3D x-ray fluorescence microscopy using fabricated micro-channel arrays
x-ray optics, x-ray fluorescence, confocal, nanolithography, DRIE, x-ray microprobe, x-ray scan probe microscopy
We report the fabrication and characterization of lithographically-fabricated arrays of micron-scale collimating channels, arranged like spokes around a single source position, for use in 3D, or confocal x-ray fluorescence microscopy. A nearly energy-independent depth resolution of 1.7±0.1 µm has been achieved from 4.5-10 keV, degrading to 3±0.5 µm at 1.7 keV. This represents an order-of-magnitude improvement over prior results obtained using state-of-the-art, commercial polycapillaries as the collection optic. Due to their limited solid angle, the total collection efficiency of these optics is approximately 10× less than that obtained with polycapillaries. Three designs have been tested, with 1, 2, and 5-µm-wide channels ranging from 30-50 µm in depth and 2 mm in length.
In addition to characterizing the devices in confocal geometry, the transmission behavior of individual channels was characterized using a small, highly collimated incident beam. These measurements reveal that, despite taking no particular steps to create smooth channel walls, they exhibit close to 100% reflectivity up to the critical angle for total external reflection. Most of this reflected power is spread into a diffuse angular region around the specular reflection condition. These results significantly impact future designs of such collimating channels, since transmission through the channels via side-wall reflection limits their collimating power, and hence device resolution. Ray-tracing simulations, designed specifically for modeling the behavior of channel arrays, successfully account for the transmission behavior of the optics, and provide a useful tool for future optic design.
Confocal x-ray fluorescence microscopy (CXRF), refers to the use of two x-ray optics to resolve x-ray fluorescence from a microscopic, 3D volume in space. This approach largely overcomes an implicit limitation of traditional x-ray spectroscopy: that the detected signal may originate from multiple depths within a sample. The spatial resolution in CXRF is determined by the 3D intersection of the focus and field of view of the optics used for the incident and fluorescence beams, respectively. Because of the naturally low divergence of synchrotron sources, a variety of different x-ray optics may be used to efficiently focus the incident x-ray beam. For example, beam sizes of 1-10 µm are routinely achieved with diffractive, reflective, or refractive x-ray optics, and recently beam sizes of order 10 nm and below have been demonstrated. In contrast, the detection optic in CXRF must collect fluorescence from a point-like source. To do so efficiently it must collect x-rays emitted over a large solid angle, and direct them to a detector. Because of this constraint, all demonstrations of CXRF to date have employed polycapillaries as the collection optic.
Polycapillary optics routinely have large acceptance angles—upwards of 25º—corresponding to 1% of 4π steradians, and achieve focal sizes of ≈10 µm at 10 keV. This resolution is suitable for many areas of study; accordingly, the availability and use of confocal XRF has grown rapidly in the last half-decade. Highlights employing synchrotron radiation (SR) include applications in cultural heritage, biology and environmental science, and analysis of cometary dust. Recently, CXRF has been successfully combined with spectroscopic methods, significantly broadening its potential impact. Despite lower resolution and count rate, table-top-based CXRF has nonetheless significantly advanced the field, extending it to studies of liquid-solid interfaces, forensics, pharmaceuticals, and fusion research. Finally, the confocal geometry has also been utilized with proton-induced x-ray emission (PIXE). These results notwithstanding, the spatial resolution of polycapillaries represents a limitation of the technique, and improvements to CXRF resolution would enable many applications that are not currently feasible. This is particularly true in the “tender” regime of 2-5 keV, in which the best reported polycapillary spot size is upwards of 20 µm.
Here, we demonstrate CXRF with a depth resolution of 1.7 µm, making use of a lithographically fabricated optic as the collector. Such optics, an example of which is depicted in Fig. 1, consist of an array of rectangular channels, arranged like spokes of a wheel, all directed towards a common focal point.
The critical difference between this design and a polycapillary is the use of collimating channels, rather than reflective glass capillaries, to transmit the fluorescent x rays from the sample to detector. In the limit of zero reflection from the channels, their degree of collimation, and hence the optic’s resolution, is solely determined by their length and width, rather than the critical angle for total external reflection, as is the case for polycapillaries. A second key difference between this optic and a polycapillary is that it is effectively a 1D optic; the probe size parallel to the channel depth dimension is determined solely by the incident beam. Although the idea of using cylindrical, collimating channels as a collection optic for CXRF has been previously proposed, ours is evidently the first experimental realization of this approach.
After describing design considerations and fabrication details in section 2, we provide experimental details in section 3. Briefly, the optics are characterized both by measuring the transmission of a highly collimated beam through individual channels and by employing them in CXRF mode.
In section 4.1, we present results of transmission measurements on three optics, having nominal channel widths of 1, 2, and 5 µm.
In section 4.2, we demonstrate the application of the 2 µm optic to CXRF, and achieve a nearly-energy-independent depth resolution of 1.6±0.1 µm from ≈4-10 keV, representing a 3D probe volume of ≈13 µm3. At this resolution, the stacking sequence and approximate thickness of four distinct metal films, each ≈100 nm thick, is measured directly. The resolution and sensitivity of this optic is compared directly to those of two polycapillary optics in otherwise identical configurations.
2. DESIGN AND FABRICATION
The two critical parameters of a collection optic for CXRF are its spatial resolution r and efficiency η, the ratio of detected to emitted fluorescent photons. In the ray-optic limit, an estimate of r from simple geometric considerations is given by:
w and δ are the channel width and angular acceptance, respectively, and
f is the working distance from the front edge of the channel to the probe volume.
A key requirement for this approach to achieve both high resolution and practical working distances is that the channels act as good collimators. To do so, the walls of the channels must absorb, not reflect incident photons. Below we will show that this is not the case for walls created by deep reactive ion etching (DRIE); nevertheless we proceed here by describing the properties of ideally collimating channels. In this case, δ = 2 tan−1(w/l) ≈ 2w/l, where l is the channel length, so that the equation in above becomes r = w(1 + f /l). Thus to achieve r ≤ 1.5w, one must select f /l ≤ 1/2.
Continuing with the assumption of perfectly collimating channels, the efficiency of these optics is the total solid angle of the channels divided by 4π. An approximate efficiency is thus given by
where N and d are the number and depth of the channels, respectively. From above equation, it is clear that for a given resolution determined by w and f /l, maximizing efficiency corresponds to increasing N and d while minimizing l. In practice, the number of channels N is limited by geometric constraints involving the sample and detector.
Maximizing d corresponds to maximizing the aspect ratio of the channels. Typical aspect ratios for channels produced by DRIE are 15-20, but much higher aspect ratios have been demonstrated, up to 70:1 for 0.8µm trenches, and the ultimate technological limits are unknown. We also observe that while the efficiency increases with decreasing l, the channels must be sufficiently long that the un-etched areas between channels absorb unwanted photons, i.e. those originating on the path of the incident beam but outside the probe volume.
Specifically, we require the attenuation length α(E) « l for all desired E.
Even for perfectly-collimating channels, above equation will break down for sufficiently long or narrow channels due to diffraction. Specifically, diffraction-induced spreading will increase the interaction between the beam and channel walls, and thus the probability of absorption. To estimate the onset of this effect, we calculate a critical channel length lCR at which the diffraction-limited size of a photon entering the center of and parallel to a channel becomes equal to the channel width w. Employing the Fraunhofer limit for single-slit diffraction, the first minimum of the central lobe occurs at sin(θ) = λ/w. Setting sin(θ) ≈ w/2l yields
The quadratic dependence of lCR on w significantly constrains the ultimate achievable resolution of CXRF using a collection optic based on collimating channels. In particular, for w = 1 µm and λ = 2.5Å (E ≈ 5 keV ), lCR = 2 mm. Thus we expect Eq. 2 to be reasonably accurate provided l <lCR . But for w = 0.5 µm , lCR = 0.5 mm.
The attenuation length in silicon for 10 keV x-rays is only ≈ 0.134 mm. Thus for 0.5 µm-channels in silicon, it may be impossible to simultaneously satisfy l <lCR and l » α(E) for a practical range of energies.
As a first demonstration of this approach, we designed and fabricated three types of channel arrays in silicon, with nominal channel widths w of 1, 2, and 5 µm and length l = 2 mm. Since the reflection properties of side-walls produced by DRIE in the x-ray regime have not previously been characterized, we allowed for the possibility that the channels would not behave as ideal absorbers. In this case, one could expect high reflection efficiency up to the critical angle θc for total external reflection, so that δ = 2θC . In the x-ray regime, the critical angle is inversely proportional to photon energy, and for silicon, is approximately 3 mrad at 10 keV. Thus, a working distance f = 0.2 mm was chosen such that the resolution r for the 1-µm channels would, according to Eq. 1, still be close to 1.5 µm at 10 keV.
The arrays were fabricated using tools housed at the Cornell NanoScale Science and Technology Facility (CNF). The pattern was written as a 5X mask using the Heidelberg DWL66 Laser Pattern Generator and Direct Writer with a 4 mm write head. Among the considerations for using this tool were the triangular-shaped geometry (see Figs. 1A, C) and that the smallest feature sizes were about 1 µm. The samples were processed on 100 mm diameter n-type (1-20 Ωcm) single side polished <100> silicon wafers. For photolithography, the wafers were first primed with a 20% mixture of hexamethyldisilazane in propylene glycol monomethylether acetate (P-20), which was spin-coated onto the wafers at 5000 rpm for 30 s. Shipley Megaposit positive photoresist (SPR220-3.0) was then spin-coated on top of the P-20 layer at 5000 rpm for 30 s and baked on a hotplate at 115°C for 90 s. The pattern transfer was accomplished using the GCA Autostep 200 (λ =365 nm) exposure tool. After a post-exposure bake at 115°C for 90 s, the wafers were developed with AZ 300MIF using the Hamatech-Steag wafer processor for 60 s. This was followed by a 15 s treatment with the Gasonics Aura 1000 to remove residual photoresist in the pattern trenches. Finally, wafers were baked for an additional three hours at 90°C to remove any remaining solvent and harden the photoresist.
The channels were fabricated by employing the deep reactive ion etching (DRIE) technique using the PlasmaTherm Versaline Deep Si Etcher. This tool employs the Bosch process, consisting of alternating steps of etching with SF6 and passivation with C4F8. These steps were programmed in a loop cycle where the process ing conditions were 25 kW inductively-coupled plasma (ICP) delivered power, 2.5 kW forward power and bias voltages of 10 and 450 V during the passivation and etching steps, respectively. The flow rate of the input gases were 150 sccm for C4F8, 250 sccm SF6 and 30 sccm Ar. The back helium cooler flow was set at 1.92 sccm with a pressure of 3000 mTorr. The electrode, spool and lid temperature of the chamber were 20°C, 180°C and 135°C.
The optics described here were each etched for 180 cycles. Figure 2 shows different SEM micrographs of a resulting 2-µm channel array.
The depth and width of the channels was characterized using micrographs such as Fig. 2C. As is generally observed for DRIE, the etch rate depends on channel width, and modest side-wall etching was observed for all channels. The nominal 1, 2, and 5 µm channels had measured widths of 1.15±0.05, 2.35±0.15, and 5.7±0.2 µm, and depths of 27±0.5, 37±0.5 and 49±0.5 µm.
The optics’ x-ray properties were characterized in transmission geometry as indicated in Fig. 3A using a 10.0 keV x-ray beam varying from 0.05×0.05 mm2 to 0.1×0.2mm2.
Also, collimating slits were used to set the divergence of the incident beam in the plane of the channels to be less than that of their geometric collimation 2w/l. The optics were mounted face-down on a sample goniometer such that the handle portion of the optic (see Fig. 1) and sample holder blocked all of the incident beam not transmitted through a channel. Alignment of the optic utilized two translation axes and two rotation axes, one of which, labeled φ in Fig. 3A, is perpendicular to the plane of the optic and aligned with both the beam and the focal point of the optic. The data represented by Figure 4 were obtained at station F3 with an ion chamber.
Data in Figs. 5 and 6 were obtained at station G2 with a photon-counting point detector. Some of the data in Figure 5, described below, were obtained with a Ge (111) analyzer between the optic and detector (see Fig. 3A), providing an angular resolution of 0.02°.
Data in Figs. 7, 9 and 10 were obtained at station G1. For CXRF geometry, shown schematically in Fig. 3B, the optics were mounted in a custom-fabricated aluminum holder incorporating an aluminum shield immediately above the optic. This was necessary to block background signal from reaching the detector by passing above, rather than through the channels.
The characteristics of our channel arrays in CXRF mode were compared directly with two commercial poly capillaries from X-ray Optical Systems (XOS, Albany, NY), with working distances of 4.5 and 2.5 mm. From their test reports, the 4.5 mm optic has an angular acceptance δ of 25◦ and transmission efficiency of ≈15% at 8 keV. Similarly the 2.5 mm optic has a angular acceptance of ≈33° and reported transmission efficiency of ≈6% at 8 keV. The total efficiency of these optics is the fraction of 4π steradians captured by the optic, (1 −cos(δ/2))/2, multiplied by the transmission efficiency. Thus at 8 keV the 4.5 and 2.5 mm optics are expected to have total efficiencies of 0.18% and 0.12%, respectively.
Figure 4 shows data obtained from rotational scans about the φ axis for each of the three optics, in the experimental configuration shown in Fig. 3A. As the optic rotates, different channels become aligned with the incident beam, allowing x-rays to reach the detector. The 5, 2, and 1-µm channel-optics have 19, 49, and 99 channels, respectively. The conspicuous inhomogeneities in intensity through the channels arise entirely from errors in the mask, resulting in un-etched areas, specifically the lettering visible in Fig. 2A, between the channels and detector. Apart from this, the channels show nearly uniform transmission.
Figure 5 shows scans of only the center-most channel of the same three optics as in Fig. 4. Each plot shows data from two scans, obtained with and without a Ge analyzer as shown in Fig. 3A. Points represent measured data, while the lines are the results of simulations described below. Scans obtained with the analyzer in place measure only x-rays that exit the optic parallel to the incident beam. Clearly, this includes x-rays that go straight through the optic, corresponding to the triangular-shaped peaks in the center of each scan. It also includes x-rays that experience an even number of specular reflections from the channel walls, clearly visible as side-lobes in Figs. 5A-B. We note that the lobes for each optic have maxima at φ values at which the incident beam illuminates the upstream half of one wall of a channel. At this angle, all of the specularly- reflected x-rays will strike the downstream half of the opposite side-wall and, if reflected, exit the downstream end. This value of φ is twice the angle at which the directly-transmitted beam is occluded by the channel, i.e. where the triangular-shaped peak of the directly-transmitted beam drops to zero.
Data represented by circles in Fig. 5 was obtained with the Ge analyzer removed from the system, so that the detector captured all x-rays that exit the channel, regardless of angle. The difference between the two data sets arises from scattered, or diffusely-reflected photons from the channel walls. That the integrated intensities of the reflected photons is comparable to or larger than the directly-transmitted beam for all three optics means that the channel walls are relatively efficient reflectors, rather than absorbers. More specifically, the data show directly that the angular acceptance of the channels is much larger than their geometric collimation. Instead, the angular acceptance of all three devices is approximately 6 mrad, which is close to 2θc for silicon at 10 keV.
To extract additional information from Fig. 5, we first reiterate that the divergence of the beam for these measurements was selected to be less than the geometric collimation of the channels. Specifically, for these data, the beam (in the plane of the channels) was defined by two, 0.1 mm slits, approximately 450 mm apart. This gives an incident-beam divergence of 0.22 mrad, compared to 0.5 mrad for the 1-µm channels. Because the beam divergence is smaller than the channel collimation, the channels do not further collimate the beam, and the peak height in each plot in Fig. 5 represents the total flux incident on the channel. As a result, an approximate value for the probability of specular reflection, RS, is obtained by equating the height of the lobes in Figs. 5A-B to RS2. The lobes in Fig. 5A have an approximate height of 0.15, corresponding to RS = 0.39 at φ = 1.44 mrad, while the lobes in Fig. 5B give RS = 0.22 at φ = 2.4 mrad. Figure 5C does not exhibit lobes, indicating that the reflectivity of these channels is small at the angle φ = 6 mrad, which would correspond to the same condition where the lobes occur in Figs. 5A-B.
For a more direct measure of RS, we take advantage of the fact that the 5-µm channels are wide enough to allow most specularly-reflected beam to exit the channels well beyond θc. Figure 6 shows a traditional reflectivity scan through a single, 5-µm channel, performed by scanning the detector by twice the angle φ of the channel, with the Ge analyzer in place. For w = 5 µm, the incident beam illuminates an entire wall of a channel until φ = 2.5 mrad, at which angle the downstream end of one channel wall will just enter the shadow of the upstream edge of the opposite wall. If the reflectivity were constant, the detected signal would drop linearly above this angle, reaching zero at φ = 5 mrad. Instead, the intensity is nearly constant from φ =1–3 mrad, and shows a steep drop near φ = 3 mrad, clearly corresponding to θc. Additionally, at φ = 2.5 mrad (again assuming w = 5µm), the intensity in Fig. 6 is an exact measure of RS. The value RS = 0.3 is in approximate agreement with the conclusions based on Fig. 5.
To corroborate our interpretation of Fig. 5, and to model new channel designs, we developed software to simulate the performance of channel arrays. A simple, Monte Carlo approach was employed to simulate photon interactions with the channels. When a photon intersects a channel wall, the algorithm uses a series of random numbers and parameterized distribution functions to evaluate the outcome. The program decides, first, whether the photon is reflected or absorbed and, if reflected, whether the reflection is specular or diffuse. Finally, if diffuse reflection occurs, the program selects a reflection angle based on a distribution of local surface slopes. The input parameters are θc, the attenuation length α, and distribution widths σR, σsp σslope, for absolute and specular reflection probabilities, and the local surface slope, respectively. An additional parameter, RS,max corresponds to the maximum probability for specular reflection.
The solid lines in Fig. 5 result from the simulation described above. In analogy with the experimental data, each plot shows a single simulation, evaluated both with and without an analyzer for the exit beam. The lines show good agreement with the data, including the overall shape of each of the peaks and side-lobes. Most input parameters are identical for the three simulations: θc = 3.2 mrad, σR = 0.8 mrad, and σsp = 1.5 mrad. Similarly, a value for α of 0.1 mm for all three simulations was chosen as the approximate attenuation length for silicon at 10 keV.30 For optimal agreement, values of σslope were 2 mrad, 2.2 mrad, and 2.5 mrad for the 1-, 2-, and 5-µm channels, respectively. Also, RS, max was 0.3 for the 1-µm channel, but 0.22 for the 2- and 5-µm channels.
The width of the triangular-shaped peaks in Figs. 5 is a direct measure of the projected channel width perpendicular to the propagation direction. This measurement is thus more reliable than the SEM measurements described in section 2, which only measure the dimensions of the end of a channel. Nonetheless, from the simulations, the actual channel widths wm of the three optics are evidently 1.35, 2.5, and 5.5 µm, in reasonable agreement with the SEM measurements.
Having characterized the channels for each channel array, we can calculate the expected resolution of the three different optics with the aid of Eqs. 1. From Figs. 5, the angular acceptance δ (FWHM) of the 1-, 2-, and 5-µm optics are ≈ 4.8, 5.6, and 6.2 mrad. The working distance f is 0.2 mm in each case giving r = wm + δf /2 =1.85, 3.05, and 6.15 µm.
If the channels were perfect absorbers, we could calculate the efficiency η of each of the optics with Eq. 2, using the channel widths and depths found above. Doing so results in ideal efficiencies of 0.006%, 0.0075%, and 0.0084% for the 1-, 2-, and 5-µm optics, respectively. However, in view of Fig. 5, we must modify Eq. 2 to account for non-ideal channels. Radiation from a point source will evidently reach the detector provided it both enters a channel and is within the channel angular acceptance δ. The 1-, 2-, and 5-µm channels, each 0.2 mm from the source, correspond to angular apertures of 5, 10, and 25 mrad, respectively. Since the angular acceptances δ from Fig. 5 are all less than or nearly identical to these values, we use the values of δ, rather than the channel apertures, to calculate the channel efficiency. Replacing w/(f + l) in Eq. 2 with δ, we have
Using this equation, we find efficiencies for the 1-, 2-, and 5-µm optics of 0.046%, 0.037% and 0.02%, respectively. The difference between these efficiencies and those calculated for ideal channels corresponds precisely to the increased angular acceptance of the channels due to diffuse reflection.
4.2 Comparison of Spoked Channel Arrays with Polycapillaries
For a direct comparison of our channel-array optics and polycapillaries, we performed side-by-side measurement of resolution and flux in CXRF mode. To demonstrate the improved resolution of the arrays, an incident beam close to 1 µ in size was required. Single-bounce, monocapillary optics are fabricated at CHESS and frequently employed to achieve beam-sizes of 10-50 µm in diameter. In this case, a custom optic, was designed and fabricated to obtain a much smaller beam. The optic is 2 cm in length, with a tip-to-focus distance of 12.2 mm and output divergence of 7.8 mrad. The beam-size at the sample positon was determined by detecting fluorescence intensity from a knife edge scanned horizontally and vertically through the focus. As shown in Fig. 7, these scans give a beam size of of 2.7×2.8 µm2. To obtain this spot size, both the size and divergence of the incident beam on the capillary was reduced from the full beam available at G1, resulting in a typical incident intensity in the focus of 6.6×108 photons/s.
CXRF alignment was performed using a sample consisting of four thin-metal films deposited on a silicon wafer, each having a nominal thickness of 100 nm. Because the illuminated area just under 3 µm in diameter, the 2-µm channel array was chosen for comparison to the two polycapillaries described in section 3. Figure 8 shows top views of the aligned CXRF setup with the same monocapillary and sample, but with three different collection optics.
We note that the channel array in the left-most image of Fig. 8 appears to be touching the sample. In fact there is a small but finite gap when the channel array is aligned, as verified by the fact that it is possible to scan through the ideal focus of the optic by ≥14 µm (see Fig.10B below).
Figures 9 shows raw fluorescence data obtained from depth scans (perpendicular to the sample surface) using the three configurations shown in Fig. 8. Because the metal films are very thin compared to the incident beam or optics’ field of view, they constitute measurements of the depth resolution dr of each system, which is a conventional metric in CXRF geometry. Each scan shows four pairs of K-lines from the four metals in the sample: titanium, copper, zinc, and chromium. Data from the channel array also shows non-localized peaks at ≈ 2.95 keV and 9.9 keV. These peaks correspond to background air-scattering (Thompson scattering, Compton scattering, and Argon fluorescence). Most, but not all such scattering is blocked from reaching the detector by the optic mount; however a small amount reaches the detector by passing over the optic. Weak peaks near 2.8 keV and 3.7 keV are Si escape peaks arising from the Ti and Cr Kα lines at 4.5 and 5.4 keV, respectively. Finally, the peak at 1.7 keV corresponds to Kα fluorescence from the Si substrate.
The gray scale for each plot in Fig. 9 are scaled differently to maximize contras, but the vertical scales of all three plots are equivalent. This representation illustrates the dramatic improvement in resolution using the channel array. The vertical extent of the peaks is approximately 20 µm for the 4.5 mm polycapillary, to 10 µm for the 2.5 mm polycapillary, to close to 2 µm for the channel array. Thus the channel array gives rise to an order-of-magnitude improvement in dr. An additional advantage of the channel arrays compared to the polycapillaries is manifested by the fact that dr decreases with increasing energy in Figs. 9B-C. This is due to the energy-dependent resolution of the polycapillary, and is evidently not present or greatly reduced for the channel array. Finally, we note that the Si Kα peak is far more conspicuous for the channel array data than the polycapillaries. This is likely due to the fact that the distance between the sample and detector for the channel array is only 5 mm, compared to upwards of 2 cm for the polycapillaries, resulting in significantly less attenuation by air.
Further inspection of Fig. 9A indicates slight, vertical displacements among the different peaks, corresponding to height displacements among the layers. To illustrate this more clearly, Fig. 10A shows vertical projections of the thin-film Kα lines in Fig. 9A. The curves vary only slightly in FWHM, from 1.7 µm to 1.5 µm. Although this resolution is much larger than the nominal, 100 nm thickness of the films, it is sufficient to determine that the sequence of the films is Ti/Cu/Zn/Cr from top to bottom.
We can compare these measurements with the expected outcome based on the section 4.1. In that section, we calculated an expected resolution of individual channels in the 2-µm array of 3 µm. This represents the field of view of an individual channel, whose intersection with the incident beam constitutes the volume probed by that channel. The actual probe volume is the sum of overlapping probe volumes from all the channels. Finally, dr corresponds to half the projected length of this probe volume onto the scan direction. Defining a as the horizontal size of the incident beam, we can approximate dr as dr = 0.5 × √(r2 + a2). Using r = 3 µm and a = 2.7 µm gives dr = 2 µm. Although this agrees reasonably well with the measured value of 1.6±0.1 µm, we conclude that one or both of our values for r and a are overestimates. Reducing either of these values from ≈3 to 2 µm would reduce dr to 1.7-1.8 µm.
Figure 10B shows the Si Kα intensity from the same scan, as well as a fit to these data to an exponentially decaying error function. This is the theoretical shape of fluorescence as a function of depth, and the fit yields a resolution at 1.7 keV of 3±1 µm. Thus the resolution at 1.7 keV is measurably larger than that at 4.5 keV and above, yet still small compared to the polycapillary resolution. The decay constant of the fit is 9±1.5 µm, which corresponds to self-absorption of Si Kα radiation by the substrate. Because the sample is at an angle of 37◦ from the incident beam, this decay constant must be divided by cos(37◦) to obtain the attenuation length α. Doing so yields 11.3 µm, which is in excellent agreement with the theoretical value of 11.5 µm.
Figure 11 compares both the resolution and efficiency of three optics presented in Fig. 9 as a function of energy. Figure 11A quantitatively illustrates that the resolution obtained using the 2-µm-channel array is significantly smaller than that obtained using polycapillary optics, particularly at low energy. In addition, the CXRF resolution using a channel array is essentially constant from 4.5 to 10 keV.
Figure 11B compares the peak intensity as a function of energy for the three optics. In this plot, counts have been normalized to an absolute integrated incident flux of 6×108 photons. To interpret these data, recall that the expected, total efficiency of the 2.5 and 4.5 mm polycapillaries (see Sec. 3) are estimated to be 0.12% and 0.18% at 8 keV, respectively, while that of the 2-µm channel array is 0.037%. Thus the intensity collected by the two polycapillaries should differ by a factor 1.5. Instead, we find that the intensities of the two polycapillary optics are essentially equivalent, suggesting one or more small errors the quoted values for angular acceptance or single-photon transmission efficiency for the two optics.
The intensity collected by the channel array is expected to be 0.18%/0.037% = 5× less than that of the 4.5 mm polycapillary, but Fig. 11 shows that, near 8 keV, this ratio is ≈15. Part of this difference may arise from the fact that the projected size of the incident beam on the sample is larger than the channel-array resolution.
Because the sample is tilted by 37◦ from the incident beam (see Fig. 8), the 2.7-µm beam appears to be 3.6 µm on the sample when viewed by the channel array. Since the field of view of the channel array is estimated to be 3µm, it should detect fluorescence from 80% of the illuminated spot. Moreover, if r is closer to 2 µm—small enough to account for the measued dr of 1.7 µm—then the channel array only sees 55% of the illuminated spot. Correcting for this reduced field of view corresponds to increasing the intensity measured by the 2-µm channel-array in Fig. 11 by a factor 1.2-1.8. Doing so would reduce the efficiency ratio of the two types of optics to as little as 8.3. We speculate that the remaining discrepancy between this and the expected ratio of 5 is due to cumulative uncertainties in our estimates of polycapillary efficiency and channel geometry. Characterization of future channel array designs will employ precisely-calibrated test samples, allowing efficiencies to be placed on an absolute scale and determined with greater precision.
In this article, we have described the fabrication, characterization, and application of a new type of optic allowing 3D scan-probe x-ray fluorescence with resolution on the micron scale. The optic consists of arrays of channels in silicon, created using lithographic techniques, which direct x-rays from a point source towards a detector. We have successfully demonstrated the application of this optic to CXRF, achieving a depth resolution of 1.7 µm from 4-10 keV, and 3 µm at 1.7 keV.
The 2-µm channel arrays described here had an efficiency approximately 10× less than that of the two polycapillaries with which they were compared at 8 keV. Despite this decreased efficiency, we note that the measured count rates in CXRF mode are very reasonable: Fig 11B shows count rates of several hundred photons from approximately 100 nm metal films and an incident flux of 6×108 photons. Considering that microprobe beamlines at 3rd generation synchrotron sources routinely generate flux densities of upwards of 1011 photons/s in a similarly sized spot,31 one can imagine count rates of 105 counts/s from similar samples, allowing 3D scan-probe work to be performed in reasonable times at the 1 µm3 scale.
Nevertheless, improvements in the efficiency of channel arrays would significantly impact the minimum detectable concentration levels, and therefore the applications for CXRF at this length scale. The channel dimensions of the optics described here have aspect ratios of 21, 15, and 9 for the 1-, 2-, and 5-µm channels. Because DRIE technology is still very much in development, significant improvement in the aspect ratio of trenches, and hence optic efficiency, may be possible.
Among the key findings of this work are that straight channels created using DRIE act not as ideal absorbers, but rather as diffuse reflectors that reflect nearly 100% of the incident beam that enters channels up to the critical angle θc for total external reflection. As a result, our demonstrated resolution was only possible by employing a working distance of just 0.2 mm. Because the optics are also 0.2 mm wide at their entrance, this leads to an impractically-small working distance between a planar sample and the corner of the array. Modifications to the design and/or fabrication techniques for the channel walls should greatly increase their absorbance, allowing larger working distances to be achieved without loss of resolution.