Phase-sensitive specular neutron reflectometry for imaging the nanometer scale composition depth profile of thin-film materials

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Abstract

Neutron reflectometry is a powerful method for probing the molecular scale structure of both hard and soft condensed matter films. Moreover, the phase-sensitive methods which have been developed make it possible for specular neutron reflectometry to be effectively employed as an imaging device of the composition depth profile of thin film materials with a spatial resolution approaching a fraction of a nanometer. The image of the cross-sectional distribution of matter in the film obtained in such a way can be shown to be, in most cases, unambiguous to a degree limited primarily by the range and statistical uncertainty of the reflectivity data available. The application of phase-sensitive neutron reflectometry (PSNR) to the study of several types of soft matter thin film systems are illustrated by a number of specific examples from recent studies. In addition, new software tools available to the researcher to apply PSNR methods and analysis are discussed.

Graphical abstract

Highlights

► Phase-sensitive neutron reflectometry (PSNR) is a powerful probe of film structure. ► Specular PSNR is sensitive to the compositional depth profile along the film normal. ► Specular PSNR is capable of nanometer scale resolution under ideal conditions. ► Specular PSNR is particularly applicable to soft condensed matter film systems. ► In the specular PSNR method, the retrieval of phase information minimizes ambiguity.

Introduction

Over the past quarter century or so, neutron reflectometry (NR) has become an established probe of the nanometer scale structure of materials in thin film and multi-layered form. NR has contributed to our understanding of layered systems of soft condensed matter of interest in polymer science, organic chemistry, and biology and of magnetic and superconducting hard condensed matter film systems [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. In general, neutrons are especially sensitive to hydrogen and atomic magnetic moments, thereby potentially complementing subsurface structural information that can be obtained from X-ray reflectivity measurements. In particular for NR, the scattering length density (SLD) depth profile along the surface normal, averaged over in plane, can be deduced from specular neutron reflectivity measurements (wavevector transfer Q normal to the surface). (The SLD is the sum of the individual products of the number of atoms of each isotope per unit volume and its corresponding neutron scattering strength as characterized by a scalar number called the coherent scattering length. This number may be complex if absorption occurs.) Under nearly ideal conditions, neutron reflectivities as low as 10 8 out to a Q of 0.7 Å 1 from a lipid bilayer membrane have been measured with a corresponding spatial resolution in the SLD profile of half a nanometer [16]. The SLD profile is directly related to the corresponding material composition distribution — and if polarized neutron beams are employed, the vectorial magnetization depth profile of magnetic materials can be obtained as well.

Moreover, it has been shown relatively recently that in specular neutron reflectometry the phase can be determined exactly using reference structures, thereby enabling a first-principles inversion, and thus ensuring a unique result for the SLD profile [17], [18], [19], [20], [21], [22], [23]. (Other schemes for retrieving phase information in reflectivity measurements have also been developed [24], [25], [26], but these do not enable the direct inversion described here.) The ability to establish an unambiguous correspondence between reflectivity data and a SLD profile is immensely powerful and one of the most important factors in making an accurate structure determination. The experimentally determined reflectivity is the reflected intensity divided by that of the incident beam. Because the reflectivity is the square of the modulus of the complex reflection amplitude, it cannot explicitly express any information about the phase of the reflected wave. The phase of the reflected wave contains essential structural information without which a unique solution for a given structure cannot be determined in all cases. Some examples of non-unique SLD profiles associated with single reflectivity data sets are presented in [27], [28], [29]. The phase-sensitive methods which have been developed allow specular neutron reflectometry to be effectively employed as an imaging device of the composition depth profile of thin film materials with a spatial resolution approaching a fraction of a nanometer. The image of the cross-sectional distribution of matter in the film obtained in such a way can be shown to be, in the vast majority of cases, unambiguous to a degree limited primarily by the range and statistical uncertainty of the reflectivity data available [30]. The uniqueness follows from the mathematical one-to-one correspondence which exists between the reflection amplitude and the scattering length density (SLD) distribution of the film structure along the surface normal. This is an extraordinary relationship for what is fundamentally a diffraction process and one which is enabled by the use of external reference media placed adjacent but external to the film of interest — the SLD depth profile of which is initially unknown. The reference media may be a variable “fronting” or “backing” medium on either side of the film of interest (one of which can also serve as supporting substrate) or a separate, variable reference film of finite thickness (such as a saturated ferromagnetic film). This one-dimensional holographic (interferometric) technique can be applied to film materials of both hard and soft condensed matter and is especially sensitive to hydrogenous organic and magnetic systems. In cases involving organic films where deuterium substitution can be performed isomorphically, the phase-sensitive methods applied to both protonated and deuterated versions of the sample can enhance the accuracy of the structural information deduced from the reflectivity measurements. For example, if two segments of the depth profile of an organic film have different chemical compositions but happen to have nearly the same SLD, then deuterating one segment and protonating the other isomorphically would in principle enable NR to distinguish one from the other. Alternatively, the isomorphic nature of such an exchange can be validated in a structure that is already known a priori. General discussions of PSNR methods can be found, for example, in [31], [32].

One of the principal aims of this article is to enable the researcher to access the tools now available to apply these phase-sensitive neutron reflectometry (PSNR) methods to current materials research problems involving thin film systems. Although numerous “proof-of-principle” demonstration experiments and analyses have been performed [33], [34], [35], [36], [37], application of phase-sensitive methods to scientific problems on the forefront of current research has not yet been widespread. Possible reasons for this include the relatively formidable mathematics of the inversion procedure and stringent requirements on the quality of the sample (particularly regarding in-plane homogeneity). The former potential obstacle has been largely removed with newly available software packages for performing such calculations and by the introduction of an alternative means of analysis which employs simultaneous fitting of multiple data sets. The latter impediment can be eliminated to a certain extent by high-quality, well-characterized standard reference substrates. Efforts to develop, and make available for general use, such substrates are currently underway at the NIST Center for Neutron Research (NCNR), e.g., magnetic Permalloy and Au layers on Si. No matter how accurately the NR measurements are performed, the quality of the result can be no better than that of the preparation of an appropriate sample. In this review of the technique, we will focus on several examples, namely a photovoltaic thin film, a biocompatible film coating, and a biomimetic lipid bilayer membrane system to demonstrate the power of the method. We will show how a direct inversion is performed as well as an indirect alternative involving simultaneous fitting of the same two composite system (“unknown film of interest” plus a given reference) reflectivity data sets (employed in the direct inversion. We will also consider methods for determining uncertainties in the structural parameters used to describe the SLD depth profile associated with the reflectivity data. All of the programs applied in the paper are publicly available on the web [38].

Section snippets

Analysis of PSNR measurements of a photovoltaic film: variation of backing medium

As a first example of how phase-sensitive neutron reflectometry can be applied to study a film system of current scientific and technical interest, consider the organic photovoltaic (PV) film system investigated by Jon Kiel et al. and originally reported on in [39], [40].

In polymer based solar cells, device performance is largely determined by the morphology of the active layer components on a length scale of nanometers. However, structural characterization by X-rays is difficult because the

Bio-compatible films: variation of fronting medium

The second example of a PSNR study involves a cell membrane mimic system originally reported on by Perez-Salas et al. [44]. Lipid membranes are of general interest because of the important role they play in mediating many biological processes on the cellular level. Supported cell membrane mimics are of specific practical interest because they enable functionalization of inorganic materials by creating biocompatible surfaces — e.g., coatings for artificial organs or other implantable objects

Bio-mimetic lipid bilayer membrane system: variation of buried reference film

In a series of articles, Le Brun and Holt et al. demonstrated how PSNR could be practically applied to the study of biomembranes involving antibody-binding membrane protein arrays [46], ion-channels [47], and engineered biosensor surfaces [48]. Here we will focus on the study of the ion-channel-containing model membrane and the determination of its structure along the membrane normal [47]. For a critique of NR studies of other biomembrane systems, see the reviews by Krueger and Wacklin [7], [9]

Conclusion

Phase-sensitive neutron reflectometry (PSNR) is a technique that is especially well-suited for studying the molecular scale structure of layered thin film materials. In particular, specular PSNR, in which the momentum and wavevector transfer is normal to the surface, can accurately reveal detailed features of the compositional depth profile with a spatial resolution approaching a fraction of a nanometer under proper conditions. Although specular PSNR is fundamentally a diffraction method, the

Acknowledgments

We would like to acknowledge our many colleagues with whom we have worked performing neutron reflectometry studies of soft matter systems over the years and who have contributed greatly to this research.

A number of key translations of code written in a variety of different computer languages to Python were performed. Pikaia was translated from FORTRAN by Mathieu Doucet; Snobfit was translated from Matlab and GEPORE was translated from FORTRAN by Ziwen Fu; Particle Swarm and Random Lines were

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