X-ray reflectivity with a twist: Quantitative time-resolved X-ray reflectivity using monochromatic synchrotron radiation

X-ray reflectivity (XRR) is a well-known method for determining the structure of interfaces and thin-films with both high accuracy and atomic-scale precision.¹ Like many x-ray scattering methods, XRR is particularly attractive for in-situ studies because it is a remote probe and can be performed in the presence of environments including atmospheric pressure and liquids.² On the other hand, applications of XRR to time-resolved processes are limited. Because XRR is typically performed by scanning both the sample and the detector,³ a single scan usually requires several seconds or minutes,^4,5 depending on the details of the setup and scan parameters.

Although many variations of XRR, referred to broadly as quick XRR (qXRR),⁶ have been developed to overcome this limitation, they generally place severe constraints on the source and/or sample, which make them incompatible with certain applications. For example, one approach to qXRR, known as convergent beam x-ray reflectivity (CBXR),^7–9 permits the use of monochromatic radiation but generally requires a highly diverging incident beam and thus cannot exploit the high intensity, but also highly collimated, beams provided by synchrotron sources. Recently, we demonstrated an approach to CBXR that makes use of a polycapillary (PC) optic to overcome this restriction and permit the use of monochromatic synchrotron radiation.¹⁰ Although this method greatly broadens the potential scope of qXRR, our implementation, similar to other implementations of CBXR, is limited due to the overlap of the sharp XRR signal with the diffuse scatter from the surface.

Recently, making use of a lab-based source, Voegeli et al.¹¹ demonstrated that the background from diffuse scatter can be reduced, improving the resolution obtained with CBXR, by rotating the sample such that the surface normal is out of the plane of the incident beam. Here, we demonstrate the combination of this low-background geometry with our PC-based method¹⁰ at the Cornell High Energy Synchrotron Source (CHESS). We demonstrate that we can record, on a single detector image, a portion of the reflectivity curve in good agreement with traditional Parratt XRR and with the time resolution as low as 10 ms. We also demonstrate this technique by showing qXRR during the annealing of an Al/Ni multilayer (ML) with detector framing at 9 Hz.

The qXRR measurements were performed at CHESS, primarily the G3 station using an 11.4 keV beam.¹² The experimental geometry is shown schematically in Fig. 1(a). A PC x-ray optic¹³ is used to create a converging fan of radiation in the horizontal plane, with an angular range of Δμ ≈ 2.5°. The sample is placed at the focal point of this beam. For these experiments, everything upstream of the sample is identical to that described in Ref. 10 with the exception of a vertical slit placed just upstream of the sample, added to reduce the vertical divergence of the incident fan out of the PC. The sample normal, $n̂$⁠, is tilted out of the plane of the incident beam fan by angle ψ = 90° − χ so that the incident rays strike the sample with a range of incident-beam angles, $Δα=Δμ sin (χ)$⁠, relative to the sample surface and a range of azimuthal angles, $Δϕ=Δμ cos (χ)$⁠, about $n̂$ [see diagrams at the upper and lower right of Fig. 1(a)]. Experimentally, this is achieved by using a goniometer (shown schematically in supplementary material Fig. S3) that comprises two rotational stages: a semicircle (Huber 5202.40) with a horizontal rotational axis, acting as the χ degree of freedom, on top of a rotation stage (Huber 410) with a vertical axis, the θ degree of freedom used to set $α0=arcsin[sin θ sin χ]$⁠. For this work, we use χ = 45°. The two stages are aligned with each other such that the center of rotation of the upper stage was along the rotational axis for the lower stage. These two stages are then aligned using a set of linear stages, vertical and transverse to the beam, such that the focal point of the focused beam is coincident with the center of rotation of the goniometer. The sample is mounted such that the surface is parallel to the χ rotation axis. A linear translation stage is used to move the sample surface to the center of rotation. Following the usual conventions, we define α and β as the angles between the sample surface and each incident beam vector, k_in, and exit beam vector, k_out, respectively, and their difference as Ω = β − α. The central ray of the incident fan, k₀, is at angle α₀ from the sample surface. An area detector is placed downstream to collect the diffracted intensity. For these measurements, we used a low-noise, photon counting area detector (Dectris Pilatus 300k), placed around 1.8 m downstream of the sample (D_SD). It is positioned by means of vertical and horizontal linear translation stages. Figure 1(b) shows a portion of a detector image. ν and δ refer to the horizontal and vertical scattering angles measured from k₀, respectively. Given that χ = 45°, the specular condition is met for all rays in the incident fan when $νspec=2α0/2$⁠. The specular reflections, which form the bright vertical feature on the detector, appear 90° from the plane of the incident fan (spillover from which is seen on the lower right of the detector image).

As discussed by Voegeli et al.,¹¹ this geometry separates the specularly reflected beam from the brightest portion of the diffuse scattering. This diffuse scatter may emanate either from surface roughness¹⁴ away from Bragg peaks or crystalline disorder (such as Huang scatter¹⁵) around Bragg Peaks. At the critical angle, there will be additional enhancement of the diffuse scatter due to dynamical effects. In all cases, this diffuse scatter is predominately confined to planes, which we will refer to as scattering planes, defined by the incident beam vector and $n̂$⁠. This effect is illustrated in Fig. 1(c): the image is a sum of three separate measurements obtained with the same sample and detector geometry as in Fig. 1(b), but with a collimated incident beam at three different μ angles. This image thus simulates a single, qXRR snapshot obtained with three, discrete converging beams rather than a continuous fan. As in Fig. 1(b), the specular reflections are along a vertical line. Emanating from each of the specular features, along a line perpendicular to the sample horizon, is a streak of diffuse scatter which falls along the scattering plane belonging to each k_in. The diffuse scatter in Fig. 1(b) is composed of a continuum of these intense streaks of diffuse scatter. The origins of these features are described in detail in supplementary material Sec. S1 although in short there is a dilatation of the q resolution along the scattering plane versus perpendicular to it. For instance, if we consider incident vectors with α = 1°, the resolution along the scattering plane is nearly 60 times higher than that perpendicular to the scattering plane. In our implementation, given the width of the specular features, at this angle, only diffuse scatter emanating from in-plane correlation lengths of less than ∼36 Å will produce intensity outside of these scattering planes; in general, this intensity is negligible.

In order to extract XRR curves from images, such as Fig. 1(b), we make use of the above observation. We ignore contributions to scattering which do not fall along the scattering plane corresponding to their respective incident ray. Specifically, we assume that each 45° line parallel to those in Fig. 1(c) corresponds to a unique value of α and a range of values of Ω. Then, every point on the detector can be addressed with a unique q_z and q_y based on its coordinates, d_h, horizontal, and d_v, vertical, relative to the location where k₀ intercepts the detector plane (diffraction is in the positive d_h and d_v directions)

where

d_h,spec is the horizontal specular position on the detector [$dh,spec=DSD tan (νspec)$⁠, constant for each image] and D_SD is the distance from the sample to the detector plane.

The process of qXRR extraction begins by normalizing the detector images to the average incident intensity (for time resolved data). For some measurements, a Si wafer was used to attenuate the scatter on a portion of the detector, extending its effective dynamic range; if applicable, we then correct for this partial attenuation. Images are additionally corrected for the variation in intensity as a function of α. This variation was measured by imaging the direct beam from the PC. The correction was performed under the assumption that 45° lines on the detector have a constant α angle as described above. Using the algorithm in Ref. 16, we then re-map the data from linear detector coordinates to 2α and Ω space according to Eqs. (3) and (4) (see supplementary material Fig. S2). In this coordinate system, the diffuse streaks are perpendicular to the specular direction. This is a more convenient coordinate system to work in, as opposed to remapping to q_z and q_y space, as the detector remaps to a relatively equally spaced grid. For data where there is a lot of background or diffuse scatter, background subtraction is performed by applying a linear fit to the background, line-by-line, along the specular direction. Finally, the reflectivity curve is generated by summing across the width of the specular feature, and 2α is converted to q_z.

To demonstrate the accuracy of our measurement method, we show XRR from two different samples, by both the traditional Parratt XRR and the qXRR method described here. The Parratt reflectivity measurements were taken at the CHESS G2 station with the diffraction measurement done in the vertical direction. X-rays are fed to the station from a Be side bounce monochromator with a 0.1% ΔE/E bandpass, and the beam is slit down to <0.1 mm in the vertical direction. Reflectivity was recorded using a 1D strip detector (Dectris Mythen 1 K) with the detector strip in the vertical direction to enable background subtraction. Figure 2(a) shows reflectivity from a trilayer film, grown by the optics group of the Advanced Photon Source, containing nominally 200 Å of Mo, 200 Å of B₄C, and a capping layer of 67 Å of Mo. We show qXRR collected over 4 decades of integration time, from 10 s to 10 ms. The Parratt XRR was fit to a model using GenX.¹⁷ It suggests that the layers are 195, 250, and 33 Å, respectively. For the 10 s and 1 s curves, there is good agreement between the two XRR curves other than in the lowest intensity portions of the curves in the troughs between fringes. When collecting the 100 ms and 10 ms data, a piece of Si wafer was placed in front of part of the detector in order to extend its effective dynamic range by attenuating the brightest part of the diffracted intensity. These curves have some additional background although significant noise is only found at the lowest intensity parts of the 10 ms curve.

In Fig. 2(b), we show XRR from a 10 bilayer thick Al/Ni ML film on SiC. The MLs were deposited in a custom deposition system.¹⁸ The films were grown from an Al 1100 alloy target and a Ni target with 7 wt. % V. The MLs were fabricated with the aim of achieving a 1:1 atomic ratio of Al to Ni-V which results in a 3:2 thickness ratio for the alternating layers. The films were grown on 6H-SiC wafers with an on-axis c-plane surface. Again, the qXRR with χ = 45° agrees well with the Parratt reflectivity. For this film, with a bilayer thickness of 105 Å, the qXRR has a resolution sufficient to capture the Kiessig fringes throughout the range of the measurement. There are some differences in the absolute intensity of some of the Kiessig fringes past the 2nd ML peak although the intensity of the ML peaks is well captured. Between the 3rd and the 4th ML peaks, the Kiessig fringes are still visible but are damped due to the higher background. For comparison, qXRR at χ = 90° is also shown (extraction of qXRR in this geometry is described in detail in Ref. 10). Again, the qXRR matches the Parratt XRR through the 2nd ML peak. At higher q_z, there is a large amount of additional signal intensity due to diffuse scattering. Between the 3rd and the 4th ML peaks, the Kiessig fringes are largely inseparable from the noise. Because of the geometry, the measurement at χ = 45° does not suffer from the same degradation of the XRR signal. An additional example of this effect is shown in supplementary material Fig. S5. With changes in the experimental implementation, such as using an optic with a shorter WD, improvements including reducing requirement on the incident beam width, increasing Δα, and improved q_z-resolution can be realized.

To demonstrate the time resolved ability of this technique, we measured qXRR from Al/Ni MLs on SiC while heating from room temperature to above 575 K at rates of up to 90.9 K/s. This was achieved by incorporating a custom designed low thermal mass heating stage into the goniometer (see supplementary material Fig. S3). The heater itself is an aluminum nitride-based heating plate with output of up to 580 W at temperatures up to 673 K. The heater was mounted in a Macor ceramic block. The samples are held onto the heater by 316 stainless steel clips, which are insulated from the sample by pressed mica sheets. The clips are separated from each other by about 7 mm. A foil thermocouple is placed between the sample surface and the mica insulation on one side to measure the temperature of the film. Al and Ni have a negative enthalpy of mixing, and therefore, when the film is sufficiently hot, the films intermix relatively rapid. This intermixing can be readily measured by XRR. Figure 3(a) shows the evolution of the qXRR as a function of time during the heating, and Fig. 3(b) shows the intensity of the 1st ML reflection, I, and temperature, T, as a function of time, t. Frames were recorded with an integration time of 100 ms with the detector framing at 9 Hz. As the sample is heated, there is a loss of intensity of the ML peak due to weakening of the periodicity of the film and therefore the Fourier amplitude. It should also be noted that there is no change in the frequency of the Kiessig oscillations throughout the measurement since there is little change in the thickness of the film. There is some change, however, in the shape of the qXRR curves—for instance, the change in the slope between the 2nd and the 3rd ML peaks at 625 K. We attribute this to the formation of a surface oxide, resulting in a low frequency Kiessig oscillation. Only by collecting XRR curves over a range of q_z-values can we accurately measure the intensity of the ML peaks or visualize the changes to the XRR due to oxidation. XRR with this type of time resolution can only be performed using a synchrotron based method of qXRR.

By looking at I(t) over time, we can extract the diffusivity. DuMond and Youtz¹⁹ derived an equation relating the relative intensity of a ML reflection to the interdiffusion constant, $D̃$⁠, during annealing at a constant temperature

Here, Λ is the bilayer spacing and I₀ is the initial intensity. We can apply this equation to our measurements during heating by using its derivative form,^20,21

treating each point during heating as an infinitesimally short isothermal diffusion period. To apply a derivative to relatively discrete data, we applied a smoothing spline²² (P = 0.99) to the extracted I(T). The resulting interdiffusion constants are plotted in Fig. 3(c) as a function of temperature. As seen in the plot, at low temperatures, the diffusivity has an Arrhenius relationship with temperature. Fitting this low-temperature region gives an activation energy, E₀, of 34.0 kJ/mol. We attribute the deviation from Arrhenius behavior at higher temperatures and longer times to a decrease in the rate of intermixing as the system approaches equilibrium and the concentration gradient between layers decreases. This effect should be mitigated, increasing the accuracy of the measurement, by increasing the bilayer thickness or increasing the temperature ramp-rate, maintaining the concentration gradient through higher temperatures. We then repeated the previous measurement 4 more times with a range of heating rates down to 34.5 K/s and found the results to be relatively consistent regardless of the ramp rate (the data can be found in supplementary material Fig. S6 and Table S1). The average E₀ was 36.3 ± 2.50 kJ/mol. Reference 23 has a table of experimentally measured E₀ values obtained using a variety of methods by a variety of research groups; they vary from 17.4 to 523 kJ/mol.

In summary, we have demonstrated an improved geometry for qXRR, with data quality suitable for quantitative analysis at acquisition times reaching 10 ms. We then applied this approach to the study of intermixing in metal-metal nano-scale MLs. With a time resolution of 100 ms, we recorded XRR curves during annealing of the MLs and were able to generate Arrhenius curves for each reaction.

See supplementary material for additional calculations, schematics, and data. A detector movie showing a change in the qXRR as a function of χ is also provided.

This research was funded by and conducted at the Cornell High Energy Synchrotron Source (CHESS) which is supported by the National Science Foundation under Award No. DMR-1332208. The authors thank the CHESS technical staff for their assistance, particularly, J. Houghton, C. Bagnell, J. Hopkins, and E. Edwards for assisting in constructing components of the experimental set-up. We thank R. Conley and A. Macrander (Advance Photon Source) for growing the tri-layer film. We also thank T. Hufnagel (Johns Hopkins) for his useful discussion and loaning us proof-of-concept films.