Statistical Characterization of the Chemical-Mechanical Polishing Process A Presentation at the XVI Oklahoma State University Research Week Prahalada K Rao School of Industrial Engineering and Management
Introduction: Why CMP • Conventional semiconductor manufacturing processes (CVD) have flaws. • Notably planarity concerns. Notice the “bird beak” structure in the adjoining figure (Zantye, 2004). • CMP is the only known method to achieve both local and global planarity and thus facilitate miniaturization. • The basic principle: Use a chemical reaction to soften material and then mechanically polish off this layer. IEM-MAE OSU
The Advantages and Challenges • Excellent Planarization. • Indifference to wafer surface. • Reduce defects. IEM-MAE OSU Zantye, 2004
Resources LapMaster Lapping M/c Wafer Carrier Polishing Pad Strasborough CMP M/c Retaining Ring IEM-MAE OSU
Challenges in CMP • Complexity of CMP Process IEM-MAE OSU
Method of Analysis • The material in these slides is presented using the Theory of Constraints approach. • The data used for this research is primarily sourced from US patent 6564116 B2.The objective of the research can be briefly summarized as follows. • Part 1- Classification: To understand the behavior of key process input variables (KPIV’s). • Part 2 – Correlation : To illuminate the effect of the KPIV’s on key process output variables (KPOV’s) namely MRR and Within-wafer-non uniformity (WIWNU) . • Part 3 – Effect-Cause-effect : Contribute to the physical understanding of the process. IEM-MAE OSU
Design of Experiment and ANOVA - US patent 6564116 B2. (Wang et al, 2001) IEM-MAE OSU
Part 1: Classification. The main factors that affect the MRR and WIWNU are classified – What’s happening?
Part 1: Classification for MRR • Platen Speed, Down Force • and Solid Content are the • KPIV’s that affect MRR most. • Back Pressure and Time are • relatively benign KPIV’s. IEM-MAE OSU
Part 1: Classification for WIWNU Most significant A: Solid Content B: Down Force C: Back Pressure D: RPM E: Time • Platen Speed and Back Pressure • are KPIV’s that affect WIWNU most. • Solid Content and Down Force are • relatively benign. • Interaction effects are more significant • than the KPIV’s (knobs) themselves. Least Significant IEM-MAE OSU
Part 1: Classification for WIWNU – how the variables behave. A: Solid Content B: Down Force C: Back Pressure D: Platen speed E: Time Needs further investigation Non Linear Non Linear Non Linear Monotonically Increasing • MRR and WIWNU are governed by different set of factors (variables), some of them acting in opposition in each response. IEM-MAE OSU
Part 2: Correlation Correlate the KPIV’s to the KPOV’s. How is it happening?
Part 2: Correlation for MRRA: Solid Content (wt%), B: Down Force (psi), C: Back Pressure (psi), D: Platen Speed (RPM), E: Time (Sec) • The regression equation for mean MRR obtained as a results of the statistical analysis can be written as A: Solid Content B: Down Force C: Back Pressure D: Platen speed E: Time IEM-MAE OSU
Model Validation for MRR IEM-MAE OSU
Explaining Significant Interactions – MRR IEM-MAE OSU
Part 2: Correlation for WIWNUA: Solid Content (wt%), B: Down Force (psi), C: Back Pressure (psi), D: Platen Speed (RPM), E: Time (Sec) • On the basis of a regression model connecting the mean WIWNU with the various factors can be written as… • Notice the three way interactions in the equation, these are not seen in the MRR equation. A: Solid Content B: Down Force C: Back Pressure D: Platen speed E: Time IEM-MAE OSU
Model Validation for WIWNU IEM-MAE OSU
Significant Interaction effects for WIWNU IEM-MAE OSU
Logarithmic Regression • The data was subjected to a logarithmic regression procedure. • The regression equation is • The equation above is in close conjunction with the Preston’s equation. It is imperative to note that a time domain is considered. Preston’s Equation Form C: Solid Content. P: Down Force V:RPM t: Time γ:Back Pressure IEM-MAE OSU
Part 3: Effect- Cause-Effect Leverage the understanding, optimize towards the goal and stretch the correlation.
Part 3: Effect-Cause-Effect - MRR IEM-MAE OSU
Effect-Cause-Effect - WIWNU IEM-MAE OSU
Statistical and Dynamic Comparison to the Lapping Process Take a designed experiments approach to characterize the lapping process Extrapolate results to the CMP process.
Motivation and Introduction • Can we provide an experimental basis for our conclusions regarding CMP? • A study of a similar process and analysis of the same would provide an excellent starting point. • Lapping is a super finishing process, utilized to achieve submicron surface roughness. Prominent researchers contend Lapping and CMP are closely related. • Material removal mechanisms have been shown to match. IEM-MAE OSU
KPOV = f (KPIV) KPIV KPOV IEM-MAE OSU
Lapping Machine Polishing Pads Sensor DAQ system 8728 A 500 Kistler Accelerometer IEM-MAE OSU
How do we decide the KPIV’s and KPOV’s Customer Requirement IEM-MAE OSU
Results from DOE (Taguchi L8) analysis. • Cannot just predict roughness given parameters alone. BAD! IEM-MAE OSU
Sensor Based Modeling DOE doesn't work that well, so what do we do?
Principal Component Analysis- PCA • The following features were extracted from the sensor based data. • Peak to Peak amplitude – P2P • Energy • Variance • Kurtosis. • A grand matrix consisting of these features was constructed. • This matrix, also called the features matrix is subjected to a PCA, to recognize the most telling features IEM-MAE OSU
The Features Matrix IEM-MAE OSU
Underlying Hypothesis and Results. • Implicit Conclusions • Cannot predict the process based on parameters alone • Process is essentially non-linear • Need sensor based modeling IEM-MAE OSU
Summary of results from Hypothesis 3 Notice closeness With CMP IEM-MAE OSU
System Development Based on: Dornfeld et al , ‘An investigation of material removal mechanisms in Lapping’ ,Journal of Manufacturing Science and Engineering, ASME , Vol 122 pp. 413- 2000 From Hanna-Tobias machine tool dynamics model IEM-MAE OSU
Model development Measuring this Simulink Model Block Diagram IEM-MAE OSU
Simulation parameters. • %------------------------------------------------- • %M-File for 'tuning' the model to observed results • %------------------------------------------------- • m =1 %mass of the system in kg • lambda =1.485e7 %hanna tobias stiffness fcn • HW =45 %VHN of aluminium • beta1 = 350000; %nonlinear constant coeff • beta2 = 350000; %nonlinear constant coeff • HP =91 %Hardness of Plate - VHN of Silicon Carbide • A = (pi*9/4)*2.56/100 %surface area exposed to lapping - 3" dia workpiece • Dm = 78e-3 %mean dia of abrasive in mm • Dmin = 25e-3 %min dia of abrasives in mm • Dmax = 125e-3 %max dia of abrasives in mm • Dsigma = (Dmax-Dmin)/2.99 %stdev of the grain size in mm • alpha = 0.95; %geometric coeffcient • T = alpha*HW/((1+(HW/HP)^2)^0.5) • P = 3.2e3 %density of Silicon Carbide Grit kg/m3 • Pd = 1000 %density of water kg/m3 • M = 0.16 %grain to fluid work ratio • K = (1+(P/(Pd*M))) • N = 6*A*Dmax/(pi*((Dm)^3)*K) • G = N*T • dint = 0.001; %initial displacement • h =1008050 %Hysteresis damping coefficent • w = 10 %Region where energy peaks are observed in the data IEM-MAE OSU
THEORY REALITY IEM-MAE OSU
Reality Theory IEM-MAE OSU
My Research tool kit. • Designed Experiments • Response Surface methodology. • Regression modeling. • Theory of Constraints. • Process Simulation. • Process Modeling • Six Sigma Approaches. • Principal Component Analysis. • Sensor based monitoring and modeling. Future focus • Illuminate the reason for the interactions. • Provide a physical model for CMP. • Introduce sensor based control techniques. IEM-MAE OSU
Acknowledgements • Dr R. Komanduri. http://www.okstate.edu/MAE/maerl/mpmrl.html http://www2.mae.okstate.edu/Faculty/koman/koman.html • Dr S.T.S. Bukkapatnam. http://www.okstate.edu/ceat/iem/iepeople/bukkapatnam/default.htm • We thank the National Science Foundation (Grant # 0427840) for their generous support of this research. • WenChen Lih – PhD Student, MAE. IEM-MAE OSU