Thermodynamic and Kinetic Stability of Nanobubbles at the Water-Solid Interface: A Modeling and AFM Study

Transcription

1 Thermodynamic and Kinetic Stability of Nanobubbles at the Water-Solid Interface: A Modeling and AFM Study B. Budhlall, X. He, I. Hyder, S. Mehta, G. Parris International Symposium on Immersion & 157nm Lithography. 3 August 2004

2 Topics Importance of nanobubbles at the waterphotoresist interface. Macroscopic model results for microbubbles Nanoscale modeling results for attachment of nanobubbles on hydrophobic surface AFM Studies Conclusions 2

3 Topics Importance of nanobubbles at the waterphotoresist interface. Macroscopic model results for microbubbles Nanoscale modeling results for attachment of nanobubbles on hydrophobic surface AFM Studies Conclusions 3

4 Importance of Nanobubbles at the Water-Photoresist Interface Liquid Immersion Lithography using water as fluid postpones major capital investment in 157nm, EUV. NA up to refractive index of water allows resolution enhancement: 45nm ½-pitch with Immersion, 32nm ½-pitch using PSMs. At the 1 st 193i Sematech Workshop (Fall 2002) the effects of bubbles made the Top 10 list of potential problems. Formation, control, removal of micro-bubbles Scattering and defects 4

5 Importance of Nanobubbles at the Water-Photoresist Interface, cont d Since then researchers at RIT, MIT, UNM, Univ. Wisconsin and others have studied nano/microbubble control. Resist topogrphy and outgassing Gas entrainment from jets Fluid surface tension and wettability issues While theoretical studies differ on feasibility of nanobubbles existence, AFM studies by Attard (Univ. SA) ascribed long-range forces to bubbles at waterhydrophobic surface. Nanobubbles at the water-photoresist interface are potential source of defect formation during exposure in optical lithography. 5

6 Focus of Study Develop a model to assess the attachment and growth of nano/micro-bubbles at water-solid interfaces. Expand our Atomic Force Microscopy methods to identify and measure nanobubbles at the water-193 nm photoresist interface. 6

7 Topics Importance of nanobubbles at the waterphotoresist interface. Macroscopic model results for microbubbles Nanoscale modeling results for attachment of nanobubbles on hydrophobic surface AFM Studies Conclusions 7

8 Macroscopic Model Approach R Bubble attached to hydrophobic surface (Semi-infinite domain) r θ Assumptions Bubble maintains spherical cap with radius of curvature, R θ is constant during the diffusion process. Parametric study for water on hydrophobic surface: Dissolved gas content Bubble radius Contact angle Solve the diffusion equation for mass transfer from the bubble to bulk liquid Stationary interface: Diffusion is slow Stability analysis of the bubbles Time scales for the bubble life 8

9 Validation of Macroscopic Model Results Simulation of mass diffusion of single bubble in a bulk fluid agree well with theory R/R simulation analytic t (s) 9

10 Contact Angle Affects Bubble Life For a given radius, reducing contact angle helps bubble dissolution Time for Dissolution (s) theta = 120 theta = 90 spherical 10 r = 100 µm Saturation

11 Contact Angle Effect on Bubble Dissolution Based on the classic diffusion model, micron size bubbles would dissolve within seconds. 100 dissolution time (s) 10 1 theta = 120 theta = 90 spherical saturation degree 11 r = 10 µm

12 Topics Importance of nanobubbles at the waterphotoresist interface. Macroscopic model results for microbubbles Nanoscale modeling results for attachment of nanobubbles on hydrophobic surface AFM Studies Conclusions 12

13 Approach(s) Macroscopic Solve the diffusion equation for mass transfer from the bubble to bulk liquid Conclusion: Diffusion is fast, bubbles will disappear in microseconds Microscopic Intermolecular effects close to the surface. Modify Laplace-Young Equation Include van der Waals dispersion forces Model does not include electrostatic forces Random alignment of electrostatic forces in liquid and solid tend to cancel or become very small 13

14 Microscopic Model Using Intermolecular Surface Forces van der Waals potential energy C u att = 6 r Near-surface forces Range < 5 nm Non-retarded vw forces Range 5-30 nm Retarded vw forces These forces leads to a disjoining pressure: Disjoining pressure: P d = ( ρ C sl = ( ρ C sl = ( ρ C sl sl sl sl ρ C ρ C ll ρ C ll ll ll ll ll ) r dr 6 r ) [ h 0 π ) 3 6h 2πξ ( z 2 A = 3 6πh dξ 2 + ξ ) 3 ] dz 14

15 Pressure Near Solid-Liquid Interface P l P l c P l 1~10nm P d = ( A Sl A ll ) π 3 6h P d P d c P + i l P d Negative P d A P Sl d A < 0 ll < 0 Positive P d A P Sl d A > 0 ll > 0 Gas will diffuse towards the surface when the disjoining pressure is negative. 15

16 Hamaker Constants for Homogeneous Media Liquids A 11 (x10 20 J) EST (dyne/cm) Water Glycerol Ethanol Hexane Solids SiO NA CaF NA PTFE 3.8 NA Gases N x10-6 NA 16

17 Hamakar Constants for Various Solid-Liquid Contact A = A ll A sl = A ll A ll A ss A*10 20 (J) Liquid\Solid SiO2 CaF2 PTFE Water Glycerol Ethanol Hexane Negative value gives stable bubble 17

18 Critical Height Based on Vapor Pressure h c = A 6 ( ) ll Asl π patm pv 1/3 Liquid\Solid Water Glycerol Ethanol Hexane Bubble Height (nm) SiO2 PTFE

19 Topics Importance of nanobubbles at the waterphotoresist interface. Macroscopic model results for microbubbles Nanoscale modeling results for attachment of nanobubbles on hydrophobic surface AFM Studies Conclusions 19

20 AFM Tapping Mode Images of 193 nm Resist Surface Using a Si3N4 Tip In air In degassed water In air saturated water 20 Si Coated Wafers

21 Nanobubbles on 193nm Resist in Tapping Mode - Effect of Solvent Degassed Water Air Saturated Water Air Saturated Ethanol force curve damage After imaging nanobubbles in water, fluid cell was filled with Ethanol. Water contact angle is ~ 70. Ethanol contact angle is 29. TM images show no nanobubbles in Ethanol. Nanobubbles returned upon re-filling cell with air saturated water. No jump-to-contact or strong adhesion were found in EtOH. 21

22 Contact Mode AFM on 193nm Resist in Air Saturated Water Si 3 N 4 Tip CM-Low Force CM-High Force After CM 10um Scan force curve damage 22

23 Height Analysis After Contact Mode Force Curve and Tapping Mode Image Nanobubbles are approx. 13 nm high. CM imaged area shows clearing and coalescence of bubbles on the 193nm resist. Large bubbles on sides of square area are ~ 60nm in height. 23

24 Tapping Mode Image and Contact Mode Force Curve for Graphite in Air Image is 5um x 5um, obtained using ozonized Si 3 N 4 AFM tip. 24

25 Topics Importance of nanobubbles at the waterphotoresist interface. Macroscopic model results for microbubbles Nanoscale modeling results for attachment of nanobubbles on hydrophobic surface AFM Studies Conclusions 25

26 Conclusions The macroscopic diffusion and mass balance equations predict rapid dissolution of micro-bubbles attached to water-hydrophobic interface. The disjoining pressure at the interface of the water-hydrophobic surface leads to stabilization of nanobubbles. Liquid-solid interactions with negative disjoining pressure may exhibit presence of nanobubbles. In AFM studies, nanobubbles are eliminated from 193 nm photoresist in degassed water or lower surface tension liquids. 26

27 Acknowledgement The authors wish to thank Air Products & Chemicals, Inc. for permission to present this study, and the following persons for their contributions to this work: Zarka Zarkov, John Marsella, Bobby Chen and Carlos Valenzuela Peng Zhang and Leslie Barber 27