Spectral Analysis for Resonant Soft X-Ray Scattering Enables Measurement of Interfacial Width in 3D Organic Nanostructures

Interfaces are of critical importance to many materials and phenomena yet are difficult to probe. This difficulty is compounded in three-dimensional nanostructures and with delicate organic materials. Here we demonstrate a quantitative spectral analysis of resonant soft x-ray scattering that can accurately measure properties of buried nonplanar interfaces within polymeric systems. We measure the scattering invariant on an absolute scale to quantify the interfacial volume and width involved in mixing at the interface of block copolymer nanostructures. Using continuous contrast tuning, this spectral analysis enables the separation and identification of any number of unique scatterers in complex nanostructures.

Figure 1

(a) Complex optical constants for PS and PMMA. (b) Contrast functions $C=E^4\mathrm{\Delta }{n}_{\mathrm{AB}}^2$ for three modeled domains: PS, PMMA, and vacuum (arising from surface roughness). Circles indicate photon energies where RSOXS was measured.

Figure 2

(a) Scattering intensity ($*q^2$ to accentuate features) as a function of both $|\mathbf{q}|$ and $E$. (b) Individual scattering profiles at select energies normalized to the BCP $q^{*}$ peak. (c) Total scattering intensity as a function of energy.

Figure 3

(a) Transmission scattering geometry enabling measurement of reciprocal space maps with one CCD exposure. $k_0$, $k_f$ are the incident and scattered wave vectors, respectively. (b) Atomic force microscopy phase images and corresponding reciprocal space maps ($E=285.1\mathrm{eV}$) of a lamellar (left) and hexagonal close packed cylinder (right) BCP nanostructure.

Figure 4

Example fit of the TSI data to the combined Eqs. (1) and (2). Dashed are terms in the sum for the combined model defined in the text. Uncertainties are derived from detector statistics for scattering and optical constants.

Figure 5

(a) Partial invariant corresponding to domain scattering plotted against sample PMMA volume fraction ${\varphi }_M$. Data (black circles) compared to calculation (line) assuming sharp interfaces. (b) Calculated interfacial width modeled as an error function. Average value (line) and standard deviation (dash) are shown. Uncertainties are propagated from fit results and absolute scattering calibration.