Jianfeng Luo, David Dornfeld Effect of Particle Size Distribution in Chemical-Mechanical Polishing: Modeling and Verification SFR Workshop November 8, 2000 Jianfeng Luo, David Dornfeld Berkeley, CA 2001 GOAL: To build an integrated CMP model for basic mechanical and chemical elements by 9/30/2001. 11/8/2000

Modeling of Abrasive Geometry and Size Two Abrasive Geometries Spherical Shape for Obtuse Abrasives Conical Shape for Sharp Abrasives 100nm     X X Schematic of Spherical and Conical Abrasive Shapes in the Model   SEM Picture of Slurry Abrasives for Si CMP (Moon, PhD Thesis, 1999) y Abrasive Size and Size Distribution Nano-Scale Size X Normal Distribution (Xavg , ) and p((Xavg , ) Xavg, Xmax and Standard Deviation  Xmax Xavg Portion of Active Abrasive Schematic of Abrasive Size Distribution 11/8/2000

Role of Abrasive Size in the Architecture of the Integrated CMP Model Contact Mechanics( Pad Topography/Abrasive Size/Pressure ) ? Chemical Reaction Slurry pH Value and so on a12= F2/Hw  V = Vol Abrasive Geometry Material Removal Rate Function: MRR= N Vol= C1Hw-3/2 {1-(1-C2P01/3}P01/2V. Correct on both average scale & local single points Schematic of Wafer-Chemical-Abrasive-Pad Interaction to Model the Volume Removed by A Single Abrasive 1 Surface Damage N Contact Mechanics( Pad Topography/Abrasive Size/Pressure ) Abrasive Size Distribution Abrasive Geometry WIWNU a22= F2/Hp Pad Hardness Xmax-Y=2 Pressure and velocity distribution over wafer-scale WIDNU n Schematic of Wafer-Abrasive-Pad Interaction to Model the Number of Active Abrasive Number Pattern Density Detailed Fluid Model 11/8/2000

MRR As A Function of Particle Size Distribution Before Saturation (Luo & Dornfeld, 2000) MRR as A Function of Down Pressure and Velocity: MRR= N Vol= C1Hw-3/2 {1-(1-C2P01/3}P01/2V. MRR= C3: A Function of Down Pressure, Velocity, Weight Concentration etc. C4: 0.25(4/3)2/3(1/Hp)Ep2/3/b1P01/3 A Function of Down Pressure, Pad Hardness and Pad Topography. Function p: The probability of the appearance of abrasive size Function : Probability density function. Contribution of Active Particle Number Contribution of Active Particle Size (Larger than Xavg) Contribution of Total Number of Particles over the Wafer-Pad Interface MRR as A Function of Particle Size and Size Distribution 11/8/2000

Particle Size Distribution Measurement Dynamical Light Scattering Mean Size (m) Standard Deviation (m) AKP50 0.29 0.070222 AKP30 0.38 0.118959 AKP15 0.60 0.210633 AA07 0.88 0.288768 AA2 2.00 1.056197 *Bielmann et. al. 1999 11/8/2000

Particle Size Dependence on MRR: Experiment VS. Model Predictions (0.29, 0.07022) (0.38, 0.118959) (0.60, 0.210633) (0.88, 0.288768) (2.0, 1.056197) C4: 0.25(4/3)2/3(1/Hp)Ep2/3/b1P01/3= 0.015 *Bielmann et. al. 1999 11/8/2000

Fraction of Active Particles Based on Model Prediction [0.726, 0.737m] 0.1827% [1.213, 1.231m] 0.1798% [1.720, 1.746m] 0.1815% [0.49, 0.50m] 0.19105% [5.091, 5.169m] 0.1719% 11/8/2000

Relationship between Standard Deviation and MRR Based on Model Prediction Number Dominant Region Size Dominant Region 11/8/2000

2003 Goals   Develop comprehensive chemical and mechanical model. Perform experimental and metrological validation, by 9/30/2003. Down Pressure Wafer Smaller contact area Larger contact area H H a 11/8/2000