PRINCIPLES AND APPLICATIONS OF ZONE PLATE X-RAY MICROSCOPES Malcolm Howells1, Chris Jacobsen2 and Tony Warwick1 1Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California, USA 2Department of Physics & Astronomy, Stony Brook University, Stony Brook, New York, USA CONTENTS 1. INTRODUCTION 1. Background 2. X-ray interactions 3. Focusing optics 2. FRESNEL ZONE PLATES 1. Introduction 2. Zone plate image quality: a. Optical path function analysis b. Ray aberrations c. Spherical aberration d. Astigmatism and field curvature e. Coma f. Relative size of aberrations 3. Zone plate efficiency: a. Idealized structures b. Real structures 4. Zone plates: fabrication and examples a. Fabrication technique b. Resolution-determining zone plates c. Condenser zone plates d Zone plates with shaped grooves e Hard x-ray zone plates f Thick zone plates 3. X-RAY MICROSCOPES 1. Microscope Layouts and illumination schemes a Transmission x-ray microsope (TXM) layout b TXM phase contrast layout c Scanning transmission x-ray microscope (STXM) layout d Scanning fluorescence x-ray microprobe (SFXM) layout 2. Fundamentals of contrast 3. Partial coherence a. History b. Fourier Optics treatment c. Contrast Transfer d. Reciprocity e. The influence of coherence on resolution f. Coherence in dark field and Zernike phase contrast g. Propagation-based phase contrast 4. Tomography in x-ray microscopes 1 5. X-ray spectromicroscopy 4. APPLICATIONS 1. Biology 2. Environmental Science 3. Materials Science 4. Magnetic Materials 5. CONCLUSION 6. ACKNOWLEDGEMENTS 7. TABLES 8. REFERENCES 2 1. INTRODUCTION 1.1. Background In the 1949 issue of Scientific American, an article by Stanford physicist Paul Kirkpatrick on “The x-ray microscope” [Kirkpatrick 1949] was described by the editors as follows: "It would be a big improvement on microscopes using light or electrons, for X-rays combine short wavelengths, giving fine resolution, and penetration. The main problems standing in the way have now been solved". With the perspective of a half century, we might change “improvement on” to “complement to,” and say that further problems were solved after 1949, but here in essence is the character of x-ray microscopes. In this chapter, we outline some of the properties of x-ray microscope systems in operation today, and highlight some of their present applications. We will not discuss the history of x-ray microscopes prior to about 1975 but instead refer the reader to a series of conference proceedings known as "X-ray Optics and X-ray Microanalysis", which began in 1956. Originally these had valuable material on x-ray microscopy but this diminished after about 1970. The first five were at Cambridge (1956) [Cosslett 1957], Stockholm (1959) [Engström 1960], Stanford (1962) [Pattee 1963], Orsay (1965) [Castaing 1966] and Tubingen (1968) [Molenstedt 1969]. We also recommend the historical perspectives by A. Baez [Baez 1989, Baez 1997] and the book by Cosslet and Nixon [Cosslett 1960]. There is a recognisable thread of continuity between today’s status of the field and efforts that began slowly around 1975 [Niemann 1976, Parsons 1978, Kirz 1980c, Parsons 1980] and blossomed with the availability of synchrotron light sources and nanofabrication technologies; this thread can be traced in part via the proceedings of another conference series that began in 1984 [Schmahl 1984a] and has continued until today [Sayre 1988, Michette 1992, Aristov 1994, Thieme 1998b, Meyer-Ilse 2000b, Susini 2003]. Zone-plate x-ray microscopes now exist at roughly two dozen international synchrotron radiation research centers, and commercial lab-based instruments are also available. Three types are in especially widespread use. Transmission x-ray microscopes (TXMs) specialize in the rapid acquisition of 2D images using high flux sources, and in the collection of tilt sequences of projection images for 3D imaging by tomography. Scanning transmission x-ray microscopes (STXMs) specialize in the acquisition of reduced dose images and point spectra with high energy resolution for elemental and chemical state mapping, and require high source brightness. Scanning fluorescence x-ray microprobes (SFXMs) are similar to STXMs except that fluorescence x-rays are collected by energy-resolving 3 detectors for trace element mapping. All three approaches are now working below 100 nm resolution, to the point of reaching 15 nm resolution in some demonstrations [Chao 2003]. While many of the new technical developments continue to be pursued by specialists in x-ray optics and microscopy, much of present-day activity comes from scientists in other fields of research who are using x-ray microscopes to address their particular questions. This chapter is aimed at scientists from the latter group as well as those from the other communities represented in the content of this series of books. 1.1. X-ray interactions A microscope requires illumination, magnification, and contrast. The characteristics of x-ray interactions with matter affect all three. In Fig. 1 we show the cross section [Hubbell 1980] for photoelectric absorption, coherent (elastic or Thomson) scattering, and incoherent (inelastic or Compton) scattering. Below 10 keV, absorption dominates, so multiple scattering is usually not of concern (an x ray is much more likely to be absorbed following any scattering event than scattered again) nor is inelastic scattering. However, what is neglected in Fig. 1 is the fact that the propagation of x-rays in materials can also include refractive effects, and in fact it was Einstein [Einstein 1918] who first pointed out that the refractive index is slightly less than unity. The x-ray refractive index for a wave forward propagated as exp $!i knx! ! "# & is often written as n! = 1! " ! i# where δ represents % ( )' the phase-shifting part of the refractive index and β represents absorption according to a linear coefficient µ = 4"# / ! in the Lambert-Beer law I = I 0 exp[! µt]. In an anomalous dispersion model, 2 the refractive index terms can furthermore be written as ($ + i# )= !" (f1 + if 2 ) with " = na re / 2! , -15 where na = !N A / A gives the number density of atoms, re=2.82×10 m is the classical radius of the electron, and (f1 + if 2 ) represents the frequency-dependent oscillator strength of an atom. This oscillator strength (f1 + if 2 ) has been tabulated with very good absolute accuracy for all elements by Henke, Gullikson et al. [Henke 1993] over the energy range 10-30,000 eV (see Fig. 2). In examining Fig. 2, two features immediately jump out: f1 is somewhat constant except near absorption edges, so the thickness t$ = " / 2# =1/(2!" f1 ) needed to provide a phase advance exp[ik!t! ] equal to π increases as !1 !2 2 " , while, because f2 scales as E or " , the thickness 1/ µ =1/(4!"# f 2 ) that produces an attenuation 4 of 1/e increases as E 3 or !"3 . As a result, phase contrast becomes the dominant contrast mechanism as one goes to shorter wavelengths [Schmahl 1987]. Much of modern x-ray microscopy centers on the exploitation of x-ray absorption edges. X-ray absorption edges arise when the x ray photon reaches the threshold energy needed to completely remove an electron from an inner-shell orbital. The energy at which this occurs is approximately given by the 2 2 Bohr model as En=(13.6 eV)(Z-zshield) /n , where Z is the atomic number, zshield approximates the partial screening of the nucleus’ charge by other inner-shell electrons (zshield≈1 for K edges), and n is the principal quantum number (n=1 for K edges, 2 for L edges, and so on). This produces the step-like rise in the cross section for photoelectric absorption that can be seen in the plots of f 2 in Fig. 2. If one takes one image I1 at an energy E1 just below an element’s absorption edge where the incident flux is I01, and a similar image I2 at an energy just above an absorption edge, one can recover the mass per area mx / A of the element x from [Engström 1946] 3 m (E1 / E2 ) ln(I1 / I01 ) " ln(I2 / I02 ) x = ! . (1) A 3 µ2 " µ1 (E1 / E2 ) This approach works well for mass concentrations greater than about 1%. Another way in which x-ray absorption edges are exploited is by means of the “water window.” At x-ray energies between the carbon and oxygen absorption edges at 290 and 540 eV, respectively, organic materials show strong absorption contrast while water layers up to several µm thick are reasonably transmissive [Wolter 1952]; this is particularly valuable for imaging hydrated biological and environmental science specimens. For those elements which have absorption edges below the energy of incident x rays so that inner-shell ionization occurs, the aftermath of absorption involves the emission of either a fluorescent photon or an Auger electron of characteristic energy. The energy of these fluorescent photons, and the fluorescence yield [Krause 1979] (the fraction of events which result in fluorescence rather than Auger electron emission), are both shown in Fig. 3. At x-ray energies below 1 keV, Auger emission dominates, and scanning photoemission microscopes (SPEM) use electron spectrometers to exploit these electrons for surface studies [Ade 1990a, Günther 1997, Warwick 1997, Ko 1998]. At higher energies, the fluorescence signal dominates and detection of these characteristic x rays provides information on the concentration of various elements in the specimen. Most scanning fluorescence x-ray microprobes 5 (SFXM) [Horowitz 1972, Sparks 1980] use energy dispersive detectors where the number of electron- hole pairs created by each fluorescent photon is used to measure its energy, though crystal-based wavelength dispersive spectrometers can also be used. Exact quantitation of the elemental concentration requires accurate knowledge of a number of factors, including the solid angle acceptance of the detector and its quantum efficiency, the degree to which fluorescent photons are reabsorbed in the specimen, and other factors, so that in most cases comparison is made with standards with known elemental concentration and matrix concentration similar to that of the specimen under study.