Numerical analysis of x-ray reflectivity data from organic thin films at interfaces

Abstract

Articles you may be interested inXray reflectivity study of behenic acid Langmuir-Blodgett mono and multilayers on SiO2 surfaces asdeposited and after thermal treatment: Influence of substrate/film interactions on molecular ordering and film topology Static and dynamic structural analysis of a saturated solution of ZnBr2 in water: Anomalous xray diffraction and molecular dynamics simulations Near edge xray absorption fine structure investigation of the orientation and thermally induced order-disorder transition in thin organic films containing long chain hydrocarbons Higher order structure analysis of nanomaterials by spectral reflectance of laserplasma soft xray AIP Conf.An efficient numerical analysis procedure of x-ray reflectivity data from ultrathin organic films at interfaces is presented. It allows virtually exact modeling of reflectivity data in the entire q-vector range including the critical angle and below with minimum fit parameters and calculation effort. The electron density profile is interpreted as a linear superposition of the air/film interface, the internal film structure, and the film/substrate interface. The reflectivities at the interfaces are calculated from the accurate Fresnel reflectivities. The internal film structure is parameterized in a Fourier series and its reflectivity contribution is calculated from refraction-corrected, approximated ͑linearized͒ Fresnel reflectivities. Additionally, a new way of weighing measurement errors is introduced. It allows the selective optimization of the fit in those data sections which are considered especially significant. Finally, we show further how to determine the degree of correlation ͑interdependencies͒ between the fit parameters and how to obtain absolute errors ͑the significance͒ of all fit parameters.

Interface effects on moisture absorption in ultrathin polyimide films

“…The error in the fitted parameter t Å 176.5 Å is estimated at D t Å 0.01 Å by the fitting procedure, For example, if the existence of the 30 Å , moisture-rich layer observed in the initial NR 10 experi-which is based on a Marquart-Levenburg fit that minimizes a merit function, x 2 , through variation ments is a universal characteristic of BTDA// ODA/MPD films on silicon substrates, the mois-of a group of specified parameters. 20- 22 The small magnitude of the error estimate D t is a partial ture absorption in thinner films should appear to be greater than in thicker films for which the consequence of this fitting procedure, which minimizes x 2 based on a set of optimized parameters moisture-rich layer constitutes a smaller fraction of the total swollen film thickness. This line of whose individual errors small but correlated.…”

“…This line of whose individual errors small but correlated. 22 The parameter set for fitting of the reflectivity reasoning depends on the important assumption that the film structure is not a function of film data discussed in this study include the thicknesses of the polyimide and oxide films, the elec-thickness. This condition is met for the BTDA// ODA/MPD chosen for this study due to its com-tron density of the polyimide film, and the roughness at the polyimide/vacuum and polyim-pletely amorphous character, 4 but is unlikely to hold for more highly structured polyimides.…”

Surfactant-Encapsulated Clusters (SECs): (DODA)20(NH4)[H3Mo57V6(NO)6O183(H2O)18], a Case Study

“…It was not possible to fit the reflectance curves by a simple periodic electron density function and to retrieve the profile of the superlattice. [19] More insight into the structure of the thin films of 2 was obtained by transmission electron microscopy.…”

Temperature dependence of interfacial fluctuations of polymerized fatty acid salt multilayers

“…7. 47,48 But the alkyl chains in our film are cross linked by polymerization. But as with the reflectivity, the transverse diffuse scattering varied only a little with temperature when the sample is in air.…”