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Modeling the polarized X‐ray scattering from periodic nanostructures with molecular anisotropy
Author(s) -
Liman Christopher D.,
Germer Thomas A.,
Sunday Daniel F.,
DeLongchamp Dean M.,
Kline R. Joseph
Publication year - 2017
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s160057671701408x
Subject(s) - scattering , orientation (vector space) , nanostructure , anisotropy , inverse scattering problem , optics , biological small angle scattering , measure (data warehouse) , computational physics , physics , position (finance) , materials science , mathematics , geometry , small angle neutron scattering , computer science , quantum mechanics , neutron scattering , database , finance , economics
There is a need to characterize nanoscale molecular orientation in soft materials, and polarized scattering is a powerful means to measure this property. However, few approaches have been demonstrated that quantitatively relate orientation to scattering. Here, a modeling framework to relate the molecular orientation of nanostructures to polarized resonant soft X‐ray scattering measurements is developed. A variable‐angle transmission measurement called critical‐dimension X‐ray scattering enables the characterization of the three‐dimensional shape of periodic nanostructures. When this measurement is conducted at resonant soft X‐ray energies with different polarizations to measure soft material nanostructures, the scattering contains convolved information about the nanostructure shape and the preferred molecular orientation as a function of position, which is extracted by fitting using inverse iterative algorithms. A computationally efficient Born approximation simulation of the scattering has been developed, with a full tensor treatment of the electric field that takes into account biaxial molecular orientation, and this approach is validated by comparing it with a rigorous coupled wave simulation. The ability of various sample models to generate unique best fit solutions is then analyzed by generating simulated scattering pattern sets and fitting them with an inverse iterative algorithm. The interaction of the measurement geometry and the change in orientation across a periodic repeat unit leads to distinct asymmetry in the scattering pattern which must be considered for an accurate fit of the scattering.