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?