1 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?Why do we care?

4 Roughness Roughness affects the way a surface reflects.Roughness affects the way a surface reflects.

5 Characterization of Roughness The easiest way to characterize roughness is to measure it directly.The easiest way to characterize roughness is to measure it directly. ATOMIC FORCE MICROSCOPYATOMIC FORCE MICROSCOPY

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 physics research if it were this simple.It wouldn’t be 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?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?

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

10 Solution: Model it Different types of rough surfacesDifferent types of rough surfaces Change horizontal length scalesChange horizontal length scales Change correlation lengthChange correlation length Change magnitudesChange magnitudes Different types of tipsDifferent types of tips Change tip shapeChange tip shape Change tip sizeChange tip size

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

12 Changing Tip Sizes

13 Changing Tip Sizes tip width = 10 nm tip width = 15 nm tip width = 20 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)

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.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) The real RMS roughness of our surface could be up to 2.7 times that measured by the AFM (up to 11.6 nm).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?

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.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%.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.This discrepancy could be fatal to our calculation of optical constants for that material.

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