Figure 1. A schematic drawing of the thin film diffractometer used at NIST (larger view 146 k).

The apparatus used for GIXR measurements is shown schematically in Fig. 1. A highly collimated monochromatic beam is formed using appropriate crystal optics. The beam is reflected off of a sample aligned in the grazing incidence configuration, and captured by a detector. An analyzer crystal placed in front of the detector decreases scatter and enhances resolution. There is a constant 1:2 ratio between the sample angle, theta, and detector angle relative to the incident beam in a reflectivity measurement. For incidence angles below the critical angle for reflection, total external reflection occurs and the reflectivity is approximately 1. For angles of incidence above the critical angle, the reflectivity falls off as -4 and the signal usually disappears within a few degrees.

Non-specular scans can be taken to determine the smoothness of a thin film interface. The initial sample alignment is the same as is described for GIXR measurements. In this type of scan, typically the detector is held at a fixed position and the sample is rocked. Only a rough surface will produce diffuse scatter from an interface, thus a distinction between interdiffusion and roughness can be made.

Thin Film Relectometry How does x-ray reflectometry work? What does it see? Figure 1 shows the geometry a simple reflectometer. Competent reflectivity measurements require an incident x-ray beam having both a narrow spatial extent (in the plane of the figure) and a small angular divergence, typically of the order of 0.01° or less. This input beam is scanned in angle with respect to the sample surface over a range of grazing angles from zero through about 6°. Reflected radiation is detected by the counter shown through a pair of slits with a small spatial extent (in the plane of the figure. The reflectivity, R, is the ratio of reflected to incident intensities. For our purposes, a reflectivity profile is obtained at fixed incident x-ray wavelength as a function of the (grazing) angle of incidence.	Figure 2. Diagram of an elementary x-ray reflectometer.
Some experimental details of higher performance reflectometers Although there are several commercial systems available for x-ray reflectometry, our instruments were mainly assembled from components at hand, or built for this application. The flexibility offered by this approach has allowed consideration of a variety of x-ray optical arrangements. The main design challenge arises from the large dynamic range of reflectivity encountered in the analysis of thin films. This reflectivity range leads to a correspondingly large range of x-ray counting rates. Since most of the important structural information is found in the region of low reflectivity, the x-ray source and beam forming optics need to aim for high incident flux on the sample reflectivity, the x-ray source and beam forming optics need to aim for high incident flux on the sample. At the same time, the rapid falloff of reflectivity with angle ( -4) means that the beam forming optics as well as the analysis optics need to have collimation profiles in which the wings of the window function are highly suppressed, i.e., fall off much faster than -4. The collimation requirements can be effectively met by carefully designed slit arrangements if the angular resolution requirements are modest. For our purposes, in order to achieve the angular resolution needed to map relatively thick stacks (~ 1 µm), multiple crystal reflections are needed. Such multiple reflection x-ray optics are conveniently realized by using channel-cut crystals, such as is illustrated in Fig. 2a where we use "four-bounce" geometry for both the preparation and analysis optics. One simple modification of the symmetric channel in Fig. 2a is realized by introducing an asymmetric initial reflection. Such an asymmetric reflection increases the angular range accepted by the collimator with a considerable gain in counting rate as in Fig. 2b. One less desirable aspect is that it also broadens the beam spatially, thereby limiting the systems utility at very small incidence angles. Still further intensity gain (with still greater spatial broadening) is realized by introducing a graded-spacing parabolic mirror as illustrated in Fig. 2c.	Figure 3. Comparison of several beam-conditioning optical arrangements offering improvements over simple slit collimators.
Figure 4. Effectiveness of counting rate linearization using a single dead time model.	High x-ray flux levels can be obtained either by combining the optical design exercises described above with a stationary anode x-ray tube, or a more powerful (and costly) rotating anode source. In either case, data rates in the region of high reflectivity rapidly exceed the counting rate capability of the usual NaI scintillation detectors and the capabilities of even the newer high speed counters that use YAP crystals. For the present, we have chosen to reduce the x-ray tube power and operate within the rate capacity of the available detector using a single dead-time correction function as indicated in Fig. 3. A simple upgrade providing automatic insertion of x-ray attenuators will allow full utilization of the available dynamic range of 108.
X-ray measurement options X-ray reflectometry (GIXR) thickness, density, etc. Diffuse x-ray scattering (GIXS) roughness spectra X-ray diffractometry (XRD) crystal structure info Grazing x-ray fluorescence (GIXF) depth profiling All are non-destructive, non-invasive, and work in air.