應用順滑模態理論操作化學機械研磨製程

全文

(1)國. 立. 交. 通. 大. 學. 機械工程研究所碩士論文. 應用順滑模態理論操作化學機械研磨製程 Dynamic Tuning of Chemical-Mechanical Planarization Operation via Sliding-Mode Theory. 研究生 : 紀建宇指導教授 : 林家瑞. 中華民國九十三年六月.

(2) 應用順滑模態理論操作化學機械研磨製程 Dynamic Tuning of Chemical-Mechanical Planarization Operation via Sliding-Mode Theory 研究生: 紀建宇. Student: Chien-Yu Chi. 指導教授: 林家瑞博士. Advisor: Dr. Chia-Shui Lin. 國立交通大學機械工程研究所碩士論文計畫書. A Thesis Submitted to Institute of Mechanical Engineering College of Engineering National Chiao Tung University in Partial Fulfillment of the Requirement for the Degree of Master of Science in Mechanical Engineering June 2004 Hsinchu, Taiwan, Republic of China 中華民國九十三年六月.

(3)

(4) 應用順滑模態理論操作化學機械研磨製程. 學生: 紀建宇. 指導教授: 林家瑞博士國立交通大學機械工程學系碩士班. 摘要. 化學機械研磨製程技術發展至今，多階段研磨的方式普遍被使用在實際製造上以獲得更佳的效能。由於研磨效能與製程操作存在的直接關係，在本研究中，將針對製程動態操作的機制加以探討建立，而實現的方式將採用順滑模態控制。因為現有機台的操作機制無法符合設計要求，用以印證動態調整的實驗仍未進行，這一部分也許需要進一步與設備廠商合作才得以完成。經由數值模擬的方式驗證下，結果顯示在維持相同移除能力的情況下，使用動態調整的方式操作所得之平坦化效果比典型的固定輸入方式操作要來得優異。. I.

(5) Dynamic Tuning of Chemical-Mechanical Planarization Operation via Sliding-Mode Theory. Student: Chien-Yu Chi. Advisor: Dr. Chia-Shui Lin. Institute of Mechanical Engineering National Chiao Tung University. ABSTRACT. The development of chemical mechanical planarization (CMP) to date relies on multi-stage polishing for better performance.. The straight. relationship between performance and operation provides a new method for control of CMP process.. The strategy of dynamic tuning is proposed. in this paper and one possible operation profile is established via sliding-mode theory.. Because of the lack of operation mechanism of the. equipment in existence, more elaborate experimental verification of the strategy is yet to follow.. We may need to work with some equipment. suppliers for future work.. Based on the proposed strategy, lower dishing. and more efficient copper step height reduction can be verified from some numerical simulations.. Simulation results show better performance. under the same throughput/removal-rate.. II.

(6) TABLE OF CONTENTS ABSTRACT (Chinese). Ⅰ. ABSTRACT (English). Ⅱ. TABLE OF CONTENTS. Ⅲ. LIST OF FIGURES. Ⅵ. LIST OF TABLES. Ⅸ. CHAPTER 1. INTRODUCTION. 1. 1.1 Planarization in Integrated Circuits (IC) Fabrication. 1. 1.2 Literature Survey. 3. 1.2.1 Modeling of CMP Process (Mechanical). 4. 1.2.2 Modeling of CMP Process (Chemical). 5. 1.2.3 Parameters Characterization. 6. 1.2.4 Consumables Approach. 7. 1.2.5 CMP Operation. 7. 1.2.6 Emerging Approach for Metal(EP/ECP). 8. 1.3 Objective. 9. CHAPTER 2 CHEMICAL MECHANICAL PLANARIZATION (CMP) 11 2.1 Chemical Mechanical Polishing System. III. 11.

(7) 2.1.1 Schematic CMP System. 12. 2.1.2 Consumables. 12. 2.1.3 Endpoint Detection System. 14. 2.2 Chemical Mechanical Planarization Process. 15. 2.2.1 Process Parameters. 15. 2.2.2 Performance Indexes. 16. 2.2.3 CMP Models/Mechanisms. 18. 2.3 Process Control in Chemical Mechanical Planarization Process 22. CHAPTER 3. OPERATION OF CMP VIA SMC. 24. 3.1 Variable Structure Control. 24. 3.2 Sliding Mode Control. 26. 3.3 Operation Profile Setting. 29. CHAPTER 4. 3.3.1 Problem Statement. 30. 3.3.2 Operation Profile Setting. 32. 3.3.3 Results. 35. VERIFICATION BY NUMERICAL SIMULATION 38. 4.1 Operation Input Concretization. IV. 38.

(8) 4.2 Verification. 41. 4.3 Discussion. 43. CHAPTER 5. CONCLUSION AND FUTURE WORKS. 46. 5.1 Conclusion. 46. 5.2 Future Works. 46. REFERENCES. 49. APPENDIX Ⅰ. 73. APPENDIX Ⅱ. 75. V.

(9) LIST OF FIGURES Fig. 1.1. Various forms of planarization. 53. Fig. 1.2. Etchback process. 54. Fig. 1.3. Schematic of CMP benefit. 54. Fig. 1.4. Illustration of CMP fabrication process. 55. Fig. 1.5. Framework of integrated CMP model. 55. Fig. 2.1.1. Schematic of CMP polisher (CMP on Rotary Tool). 56. Fig. 2.1.2. Schematic of CMP polisher (CMP on Orbital Tool). 56. Fig. 2.1.3. Schematic of CMP polisher (CMP on Linear Tool). 57. Fig. 2.2. Effects of slurry flow rate on CMP process. 57. Fig. 2.3. Pad conditioning. 58. Fig. 2.4. Dishing and Erosion. 58. Fig. 2.5. Planarization efficiency. 59. Fig. 2.6. Copper CMP Defects. 59. Fig. 2.7. The Run-to-Run Concept. 60. Fig. 3.1.1. All possible situations of system by traditional design. 60. Fig. 3.1.2. VSC system response of a simple second order system. 61. Fig. 3.2. Generation of sliding-mode. 61. Fig. 3.3. The system trajectory in sliding mode. 62. VI.

(10) Fig. 3.4. Effects of pressure and speed on dishing and erosion. 62. Fig. 3.5. Conceptual description of soft landing. 63. Fig. 3.6. Simulation results of CMP operation via time optimal control. 64. Fig. 3.7. Equilibrium control. 65. Fig. 3.8. Simulation result_Sliding Function. 65. Fig. 3.9. Simulation result_Phase-Plane Plot. 66. Fig. 3.10. Simulation result_Control Input. 66. Fig. 3.11. Simulation result_State Variables. 67. Fig. 4.1. Removal rate (A/min) as a function of oxidizer concentration for different pressure and speed settings. Fig. 4.2. 67. Effect of H2O2 concentration on the value of Rc with specific slurries from Rodel. 68. Fig. 4.3. Dynamic tuning operation of CMP process. 68. Fig. 4.4. (a) Comparison of dishing between dynamic tuning and corresponding constant input (copper removal). 69. (b) Variations of parameters (Kcu, B and Rc are normalized. Fig. 4.5. forms). 69. Effect of over polish on the extent of dishing. 70. VII.

(11) Fig. 4.6. (a) Comparison of step height reduction between dynamic tuning and corresponding constant input (removal rate). 71. (b)Variations of parameters (Kcu, B and Rc are normalized forms). 71. VIII.

(12) LIST OF TABLES Table 1.1. Comparison between common planarization techniques. IX. 72.

(13) CHAPTER 1 INTRODUCTION. As ultra-large scale integration (ULSI) technology progresses, the feature size decreases while the chip size and the number of device increases.. Multilevel. interconnection technique plays a critical role in Integrated-Circuit (IC) fabrication. The present state of Chemical Mechanical Polishing/Planarization (CMP) is the result of semiconductor industry’s needs to fabricate multilevel interconnection for increasingly complex, dense, and miniaturized devices and circuits. This need is related to improving the performance while adding more devices, functions, etc. to a circuit and chip. Several methods are known to achieve a higher level of planarization: (chemical-mechanical) polishing, laser reflow, coating with spin-on glasses, polymers, and resists, thermally reflowing materials, dielectric deposition, and flowable oxides. In these methods, CMP needs fewer steps compared with the others.. Furthermore,. CMP uses nontoxic substances, has good removal selectivity, and a good removal rate control [3].. Above all, the main advantage of CMP lies in the global planarization.. At the present time, the global planarization can only be achieved by using CMP. Certainly, CMP process becomes a heavy subject of investigation in IC fabrication technology.. 1.1. Planarization in Integrated Circuits (IC) Fabrication. To increase factory productivity in semiconductor production, manufacturers are finding way to reduce chip size and add more levels of interconnecting wires. 1. In.

(14) the fabrication of integrated circuits (IC), the problem of planarity is well known. During IC fabrication, successive deposition and etching of dielectric and conductor layers increasingly modify the substrate topography. Problems caused by variations in relief arise mainly during lithographic processing and metallization and include linewidth variations and step coverage.. Therefore, the problem of planarity has been. addressed using numerous planarization approaches involving the materials and/or techniques [25]. Over the years many methods have evolved for planarizing wafers. Basically, all of the alternatives to CMP consist of reflow, spin-on film smoothing and etchback techniques. In these methods the wafer is coated with, for example, an oxide. Since the underlying topology is uneven, the wafer is baked at a temperature high enough to enable the oxide to vitrify and flow.. To lower the temperature at which flowing can. take place, the oxide is typically doped with phosphorous and boron.. However, the. introduction of these impurities leads to problems such as crystallization and moisture adsorbance. In addition, each time the wafer is subject to high temperatures the thermal budget is consumed, thus affecting the underlying device performance. Unfortunately, even when all of these problems are addressed, the resulting surface morphology is only locally planar, i.e., barely planar enough to meet the needs of today's processing technology.. Further reduction in device geometry mandating. additional levels of interconnects renders present non-CMP based planarization techniques inadequate. Fig. 1.1 shows various forms of planarization. Additionally, the common planarization method, etchback, is showed schematically in Fig. 1.2.. After metal wirings are formed, deposit thick oxide film. and spread photoresist on the surface. plasma etching.. Then, the planar surface is derived by dry. First, the thinner photoresist will be removed and etching. downward continuously.. The exposure oxide film and inner photoresist on the caves 2.

(15) will be etched.. Whole etchback process stops when all the photoresist removed.. Moreover, other familiar methods are listed on Table 1.1 in comparison. Multilevel interconnection keeps playing a critical role in the next generation of ULSI fabrication.. Furthermore, global planarization is the key point of realization of. multilevel interconnection technique. is the only way to go.. Employing CMP into the fabrication process. After the discussion on planarization techniques above, it is. clear that CMP will play an important role in IC fabrication.. Fig. 1.3 shows the. difference in planarization between IC with CMP and without CMP.. A simple. illustration of this part of semiconductor fabrication process is shown in Fig. 1.4.. In. next chapter, the framework of CMP will be illustrated in detail.. 1.2. Literature Survey. CMP. is. the. planarization. technique. required. for. meeting. stringent. photolithography depth of focus requirements for small device multilevel interconnection geometry.. At the present time, it appears that the global. planarization necessary for establishing reliable multilevel interconnects can only be achieved by using CMP.. However, the fundamental physics and chemistry of CMP. are not well known, the reason being the difficulty in obtain quantitative information about the pad surface, and what happens to the interface between pad and wafer surface during polishing.. In past ten more years, lots of research works are focused. on detailed removal mechanism (e.g., chemical and/or mechanical factors) and the influences of process parameters (e.g., slurry components and recipe setting). For improving the performance of CMP process, there exist different ways of modeling or characterization.. One of them is operation/control aspects of CMP process. In last. decade, much less work has been done on the operational aspect of CMP, especially 3.

(16) the process control side of CMP operation.. 1.2.1 Modeling of CMP process (Mechanical). In order to control a system well, it is necessary to understand the objective. To know what happens in a system, the most general way is to establish an explicit mathematical model.. Among research of CMP, a lot of works focus on establishing. model (or parameters identification).. Because of the complexity of whole process. (due to the consumables), a model which can describe the entire CMP process is not derived yet. But in last decade, great progresses in CMP modeling have been made. In modeling of CMP process, the most representative model is that brought up by F. W. Preston [1] for glass planarization in 1927, that is R = k ⋅ P⋅ V. (1.1). where R represents removal rate of the target material to be removed, P is the pressure applied to the material, V is the relative velocity between the pad and the target material and k is the constant of polishing.. This model represents the. intuitive mechanism of polishing and the most important mechanical parameters of polishing process, P and V .. CMP was first proposed for planarization of. large-scale integrated circuit (LSI) features by Kaufman and others [2] in 1991, and since then played a key role in the rapid advance of LSI technologies for multilevel interconnection.. Henceforward, there are many people trying to establish the. mathematical model (or removal mechanism) of CMP process in various research. G. Nanz and L. E. Camilletti [3] surveyed CMP process modeling which are established before 1995.. It turned out that only a few models exist, and that almost. none of them are applicable in general sense. Note that all of the models mentioned in that survey paper are related to mechanical effects. 4. In the same manner, there are.

(17) some models related to mechanical effects and based on Preston’s equation.. A. model which is a modification to Preston’s equation was developed by W.-T. Tseng and Y.-L Wang [4] to re-account the dependence of removal rate on the down force (pressure) and relative rotation speed during the CMP process.. F. Zhang and A.. Busnaina [5] established a model which is based on the plastic deformation of the polished material and incorporated the important contribution of particle adhesion forces.. In the work by B. Zhao and F. G. Shi [6], there can exist a threshold pressure. in the CMP process due to tribological interaction among abrasive particles, the polished wafer surface, and the polishing pad. H. Hocheng et al. [7] derived an analytical model which contains the effects of the applied pressure and the relative polishing velocity between the wafer surface and the pad surface.. In that model, the. chemical reaction as well as the mechanical bear-and-shear process is also considered. Moreover, the abrasion mechanism in solid-solid contact mode of the CMP process is investigated by J. Luo and D. A. Dornfeld [8] in detail. In their work, based on assumptions of plastic contact over wafer-abrasive and pad-abrasive interfaces, the normal distribution of abrasive size and an assumed periodic roughness of pad surface, a model is developed for mechanical material removal in CMP. It needs to be mentioned that Preston’s equation is effective in describing the average behavior of a process but is ineffective in providing fundamental understanding and locally relevant information regarding a chosen process.. Recently, a locally relevant expression for. material removal rate based on Preston’s equation was presented by D. Castillo-Mejia and S. Beaudoin [9].. 1.2.2 Modeling of CMP process (Chemical). Preston’s equation is nonetheless flawed, as it is solely based on concepts. 5.

(18) derived from mechanical polishing [10].. As the requirement of planarization and the. use of copper increases, chemical effect (slurry components) plays a more and more important role in CMP process.. Actually, the mechanism presented by Kaufman et. al. [2] in 1991 contains consideration of chemical effect. Furthermore, a two-step model of copper CMP involving mechanical abrasion of copper surface followed by removal of the abraded material from the vicinity of the surface is established by R. J. Gutmann et al. [11] in 1995 through PH value and electrochemical potential of slurry. Q. Luo et al. [34] and J. Luo and D. A. Dornfeld [8] included chemical effects in their mathematical model of CMP. Recently, J. Luo [12] concluded the development of CMP modeling, see Fig. 1.5.. 1.2.3 Parameters Characterization. Except for process modeling mentioned above, there are still a lot of researches which are focused on the investigation of consumables (especially in slurry components) or parameters characterization of CMP process. Note that a lot of works are related to copper or barrier layer, e.g. Tantalum (Ta) or Titanium (Ti), because of the employment of copper in IC fabrication.. Electrochemical. potentiodynamic measurements, obtained under static conditions and during polishing, were used by D. Zeidler et al. [13] to explain the CMP performance.. In their. investigation, an increasing H2O2 concentration leads to both lower wet etch rates and polish rates of Cu.. V. Nguyen et al. [14] investigated the influence of slurry. chemistry and thickness of the copper layer on dishing and found that the concentration of the oxidizer and the thickness of copper layer have a strong impact on dishing.. Furthermore, surface chemistry studies of CMP of copper were. 6.

(19) presented by J. Hernandez et al. [15] and revealed that the removal of copper during CMP is affected by the presence of copper oxides on the surface.. On the other hand,. V. S. Chathapuram et al. [16] and S. Ramarajan et al. [17] investigated the polishing of barrier layer of Ti and Ta, respectively.. 1.2.4 Consumables Approach. In recent year, some methods were brought up to improve the performance of CMP process. Instead of investigation of parameters and establishing of model, employing other approaches is researched and developed. The use of slurry with no abrasive and pad with fixed grit are two promising approaches.. V.H. Nguyen et al.. [18] presented the technique of copper CMP using fixed-abrasive pad. S. Kondo et. al. [19] and Y. Yamada et al. [20] worked on development of abrasive-free chemical polishing (AFP) for CMP process.. In their experimental study, the method reveals. great performances, lower line resistance, lower over-polishing sensitivity and cost reduction.. 1.2.5 CMP Operation. However, except investigation of details of CMP process and employment of other approaches, process control/operation is a candidate for solving the uncertainty of the process. Among public research archives, there are less works which are focused on control/operation aspects of CMP process. developed a EWMA controller and applied to CMP.. A. Chen and R.-S. Guo [21] L. Da et al. [22] analyzed the. performance of Run-to-Run control schemes and proposed a self-tuning predictor-corrector controller (PCC) for CMP process.. In their development of. process control, process statistics plays a key role and the performance within a wafer 7.

(20) is not clearly displayed in their result.. The experimental data of Wijekoon et al. [23]. indicates that the important defect, dishing, would vary linearly with operation condition (e.g. down pressure and relative velocity).. Therefore, to control the. within-wafer performance, taking care of the operation of the process is necessary. J.-B. Chiu et al. [24] established an analogy between soft landing of a spacecraft and CMP operation. In that work, the CMP operation was solved as a minimum-time optimal control problem and a two-stage CMP operation procedure was devised to ensure robustness of the controller. Besides, bang-bang control law was employed for preventing measurement uncertainties.. 1.2.6 Emerging Approach for Metal(EP/ECP). Several schemes for dielectric planarization have been developed and obtain good enough performance these years.. As the number of metal levels in electric. circuits increases, the need for improved planarization also increases at both chip and package levels.. An Electrochemical Planarization (EP/ECP) technology involving. electroplating followed by electropolishing was proposed by R. J. Contolini et al. [44] in 1994.. Later in 1995, copper electropolishing is discussed in detail from. experimental findings and theoretical interpretation. [45]. Recently, this method is. further demonstrated by integrating Cu electropolishing (removal of electroplated Cu to barrier layer) with CMP or dry etching (removal of remaining Cu and the barrier metal). [46, 47, 48]. The unique advantage of EP/ECP compared with CMP is that no. mechanical stress will be applied to the substrate and it might be important especially with the usage of low-k dielectric materials.. 8.

(21) 1.3. Objective. From the brief survey of CMP research mentioned above, it is clear that major research is focused on modeling, especially in mechanical aspects.. Parameters. characterization will help to increase knowledge of the complicated process and establish the model.. New approach and invention is always taken up in the industry. more than in academia because it needs a lot of experiments.. The approach of. operation aspect of CMP process presented by J.-B. Chiu et al. [24] provides a potential way for making a big stride in CMP, i.e. employing more process control in CMP process may be a promising way for deriving better performance. (see section 2.3) Note that there may be also some problems in EP/ECP, like non-uniformity. In the research of D. Padhi et al. [48], to gradually increase the electrolyte flow with time is suggested to avoid the inherent flaw of EP/ECP. This suggestion includes the concept of improving process performance by appropriate process operation. In typical operation, some limitations (due to constant input) will be led into the process. Based on the existing knowledge and the typical operation, some new operation methods are figured out, like two or three stage polishing.. The multi-stage. method is widely used in real production but it seems not good enough in the growing requirement of planarization.. On the basis of the qualitative and quantitative. research on CMP, a new operation strategy is proposed in this thesis.. In order to. increase the degree-of-freedom/flexibility of CMP process and further improve the performance of the process, the method of “Dynamic Tuning” will be tried and the operation profile will be set via sliding mode theory of variable structure control (VSC).. The details will be presented in following chapters.. For control system design, a dynamic model which is not too complex and can. 9.

(22) describe the system behavior reasonably is necessary.1. Among the research efforts. which have been reported on modeling the CMP of copper, ILD, or STI, there is no dynamic model with physical meanings of CMP process except the conceptual description used in the works of J.-B. Chiu et al. [24].. Therefore, Chiu’s dynamic. model will be employed for setting “dynamic tuning” operation profile via sliding mode theory.. Some models/mechanisms with physical meanings will be employed. to simulate this “dynamic tuning” operation strategy for CMP process.. 1. “Dynamic Tuning” is referred to within-wafer control of process control, so the process must be treated as a dynamic system. 10.

(23) CHAPTER 2 CHEMICAL MECHANICAL PLANARIZATION (CMP). A novel technique for planarization has drawn more attention, since conventional planarization methods such as reflowing-oxide-layers do not give the required global planarity for advanced processes.. Multilevel interconnects and the. use of 3-D packaging requires sophisticated methods to planarize the surfaces of wafers for subsequent device processing.. (e.g. For multi-layers of a logic device at. least one layer should be perfectly planar.) Lack of planarity may lead to severe problems for lithography (insufficient focus depth).. Chemical Mechanical. Planarization (CMP) evolves as the only way to achieve global planarization in IC fabrication.. In this chapter, CMP will be explained from the views of. system/configuration and process.. 2.1. Chemical-Mechanical Polishing System. As implied by the name, Chemical-Mechanical Polishing, the system must perform mechanical abrasion and chemical erosion to wafer surface of various materials. Mechanical abrasion is mainly provided by contact force of fluid or solid objects, i.e. slurry, abrasive and pad. However, chemical erosion is provided by slurry which is composed of specific chemical agent. coupled to each other.. These two chief effects are. It is this reason why CMP technique is treated as an. engineering ‘art’ rather than an engineering ‘science’.. 11.

(24) 2.1.1 Schematic CMP System. The design goals of all the CMP polishers include high throughput (multi-heads), “dry-in/dry-out”, easy control, endpoint detection and high quality of polished surface.. The CMP equipments/systems are fabricated by ten more suppliers. and all of these equipments have different configurations.. However, the main. mechanism of these polishers can be separated into three forms.. Fig. 2.1.1 shows the. most common kind of polisher framework-rotary tool.2 The wafer is held on a rotating carrier (holder) while the face being polished is pressed against a resilient polishing pad attached to a rotating platen disk. The abrasive contained in slurry and the slurry is carried to the wafer by the porosity of the polishing pad. Another configuration which is different to rotary tool is orbital tool, as shown in Fig. 2.1.2. The major differences between these two frames are slurry supply system and platen motion.. The slurry is fed from platen and the platen is oscillating during polishing.. The third configuration is announced by Lam Research, Linear Planarization Technology. TM. (LPTTM), as shown in Fig. 2.1.3.. These three equipments have. respective advantages and disadvantages.. 2.1.2 Consumables. CMP combines both chemical action and mechanical forces to planarize wafer surface.. The critical components required for CMP are a reactive liquid medium and. a polishing pad surface to provide the mechanical control required to achieve planarity. Either the liquid or the polishing surface may contain nano-size inorganic particles to enhance the reactive and mechanical activity of the process.. Because of the great. quantity of consumables requirement, CMP turns into one of the most expensive steps 2. In this work, the rotary tool will be investigated. 12.

(25) in the IC production. Besides, it is well known that consumables, slurry and pad, play significant roles in CMP.. Therefore, consumable suppliers and many. researchers are devoted to improve the stability and efficiency of consumables.. Slurry. Typically, slurry consists of two phases, namely, liquid and solid phases.. Liquid. phase consists of deionized (DI) water with several additives like oxidizers, complexing agents, inhibiting agents, and surfactants (Different components have distinct characteristics and are used to polish different materials).. Solid phase is. comprised of abrasives, which are usually inorganic oxides, e.g., alumina, silica, ceria, zirconia, titania, magnesia (Different sizes and types of abrasive have different effect on polishing).. While recent advances in abrasive-free slurries and fixed abrasive. CMP offer great potential, several challenges remain.. In CMP process, slurry is. dispensed in-between polishing pad and wafer to play a part in planarizing.. Slurry. flow rate is an important factor in supplying slurry. Fig. 2.2 shows the effects of slurry flow rate on the CMP process. According to that figure, slurry flow rate affects removal rate.. In oxide CMP, removal rate will increase with increased slurry. flow until saturation effect occurs. In metal CMP, removal rate will increase with increased slurry flow first and then decrease when lubrication effect occurs, i.e. slurry forms hydroplane between wafer and pad.. Pad. All polishing pads used in IC production are polyurethane pads. Based on the structure/composition, a polishing pad can be classified into the following types: solid polyurethane pad, polyurethane with filler or void, fiber felt impregnated with 13.

(26) polyurethane, and poromeric pads.. Each type of pad uses a unique manufacturing. process and therefore has its own unique characteristics. For example, poromeric pads are widely used for buffing and tungsten plug polishing because of their capability to deliver good local uniformity and low cost.. For the applications. required long range planarity, pads consisting of polyurethane with filler, such as Rodel’s IC pads, are the most commonly used pads.. Because of lack of long-range. planarity and/or excess dishing for large geometry features, older pads made of fiber felt impregnated with polyurethane are limited to sub-pad and tungsten plug polishing applications [27].. According to the same literature [27], pads are investigated for. groove effects and there are different influences by different forms of groove.. They. also mention that pad elasticity is also an important factor in CMP processing.. Conditioner. Pad conditioning, or pad “dressing”, is a critical component of the CMP process. It refers to the process of refreshing the polishing pad surface during CMP.. In the. process, a pad is conditioned by contacting its surface with a diamond abrasive disc or wheel. Generally, the conditioning disc is mounted on a powered rotating chuck that can be lowered onto the pad surface.. Well conditioning of a pad can increase pad. life and performance of polishing.. Fig. 2.3 shows the conditioning effect. schematically.. 2.1.3 Endpoint Detection System. To date, the design of CMP system is quite different from before, including the design of “dry-in/dry-out”, multi-platen and so on.. In spite of the advances of. configuration setting, robust sensor for end point detection (EPD) of polished material 14.

(27) is still a problem for process control of CMP.. Endpoint detection is an in-line. method of determining the termination point of wafer polishing based on metrological (i.e. film thickness) or physical (i.e. tool hardware) signals obtained during the CMP process.. The end of the polishing step is traditionally determined by setting a time. limit in the process. Changes in removal rate due to the normal pad life cycle, variation in slurry and pad lots, conditioning issues and a myriad of other potential variables, can result in under- or over-polish3 errors.. Additionally, the incoming. initial oxide or metal layer thickness may fluctuate from wafer to wafer.. All the. possible errors have to be compensated by valid in-line sensors [29]. To control CMP process well, a good and accurate in-line sensor is indispensable. In past few years, endpoint detection is developed through many methods, optical, thermal, vibration, acoustic, electrochemical and motor current (frictional). Some commercialized transducers were announced, ISRMTM (Applied Materials), SentinelTM (Novellus) and PRECICETM (KLA-Tencor) and so on.. 2.2. Chemical-Mechanical Planarization Process. After introducing the configuration of CMP system, the CMP process itself will be discussed briefly.. 2.2.1 Process Parameters. To improve CMP performance, understanding this process comprehensively is necessary.. Finding out what parameters and how they contribute to the. mechanical-chemical actions is critical for understanding of CMP. 3. There are so. Under-polish and over-polish mean that the process is proceeding before oxide is exposed and until oxide is exposed, respectively. 15.

(28) many parameters related to CMP process.. Dozens of parameters are dominant in the. process. On the polishing tool side, down pressure/force, platen temperature, slurry flow (supply) rate, platen and carrier speed are all dominant factors in CMP process. On the slurry side, chemical components, PH value, concentration of Oxidizer, kind and size of particles and stability of suspension are all very important factors of the process.. On the polishing pad, elasticity, hardness, groove, pore structure,. construction, age and conditioning of pad are very critical in CMP process.. Finally,. materials and structure (pattern) of wafer surface, wafer carrier and endpoint detection system et al. all influence CMP process.. It is important to note, coupling effects. exist among these parameters, between chemical and mechanical factors. It is a very complicated task to investigate CMP.. 2.2.2 Performance Indices. Because CMP is a planarization method, it is clear that the most important index of polishing performance must be “how flat” of the polished wafer. The planarity is usually represented by within-wafer non-uniformity:. Non − Uniformity =. ∆max − ∆min 2 ∆mean. (2.1). where ∆ is removed thickness per minute. To maintain a high throughput of CMP process, removal of excess material of polished wafer must be accomplished in a specific time, i.e. the removal rate must be sustained on a reasonable level. For Cu CMP4, thickness of Cu film is calculated by dividing the film resistivity with its measured sheet resistance. The relation between thickness and resistivity is. 4. In this thesis, copper material will be considered. 16.

(29) ρ ∝ RS ⋅ T. (2.2). where ρ is the resistivity ( µΩ ⋅ cm. ( mΩ. unit-area), RS is the sheet resistance. unit-area) and T is the copper thickness (kÅ).. Sequentially, CMP. removal-rate can be represented by. Removal Rate =. (Pre - CMP Thickness) − (Post - CMP Thickness ) Polish Time. (2.3). In fabricating Cu damascene interconnects, CMP of Cu and barrier metals is one of the most important techniques. SiO2 erosion and Cu dishing are serious problems of CMP. This erosion is defined as oxide loss around the patterned Cu area and dishing is defined as Cu thickness loss inside the Cu pattern. Fig. 2.4 shows schematic dishing and erosion. Any dishing and erosion and the resulting decrease in cross section area due to thinning (dishing plus erosion) of the long interconnect line during polish has a significant effect on circuit delays due to the increase in the RC constant.. Therefore, to achieve the benefits of the low RC. intended with the use of Cu, there is an increased need to minimize and control dishing and erosion across the wafer during Cu CMP process.. In the previous. literature, Steigerwald et al. [28] found that Cu dishing is a strong function of line width, but is only weakly dependent upon pattern density. Moreover, to specify dishing, they defined planarization efficiency (PE) PE = [1 - (∆down ∆up )] × 100%. (2.4.1). where ∆down and ∆up are the thickness differences of the inside and outside of the feature after planarization processes, as shown in Fig. 2.5. planarization efficiency can be expressed as. 17. In other words,.

(30) PE = 1 − R r_bottom R r_top = Step Height Reduction R r_top. (2.4.2). where R r_bottom and R r_top is removal rate of lower and higher area, respectively.. Wafer roughness which is measured by AFM (Atomic Force Microscope) can be defined by. Rq =. ∫. L. 0. y 2 ( x )dx. (2.5). L. where L is the distance of scanning and y is the difference between probe point and average height. The defects after copper CMP are shown in Fig. 2.6. In that figure, Cu puddle, corrosion and scratch are not caused by CMP, they just might appear as after effect of polishing [39].. 2.2.3 CMP Models/Mechanisms. Establishing model/mechanism, much more works are focused on mechanical effects, just like what mentioned at section 1.2.1 and 1.2.2. Based on Preston’s equation (1.1), the generalized form. R = k ⋅ P α ⋅V β. (2.6). is widely accepted and used [30]. The value α and β are fitted parameters that vary depending on the process and the consumable set (pad, slurry) used. However, the models derived from Preston’s equation are ineffective in providing detailed fundamental understanding and locally relevant information regarding a chosen process.. To date, there are very few wafer-scale, quantitative models for CMP. removal rate and uniformity. This fact, combined with the resiliency of Preston’s. 18.

(31) equation, makes a strong argument for a locally relevant expression for material removal rate [9, 31] R ( x, y ) = k ⋅ P ( x, y ) ⋅ V ( x, y ). (2.7). where the removal rate R at point (x, y ) on the wafer surface is a function of the local pressure P( x, y ) and the local pad/wafer relative velocity V ( x, y ) . It has to be mentioned again that Preston equation is nonetheless flawed because of the neglect of chemical effects. Except for mechanical effect modeling, the chemical effect is also a very important part of CMP process, especially in polishing metal. Early in the works of F. B. Kaufman et al. [2] and R. J. Gutmann et al. [11], the mechanism related to chemical effects was discussed. The mathematical model including chemical effects was first established by Q. Luo et al. [34], that is R = ( KP + B ) V + RC. (2.8). where B is a modification term of velocity V and RC represents the purely chemical removal rate. Equation (2.8) was established by linear regression of experimental data and has greater dependence on the velocity compared to the pressure. (It may be different on different polishing tools.) J. Luo and D. A. Dornfeld [8] also derived a model with mechanical and chemical effects of CMP process. In their model, an interface between chemical effect and mechanical effect has been constructed through a fitting parameter Hw, a “dynamical” hardness value of the wafer surface. It reflects the influences of chemicals on the mechanical material removal. Usually, the model/mechanism in CMP process investigation means material removal mechanism. To further improve the performance of CMP process, e.g. copper dishing, the CMP process model has to be analyzed in more detail, too. Y. 19.

(32) Lin [42] established copper planarization (step height reduction) model and copper-dishing model based on the difference of removal rate between high and low area of wafer surface and that between copper and barrier material, respectively. The copper-dishing model is shown as. hD =. (S − 1) PH ξ ln. w w  0. S. K EV − Cu t    1 − e H     . (2.9). where hD is the dishing height; P is applied downward pressure; H is the pad thickness;. ξ is a constant defined as the conformity of the pad; KCu is the Preston constant for copper; E is Young’s modules of the pad; V is the relative velocity between the work piece and the pad; t represents the overpolish time; w and w0 are defined as the trench width and effective minimum width, respectively. (The word “effective” means that pad can contact with the lower feature.) The factor S represents the removal rate selectivity of copper to barrier material, like tantalum, defined as S=. RCu K Cu = RTa K Ta. (2.10). The step height reduction model is. hS = hS 0 e. −. K Cu EV t H. +. PH E.   w ξln   w0. K EV − Cu t     − 1 1 − e H      . (2.11). where hS is the step height of sacrificial copper; hS0 is the initial step height; t represents polish time of bulk copper here. Note that (2.9) and (2.11) are derived involving pad conformity. V.H. Nguyen et al. [32] also established a physical model for development of dishing during metal CMP.. The model is. D ( LW,t ) = t  LW 2 ∞   −t  ⋅ RBl ⋅ ∫  ∫ Φ ( rC ) drC + exp   ∫ Φ ( rC ) drC  dt  LW ⋅ K  LW 2  0   0. 20. (2.12).

(33) where D(LW,t ) is dishing, LW is line width, RBl is the blanket removal rate, t is over-polish time, Φ(rC ) is the distribution of contact size, rC is the average contact radius and K is the only adjustable parameter. Note that this model was derived including pad morphology.. G. Fu and A. Chandra [33] also derived an analytical. model for dishing and step height reduction in CMP. These models/mechanisms shown above are established in steady-state. However, one appropriate dynamic model is necessary for setting the operation profile via strategy of dynamic-tuning. The only dynamic model is the conceptual model proposed by J.-B. Chiu et al. [24], shown as ~ dh = −R dt. (2.13). dR =u dt. (2.14). x = Ax + b u + d ( x ,t ). (2.15). ~ where h represents the thickness of copper to be removed, R is the removal rate and u is the system input. For convenience, (2.13) and (2.14) are further changed into the following state equation:. [. ~ where x = h. ]. T 0 − 1 0  − 0.1t  R ∈ R2 , A =  , b =   and d =    . Note that the 0 0  1  − 0.1 . initial value of the system x (0) = [8000 0] . The selection of disturbances is based T. on the investigations of run-to-run controller of CMP, just like the works of L. Da et. al. [15]. In their research, the removal rate would drift down as the process proceeds because of pad wearing and slurry dilution. Although the problem of pad wearing can be adjusted by conditioning during the CMP process, the slurry concentration can be kept constant by pre-mix before delivering onto platen and they might not be too obvious during a single wafer polishing, the disturbance d is also added into the simulation to model the uncertainties during CMP process processing. Note that the coefficients are assigned small values arbitrarily. This model will be used to design 21.

(34) the “dynamic tuning” operation profile via sliding-mode theory in chapter 3. In following sections, some of these models will be used to verify the ability of dynamic-tuning operation by numerical simulations.. 2.3. Process Control in Chemical-Mechanical Planarization Process. Most of people who are devoted to do research on the CMP process focus their works on process improvement, i.e. finding the perfect composition of process parameters, namely, “Golden Recipe”.. “Golden recipe” means: through fixed. perfect parameters setting the perfect performance will be derived. For example, in the CMP process, the perfect performance is complete flat. Nevertheless, it can not be realized at most case in real world because of existence of a lot of disturbances, noise and uncertainties. The inherent characteristics/flaws of equipments may cause some imperfections in products. (That may be one of the reasons why control theories were developed for.) Continuous control for CMP process seems necessary. Here, one question is raised: Is it more complete if the “Golden Recipe” contains an appropriate operation pattern? CMP process control covers both consumables and equipments to improve performance of CMP process. Run-to-run control is the only one control method with specific control algorithm/law in the CMP process and is thought to be the only viable scheme in most semiconductor manufacturing processes because of the lack of in-situ measurements of the product quality of interest [22].. The method of. run-to-run control is based on statistic data of process performance.. Besides, the. name “run-to-run” means the control object is a single run, one specific number of wafers (ten, five or less number of wafers). The concept of run-to-run control is shown in Fig. 2.7. 22.

(35) As the requirements of degree of planarization increases, within-wafer CMP process control becomes necessary. Little effort has been tried to move forward to within-wafer control because of the complexity of CMP process. In this thesis, it will be attempted based on the knowledge of CMP process.. 23.

(36) CHAPTER 3 OPERATION OF CMP VIA SMC. The theory of sliding-mode control (SMC) has been developed for a long time and has been known as an effective control method for many advantages. One of the most unique aspects of sliding mode is the discontinuous nature of the control action whose primary function of each of the feedback channels is to switch between two distinctively different system structures (or components) such that a new type of system motion, called sliding mode, exists in a manifold.. This intriguing system. characteristic is claimed to result in superb system performance which includes insensitivity to parameter variables, and complete rejection of disturbances [35]. However, a serious problem is also generated due to this characteristic, namely, chattering.. Fortunately, many methods were proposed to reduce the chattering. phenomenon. In this paper, the sliding-mode theory is employed to operate CMP process, i.e. to set the removal rate during a single wafer (within wafer) polishing. In this chapter, VSC and SMC will be introduced briefly and the presentation of controller design for the conceptual CMP model will be followed by some simulation results and discussions.. 3.1. Variable Structure Control. Variable structure control (VSC) with sliding mode control (SMC) was first proposed and elaborated in the early 1950’s in the Soviet Union by Emelyanov and several co-researchers. This method did not catch researchers’ attention widely until the publication of the survey paper in 1977. Significant interest on VSC and SMC 24.

(37) has been generated in the control community worldwide [35].. To illustrate the. advantage of VSC, a concise and acceptable example is generally used, that is, linear second order system [37]. Consider the second order system x+ x = u,. x(0 ) = 1, x (0 ) = 0. (3.1). Let control input u = − ax , where a ≥ 0 . The control goal is to design parameter ‘a’ and let system approach zero (get into x(t ) ≤ ε ) in shortest time and not exceeding zero (not across t-axis). Traditionally, the design is to choose a fixed value ‘a’ for acceptable response. According to VSC theory, the best performance will be derived easily by switching the system between two subspaces. Fig. 3.1.1 is all possible situations in traditional design and Fig. 3.1.2 shows the system response via VSC design. The system which is shown in Fig. 3.1.2 can also be called variable structure system (VSS). The VSS is defined as followed: one system which consists of more than two subsystems (a set of subsystems) together with suitable switching logic. In the example above, the value ‘a’ which is equal to zero or larger than two form two subspaces. Besides, the switching logic/condition is magnitude of ‘x’, ‘a’ is zero or two while ‘x’ is larger or smaller than ε, respectively. To date, VSC has developed into a general design method being examined for a wide spectrum of system types including nonlinear system, multi-input/multi-output systems, and stochastic systems.. In addition, the objectives of VSC have been. greatly extended from stabilization to other control functions.. The most. distinguished feature of VSC is its ability to result in very robust control systems, in many cases invariant control systems result.. Conceptually, the term “invariant”. means that the system is completely insensitive to parametric uncertainty and external disturbances [36]. Today, research and development continue to apply VSC to a wide variety of engineering systems. 25.

(38) Recently, the VSC and SMC are almost synonymous nouns, and the key difference between VSC and SMC is the existence of sliding-mode in the system. From the viewpoint of mathematics, sliding-mode is a system behavior in “hyperspace.” (The main feature is described in the beginning of this chapter.) It should be mentioned that the system performance will not be influenced by any matched disturbances5, and the control strategy provides an effective and robust means for certain classes of nonlinear systems subject to modeling uncertainties in the sliding mode. In next section, more detailed descriptions of SMC will be introduced.. 3.2. Sliding Mode Control. SMC is a robust nonlinear control algorithm that employs discontinuous control to enforce a system state trajectory on some prescribed sliding surface. The SMC includes several different continuous functions that map plant state to a control surface, and the switching among different functions is determined by plant state which is represented by a switching function. In general, a variable structure system can be described by x = f ( x , u( x )). (3.2). where x ∈ R n is the state variables of the system, u( x ) is the control input, and the timing of switching is governed by x (a specific form of combination of state variables, namely, switching function). In addition, the equilibrium point of the system is supposed to be x = 0 , which is the system design target (the control goal). For a single input system, the switching condition of control input is represented by 5. Matched disturbances mean that the disturbances which can be affected by system control input directly. 26.

(39) u + ( x ) u( x ) =  − u ( x ). s( x ) > 0. (3.3). s( x ) < 0. where u + ( x ) ≠ u − ( x ) , and s ( x ) is a switching function. The switching function s ( x ) collocate the switching condition, and divides the system state space into three. sub-spaces: s ( x ) > 0 , s ( x ) = 0 , and s ( x ) < 0 . It is important that the hyperspace, s ( x ) = 0 , must be continuous and contain the equilibrium point x = 0 , i.e. system in. this specified hyperspace must be stabilizable. The main objective of the system design is to generate a sliding mode in the hyperspace s ( x ) = 0 . Note that s ( x ) is also called sliding function, and s ( x ) = 0 is the so-called sliding-surface6. The most important thing in SMC design is to generate (specify) a sliding-mode (sliding-function). There are two procedures in sliding-mode generation: (1) When system is outside of hyperspace s ( x ) = 0 , it must be ensured that the trajectory of system states would reach the hyperspace in a finite time th; (2) After the trajectory getting into the hyperspace, the trajectory will never depart from the hyperspace and move toward the equilibrium point x = 0 . The system behavior of first procedure is called approaching-mode, and the second one is named sliding-mode. illustrates this generation of sliding-mode.. Fig. 3.2. In order to ensure the procedures. mentioned above being workable, one condition must be satisfied, that is ss < − σ s. (3.4). where s ≠ 0 , and σ is a positive constant which can guarantee the system trajectories to hit the sliding surface in a finite time. Note that (3.4) is also called “reaching/approaching and sliding condition.” Further looking into the behavior of system in the sliding mode, if the switching condition (3.3) can be realized perfectly, 6. The derivation of “sliding-surface” is due to the existence of sliding-mode in the hyperspace. 27.

(40) i.e. the infinite frequency of switching exists, the ideal sliding mode exists, too. Unfortunately, the system in real world can not provide such a high-frequency switching. To display the situation of system in the sliding mode schematically, a very small layer7 covering the sliding surface is often employed, as shown in Fig. 3.3. To design a controller via SMC, the procedure can be concluded into two steps8, that is: (1) Specify a sliding function s ( x ) which will let the system to move toward control goal while the system is in the sliding mode; (2) Determine the control input u which will force the system to hit the sliding surface and generate the sliding mode in a finite time. For a simple single-input system in controllable canonical form x 1 = x 2 x 2 = x3 . . x n −1 = x n x n = a1 x1 + a 2 x 2 + ⋅ ⋅ ⋅ + a n x n + u + d ( x ,t ). where x = [x1. x2. (3.5). . . . x n ] is system states, u is control input, and d ( x ,t ) is T. the disturbance of system. There are several ways to choose sliding function, for the simple case, the easiest way is setting sliding function as s ( x ) = cx. where c = [c1. c2. (3.6) . . . c n ] . Through some calculation, the value of ‘c’ will be. derived, and then the sliding function is obtained. At the second step, based on the important condition (3.4), the control input can be determined as. 7. In SMC design, the setting of layer namely sliding-layer is an important and effective way to reduce so-called chattering phenomenon. 8 Note that the two steps are concluded based on the procedures of generating sliding-mode mentioned above. 28.

(41) u = − a1 x1 − (c1 + a 2 ) x 2 − ... − (c n −1 + a n ) x n − (δ ( x ,t ) + σ ) sign(s ). (3.7). where δ ( x ,t ) is the maximum value of disturbance d ( x ,t ) and σ is the value to be designed. Note that the value of δ is determined by estimating or deciding among the measured data.. The control input (3.7) contains an ideal switching. function sign(s ) , which can not be realized in real world.. Besides, the ideal. switching function sign(s ) is the main reason of existence of chattering phenomenon. The easiest and effective way to reduce chattering is to replace sign(s ) by saturation function 1  sat (s, ε ) =  s ε − 1 . s>ε s ≤ε. (3.8). s < −ε. where ε is the thickness of sliding-layer mentioned above, and the system trajectory will be limited in s < ε . It should be mentioned that employing of sliding-layer would reduce the chattering but it can induce the loss of precision of the controller. This controller is actually a continuous approximation of the ideal relay control. The consequence of this control scheme is that invariance property of SMC is lost. The system robustness is a function of the width of the boundary/sliding layer. Robustness is decreased as width is increased.. Next, dynamic tuning of CMP. process based on SMC is presented.. 3.3. Operation Profile Setting. Before designing the setting of removal rate of CMP process, some preliminary research results and statement will be recounted first.. 29.

(42) 3.3.1 Problem Statement. In copper CMP, copper dishing and oxide erosion are critical problems and have to be solved urgently due to the serious influence on RC constant and surface uniformity, especially the copper dishing. (see section 2.2.2.) From the research by K. Wijekoon et al. [23], the operation parameters (applied downward pressure, P, and relative speed between wafer carrier and platen table, V) have direct influence on copper dishing and oxide erosion, as shown in Fig. 3.4. Furthermore, in the investigations by Y.-C. Kao et al. [38], a robust operation region is located on the base of copper removal rate curve. Note that the robust operation region means low-sensitivity to parameters change.. In their works, some. operation-relevant models and an overall strategy of polishing are established, and the strategy setting is subject to the copper dishing (Note that the strategy, soft landing, is related to the work by J.-B. Chiu et al. [24]. The conceptual description of the strategy is shown in Fig. 3.5). Based on these results, better operation profile of the process might be a candidate to improve CMP process, especially in reducing the copper dishing.. In other words, the copper dishing might be suppressed by. accurately tuning the process parameters during a single wafer polishing. Furthermore, the works by V. Nguyen et al. [14] [32], G. Fu and A. Chandra [33] and Y. Lin [42] reveal that the copper dishing is a function of over-polish time and process parameters. Consequently, the feasibility of this idea is greatly strengthened. In detail, it is clear that the process parameters, like P and V, play important roles in the forming of dishing besides the feature size, polish time and properties of pad, in reference to equation (2.9).. Equation (2.12) reveals that dishing will be also. suppressed directly during overpolish stage if the blanket wafer removal rate drops down. From many investigations, the removal rate in CMP process can be related to 30.

(43) process parameters including the parameters which can be operated in process. One of methods of reducing critical problems occurred in CMP process is to optimize the recipe of wafer processing through setting of these process parameters. In this thesis, the other way is considered to improve the performance of CMP process, that is, dynamic tuning of the operation parameters during CMP process run in an appropriate form/scheme. Generally speaking, to maintain high throughput high removal rate recipe has to be used, but that can cause more damages in most cases. On the other hand, the recipe of low removal rate often cause better surface profile but that will make low throughput, too. Obviously, to achieve balance between high throughput and good surface profile is an important topic. In the discussion in section 2.3, very few works have been done via the strategies of control theory except the work by J.-B. Chiu et al. [24]. In the works of J.-B. Chiu et al. [24], the control law of time optimal control, is employed, and an analogy between the soft landing of a spacecraft and the CMP process is illustrated for CMP operation.. The purposes of citing this analogy is for. reducing the copper dishing and handling the uncertainties, the undetermined initial thickness of copper (measurement uncertainties), and the bang-bang control law is used to implement this idea. Fig. 3.6 shows their simulation results. Note that the timing of stopping the process is determined by the endpoint detection. From the first plot of Fig. 3.6, it is clear that the removal rate has to increase to 9000 A/min at once while the process is starting, and drop to 2000 A/min while the process is going for 40 seconds. There are two reasons of setting second step (based on the concept of soft landing), one is for better surface profile and the other is for handling uncertainties.. Looking into the ability of uncertainties handling, using lower. removal rate can be a “conservative” method. 31. In general, the over-polishing is.

(44) necessary to remove the barrier layer (in copper CMP) and make sure that copper residue is cleared entirely. However, many damages may occur if the over-polishing is not controlled well. For this reason, to reduce the damages which might occur at the final stage of the process, lower removal rate recipe has to be employed. Additionally, it is known that this strategy is employed in practical production, too. Even though this method seems to be pretty good, two questions remains: (1) How small is the value of second step (after 40 seconds) will be enough? (2) Do the unstable/discontinuous situations, like the period of rising and dropping the removal rate immediately, will cause any undesired damages?(e.g. vibration of platen or turbulence of slurry). To avoid these two problems, a more continuous/smooth. operation strategy will be established via SMC algorithm.. Furthermore, the. mechanism of operation profile will be proposed to not only solve the above two problems but derive better planarization (dishing and step-height reduction). Note that it should be not sufficient to improve the performance by adjusting mechanical loads (P and V) only.. From the investigations on CMP process. mentioned in section 1.2, the chemical loads should be important factors, like PH value, etcher, inhibitor and oxidizer.. In this thesis, only the oxidizer (H2O2). concentration will stand for chemical load, i.e. the oxidizer concentration is the only chemical factor which is discussed in this thesis. (see chapter 4). 3.3.2 Operation Profile Setting. There are two steps in SMC design: first, a stable sliding mode/surface/function has to be specified, and the system will move along sliding surface toward equilibrium point (control goal); next, a control input which will force the system to hit sliding surface in a finite time has to be derived. From Chen and Chang [37],. 32.

(45) there are three methods which are generally used in designing sliding function, Transformation. Matrix. method,. Lyapunov-based method.. Eigenstructure. Assignment. method. and. Similarly, in establishing control law, there are. Hierarchical Sliding-mode Control and Integral Sliding-mode Control and so on. In this work, a convenient and powerful method which is also proposed by Chen and Chang [40], namely, Virtual Eigenvalue method is used in controller design. In this conceptual model of CMP shown in (2.15), just one sliding-mode eigenvalue and one virtual eigenvalue instead of two set of them have to be selected because of the two by two system matrix.. After choosing eigenvalues first,. according to linear control theory, a state feedback control input by pole-placement method can be obtained as u = −kx. (3.9). where k is the value to be designed.. Note that this method can assign the. eigenvalues of A − bk to any desired value (Of course, it is always negative for stabilizing systems). Then, A − bk can be diagonized as −1. v   J [ A − bk ] =    c   0. 0  v  Ω  c . (3.10). where J and Ω represents sliding-mode eigenvalue and virtual eigenvalue, respectively.. Consequently, the left eigenvector corresponding to the virtual. eigenvalue has to be determined J v  c [ A − bk ] =  0   . where v = [v1. 0  v  Ω  c . v 2 ] and c = [c1. (3.11). c 2 ] are the left eigenvector corresponding to J and. Ω, respectively. Up to present, the sliding function is derived 33.

(46) s = cx. (3.12). where c is the left eigenvector corresponding to the virtual eigenvalue Ω in Eq. (3.14). To establish the control input, let the control input be u = −kx + u ′. (3.13). where u’ is the term with switching function.. Based on the concept of. approaching-mode mentioned before, differentiate Eq. (3.12) and u’ will be derived, that is u ′ = −( c δ ( x ,t ) + σ )(cb ) sat (s,ε ) −1. (3.14). where δ ( x ,t ) represents the maximum value of disturbance d ( x ,t ) and sat (s,ε ) is saturation function defined in Eq. (3.8).. Stability. Because the design of SMC is to force the system to hit the specified sliding-mode in a finite time and make it stay there forever, to analyze the stability of the system under SMC control, only the part of system which has entered the sliding mode needs to be considered. In other words, the stability of the system is equal to the stability of the system in specified sliding-mode. To analyze the stability of the sliding-mode control, an important concept has to be employed, that is, equivalent-control [37]. It is known that the trajectory of the system is continuous even in the sliding-mode. However, the continuous trajectory in the sliding-mode control is made by a discontinous switching condition. The relationship between the continuous trajectory and the discontinuous switching condition is proposed by Filippov in 1988, that is. 34.

(47) f (x ,u eq ) = µ f (x ,u + ) + (1 − µ ) f (x ,u − ). (3.15). where the meaning of u+ and u- is the same to (3.3). Fig. 3.7 shows a brief but comprehensive explanation. Then, the stability of the sliding-mode can be proved through the concept of equivalent-control. The detailed proof is shown in appendix Ⅰ.. 3.3.3 Results. Some simulations are implemented by MATLAB software package. These simulation results are the preliminary demonstration of feasibility of the controller.. Analysis. In SMC design, the first thing which has to be taken care is the convergence to the sliding surface as shown in Fig. 3.8. In Fig. 3.8, it is clear that the system reach the sliding-surface (s=0) in a finite time, about 0.6 minutes. This result represents that the design is successful, i.e. the control law (3.14) works. Additionally, to visualize whole performance of the system, phase-plane analysis is a powerful tool.(Note that the method is restricted to second-order or first-order systems.) Fig. 3.9 shows the phase-plane plot of the system, and it reveals that the thickness (horizontal axis) decreases continuously and the variation of material removal rate (vertical axis) is smooth. Besides, Fig. 3.10 shows the plot of control input (3.13) and it also varies smoothly. The last one is Fig. 3.11, and it shows time history of removed copper thickness and (copper-) material removal rate during CMP process separately. In Fig. 3.11, the more detailed profile of these two important parameters are presented. The CMP process will finish in about 1.7 minutes (102 seconds), and. 35.

(48) the removal rate will decrease to zero at about the same time.. Discussions. To summarize entire process of CMP under SMC control: Initially, the system starts from an idle situation, the platen speed and the carrier speed increase loading separately , the down pressure is increased gradually, the temperature and the oxidizer concentration of slurry is increased proportionably. After about 0.2 minutes (12 seconds), all parameters tend to decrease their value to lower the removal rate. Note that the rate of change is lower than the period of first stage (increasing removal-rate). The process keeps on going until about 1.7 minutes, and then the platen and the carrier rotation speed go down to a lower value; so do the down pressure and the chemistry of slurry. Finally, all parameters decrease to very low values, and the CMP process is accomplished at the same time. Certainly, the mechanism mentioned above is just a concept, but the description does contain some possible ways to achieve/realize the mechanism of “dynamic tuning” of operation, i.e. tuning platen and carrier rotation speed, varying down pressure, changing the temperature and oxidizer concentration of slurry and so on. Besides, the distinguishing feature of operation by dynamic tuning comes out from the description, that is, the variations of parameters are all continuous and smooth. In the operation via SMC design, not only the violent switching is avoided but the lower loads of parameters are employed. in real world.. It will make this method much more applicable. From the parameters variation during the process, the. degree-of-freedom/flexibility can be increased. Based on the existing knowledge of CMP process, it is possible to set the process parameters dynamically.. The. opportunity of further improving the performance of CMP process will be feasible.. 36.

(49) Note that detailed mechanism (including the consideration of chemical effects) which tunes the operation profile will be discussed in next chapter. Additionally, according to the works mentioned in section 3.3.1, some evidences for the capability of the operation profile has been revealed. (Note that the profile means the removal rate curve in Fig. 3.11.). Because the recipe of low. removal rate will be employed in the final stage of this operation, it will have better performance in low copper dishing [23, 24, 38]. The “deliberate” (low load on the process) at final stage will reduce the damages caused by over-polish effectively, and the over-polish time will be easier to control. [14, 32, 33, 42] simulation and verification will be shown in next chapter.. 37. The detailed.

(50) CHAPTER 4 VERIFICATION BY NUMERICAL SIMULATION. To verify the operation strategy of dynamic-tuning, some models/mechanisms which are presented in previous chapters will be employed to simulate in this chapter. Before the numerical simulations, what the operation input has to be clarified first. In last chapter, the operation profile (removal rate curve) is set and shown as Fig. 3.11. However, to realize this operation scheme coordinating the mechanical loads and chemical loads in harmony will be the critical point of “dynamic tuning” operation, i.e. decomposing the operation profile appropriately will be the critical point in forming the strategy of “dynamic tuning” operation. This strategy will be described in detail in this chapter and some verification of ability of the strategy will be followed.. 4.1. Operation Input Concretization. To clarify the control/operation input u, the mechanism which is presented in section 2.2.3 is repeated here. From the system dynamic equation (2.15) and the material removal model (2.8), the control input is shown by differentiating (2.8), and (2.15) can be formulated as x = Ax + BU + d ( x ,t ). [. ~ where x = h. ]. (4.1). 0 − 1  0 R ∈R , A=  , B=  0 0   KV T. 2. 0   dP , U =  KP + B   dt. T. dV  , dt . − 0.1t  T d= and the initial value of the system is x (0) = [8000 0] . The elements   − 0.1  dP dV and , can be transferred to the design/actuators of equipment. Note of U, dt dt 38.

(51) that constraints of applied downward pressure and linear relative velocity are not considered in (4.1). Because of the lack of model of chemical factors in CMP process, the detailed equation is difficult to be expressed here. However, from the research by Y.-C. Kao et al. [38], some experiments were carried out over wide range of oxidizer concentration. They indicated that the copper removal rate of copper CMP will follow a specific trend as the concentration increases. Coincidentally, the trend, shown in Fig. 4.1, is similar to the operation profile which is shown above (Fig. 3.11).. Therefore, the oxidizer concentration can be included into the operation. mechanism easily because of this similarity.. With the constraints of downward. pressure and relative velocity, the chemical factor, RC can be introduced into the operation mechanism. The control input and input matrix B can be reformed as  dP U =  dt. dV dt. dRc  dt . T.  0 and B =   KV. 0 0 . KP + B 1. Note that the relation. between oxidizer concentration and RC (with specific slurry) was proposed by Q. Luo et al. [34], as shown in Fig. 4.2. It should be mentioned that reduction of removal. rate at higher H2O2 concentration in both figures, Fig. 4.1 and 4.2, are due to the formation of passivation layer (copper oxide film). Because of the important interdependence of chemical and mechanical effects, it has to be mentioned that a phenomenon in changing the process parameters. The phenomenon has been proposed in the works of J. M. Steigerwald et al. [43] and Y.-C. Kao et al. [38], that is, two polishing regimes, a dissolution rate limited regime (chemical reaction controlled regime) and an abrasion rate limited regime (mechanical abrasion controlled regime), exist in CMP process. Besides, the effects of slurry chemistry on dishing have been proposed by V. Nguyen et al. [14]. They revealed that less dishing would be obtained from higher oxidizer concentration in the slurry. These investigations could be great foundations for setting the manner of the chemical 39.

(52) factor. To integrate these research achievements [14, 32, 33, 38, 43], the control inputs integration of control inputs described must be coordinated in harmony with each other. In other words, the objective mentioned in section 1.3 can be implemented with these considerations of chemical effects. The dynamic tuning operation of CMP process is then coordinated, as shown in Fig. 4.3. Fig. 4.1 above is used to illustrate the concept of dynamic tuning operation. It must be mentioned again that most superior feature of dynamic tuning operation is the higher degree-of-freedom/flexibility of the process parameters. If all of the parameters can be assigned arbitrarily during the process, the possibility of figuring out the optimal operation condition/profile is much larger. The acceleration stage in Fig. 4.3 means the increasing of removal rate (before about 0.2 minutes of second plot of Fig. 3.11). It is followed by deceleration stage after the peak value of removal rate is achieved.. Because all of the operation. parameters (means P, V and RC here) are all changeable, increasing and decreasing of removal rate can be realized by tuning them. Besides, the operation can be designed with more appropriate sequence to obtain better performance.. The proposed. sequence is to set the system at mechanical abrasion controlled regime in the beginning. At this regime, the passivation layer is formed and the rate of forming is higher than the mechanical abrasion rate. Therefore, it can be expected that lower region of wafer surface is protected by the passivation layer. Continuously, the load is increased (larger values of parameters) to raise the removal rate until the peak value of removal rate. Note that relative velocity will be the major factor in increasing removal rate because of the lower influence on dishing. In the representation of Fig. 4.3, the values of operation parameters, P, V and Rc, can be assigned with 3.5 p.s.i., 93rpm, 300nm/min, respectively. (this set of parameter represents the constraint which 40.

(53) is assigned in this thesis) As soon as the peak value is achieved, these parameters can be decreased for suppressing dishing, especially the applied downward pressure P. Moreover, higher oxidizer concentration (causes lower RC value) will cause less dishing from the results shown by V. Nguyen et al. [14] because a more effective passivation layer is formed with higher oxidizer concentration and protects the recess areas. Because the operation inputs are decomposed directly from the removal rate curve and the bound is the only one constraint for each input, the operation profile can be set in many ways. In other words, there can be infinite solutions because of three variables (P, V and Rc) and only one equation (removal rate curve, Fig. 3.11). Therefore, a new problem will be raised, what is the best tuning/operation profile? It will not be discussed in this work. Here, one possible operation profile will be chosen to verify the effect of dynamic tuning operation of CMP process.. To. formulate the dynamic-tuning operation profile at first time, the composition of parameters will be obtained by hand based on the trend of Fig. 4.3 and the mechanism of (2.8). Three process parameters, P, V and the oxidizer (H2O2) concentration, will be tuned in specific profile dynamically during single wafer polishing. The bounds of P, V and the oxidizer concentration are set by 1.7 p.s.i. to 3.5 p.s.i., 40 rpm to 95 rpm and 2% to 5%, respectively.. Note that relative velocity is transferred to. platen/carrier rotational speed. The detailed procedure of setting operation profiles is shown in appendix Ⅱ.. 4.2. Verification. The dishing model (2.9) is used to verify the ability of dynamic tuning method and the result is shown in Fig. 4.4. It is clear that dishing is suppressed from 1106Å 41.