ratio of Bad Chip 1

70 53 According to the x-ray inspection results in Figure 4-3, Bad Chip 1 has a missing solder ball near detection point A. Looking at the Error Ratio values in Figure 4-9, detection point A has an extremely large value for the Error Ratio, about This result was expected because the missing solder ball decreased the stiffness of the chip s supports, allowing higher amplitude vibration and increasing the error between the reference and the signals recorded for the bad chip. Similarly, the Error Ratio values were calculated for Bad Chip 2, as shown in Figure Point C has a very large Error Ratio value, which shows that this chip has a solder connections defect near detection point C. This is also consistent with the chip s physical defects shown in Figure 4-3. The Error Ratio at Point A is also relatively high, which indicate there might be a defect close to that point. However, that defect could not be detected by using X-ray and microscope Error Ratio A B C D Detection Point Figure 4-10: Error Ratio of Bad Chip 2

71 54 Analysis of the Error Ratio values and the waveforms show that the measurement system makes repeatable measurements that accurately represent physical defects. In addition, the data analysis algorithm provides a good measure of the physical defects of flip chips. By taking data at multiple points on the surface, the values of the Error Ratio were used to predict the approximate locations of the defects. Detecting on Top of Each Solder Joint As previously addressed, using Error Ratio analysis, only a few detection points are needed for each chip to inspect it s solder joint quality. This expedites the inspection process, and makes online inspection possible. However, by only inspecting at a few points, the inspection system can only decide whether this chip has a bad solder joint or not, but doesn t indicate where that defect is located. Even though defect location is not part of the main objectives of this research, this system has the capability to do that. Depending on how precise the defect location is desired, the number of detection points need to be adjusted. For example, to inspect the sample chip as discussed before, which has fourteen solder joints as shown in Figure 4-2, fourteen inspection points were chosen. Each inspection point is located right on the top of one solder ball. Signals are recorded at those detection points, and Error Ratio values are calculated.

72 55 As shown in Figure 4-11, Good Chip 2 has considerably small Error Ratio values at all detection points, which indicate that all solder joints of Good Chip 2 have good connection. Note that Error Ratio value at solder ball 4 is not available because there is a fiber located on top of that solder joint. Interferometer cannot detect any meaningful signal at that point. Figure 4-11: Error Ratio of Good Chip 2 on Top of Each Solder Joint

73 56 Figure 4-12 shows the Error Ratio value distribution of Bad Chip 1. It is clear that Bad Chip 1 has much higher Error Ratio values, and the maximum value is located on the top of solder ball 2, which is exactly the location of the missing solder ball. Figure 4-12: Error Ratio of Bad Chip 1 on Top of Each Solder Joint Power Spectrum Analysis in Frequency Domain In this solder joint quality inspection system, the signal source is the ultrasound generated by pulsed laser on the chip s surface. By theoretical calculation and experimental validation, the ultrasound wavelength is found to be in the order of 15mm,

74 57 which is much larger than chip s thickness, 0.528mm. Therefore, during the testing process, the chip can be modeled as a plate vibrating on top of solder supports. When a solder joint is missing, or if there is a big defect in one or more solder joints, the stiffness of the supports will change, causing the natural frequency of the plate to change. Because the acoustic wave generated by a pulsed laser is broadband, if the ultrasonic energy is strong enough, the vibration modes of the plate can be excited and the test chip will vibrate on its natural frequencies. Thus, signal analysis in the frequency domain is also important for solder joint defects detection. Fast Fourier Transform (FFT) technique was used to analyze the frequency distribution of vibration signals (Tohyama, 1998). FFT is just an efficient implementation of Discrete Fourier Transform (DFT), which transforms a series of time domain data samples x [n] into a series of frequency domain data X [k], as shown in equation N 2πi( k 1)( n 1) X[ k] = x[ n]exp[ ], k = 1,..., N (Eq. 4.2) n= 1 N The techniques for using FFT to analyze a function of time require that the time window in which the function is viewed be sufficiently large to see the function decay to a relatively small value. In addition, the sampling frequency must be considered, ensuring that it is large enough to avoid aliasing. Figure 4-13 shows the signal recorded at detection point A from one chip. The sampling frequency was chosen to be 10MHz

75 58 and a 2MHz anti-aliasing low pass filter was used because most of the signal frequencies are lower than 2MHz. Figure 4-13: Signal Recorded for Frequency Analysis Signals were recorded from the four sample chips. Power spectrum density of the signal from one of the good chips is shown in Figure 4-14.

76 59 Figure 4-14: Power Spectrum Distribution of Signal From the experimental results in Figure 4-14, and from the vibration modal analysis based finite element modeling (to be discussed in Chapter VI), the first vibration natural frequency of a good chip is about 500kHz. For a chip with a missing solder ball, the first natural frequency drops to 469kHz in modeling, and 438kHz in experiment. Therefore, a bandpass digital filter was designed with a passband from 400kHz to 600kHz, and central frequency 500kHz, as shown in Figure 4-15.

77 60 Figure 4-15: Frequency Response of the Band Pass Filter After using this digital bandpass filter, the frequency distribution of signals are shown in Figure Note that the peaks of good chip 1 and good chip 2 are very closely matched, with frequency about 500KHz. But bad chip 1 is at lower frequency, with a peak at about 440kHz. This can be easily explained. Bad chip1 has a solder joint disconnected, which decreases the stiffness of vibration supports. As a result, it s natural frequency decreases. Similarly, bad chip 2 also has a lower vibration natural frequency, because its solder ball #9 is missing. Therefore the chip s first vibration frequency can be used to determine the quality of solder joint.

78 61 Figure 4-16: Power Spectrum of Signals After Filtering Periodogram Averaging Analysis in Frequency Domain Figure 4-17 shows the raw signal recorded at detection point A from a test sample. To sample the vibration response at the flip chip surface, a low pass anti-aliasing filter with a passband up to 2MHz was used, and the sampling frequency was chosen to be 5MHz. The waveform shown here is after averaging 8 times. But it is still noisy.

79 Amplitude(V) Time(S) x 10-4 Figure 4-17: Noisy Signal Recorded by Interferometer The power spectrum density of this noisy signal is shown in Figure The noise makes it difficult to determine the chip s vibration frequency. As shown in this figure, noise is even distributed in the whole spectrum. Therefore it is white noise. Because the noise is white, it cannot be completely filtered off by simply using band-pass filter. From the experiment, the noise is also found to be random with zero means, because time domain averaging can greatly increase the signal-to-noise ratio.

80 Power Frequency(Hz) x 10 5 Figure 4-18: Power Spectrum Distribution of Noisy Signal Most of the noise is produced when the interferometer is measuring flip chip surface vibration response. The signal-to-noise ratio is mainly determined by the reflectivity of the flip chip surface. If the surface is smooth and it has good reflectivity, signals recorded by the interferometer will be clean. Unfortunately, in on-line inspection, the surface reflectivity is always changing. Therefore, a method to get rid of the noise is highly desired. For a plate vibration, the displacement at a detection point can be modeled as: ξt s( t ) = e ( K i Sin ( ω it + φ i )) i (Eq. 4.3)

81 64 where, ξ is the damping ratio, and ω i is the vibration natural frequency. For a certain structure, there are infinite numbers of natural frequencies. But usually only the first few vibration modes can be excited, so only the first few frequencies are important. After a Fourier transform, the frequency response of the signal with one mode is: S ( ω ) i ω i = K i (Eq. 4.4) 2 ( ξ + jω ) + ω 2 i For When ω >> i ξ, the power spectrum can be simplified as: 2 2 i ( ω) = K i 2 i 2 ω i 2 2 S (Eq. 4.5) ( ω ω ) + ( 2ξω ) 2 Therefore, theoretically, the power spectrum distribution should have a shape as shown in Figure (ω) S i ω i ω Figure 4-19: Theoretical PSD of a Vibration Signal

82 65 A real vibration signal with noise can be modeled as: ξt s( t ) = e ( K i Sin ( ω it + φ i )) + u ( t ) i (Eq. 4.6) where, u(t) is random noise. Because of noise u (t), the experimental power spectrum results are like those shown in Figure There are two methods that can be used to get rid of noise u (t), so that a nice PSD like shown in Figure 4-19 can be produced. One is averaging in time domain, before doing FFT. Another is the periodogram PSD estimation method. The Bartlett method, as one of the periodogram methods, is used in this system (Oppenheim, 1998). A single record of N = N 1 N 2 data is broken into N 2 sub-records of length N1each. The raw periodogram for each of the sub-records y i n]([0 : N 1],[ N : 2N 1],...,[( N 1) N : N 1]) is calculated [ I ( i) yy N1 1 1 ( ) jω e = yi[ n] e N 1 n= 0 jω 2, y i n] = y[ n + in ], (Eq. 4.7) [ 1 and then the PSD is formed as: 1 jω φ I ( e ). (Eq. 4.8) ^ N2 1 jω yy ( e ) = N 2 i= 0 ( i) yy Figure 4-20 shows the power spectrum density results only by using averaging in the time domain, compared with using the Bartlett method after time domain averaging.

83 66 The results indicate that if using time domain averaging only, about 16 averages are needed to reach a good signal-to-noise ratio. But if the Bartlett method is used, with only 4 averages, a nice clean power spectrum density plot can be generated. This means that using the Bartlett method can decrease the data acquisition time four times. This is important for increasing the system inspection speed. 2 Averages: 4 Averages: 8 Averages: Direct FFT: x x Bartlett Method: x x x Averages: Frequency(Hz) x x x Frequency(Hz) x 10 5 Figure 4-20: Time Domain Averaging Compared with Bartlett Method By using 4 averages in the time domain and using the Bartlett method, the power spectrum of signals from Good Chip 1, Good Chip 2 and Bad Chip 1 were obtained as

84 67 shown in Figure Note that the peak location on the spectrum of Good Chip 1 and Good Chip 2 are closely matched, because they are all good chips. Bad chip 1 has a lower frequency because it has a solder joint disconnected. The loss of a solder joint stiffness of the vibration supports, and thus its natural frequency decreases. x Good Chip 1: x x 10 5 Good Chip 2: x x Bad Chip 1: Frequency(Hz) x 10 5 Figure 4-21: Power Spectrum of Flip Chip Samples As discussed in this chapter, experimental procedures and data analysis techniques have been developed. In order to detect solder joint quality of a flip chip, signals are recorded at a few inspection points. Data is analyzed both in time domain and frequency domain. In time domain, Error Ratio was defined and automatically

85 68 computed. In frequency domain, Bartlett methods are used for power spectrum density estimation, which successfully increased signal-to-noise ratio and increased the inspection speed. The Error Ratio and frequency distribution accurately predict the existence of defects, such as missing solder ball. The chips physical defects, as shown by the x-ray results, validate the experimental results. Based on the above analyses, a pattern recognition method will be developed to help speed up the defect classification process.

86 69 CHAPTER V CAPABILITIES OF THE FLIP CHIP DEFECTS INSPECTION SYSTEM Capabilities of this defects inspection system are discussed in this paper. Experimental results indicate that this laser ultrasonic/interferometric system is capable of detecting various defects such as missing solder ball, undersized solder ball, misaligned solder ball, and surface defects on the silicon die, in a fast and efficient way. this chapter. Resolution of this system has also been tested. Experimental results are shown in Results from two different flip chips supplied by two companies are presented. The first type of flip chip is the same type of chip as discussed in Chapter IV, which is a mm by 2.281mm flip chip with 14 solder balls sitting on ceramic substrate. In this type of chip, solder ball size is 330 micron, and pitch size is 670 micron. The second type of flip is a 6.3mm by 6.3mm chip with 48 solder balls on FR-4 substrate, which has a solder ball size 120 micron and pitch size 457 micron. The defects in these chips were created purposely for this research.

87 70 Detection of Missing Solder Ball/Undersized Solder Ball Shown in Figure 5-1 are four testing chips, labeled Good Chip 1, Good Chip 2, Bad Chip 1, and Bad Chip 2. One solder ball on Bad Chip 1 is missing, and two solder balls on Bad Chip 2 are undersized. Good Chip 1 Good Chip 2 Bad Chip 1 Missing Solder Ball Bad Chip 2 Deformed Solder Balls Figure 5-1: Good Chips and Chips with Defects at Solder Bump Figure 5-2 shows the waveforms recorded from testing these four chips. It is clear that Good Chip 1 and Good Chip 2 have similar waveforms, because the amplitude and phase are nearly identical. The signals from Bad Chip 1 and Bad Chip 2 differ a lot from the waveforms from the two good chips, because they have a missing solder ball and two undersized solder balls, respectively. These differences help to confirm that the presence of a defective solder joint affects the chip s surface displacement response. Error Ratio values are calculated by using equation 4-1 as discussed above. Shown in Figure 5-3 are the maximum Error Ratio values from these four test samples.

88 71 The Error Ratio of Good Chip 1 is zero, because it was chosen as the reference. Error Ratio of Good Chip 2 is close to zero, but the Error Ratio values for the other two bad chips are very high, indicating that there are defects on those two chips. Figure 5-2: Signals from Four Flip Chip Samples for Solder Joints Defects Inspection

89 Max Error Ratio Good Chip 1 Good Chip 2 Bad Chip 1 Bad Chip 2 Figure 5-3: Error Ratios for Solder Joints Defects Inspection Detection of Flip Chip Surface Defects The next step is to test some chips with surface defects, such as a crack on the silicon die. Figure 5-4 shows four test chips, still libeled Good Chip 1, Good Chip 2, Bad Chip 1, and Bad Chip 2. There is a crack on one side of Bad Chip 1, and Bad Chip 2 has a crack at one of its corner. Figure 5-5 shows the waveforms recorded from those four chips. It is clear that Good Chip 1 and Good Chip 2 have similar waveforms, while waveforms from Bad Chip 1 and Bad Chip 2 are very different compared with the good chips.

90 73 Good Chip 1 Good Chip 2 Bad Chip 1 Bad Chip 2 Surface Crack Figure 5-4: Good Chips and Chip with Surface Defects Figure 5-5: Signals from Four Flip Chip Samples for Surface Defects Inspection

91 74 By using the same Error Ratio definition, the maximum Error Ratio values are calculated as shown in Figure 5-6. It is clear that the Error Ratio from chips with surface defects are much larger than from good chips Max Error Ratio Good Chip 1 Good Chip 2 Bad Chip 1 Bad Chip 2 Figure 5-6: Error Ratios for Surface Defects Inspection Detection of Misaligned Solder Ball Four other different test samples are shown in Figure 5-7. These are 6.3mm by 6.3mm flip chips with 48 solder balls sitting on FR-4 substrate, which has a solder ball size 120 micron and pitch size 457 micron, without underfill. Among those samples, two of them are good chips, while the other two are chips with solder joint misalignment defects, labeled as Bad Chip 1 and Bad Chip 2.

92 75 Good Chip 1 Good Chip 2 Bad Chip 1 Bad Chip 2 Misalignment Figure 5-7: Good Chips and Chips with Solder Joint Misaligned Similar to what has been shown before, ultrasound signals are recorded from those four testing samples by using an interferometer, and waveforms are compared as shown in Figure 5-8. As expected, Bad Chip 1 and Bad Chip 2 have ultrasound waveforms that are different from those of good chips, because they have misalignment problems.

93 76 Figure 5-8: Signals from Four Testing Samples for Misalignment Inspection Again, the Error Ratio values were calculated, as shown in Figure 5-9. By comparing the Error Ratio values, it is easy to separate chips with misalignment problems from good chips. Max Error Ratio Good Chip 1 Good Chip 2 Bad Chip 1 Bad Chip 2 Figure 5-9: Error Ratios for Misaligned Solder Ball Inspection

94 77 System Resolution Test As previously discussed, the smallest defect that can be detected by this system is mainly determined by the sensitivity of interferometer. In this set-up, the minimum detectable displacement of the interferometer is on the order of 0.25 nm. Therefore, any change in the solder joints that causes a change in the surface vibration of a least 0.25 nm can potentially be detected by the system, hence, giving the system a high resolution. Given the limited number of tests that have been performed, the limit of system resolution is still unknown. A 6.3mm by 6.3mm flip chip with 48 solder bumps sitting on FR-4 substrate has been tested. The solder ball diameter is 120 microns, and the pitch size is 457 microns. Figure 5-10 illustrates the solder ball distribution and the detection point distribution on a sample chip. As shown in this figure, a solder ball is missing at the right edge of the chip. In order to detect the effect of that missing solder ball, 36 detection points were used. Those detection points are located along the top, right and bottom edges of the chip. Each detection point is located close to a solder ball. By comparing with another reference good chip, Error Ratio values of this flip chip were calculated, as shown in Figure 5-11.

95 78 Solder Ball Detection Point Missing Solder Ball Laser Insonification Point Missing Solder 21 Ball Figure 5-10: Solder Ball and Detection Point Distribution of Test Sample Error Ratio Top Edge Right Edge Bottom Edge Figure 5-11: Error Ratio Distribution Along the Three Edges

96 79 The Error Ratio values along top edge and bottom edge are very small, because there is no defect on those two edges. The Error Ratio values along the right edge are much larger, and two extremely large values are located at detection point 18 and 19, which are the close to the missing solder ball. Therefore, from the Error Ratio distribution, the missing solder ball can be detected and localized. Experimental results shown here is not the resolution limit of this technique. With the improvement of interferometer and chip alignment system, resolution of this system can be further improved. Throughput of the System Compared with traditional solder joint quality inspection techniques, one of the most important advantages of this laser ultrasound and intereferometric system is its much higher throughput. Throughput of this system is mainly determined by the laser pulse rate, x-y stage travel speed, and the signal processing software speed, as shown in Table 5-1. With current setup, the pulse laser used to generate ultrasound has a frequency of 10Hz, however a commercial 100Hz laser is available and can be used in our system. In current setup, the x-y stage is relatively slow, and moving from one detection point to another detection point needs about 1 second. This process can be improved using commercial high speed stage. The travel time is expected to be decreased to 0.1 second /point. Also, with further integration and optimization of the signal processing program, the data process time can be decreased from 1 second to the

97 80 order of 0.1 second. Overall, with current setup, to inspect one flip chip needs about 10 seconds. But in the future, an optimized system could do that in about 1 second. The throughput can be further greatly improved if parallel processing is used. Table 5-1: Throughput Parameters of Current and Optimized System Throughput Parameters Currently Optimized Laser Pulse Rate (4 averages needed) 0.1 s/pulse 0.01 s/pulse X-Y Y Stage Travel Time (4 detection points needed) Signal Processing Total Measurement Time/Chip 1 s/point 0.1 s/point 1 s 0.1 s 10 s 1 s As shown in this chapter, the experimental results indicate that this laser ultrasound and interferometric system is capable of detecting different kinds of defects on flip chips, including missing solder ball/undersized solder ball, misaligned solder ball, and surface defects on silicon die such as crack. By using an automated inspection prototype and the Error Ratio analysis routine, those defects can be successfully detected in a fast and efficient way.

98 81 CHAPTER VI MODELING BASED ON VIBRATION MODAL ANALYSIS In this research, setting up an appropriate model is equally important as designing experimental method, because it can provide us with insight into the physics of the defect inspection process. The understanding of physics of signal is valuable for the development of the defects pattern recognition algorithm to be discussed in the next chapter. In this chapter, a finite element model based on vibration analysis was introduced to model the signal generating phenomenon when a flip chip is excited with pulses from a pulse laser. Modeling results were also validated with experimental results. Why Use Vibration Analysis for Modeling As discussed before, this flip chip solder joint quality inspection system was developed by using laser ultrasound and interferometric techniques. In this system, a pulsed laser is directed to a chip s surface, and the thermal expansion and contraction, caused by rapid laser pulses, generates ultrasound in the chip s surface. Flip chip solder joint quality can be inferred by analyzing the changes in ultrasound signals received by a detector. This phenomenon could either be modeled as a wave propagation problem, or a flip chip vibration problem. We chose to model this as a flip chip vibration problem.

99 82 An explanation of why we chose to model this as a chip vibration problem is discussed below. The ultrasound wavelength in silicon and the dimension of the silicon chip are compared. Ultrasound generated by pulse laser contains three main types of waves: longitudinal (compression), transverse (shear), and Rayleigh (surface) waves. These different types of waves propagate at different speeds. In this application, longitudinal waves are the main stress waves which are detected, because the interferometer can only pick up out of plane displacement. The speed of longitudinal waves is calculated by the following equation for materials at room temperature (Krautkramer, 1977; Miller, 1999): 1 σ C = E l ρ (1 + σ )(1 2σ ) (Eq. 6.1) In the above equation, C l is the longitudinal wave velocity, E is the modulus of elasticity, ρ is the density, σ is the Poisson s ratio. Typical values of these constants for pure silicon at room temperature are: E = 1.15e ρ = 2.33e 11 ν = 0.25 (Eq. 6.2) 3 Pa kg / m 3 Using the above values gives a longitudinal wave velocity of m/s. From the experiment, laser ultrasound is generated in a broad frequency band, mainly located between 200kHz and 1MHz, and the averaging central frequency is about 500kHz. Therefore the dominant wavelength of the longitudinal wave in pure silicon is about

100 mm. Meanwhile, the thickness of flip chip is measured to be 0.528mm. This means that the wavelength of the ultrasound generated by pulse laser in silicon die is much larger than the thickness of the silicon chip, therefore it will be impossible to model the phenomenon as a wave propagation problem, and therefore we chose to model it as a vibration analysis problem. Because vibration frequencies change is used to detect flip chip solder joint quality, the research discussed in this chapter is focused on vibration modal analysis. Theory Behind Vibration Modal Analysis A simplest one-degree-of-freedom rigid body system will be introduced as a starting point of the vibration modal analysis. A one-degree-of-freedom system can be represented by a standard mass-spring system, as shown in Figure 6-1. The mechanical properties of this system are the single element of the inertia, and stiffness of the spring, corresponding to the generalized coordinate w. During the vibration process, the displacement w must overcome the impedance of the mass M, and spring constant K.

101 84 w M K Figure 6-1: Standard Mass-Spring System For free vibration analysis, the equation of motion of this system is the single force balance equation, M w+ Kw = 0 (Eq. 6.3) Because there is no external excitation for free vibration analysis, the motion in this case results from the initial condition. The homogeneous solution of this equation is in the form w λt = (Eq. 6.4) Be where w is the the displacement, B determine the amplitude of vibration and λ corresponds to the vibration natural frequency. The constants B and λ must be determined. The characteristic equation for λ is 2 Mλ + K = 0 (Eq. 6.5) The roots of the characteristic equation are

102 85 λ = ±iω nat (Eq. 6.6) K ω nat = (Eq. 6.7) M The parameter ω nat is the natural frequency of the mass-spring system. The whole massspring system is vibrating at that frequency. If the stiffness K changes, natural vibrating frequency will change. This mass-spring system can be viewed as a simple model for a silicon die flip chip sitting on solder balls. The silicon die of flip chip is the rigid body, while solder balls are the springs. If there is one solder ball missing, the overall stiffness K decreases, causing the natural frequency the experimental result shown in Chapter IV. ω nat to decrease as well. This analysis matches The model just discussed contains only rigid body and discrete sets of elements. It will be more accurate to model a flip chip as a continuous system, rather than a simple rigid body. A continuous system will be introduced next, in which the motion is characterized by a displacement field whose value is a function of position, as well as time. Figure 6-2 shows a bar undergoing flexural displacement. The bar is supported by two springs at both ends. This model contains more information than the one shown

103 86 in Figure 6-1. The flexural displacement in this model is not from a rigid body, but from a continuous system supported by elastic springs. w ( x, t ) 0 L x K K Figure 6-2: A Bar Supported by Springs Undergoing Flexural Displacement To elucidate the vibration modal analysis, Ritz series method was used to analyze this continuous system. To derive equations of motion of this system by using Ritz series method, kinetic energy and potential energy of the system need to be worked out first. The corresponding total kinetic energy of the system is T = 1 2 L 0 w( x, t) ρadx (Eq. 6.8) We obtained the total potential energy by adding the energy stored in the spring and the bar, which leads to

104 87 L w( x, t) 1 2 V = EI ( ) dx + 2 kw( xi, t) (Eq. 6.9) 2 x 2 0 i= 1 For free vibration, the power input is zero. Once the mechanical energies, and power input have been characterized in terms of the displacement, the equations of motion can be derived by using the power balance law. We substitute the basic series expansion, which has the form N w( x, t) = ψ ( x) q ( t), (Eq. 6.10) j= 1 j j into the equations of motion, and then collect coefficients of the generalized coordinates q j. The resulting equations of motion have the form [ M ] q + [ K]{ q} = 0, (Eq. 6.11) where M K jn jn = M = K nj nj = = L 0 L 0 ψ ψ ρadx j n 2 d ψ EI 2 dx j d ψ 2 n 2 dx dx + 2 i= 1 kψ ( x j k ) ψ ( x n k ) (Eq. 6.12) In the above equations, ψ j and ψ n can be any continuously differentiable basis functions, that satisfy the geometric boundary conditions.

105 88 To evaluate the natural vibration frequencies and mode shapes of this system, complex exponentials are used to represent the homogeneous solution of the equations of motion, Eq. 6.11, so iωt {} q Re[ B{ φ} e ] = (Eq. 6.13) where B is an arbitrary complex constant. To make the generalized coordinates { q } to satisfy the equations of motion will generate the general eigenvalue problem, as 2 [[ K ] ω [ M ]]{ φ} = {0}. (Eq. 6.14) Because the Ritz series has N terms, the solution of Eq leads to N natural frequencies ω and corresponding orthogonal modes φ }. Usually, we sequence the n { n eigenvalues such that 0 ω ω ω. 1 2 N Substituting the resulting { q } into Eq yields N iωt w( x, t) = Re[ Bφ e ] ψ ( x) j= 1 jn j (Eq. 6.15) where φ jn is the as th j element of mode vector n. The above equation can be reorganized N w( x, t) = [ φ jn ψ j ( x)] B cos[ ω nt + arg( B)] (Eq. 6.16) j= 1 w( x, t) = Ψ n ( x) B cos[ ω t + arg( B)] (Eq. 6.17) n

106 89 where N Ψ ( x) = φ ψ ( x) (Eq. 6.18) n j= 1 jn j The factor Ψ (x) is called the mode function, which describes the vibration mode shape n of this system. The mode functions for most systems share a common property. The mode shapes of the system previously discussed could be like that shown in Figure 6-3. This figure displays the first four mode functions of such an elastic bar spring system. From the mode shape of each mode function, it is clear that at some locations vibration amplitudes are high, and at other locations, vibration amplitudes are low. Therefore, in order to get a strong signal from a vibration sensor, the location of detection points is critical. Ψ n ( x) Axial Distance x L Figure 6-3: Mode Functions For an Elastic Bar Supported by Springs

107 90 Although only the first few modes are shown in this figure, a real system should have infinite numbers of natural frequencies and mode functions. By using Ritz series method, we will be able to get the first N modes approximately. By increasing the number N, that approximation becomes more and more accurate. However, the computational complexity also increases for large values of N. So far, both simple mass-spring system, and continuous bar-spring system were discussed. A real flip chip can be better modeled as a continuous elastic block supported by springs, where the silicon die is modeled as an elastic block and solder joints are modeled as springs. Similar analysis procedures can also be used to model this elastic block-spring system, except that the flexural displacement w ( x, y, t) is a function of position x and y, as well as time. The mode function Ψ ( x, y) is no longer a one dimensional function, but a two dimensional function. n For each flip chip, there are usually many solder balls, and the distribution of those solder balls is not always symmetric. This makes modeling very complicated using the Ritz series method. Therefore, the finite element method was chosen to perform the vibration modal analysis of flip chips.

108 91 Modeling by Using Finite Element Method The Finite element method (FEM) is very powerful for solving vibration problems with irregular system configuration and complicated boundary conditions. A powerful FEM tool, ANSYS, was used to set up a finite element model of a flip chip. The same type of flip chip used in Chapter IV was used for finite element analysis. Finite element models of a good chip and chips with different defects were setup, and vibration modal analysis was performed on these models (Liu, 2000). Geometric Solid Modeling An elastic block sitting on 14 solder balls can represent the geometric model of the flip chip, as shown in Figure 4-1. The solder ball is a part of a sphere with its top and bottom cut out to form circular planes. This is only an estimation of the real model. Actually the chip base is an imperfect rectangle and with several layers in it. The actual solder balls are not perfect spheres, as well (Read, 1991). To accurately measure the geometric dimensions of the flip-chip, a scanner is used to grab the image of the flip chip along with a ruler. Then all dimensions can be counted by pixels, thus insuring high-level of measurement accuracy. Figure 6-4 shows the dimensions of the chip base and a solder ball height measured by this method.

109 Unit: mm Figure 6-4: Geometric Model of Flip Chip and Solder Ball Figure 6-5: Solid Model of a Good Chip

110 93 Three cases of flip chip solder joint quality have been studied: a good chip, a chip with one missing ball, and a chip with delamination at one solder joint. By using the above dimensions, a solid geometric model is set up in ANSYS, as shown in Figure 6-5. Figure 6-6 shows the solid model of a chip with one missing solder ball. Figure 6-6: Solid Model of Chip with One Missing Solder Ball Figure 6-7 shows the solid model of a chip with a defect at solder joint 2. This defect is a delamination at the contact surface between silicon die and solder ball. This kind of defect could be caused by shear stress.

111 94 Figure 6-7: Solid Model of Chip with Delamination on a Solder Joint Materials The material of the silicon die is pure silicon with the following properties: E = 1.15e ν = 0.25 ρ = 2.33e 11 3 Pa kg / m 3 All the parameters are in International Unit. The properties of solder balls are: E = 1.965e ν = ρ = e 3 Pa kg / m 3

112 95 These values come from the normal Lead-Tin alloy (95%-5%) for solder joints of this type of flip chip. Meshing The element type is chosen as: SOLID187 3-D 10-Node Tetrahedral Structural Solid. SOLID187 element is a higher order 3-D, 10-node element. SOLID187 has a quadratic displacement behavior and is well suited to modeling irregular meshes, such as those produced from this silicon die and solder ball model. The element is defined by ten nodes with three degrees of freedom: translations in the nodal x, y, and z directions, as shown in Figure 6-8. Figure 6-8: Solid 187 3D 10-Node Tetrahedral Structural Solid

113 96 After choosing the element type, the next step is to control the mesh size. Although ANSYS has its automatic mesh control tool, it is not recommended to simply use that tool when modeling an irregular-shaped system like this. The user-controlled mesh size can provide better balance between mesh size and computational complexity. Figure 6-9 shows a flip chip after meshing. Figure 6-9: A Flip Chip Model After Meshing Boundary Conditions To perform vibration modal analysis on this flip chip model, it should be a free vibration without any force input is assumed. The boundary condition is the

114 97 displacement constraints on the bottom surface of solder balls. All the solder balls are sitting on a ceramic printed circuit board (PCB). During the testing process, it is assumed that the PCB doesn t move. Therefore it is assumed that there is no displacement on the bottom surface of all solder balls. Modal Analysis Results To solve this vibration modal analysis problem by using ANSYS, both the natural frequencies and the mode shape corresponding to each frequency will be generated. Table 6-1 summarizes the first four natural frequencies for both cases. As shown in this table, the chips with defects have lower natural frequencies than good chips. This is because the defect decreases the stiffness of the vibration supports, causing the chip s natural frequencies to decrease. Table 6-1: Vibration Frequencies (khz) of Different Chips (Modeling Results) 1 st Mode 2 nd Mode 3 rd Mode 4 th Mode Good Chip Chip with One Missing Solder Ball Chip with Delamination Defect

115 98 Figure 6-10 to Figure 6-13 illustrate vibration mode shapes at the first four vibration frequencies. The mode shape provides an insight on how to design the data scanning pattern. The location of detection points should be chosen where large displacement takes place.

116 99 Figure 6-10: Mode Shape of the 1 st Vibration Mode Figure 6-11: Mode Shape of the 2 nd Vibration Mode

117 100 Figure 6-12: Mode Shape of the 3 rd Vibration Mode Figure 6-13: Mode Shape of the 4 th Vibration Mode

118 101 Experimental Verification The same flip chips as that were used in the FE model were tested in the inspection system for model validation. Because of the limited number of test samples, only the models of a good chip and a chip with one missing solder ball were validated. Images of the solder joints of three sample chips are shown in Figure The top pictures are side views taken by microscope, and the bottom pictures are x-ray images taken through the circuit board. As shown in the picture, there are two good chips, labeled as Good Chip 1 and Good Chip 2, and a chip with defect, labeled as Bad Chip 1. One solder ball of Bad Chip 1 is missing. Because of this defect, the vibration response of the bad chip will be significantly different from the good chips vibration responses. Good Chip 1 Good Chip 2 Solder Ball Bad Chip 1 Missing Figure 6-14: Solder Joints of Flip Chip Samples

119 102 Power spectrums of signals from the three test chips were obtained as shown in Figure 6-15 to Figure Note that the peak locations of Good Chip 1 and Good Chip 2 are very closely matched because they are both good chips. Bad Chip 1 is at relatively lower frequency because it has a missing solder ball, which decreases the stiffness of vibration supports, thus its natural frequency decreases. 504kHz 627kHz 784kHz Figure 6-15: Power Spectrum of Good Chip 1

120 kHz 625kHz 781kHz Figure 6-16: Power Spectrum of Good Chip 2 438kHz 776kHz 570kHz Figure 6-17: Power Spectrum of Bad Chip 1

121 104 Table 6-2 lists the first four natural frequencies for those three chips from experimental measurements. Good Chip 1 and Good Chip 2 have similar natural frequencies, but Bad Chip 1 has lower frequencies. For Good Chip 1 and Good Chip 2, the 3 rd mode is not available. A possible explanation for the missing vibration mode is that the inspection point could be near a node for the mode shape, producing a very small displacement at that point, which is impossible to detect. Table 6-2: Vibration Frequencies (khz) of Different Chips (Experimental Results) 1 st Mode 2 nd Mode 3 rd Mode 4 th Mode Good Chip N/A 784 Good Chip N/A 781 Bad Chip 1 (with One Missing Solder Ball) N/A 776 A comparison of Experimental and modeling results are shown in Table 6-3. As shown in the table, there is a good match between modeling results and experimental results.

122 105 Table 6-3: Modeling Results Compared with Experimental Results 1 st Mode 2 nd Mode 3 rd Mode 4 th Mode Good Chip 1 Modeling Experiment N/A 784 Bad Chip 1 Modeling Experiment N/A 776 From above theoretical modeling and experimental results, it is clear that the change of chip s vibration frequencies indicates the quality of solder joints. However, the type of flip chip modeled does not have many solder balls, and the ball pitch is relatively large. When a flip chip has few solder bumps, frequency domain analysis and/or time domain analysis can be used to detect defects. But when there are many solder bumps, time domain analysis must be used, and frequency domain analysis may or may not produce good results.

123 106 CHAPTER VII PATTERN RECOGNITION OF DEFECTS One of the objectives of this research is to develop a solder joint inspection system that can be used for on-line inspection. To achieve this goal, full automation of the inspection system is very important. The signal output of this system is vibration waveforms in the ultrasonic frequency range, and all the defect information is contained in these waveforms. It is difficult to automate the inspection process without advanced signal processing and pattern recognition algorithms. Therefore, an appropriate waveform pattern recognition method needs to be designed which can automatically evaluate the solder joint quality from the ultrasonic waveform. This pattern recognition method can also be used to classify defects. As discussed earlier in Chapter II, a typical pattern recognition paradigm should consist of three steps: preprocessing, feature extraction, and classification. The three components of the integrated pattern recognition paradigm mutually reinforce one another. Preprocessing The fundamental objective of applying pattern recognition methods is to develop a combination of discriminatory clues and decision rules that could efficiently separate

124 107 the feature space into different classes. We would like these clues to reflect and to capture the underlying signal physics. Unfortunately, there exist a number of confusing factors that tend to obscure or even bury the significant attributes needed for analysis. Those confusing factors may include background noise, interference, and environmental conditions. For example, in the current system, the noise could come from the interferometer because the test sample s surface is not smooth, or from the signal digitizing system. Therefore, it is imperative that some form of signal cleaning techniques be used, such as noise filtering, etc. The following approaches have been used for preprocessing in this system: 1) Band-pass filter and amplifier. A filter/amplifier unit between the interferometer and the data acquisition board conditioned the signal before sampling. The filter was configured to have a passband between 100kHz to 2MHz, cutting off noise outside the band. The amplification was set to 6dB. 2) Time domain averaging. Although a bandpass filter has been used, noise in the passband range still passes through the filter. Time domain averaging was used to further decrease the effect of random noise in that frequency range. 3) Periodogram averaging power spectrum estimation

125 108 The periodogram power spectrum estimation method was also used to get rid of random noise in the frequency domain. By using this method, less time domain averages will be required, which makes the inspection process faster. 4) Digital filtering. A digital filter was also designed to look at signals in a certain passband. The bandwidth was designed to cover only the first few vibration natural frequencies. Feature Extraction During the experimental process, a lot of raw data is recorded from test samples. Although it is possible to do classification directly on a raw data, it is not recommended because the resulting feature dimension is too high, leading to the curse of dimensionality in classifier design. Therefore, before classification, feature extraction is necessary to capture essential attributes that are useful for class separation (Liu, 1998). Since feature extraction is so important, the key to achieving robust recognition performance is the integration of good features into the classifier architecture. The good features are supposed to: capture signal attributes based on signal physics, possess good discrimination capabilities (small intra-class variance and large interclass separation), be insensitive to extraneous variables, be relatively inexpensive to measure if real-time implementation is desirable, and to be mathematically definable (Kil and Shin, 1996).

126 109 Training Samples The same type of flip chips shown in Figure 4-1 were chosen to test the pattern recognition algorithm for defects inspection. Twenty chips were chosen as training samples, and the pictures of them are presented in Figure 7-1 and Figure 7-2. Some of them are good chips, and some are chips with various type of defects, such as a missing solder ball, an undersized solder ball, and a silicon die with a crack.

127 110 Crack Good Chip Chip 1 Chip 2 Crack Good Chip Chip 3 Chip 4 Crack Crack and Solder Ball Disconnected Chip 5 Chip 6 Solder Ball Deformed Crack Chip 7 Chip 8 Solder Ball Missing Solder Ball Missing Chip 9 Chip 10 Figure 7-1: Views of Training Samples (Chip 1 to Chip 10)

128 111 Good Chip Surface Crack Chip 11 Chip 12 Crack Crack Chip 13 Chip 14 Good Chip Solder Ball Disconnected Crack Chip 15 Chip 16 Solder Ball Disconnected Crack Chip 17 Chip 18 Crack and Solder Ball Disconnected Solder Ball Missing Chip 19 Chip 20 Figure 7-2: Views of Training Samples (Chip 11 to Chip 20)

129 112 Feature Vector Design Feature extraction is important to accurate classification. The extracted features must be simple and contain a lot of useful information. One very important thing in feature vector design is that the features extraction process does not remain as a black box, but as a physical entity that is logically explainable. Good features should have physical meanings. Based on the research discussed in Chapter IV, Error Ratio can be used as one of the features for classification because it is a good quantitative measurement of the difference between a good chip and a chip with defects in the time domain. However, there are several Error Ratios for each chip because of multiple detection points. It is not necessary to use all of them for classification, so the maximum value calculated from all of the points is the final feature. The first feature is described mathematically as the following: Feature 1 = max (Error Ratio, Error Ratio 2, Error Ration N) (Eq. 7.1) where N is the number of detection points.

130 113 Using this method, the maximum Error Ratio values of all the training samples chips were calculated and are shown in Figure 7-3. Figure 7-3: Maximum Error Ratio of Each Training Sample The vibration frequency is the second feature which can be included into the feature vector. As discussed in Chapter V, chips with defects such as a missing solder ball, or delaminations, will have lower natural vibration frequencies than a good chip. Therefore vibration frequencies can be used to distinguish a good chip from a chip with defects. Although several vibration modes can be excited on one chip, the first mode is usually the dominant mode, so the first natural frequency was chosen as another feature. Feature 2 = First Vibration Frequency (Eq. 7.2)

131 114 The first vibration frequency values of the 20 training chips are shown in Figure 7-4. Figure 7-4: Dominant Frequency of Each Chip Based on the discussion, the final feature vector is finally designed as: Vi = (Max Error Ratio, Dominant Frequency) (Eq. 7.3)

132 115 The feature vectors are distributed as shown in Figure 7-5, for the 20 training chips. Figure 7-5: Feature Vector Distribution of Sample Chips Classification Once all the features are extracted, classification can be achieved. Appropriate classifier architectures need to be developed to exploit the underlying feature distribution. Classifiers are simply projection operators transforming the optimized feature subset onto a classification decision dimension. Classification parameters associated with the internal structure are estimated during training.

133 116 Region of Interest As shown in Figure 7-5, the feature vector of Chip 12 is obviously located far away from other vectors. Outlying data vectors are very easy to separate from other data vectors even without using complicated classification algorithms. In other words, when working on pattern recognition classifier design, only data inside a certain region of interest must be considered. For this type of test samples, from the modeling results discussed in Chapter 6, a good chip has the 1 st vibration natural frequency at 498kHz and a chip with one missing solder ball has the 1 st vibration natural frequency at 469kHz. From the experimental validation, good chip has the 1 st natural frequency at about 500kHz, and chip with one missing solder ball has the 1 st natural frequency at about 440kHz. All of the values are located inside a frequency band from 400kHz to 550kHz. Any test chip has a dominant frequency outside this region must be a chip with defect. Similarly, based on the experimental results, all the good chips have a Error Ratio value much smaller than 1.5. Any chip has a Error Ratio larger than 1.5 is for sure a bad chip. as Based on this analysis, as shown in Figure 7-6, the region of interest was selected and 400kHz Dominate Frequency 550kHz (Eq. 7.4) 0 Max Error Ratio 1.5 (Eq. 7.5)

134 117 Figure 7-6: Training Feature Vectors and Region of Interest Applying this definition, the feature vector from Chip 12 is located outside the region of interest, and it is easy to tell that Chip 12 is not a good chip. Figure 7-7 shows the feature vector distribution inside the region of interest. The next step is to design a pattern recognition classifier to automatically separate good chips from chips with defects.

135 118 Figure 7-7: Feature Vectors Distribution inside Region of Interest Probabilistic Neural Network Classifier Classifiers can be categorized into artificial neural networks and conventional classifiers based on the classification architecture. Neural networks can be characterized by the following: network topologies, adaptive training rules, and nonlinear node functions that include sigmoid, hard limit, and exponential functions (Lippman, 1987; Morgan and Scofield, 1991). The Bayesian classifier and its outgrowth, the probabilistic neural network (PNN), have been used successfully to solve a diverse group of classification problems. The PNN competes with the backpropagation algorithm (Rumehart, 1986). Compared with

136 119 backpropagation, the PNN offers the following major advantages (Wasserman, P. D., 1993): 1. Rapid training: The PNN process is as much as five orders of magnitude faster than backpropagation. 2. With enough training data a PNN is guaranteed to converge to a Bayesian classifier (the usual definition of optimality), despite an arbitrarily complex relationship between the training vectors and the classification. There is no such guarantee with the backpropagation, because long training periods can terminate in a local optimum that may be an unsatisfactory solution. 3. The PNN algorithm allows data to be added or deleted from the training set without lengthy retraining, whereas, any modification to a backpropagation training set will generally require a repetition of the entire training process. This characteristic of the PNN makes it more compatible with many real-world problems. As with human experience, network learning is often a continuous process. Additional input data collected during operation can improve the performance of the classifier. 4. PNN provides an output indicating the amount of confidence upon which it is basing its decision. A backpropagation system provides no such confidence indication.

137 120 The probabilistic neural network is a kind of radial basis network suitable for classification problems. Figure 7-8 shows the architecture of a probabilistic neural network which accomplishes the classification for two classes. Input Distribution Layer Pattern Layer Summation Layer Decision Layer w ij f () Z A1 x 1 Z AP S A x 2 Z B1 S B x n Z BQ Figure 7-8: Architecture of Probabilistic Neural Network As shown in Figure 7-8, an input vector X = x x... x ) to be classified is ( 1 2 n applied to the neurons of the distribution layer. This layer serves merely as a connection point; the neurons perform no computation. The pattern layer neurons are grouped by the known classification of its associated training vector. Each pattern layer neuron sums the weighted inputs from every distribution layer neuron, then applies the non liner radius function f ( ) to that sum to produce the output Z ci, where the first subscript, c, indicates the class of the associated training vector, and the second identifies the pattern layer

138 121 neuron computing that class. Each neuron in the summation layer received all the pattern layer outputs associated with a given class. In the decision layer, each neuron forms a comparison, outputting 1 if S > S, and 2 otherwise, thereby indicating the class of the a b current input vector. Compared with conventional neural networks, one thing that makes a PNN special is that the function at its hidden layer (Pattern Layer) is a radial basis function. The radial basis functions produce a localized response to input stimulus. That is, they produce a significant nonzero response only when the input falls with a small localized region of the input space. Although implementations vary, the most common radial basis function is a Gaussian kernel function of the form: ( q) ( m) T ( q) ( m) ( q) ( m) ( X V ) ( X V ) f ( X, V ) = exp[ ] (Eq. 7.6) 2 2σ m where (q) X is the q th weighted input vector, and (m) V is the m th center vector. Figure 7-9 shows a radial basis function on the plane (Looney, 1997). When (q) X is close to V (m), the radial basis function output a large value, but when they are far away from each other, the function value is very small. The parameter σ m in the equation is used to control the spread of the radial basis function so that its values decrease more slowly or more rapidly as (q) X moves away from the center vector V (m). The name, radial basis function, comes from the fact that these Gaussian kernels are radially symmetric; that is, each node produces an identical output for inputs that lie a fixed radial distance from the center of the kernel.

139 122 Figure 7-9: A Radial Basis Function On the Planar Feature Space Figure 7-10 illustrates an example with two input features and two output classes. As you can see from this example, one major shortcoming of the PNN is that it requires one neuron for each training vector. Approaches to overcome this drawback encompass feature set reduction, clustering and kernel adaptation. It is important to use a feature subset that provides maximum class separability. Clustering can reduce the number of training vectors by grouping vectors with similar characteristics measured in distance from the centroid of each cluster and by representing them with the cluster centroid. On the other hand, clustering can be combined with maximum likelihood estimation of the kernel shape associated with each cluster.

140 123 x 2 Class 1 Class 2 (a) Two-dimensional feature distribution with 7 training vectors x 1 f () w ij x 1 Decision x 2 (b) Corresponding probabilistic neural network Figure 7-10: An Example of Two Input Features and Two Output Classes Although the case shown here has only two classes, this technique can be easily extended to an arbitrary number of classes by adding a group of pattern layer neurons and a summation layer neuron for each class. A mechanism must then be provided to determine which summation neuron has the maximum output.

141 124 PNN Classifier Training A supervised pattern recognition method was used in this project. The PNN classifier has to be trained on a training set consisting of feature vectors before it can be used for classification. For a PNN classifier, the training requires very little throughput because it simply stores the training tokens and waits for testing to commence. For the training data, the target must be known. In this project, two target clusters have been defined, one is good chip cluster, and the other is bad chip. Twenty training samples were used to train the PNN classifier. After training, the classifier output is shown in Figure Decision Surface Figure 7-11: Output of the PNN Classifier

142 125 As shown in Figure 7-11, the output of this PNN classifier is either 1 or 2. If the input feature vector is located in a certain area, and the output is 1, the feature vector will be classified into cluster 1, which is the good chip cluster. If the output is 2, that feature vector will be classified into cluster 2, which is the bad chip cluster. The surface which separates the two clusters is called the decision surface. Figure 7-12 illustrates the training vector distribution and the location of the decision surface. The decision surface was automatically generated by the classifier training process. As shown in the figure, the decision surface successfully separates good chips from chips with defects. Decision Surface Figure 7-12: Training Vectors Distribution with Decision Surface

143 126 PNN Classifier Testing In order to test the performance of this classifier after training, another 5 chips were chosen as test samples. They are numbered Chip 21 to Chip 25. As shown in Figure 7-13, only Chip 22 and Chip 23 are good chips, and others have crack or missing solder ball. Crack Good Chip Chip 21 Chip 22 Good Chip Crack Chip 23 Chip 24 Missing Solder Ball and Crack Chip 25 Figure 7-13: Views of Test Samples

144 127 The classification results of the test samples are shown in Figure Chip 21 and Chip 24 are located out of the region of interest, therefore they were classified into the chip with defect cluster without going through the PNN classifier. Inside the region of interest, Chip 22 and Chip 23 were classified as good chips, and Chip 25 was classified as a chip with defect. The results match up with the chips physical characteristics as shown in Figure Figure 7-14: Classification Results of Test Samples

145 128 Further Classification For on-line flip chip solder joint quality inspection, the goal is to distinguish good chips from chips with defects. Therefore classifying chips into two clusters is enough. However for other applications such as off-line analysis for process optimization, more detailed information about the defects may be desired. In this case, further classification is necessary. The PNN classifier is simple to configure for classifying more than two clusters. In order to further separate the 20 training samples, further analysis of data is needed. For example, the 20 training samples can be separated into three clusters: a good chip cluster, a chip with a missing/disconnected solder ball cluster, and a chip with crack cluster. The reason the chip with a missing/disconnected solder ball cluster can be differentiated from the chip with crack cluster is that the missing/disconnected solder ball defect usually causes an Error Ratio change and a frequency decrease, while the chip with a crack cluster does not change frequency as much. The output of the PNN classifier, using the three output values, is shown in Figure There are three output values. When the output is one, that chip belongs to good chip cluster. An output value of two corresponds to the chip with missing/disconnected solder ball cluster, and an output value of three belongs to chip with crack cluster.

146 129 Figure 7-15: Output of PNN Classifier for Further Classification As shown in Figure 7-16, the decision surface can successfully separate those three clusters, with one exception. A chip with a missing solder ball belongs to chip with crack cluster. Because the pattern recognition method used is a statistical method, some defects close to the decision surfaces may be incorrectly classified. Error always exists and cannot be avoided.

147 130 Figure 7-16: Further Classification Results As discussed in this chapter, a statistical pattern recognition method was developed to classify the waveforms from good chips and bad chips. The automated defects pattern recognition technique makes on-line inspection possible. It also makes the identification of different defect possible.