ANDRÉ GUZMÁN POOLESV I L LE H IGH SCHOOL BR IAN MARANVILLE N IS T CENTER FOR NEUTRON RESEARCH PAUL K IENZLE N IS T CENTER FOR NEUTRON RESEARCH
Modeling off-specular x-ray scattering from patterned thin films using the Born Approximation.
• Off-specular scattering with neutrons
• Developing technique at NCNR
• Born Approximation to model other data
• SANS, Triple Axis
• Testing Born Approximation for use with off-specular
Motivation
• Permalloy is magnetically soft
• Nickel has high neutron SLD
• Patterned on silicon substrate
Patterned Permalloy Gratings
Permalloy diffraction grating
• Rocking Curves
• Vary θ, 2θ constant
• For each θ
• Measure kout intensity
• Compute Qx
X-Ray Off-specular Scattering
• Features on flat sample
tilt
tilt
4 2sin
2
sin( )
cos( )
x
z
Q
Q Q
Q Q
• Taken before Rocking Curves
• Low Q, Mid Q, High Q
• Peak θs used for Rocking Curves
• 2θ > 2 data too noisy
Specular Measurements
• Rocking curves
• Did not use specular peaks
• Incremented 2θ
• Vbscript data collection
Mesh Scans
• Approximates x-ray scattering
• Assumes weak scattering
• Fourier transform of structure
• Measuring in waves
• Real space to reciprocal Q-space
Born Approximation Fourier Transforms
( ) ( ) di tF f t e t
0
( ) dx
x
S
iq x
xFT q e x
1( () )x t x
1( ) ( )xx Å q Å
• Property of Fourier Transform
• Equation must hold true
• Detect false peaks
Preliminary Data Analysis
2Realspace
peak spacingx
x
D Åq
• Uses Born Approximation
• Equation is Fourier Transform of structure
• Parameters in equation correspond to material structure
Square Model
2
2
( )
21
( ) 12
xmax
x x x x
max
nDniq nD iq S
x
n nx max x
iFT q e e e
D n q
• Also uses Born Approximation
• Slightly more complicated
• Structure not perfect square
Trapezoidal Model
12
2 1
2
1122 2
1
( )
( )
22
2 2
2
(1 ( )) 1
(1 ( )) (1 ( ))
x x x
x x
x x x x x
x x x x x
nD iq liq nD x x x x xz
x x x
iq S l iq l
x
iq S iq S l
x x x x x x xz
x x x
e iq l nD iq nDle e
l q q
ie e
q
e iq S nD e iq S l nDl
l q q
• Bayesian Uncertainty Modeling for Parametric Systems
• General purpose fitting program
• Varies parameters
• Finds best fit for data
BUMPS Data Analysis
• Used part of lowq data
• Both stop matching at end
• Trapezoid fits more closely
• Neither works in left half
Model Comparison
• Form factor is constant over summation
• Form factor more dynamic
• Structure factor determines peak location
Structure and Form Factor
• Form factor determines shape
• Trapezoidal model works slightly better
• Born Approximation works lowq and midq right side
• Further refine data model
• Test on more complicated sample
• Test on real samples
Conclusions and Future Work
Acknowledgements
• Advisor:
• Brian Maranville
• BUMPS and C Programming Support:
• Paul Kienzle
• NCNR SHIP Coordinators
• Yamali Hernandez
• Julie Borchers
• NCNR SHIP Sponsor
• Center for High Resolution Neutron Scattering
Questions?
