SCALING OF THE ADHESION BETWEEN PARTICLES AND SURFACES FROM MICRON-SCALE TO THE NANOMETER SCALE FOR PHOTOMASK CLEANING APPLICATIONS Gautam Kumar, Shanna Smith, Florence Eschbach, Arun Ramamoorthy, Michael Salib, Sean Eichenlaub, and Stephen Beaudoin Purdue University School of Chemical Engineering Forney Hall of Chemical Engineering 480 Stadium Mall Dr. West Lafayette, Indiana 47907-100 Phone: (765) 494-7944 sbeaudoi@purdue.edu
Rationale Mask cleaning processes can be more quickly optimized if the magnitude of particle-mask adhesion forces known Mask layers and contaminants offering most difficult cleaning challenge can be identified Effects of solution properties on contaminant adhesion can be evaluated Range of adhesion forces for given contaminant/mask layer can be determined
Particle Characteristics The Academic System Polystyrene Latex Sphere (PSL sphere) 5 μm The Real World Alumina Particle Ideal geometries 5 μm Can model contact area using classic approaches Contact mechanics (JKR, DMT ) DLVO Uniform microscopic morphology Empirical, semi-empirical approaches Unusual geometry Random microscopic morphology Compression/deformation of surface asperities Chemical heterogeneities Settling (tilting, shifting) Statistical information
Macroscopic Adhesion Model: DLVO Theory F = F + A Total Adhesion Force vdw van der Waals Force F F vdw = f ( A,d,a,h) EDL A = System Hamaker constant d = Particle diameter a = Contact radius h = Particle-surface separation distance ε = Medium dielectric constant ζ = Zeta potential κ = Reciprocal double-layer thickness I = Medium ionic strength Electrostatic Double Layer Force F EDL = f ( ε, ζ, κ,d,h) ζ = f (I,pH ) κ = f (I ) F A Particle d a Surface
Electrostatic Double Layer (EDL) Force S u r f a c e Potential ψ ψ s ζ - - - - + + + Outer Helmholtz Plane + Shear Plane - Diffuse Double Layer - Distance + F EDL = εε Negative Co-Ion Positive Counter-Ion Zeta Potential, ζ Stern Layer Diffuse Layer Ions in Bulk Solution ( ψ + ψ ) 0d p s κh κh 4 κe 1 e ψ pψ s ψ p + ψ s ψ approximated by ζ e κh
van der Waals (vdw) Force F vdw = F Keesom + F Debye + F London induced-permanent permanent-permanent induced-induced Electrons Lithium atom -q l μ = ql (instantaneous dipole moment) +q Electric field lines Surface Surface Induced dipole moment μ 1 μ Surface
Particle Adhesion Measurements AFM Schematic Distribution of Forces Mounted particle cantilever Sample Sample holder and translation stage Frequency Adhesion Force Particles Mounted on AFM Cantilevers PSL Particle a AFM Force Curve Al O 3 Particle b c d e Deflection d c b e Position a Adhesion Force
Surface Roughness and Adhesion Removal Force (nn) 00 160 10 80 40 0 Modified vdw for a rough silicon surface 5 μm PSL spheres in contact with a silicon substrate in 0.03 M KNO 3 Removal Force = Adhesion Force Modified vdw for a smooth silicon surface Transition Region 1 3 4 5 6 7 8 9 ph
Geometry and Adhesion Interaction Force (N) Interaction Forces 3.E-09.E-09 1.E-09 0.E+00-1.E-09 -.E-09-3.E-09-4.E-09 (b) (c) Ideal Surfaces particle double layer Dominant dominant interaction region surface (a) van der Waals Electrostatic Combined DLVO Interaction Force (N) Interaction Forces Irregular Particles 1.E-08 5.E -09 0.E+00-5.E-09-1.E-08 (b) (c) van der Waals Electrostatic Combined DLVO (a) -5.E-09 0E+00 E-09 4E-09 6E-09 8E-09 1E-08 Separation Distance (m) -.E-08 0E+00 E-09 4E-09 6E-09 8E-09 1E-08 Separation Distance (m)
Alumina Interactions with SiO Alumina Adhesion Force (nn) 80 70 60 50 40 30 0 10 vdw Model Predictions Model Predictions Experimental Measurements 0 4 6 8 ph (Constant Ionic Strength 0.01 M) Electrostatic interactions do affect the adhesion force, which varies with ph Large area between particle and wafer out of contact Small contact area
How to Describe? du 1 = van der Waals Point-by-point additivity {( x x ) + ( y y ) + ( z z ) } 3 1 C 1 ρ ρ dv dv 1 1 1 1 5 μm Electrostatics Poisson-Boltzmann Equation κ = ψ = κ ψ e z n i i ε ε k T 0 r B io Hamaker Constant, A 1 Approximate Solutions A R F = 6h + 1 1 A R1R F = 6h R + R + 1 A F = 1πh 1 3 Computational Solutions Combination of ideal shapes κh εε d κe ( ψ + ) ( ) ( ) p ψ s ψ pψ 0 s = κh F + e κh e sphere-plate 4 1 ψ p + ψ s + + sphere-sphere plate-plate Approximate Solutions + ε r ( ψ 1ψ cosh( κ ) ψ1 ψ ) ( κh) κ ε 0 F = h sinh + ε r ( ψ 1ψ cosh( κ ) ψ1 ψ ) ( κh) κ ε 0 F = h sinh Computational Solutions
Combined vdw, ES Interaction Models Generate Mathematical Surface Representations SEM (Geometry) 3-D Reconstruction Surface Potential ζ (mv) ph IEP vdw + EDL Model Contact Surfaces AFM (Topographic Data) Compression/Deformation Load (mn) Applied Load force/depth profile Removal Force Statistics AFM Force Measurements
Geometric Models School of Chemical Engineering
Fourier transform of surface profile Reconstruction of surfaces generated with random phase angles FFT Roughness Model F(x) x π AFM scan of actual Cu surface FFT model Cu surface FFT with random phase
Validation: PSL Adhesion to Evolving Surfaces Only vdw forces needed to describe adhesion 0.4 0.35 0.3 Average Measured Value 10 nn Removal Force = Adhesion Force Average Measured Value 17 nn Frequency 0.5 0. 0.15 Range of Observed Values Range of Observed Values 0.1 0.05 0 Rough Silicon Surface Smooth Silicon Surface 1 1 41 61 81 101 11 141 161 181 01 Removal Force (nn)
PSL Interactions with SiO 300 PSL Adhesion Force (nn) 50 00 150 100 50 vdw Model Predictions Model Predictions Experimental Measurements 0 4 6 8 ph (Constant Ionic Strength 0.01 M) Electrostatic interactions do not have a significant effect at different phs Large contact area between sphere and wafer dominated by vdw
Alumina Interactions with SiO Alumina Adhesion Force (nn) 80 70 60 50 40 30 0 10 0 4 6 8 ph (Constant Ionic Strength 0.01 M) vdw Model Predictions Model Predictions Experimental Measurements Electrostatic interactions do affect the adhesion force, which varies with ph Large area between particle and wafer out of contact Small contact area
Nanoscale Adhesion Approach Measure, model micronscale adhesion Extract vdw, ES constants Measure nano-scale adhesion Model adhesion using constants from micron-scale Can measure nano-scale adhesion Can model roughness and geometry effects Can predict nano-scale adhesion
School of Chemical Engineering Silicon Dioxide Surface 30 0 10 0-10 -0 00 100 0 AFM Image 0 50 100 150 00 FFT model Regeneration 50
Silicon Nitride Particle: Micron-Scale FESEM image of a Si 3 N 4 particle mounted on an AFM cantilever Photomodeler Pro model for the nitride particle
Silicon Nitride Cantilevers: Nanoscale Sharpened silicon nitride probe Max ROC ~ 40nm Region considered in force calculations ~10nm ~ μm Geometry considered in modeling the force between nanoscale cantilevers and substrates
Silicon Nitride Adhesion to Silicon Dioxide in Air Tip ROC=1nm Tip ROC=36nm
Silicon Nitride Adhesion to Silicon Dioxide in Water Tip ROC=10nm Tip ROC=41nm
Silicon Nitride Adhesion to Quartz in Air Tip ROC=14nm Tip ROC=3nm
Silicon Nitride Adhesion to Quartz in Water Tip ROC=14nm Tip ROC=3nm
Theory and Experiment: Silicon Nitride Adhesion to Silicon Dioxide in Air Particle System MSCT OTR8 Tip ROC=36nm Tip ROC=1nm 0 0 40 60 80 100 10 140 Force (nn)
Theory and Experiment: Silicon Nitride Adhesion to Silicon Dioxide in Water Particle System MSCT Tip ROC=41nm OTR8 Tip ROC=10nm 0 4 6 8 10 1 14 16 Force (nn)
Theory and Experiment: Silicon Nitride Adhesion to Quartz in Air Particle System MSCT Tip ROC=3nm OTR8 Tip ROC=14nm 0 0 40 60 80 Force (nn)
Theory and Experiment: Silicon Nitride Adhesion to Quartz in Water Particle System MSCT Tip ROC=3nm OTR8 Tip ROC=14nm 0 1 3 4 5 6 7 8 Force (nn)
Conclusions Micron- and nano-scale particle adhesion can be described by vdw and electrostatic force models Proper accounting for roughness and geometry is required Particle adhesion characterized by a distribution of adhesion forces Reflective of the interaction of two rough surfaces Particles with highly nonuniform geometry can be influenced by electrostatic forces even when in contact with a substrate
Acknowledgements Financial support National Science Foundation CAREER grant (CTS-998460) NSF/SRC ERC for Environmentally-Benign Semiconductor Manufacturing State of Indiana 1 st Century Fund Intel Praxair Microelectronics SEZ America Stefan Myhajlenko Arizona State University Center for Solid State Electronics Research Ann Gelb Arizona State University Mathematics