1. Niki Farnsworth R. Steven Turley
Surface Roughness of Thorium and Thorium Oxide and its Effect on Optical Properties in the Extreme Ultraviolet
Niki Farnsworth
R. Steven Turley

2. Why the Extreme Ultraviolet?

3. Roughness
Why do we care?

4. Roughness
Roughness affects the way a surface reflects.

5. Characterization of Roughness
The easiest way to characterize roughness is to measure it directly.
ATOMIC FORCE MICROSCOPY
Talk about tapping mode

6. Our Data RMS roughness of 4.3 nm over a 1000x1000nm length scale.
Peak roughness at horizontal length scales on the order of 50 nm.

7. Too Good to be True?
It wouldn’t be interesting physics research if it were this simple.
Problem: What happens when the tip size is on the order of the horizontal length scales of our roughness?

8. Too Good to be True?
The tip of the AFM has a finite diameter. How different is our data from reality?

9. Now what? Do AFM measurements tell us anything about the surface?
How accurate are the RMS roughnesses it reports?
How accurate are the power spectral densities it reports?

10. Solution: Model it Different types of rough surfaces
Change horizontal length scales
Change correlation length
Change magnitudes
Different types of tips
Change tip shape
Change tip size

11. Solution: Model it Assumptions: Horizontal length scale = 20 nm.
Magnitude is a Gaussian of width 1nm around zero.
Tip shape is a parabola.

12. Changing Tip Sizes

13. Changing Tip Sizes tip width = 10 nm tip width = 20 nm
say dx=20
tip width = 15 nm
tip width = 30 nm

14. Changing Tip Sizes
Tip Size (nm)
RMS roughness of the surface (nm)
RMS roughness measured by the tip (nm) 10
0.798 15
0.776
0.566 20
1.01
0.537 30
1.13
0.415

15. Changing Tip Sizes

16. Changing Tip Sizes
tip width = 10 nm

17. Changing Tip Sizes
tip width = 15 nm

18. Changing Tip Sizes
tip width = 20 nm

19. Changing Tip Sizes
tip width = 30 nm

20. Comparing to Our Data
dx = 20 nm, tip width = 30 nm

21. Comparing to Our Data
The horizontal length scales of our surface roughness are approximately 2/3 the size of our tip.
Tip Size (nm)
RMS roughness of the surface (nm)
RMS roughness measured by the tip (nm) 30
1.13
0.415
The real RMS roughness of our surface could be up to 2.7 times that measured by the AFM (up to 11.6 nm).

22. How Does this Affect Reflectance Data?
Up to 35%

23. Conclusions
The discrepancy in the roughness measured by the tip and the actual roughness of the surface could be different by as much as 7.3 nm.
Failure to take this difference into account could change our calculated reflectance by up to 35%.
This discrepancy could be fatal to our calculation of optical constants for that material.

24. Acknowledgements Dr. R. Steven Turley Dr. David D. Allred
The BYU Thin Films Group
Physics and Astronomy Department Funding
Rocky Mountain NASA Space Grant