VIBRATION MODELING IN CMP. M Brij Bhushan IIT Madras

Transcription

1 1 VIBRATION MODELING IN CMP Jul M Brij Bhushan IIT Madras

2 Outline 2 Introduction Model description Implementation details Experimentation details Verification of simulation output with experimental data Application Summary and Conclusion Future work Acknowledgement OSU

3 What is CMP? 4 Planarizing process, combination of Chemical and Mechanical forces. Hybrid of chemical etching, mechanical abrasion and free abrasive polishing. Used on metals (Al, Cu, W, etc.), dielectrics (SiO 2, etc.) and hard ceramics (SiC, TiN, etc.) Achieves local and global planarization, most preferred in semiconductor industry. The overall CMP market exceeds $10 billion and is growing at a rate of ~ 50% per year. With wafer sizes going above 300mm and feature sizes going below 30nm, chief determinant of wafer yield and cost.

4 What is CMP? 5 Ref:

5 Quality challenges in CMP 6 Complex process dynamics and interactions among: Equipment Consumables (i.e. slurry, pad, carrier film) Process parameters Large number of parameters affecting the process High capital costs Quality Indices: Process Material Removal Rate (MRR) Repeatability Product Within wafer non-uniformity (WIWNU) Surface roughness Defects High requirement of quality vs. cost need for understanding the process dynamics and improve process monitoring

6 Prior work in CMP modeling & sensing 7 Process modeling Physical modeling Computational models Srinivas-Murthy et al. (1997) Byrne et al. (1999) Nguyen et al. (2004) CMP Pheno/Empirical models Preston (1927) Jeong et al. (1996) Lucca et al. (2001) Noh et al. (2004) Venkatesh et al. (2004) Hernandez et al. (2001) Wang et al. (2001, 03) Park et al. (2000) Analytical models Ida et al. (1964) Saka et al. (2001) Qin et al. (2004) Zhao et al. (2002) Warnock et al. (1991) Vlassak et al. (2004) Burke et al. (1991) Sivaram et al. (1992) Burke et al. (1991) Cook et al. (1990) Cho et al. (2001) Watanabe et al. (1981) Suzuki et al. (1992) Wang et al. (2005) Borucki (2002) Process monitoring End point detection Bibby and Holland (1998), Simon (2004), Saka (2004), Yu (1993,95), Moore (2004) Murarka (1997), Sandhu (1991), Sandhu and Doan (1993), Chen (1995), Mikhaylich (2004) Defect detection Tang et al. (1998) Vasilopolous et al. (2000) Surana et al. (2000) Dennison (2004) Steckenrider (2001) Braun (1998) Chan et al. (2004) Li and Liao (1996) Wang et al. (2000) Zhang et al. (1999) Xie et al. (2004) 7

7 Gaps in technical approach 8 Modeling Gaps: It is still not fully been understood how the process parameters affect the performance Significant analytical work focuses only on the static loading aspects Sensors have been used to monitor and predict process features mainly statistical Experimental gaps: MEMS wireless sensors not much explored Vibration one of the few real-time parameters, experimental data is scarce. Need for Real-time estimation of state of the process and dynamics from the sensor features advanced prediction capability for online CMP process control (active control)

8 Sensor based modeling of CMP 9 Sensors are used for process monitoring and modeling. Sensors Give information about state of the machine, process, and pad/wafer. Few real-time sensors available optical, vibration, acoustic emission, ultrasonic, thermal, etc. We used MEMS wireless vibration sensors MEMS Light-weight Robust Low energy consumption Wireless Can be placed in close proximity to the object. Flexibility Vibration Dynamic response higher than other sensors One of the best for real-time monitoring

9 Approach 10 An attempt to develop a model of CMP dynamics that can physically capture the cause of the various vibration features observed: Obtain pad parameters such as elasticity (E), curvature of asperities (κ s ), pad asperity density (η s ), etc. Obtain the mean distance of separation (d o ) for static loading conditions Use these parameters in the dynamic simulation model Verify the features of the simulation data with those obtained from the sensor signals Machine ( m, K, c, P o, λ ) Process ( E eff, η s, k s, d o, ϕ(z) )

10 Forces in CMP 11 Original position of wafer above the asperities (mean of vibrations) d 0 z x(t) Vibration Amplitude Gaussian asperity distribution ~N(0, σ 2 ) Mean of the asperity distribution (fixed) x = 0 Relatively flat, hard wafer in contact with a rough pad surface. Pad asperity heights and wafer position are measured from the mean pad surface plane. Vibrations are developed due to the elastic deformations in the pad asperities.

11 Forces in CMP 12 When the wafer rests on the pad at a distance x from the mean, the prob. of making contact with any asperity of height z(z>x) is: The expected total load is: η s is the asperity density on the surface. k s is the curvature of the asperity summits. E * is the 2-D Young s modulus of the pad material. A nom. is the nominal area of the pad surface. Ref: Greenwood, J. A. & Williamson, J. B. P Contact of nominally flat surfaces.

12 Static distance of separation (do) 13 d o was calculated using minimizing the function: Ran for various values of d o in the appropriate range to search for minima (tending to 0); d o calculated to 0.1% error; integral discretized Variation in do value with change in P o is in accordance with Greenwood s results (Greenwood & Williamson 1966)

13 Structural Excitation 14 Po Wafer mass (m) P o is the constant downforce acting on the wafer. c is the system s damping coefficient. k s is the spring constant of the additional elasticity in the system. d o is the distance of the mean position from the datum.

14 Harmonic Perturbation 15 CMP setup always has slight lack of local/global planarity. Level difference is given by: λ As θ is very small, If the wafer RPM is N, a perturbation is introduced to the disturbance given by:

15 Variation of pad elasticity with x 16 Asperity Bulk Pad material is not homogenous with deflection. Can be decomposed into asperity region and bulk region. Bulk has large effective elasticity, E eff value all air voids compressed.

16 Variation of pad elasticity with x 17 Lower down-force Higher down-force Wafer Wafer Pad Pad Greater do Lower value of E eff Large number of voids beneath the asperity layer Smaller do Higher value of E eff Lesser number of voids beneath the asperity layer.

17 Variation of structure stiffness with x 18 Additional spring-force due to the structure, introduced into the system. Stiffness also changes with x. Change in stiffness similar to E eff. SEM cross-section of a polishing pad. L. Borucki (2002)

18 Implementation details 19 Overall differential equation: mx + cx + k x d 0 = P 0 [β 0 + β 1 x + x 3 + β 2 x + x β 3 x + x 3 + ] x 3 is the harmonic perturbation introduced into the system: x 3 + 2π T 2 x 3 = 0 2 degree of freedom, non-linear model of the CMP process Model was implemented in Simulink Solver : variable step, ODE45 (Dormand-Prince) Simulation time: 0 to 40 seconds Initial conditions: Force(RHS) = P o Acceleration = 0 Velocity = 0 Displacement = d o

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20 Disturbance block: 21 Add a perturbation as a sine wave. Check whether the displacement stays above a basic minimum value (6 um, in this case). Feed the displacement into the RHS force calculation block.

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23 Experimentation details 24 Machine: Buehler Ecomet 250 grinder-polisher. Sensors: Freescale MMA62xxQ Low-g, dual-axis sensor High resolution in the range of 1.5g to 10g. Low noise Low current device Wireless communication system: Tmote sky 250kbps 2.4GHz IEEE Chipcon Wireless Transceiver 8MHz Texas Instruments MSP430 microcontroller (10k RAM, 48k Flash) Integrated ADC, DAC, Supply Voltage Supervisor, and DMA Controller Ultra low current consumption

24 Experimentation details 25 Design of experiments (DOE): Full factorial design having three factors and two levels : Run ID Load (lbf) Pad RPM Slurry ratio R :3 R :3 R :3 R :3 R :5 R :5 R :5 R :5 Wafer - Copper work piece Wafer RPM is constant at 60 Slurry - alumina slurry having an abrasive size 0.05μm Polishing pad - Microcloth pad from Buehler.

25 Experimental Data Hz

26 Region of interest in the FFT spectrum: Vibration sampled at 300Hz Region below 100Hz corresponds to the machine frequency Region above 100Hz corresponds to the process frequency and is of interest (100Hz to 150Hz)

27 28 Simulation

28 Time-domain features captured 29 Beat phenomenon, frequency 1Hz (~wafer RPM) Regions of high and low amplitudes. High amplitude bursts. Time-frequency variations.

29 Frequency-domain features captured Hz Dominant frequency Spectral shape (continuous spectrum with two dominant frequency bands) Hz

30 Effect of varying down-force 31 As P o increases, clustering increases Increased bursts at high amplitudes Amplitude difference between high and lowamplitude regions increases Energy in the Hz band increases Some harmonic distortion evident in the model

31 32 Experimental Simulation

32 Experimental Simulation

33 Effect of wear 34 The peaks of the taller asperities flatten out The mean of the asperity distribution shifts downwards Reduced height of asperity σ decreases The pad now rests at a lower d o value Assumed Gaussian distribution holds in reality, distribution gets slightly skewed (Borucki, 2002) d o do New pad Old pad

34 Effect of wear 35 Experimental Simulation

35 Anticipated applications of model 36 Enhance the predictability of the CMP process. Enable development of feed-forward control systems which have a faster action time. Tool for iterative optimization of yield, quality under changing settings.

36 Summary and conclusions 37 2-DOF deterministic, non-linear, differential equation model developed to capture the physical sources of CMP vibrations Variation of elastic properties was found to be the cause of variations and bursts in the time and frequency pattern Incorporated the beat phenomenon due to the lack of planarity of the wafer-pad interface

37 Future Work 38 Harmonic balancing Studying more about wear of the pad and its effect on vibration signals Inclusion of velocity and its effects into the model

38 Acknowledgements 39 Dr. Karl N Reid, for giving me the opportunity Dr. Satish Bukkapatnam and Dr. Ranga Komanduri for being the driving force and the guiding light for my work Research group at OSU - all the faculty and the MS and PhD students All the fellow interns from IITs and IT-BHU