Gerardo
Gamez
*,
Damian
Frey
and
Johann
Michler
Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, 3602, Thun, Switzerland. E-mail: gerardo.gamez@empa.ch; Fax: +41 33 2284490; Tel: +41 58 7656201
First published on 7th November 2011
Glow discharge optical emission spectroscopy (GDOES) has been recognized for allowing direct solid sample elemental analysis with high depth resolution. However, the lateral resolution it affords has been historically restricted to some millimetres or the diameter of the sputtered area. Recently, it was shown that one can obtain laterally resolved information from within the sputtered area by operating the discharge in pulsed power mode. The newly available data dimensions require a new approach to the collection of the GDOES signal with lateral (to recover X and Y positions), spectral (to qualify and quantify elemental information), and temporal resolution (to improve lateral resolution and allow depth profiling). Previous studies have utilized spectral imagers of whisker-broom and staring geometries. In this study we characterize the advantages and disadvantages of using a push-broom geometry hyperspectral imager for GDOES elemental mapping. The results show that the higher light throughput of the push-broom geometry allows faster image acquisition times, compared to other spectral imaging systems with the same components, and thus maintain depth resolutions below 10 nm.
However, recently it was found that one can get laterally resolved information from within the sputtered area of the sample. Hoffman and Ehrlich showed that the lateral profile of the glow discharge emission from heterogeneous samples is not homogeneous.1 In this way, it was clear that the emission from the discharge can keep some kind of “memory” of the origin of the sputtered atoms from the sample. Webb et al. showed that by operating the glow discharge in pulsed DC mode it is possible to obtain laterally resolved information from within the sputtered area.2 Gamez et al. showed this could also be accomplished with pulsed RF discharges and demonstrated the first application of the technique for analysis of proteins on blotting membranes.3
Meanwhile, it is evident that the newly available data dimensions require a new approach to the collection of the GDOES signal. The requirements are to have lateral resolution to recover X and Y position, spectral resolution to qualify and quantify elemental information, and temporal resolution to improve lateral resolution3 and allow depth profiling. Hence, this technique requires multi/hyper-spectral imaging. Previous studies have utilized spectral imagers of whisker-broom and staring geometries.1,2 In the whisker-broom configuration, one collects the light coming from one point of the object (the glow discharge) which is passed through a light dispersion system to obtain the spectral information. The collection point is then rastered throughout the object to get the full image. When using a monochromator, one has to scan in two spatial dimensions and one spectral dimension to get the full picture; when using a spectrograph, one still has to scan in two spatial dimensions. This geometry affords very high light throughput but it is very time consuming. On the other hand, in the staring geometry the object is imaged onto a 2D array detector while the collected light is passed through a bandpass filter. The two spatial dimensions are obtained simultaneously but multiple spectral information can only be obtained by using several filters sequentially or by using a dispersion system as a filter, e.g.monochromator, and scanning the spectral dimension.
In this study we characterize the utility of a push-broom geometry hyperspectral imager for GDOES elemental mapping. The push-broom configuration is analogous to the whisker-broom but it uses a spectrograph with a 2D array detector that allows collection of the spectral dimension and one spatial dimension simultaneously. In addition, the high light throughput of the whisker broom configuration is kept while only one spatial dimension has to be scanned to obtain the full picture. A comparison of the advantages and disadvantages of this geometry against others is discussed.
Fig. 1 Schematic of push-broom hyperspectral imaging system for GDOES elemental mapping. For details please refer to Experimental section in the text. |
The collection optics consist of two triplet lenses to minimize chromatic aberrations (CaF2/fused silica/CaF2, 135 mm effective focal length, f/6, Edmund Optics Ltd, UK), with a typical chromatic shift of 0.55 mm over the spectrograph's spectral window in the UV region and 0.07 mm in the Vis-NIR region, and a broadband metallic mirror (Newport Corporation, USA) with >90% reflectivity from 200–650 nm. The first triplet lens (L1) serves to collimate the light coming from the GD source. The second triplet lens (L2) serves to focus the light onto the entrance slit of the spectrograph. The mirror (M1) allows positioning the axis of the focusing lens and the axis of the entrance slit at 90° from each other. Both focusing lens and turning mirror are mounted on a motorized stage such that the image can be scanned through the entrance slit without having to move the spectrograph or the source, thus allowing push-broom scanning in a practical manner. The stage motor (MTS25/M-Z8, Thorlabs Ltd, UK) has a maximum velocity of 3.0 mm s−1, maximum acceleration of 4.5 mm s−2, bidirectional repeatability of 1.6 μm, and backlash <6 μm. It is equipped with a Hall effect encoder feedback where the linear displacement of the lead screw per encoder count is equivalent to 29 nm. The imaging system was characterized with an Hg(Ar) pencil style calibration lamp (Oriel Instruments) and a USAF 1951 negative resolution target on fused silica substrate (Edmund Optics Ltd, UK). A deuterium lamp/tungsten–bromine lamp combination continuum source (LLC2, Lambda Scientific Systems, Inc., FL, USA) was also used for spatial resolution characterization and to perform flat field correction. WinSpec32 software (Roper Scientific, USA) was used to record the images for the spectral and spatial characterization of the imaging system. A LabVIEW program (National Instruments Corporation, Austin, TX, USA), described below, was developed for the acquisition automation, display and analysis of hyperspectral cube images.
To compare the systems one can determine the geometric entendue (G), or geometric extent, of each system to describe the light collecting capabilities. In short, the entendue is a limiting function of light throughput based on the area of the source and the solid angle (for further information about geometric entendue please see ref. 4–7). The G of the system will be limited by the component with the lowest geometric entendue which in the case of the whisker- and push-broom configurations, with the components herein, is the triplet lens. The G of the lenses can be approximated by G ≈ As × AL/DLS, where As is the area of the entrance slit, AL is the illuminated area of the lens, and DLS is the distance from the lens to the entrance slit. In the spectrograph the area of the slit is equivalent to the area of one camera pixel (0.0256 × 0.0256 mm, when binned 2 × 2) which is the same for both whisker- and push-broom configurations to maintain the same spectral and spatial resolution. The effective diameter of the lenses is 22.5 mm and DLS is the same as the focal distance of the lens. In the case of the staring geometry with a monochromator as a filtering device AL is equivalent to the area of the entrance slit because this is the component acting as the limiting aperture stop. The width of the slit would be 0.0256 mm, to keep the same spectral resolution, but the height can be the maximum allowed by the system which is 8 mm in this monochromator. As, in this case, would also be equivalent to the area of one camera pixel which is 0.0256 × 0.0256 mm to maintain the same spatial resolution between the systems. These conditions yield G that is higher in the whisker- and push-broom configurations by more than three orders of magnitude compared to the staring configuration based on a monochromator as a filter.
In terms of time required to collect a 2D image at a given wavelength, one would have to restrict the spatial and spectral resolution, as well as the pixel exposure time, to compare image acquisition times between systems. If one were to obtain an image of 512 × 512 pixels, then one would need to scan over 512 columns in the push-broom system but one would have to raster over 262′144 positions with a whisker-broom system. In theory they both have the same geometric entendue; thus it would take 512 times as long to collect an image with the whisker-broom configuration compared to the push-broom configuration at a single wavelength. In the case of the staring configuration it would take three orders of magnitude more exposure time to capture the same amount of light per pixel compared to the whisker- and push-broom systems, according to the geometric entendue calculations above. However, this is not the whole story because the staring configuration would give a full 2D image at a given wavelength but one would still have to scan or raster in the other configurations to get a full 2D image. Nevertheless, to get one monochromatic 2D image it would still take about twice as long as in the staring configuration compared to the push-broom configuration in spite of the scanning requirements. On the other hand, the push-broom configuration does not only yield one monochromatic image but it gives many monochromatic images over the spectral window (68.5 nm, under current operating conditions) of the spectrograph. Taking the linear dispersion and pixels size into account one could estimate the bandpass at ∼0.5 nm (or 3 pixels). In principle, this push-broom configuration would allow easily getting more than 100 monochromatic 2D images simultaneously and to get the same amount of information with the staring geometry one would have to spend more than 200 times as long.
A step further in the comparison would be to take into account how this applies directly to the GDOES case. For example, typically, commercial GDOES instruments are equipped with a polychromator that allows simultaneous measurement of up to 60 channels from around 100 nm to 800 nm. Thus, it is clear that the number of simultaneous bands which the push-broom system affords is above the typical requirements but it is also evident that the spectral window here falls short of the typical requirements. Thus, one can take a specific spectral window, for example from 220 nm to 288.5 nm, and see that the emission lines of approximately 12 elements typically used in GDOES lie within this window, plus about 12 more emission lines from different elements which are not so typically used.8 Then, one could say that with the staring geometry (monochromator-based) one could get the same amount of useful GDOES images in about 50 times as long as with the push-broom geometry (with the same spectral and spatial resolution, and the same amount of light collected), hence the use of a push-broom spectral imaging system. It is worth noting that other types of staring or push-broom imagers may perform better but going over every single type of configuration is outside of the scope of this manuscript.
Fig. 2 (A) Spectral image of the spectrograph slit illuminated with the Hg(Ar) pen lamp. (B) Spectral image of a grid on the spectrograph slit illuminated with a continuum lamp. (C) and (D) are taken under same conditions as (A) and (B) but with a grating mask that only allows an 8 mm × 8 mm central portion to be illuminated. |
A way of getting around the smile problem is to make the unit pixel size in the spectral dimension big enough to make the smile insignificant with respect to the size of the wavelength channel (in other words degrade the image to have a uniform point spread function), however, this would come at a premium cost of spectral resolution.11 There are several methods to correct for the smile;12 herein the smile is corrected by projective transformation.13 In short, the method uses a function to chart and amend distorted images. In the case of the smile, a polynomial function is justified due to the dependence of the curvature on the square of the vertical position.4 The polynomial function is obtained by establishing control points in the sample image that correspond to model positions in an ideal image. For this purpose, a spectrum of the Hg(Ar) pen lamp was measured. Line peak positions for each spatial position were obtained with a Matlab (R2011a, The MathWorks, Inc., Natick, MA) program called iPeak,14 thus giving a set of control points. This was followed by resampling the spectra for all the spatial positions to the central spatial position parameters (across the track row corresponding to the pixel where the aberrations are at a minimum and thus the spectral and spatial resolution is highest) which gave a set of model points. The sets of points serve as input in Matlab which can yield the appropriate structure (viacp2tform) that can then be used for the image transformation (via imtransform).
It should be noted that before the smile correction the image is rotated to correct for the remaining camera rotation misalignment (in this case 0.38 degrees). This is characterized via imaging a section of a USAF 1951 target mask illuminated with the deuterium/tungsten halogen continuum source onto the spectrograph's entrance slit. The same images can be used to measure the keystone distortion, which is a change in magnification with the spectral channel. Fortunately, our system does not have an observable keystone distortion.
However, in a push-broom system one obtains a spatial and a spectral dimension and so the ideal flat-field source would have to be homogeneous in these two dimensions for the correction to take the effects of the imaging system into account. A source that emits a perfectly even intensity through a large wavelength range is not accessible but some alternatives can be pursued. In our case, the emission from the D2 lamp is spatially homogenized via a “spatial averaging”17 optical collection system and imaged onto a diffuser. The spectral heterogeneity, which should not be extreme within the spectrograph's wavelength window, can be removed by obtaining an average spectrum from the smoothed spectra over the spatial dimension and dividing element-wise the original image over the average spectrum. The resulting image is the one used for flat-field correction.
Fig. 3 (A) Hyperspectral data cube of a transmission 1951 USAF target situated at the position of the cathode surface in the GD cell and illuminated with the Hg(Ar) pen lamp. (B) Monochromatic 2D image from data above at 404.7 nm. |
Fig. 4 GDOES elemental mapping of Cu pin in the Ni substrate sample without a grating mask. (A) Monochromatic image of the GD at 324.7 nm. (B) Monochromatic image of the GD at 341.5 nm. |
Fig. 5 GDOES elemental mapping of Cu pin in the Ni substrate sample with a 8 mm × 8 mm grating mask. (A) Monochromatic image of the GD at 324.7 nm. (B) Monochromatic image of the GD at 341.5 nm. |
To have an idea of the expected depth resolution under the current operating conditions one must take into account the erosion rate. The erosion rate for a pure Cu sample under the same conditions for a period of 8 h was measured to be 12.5 nm min−1. In our case, a 7 mm scan (size of the anode) takes approximately 14.1 s (0.5 mm s−1motor speed, plus acceleration and deceleration time), which means that the size of one pixel in the depth dimension is equal to 2.9 nm for Cu. This shows that the resolution in the depth dimension is still very high and, in fact, this is not the limit. The depth resolution could be improved by optimizing the glow discharge operating parameters such as pulse width, voltage, or pressure, as well as the ICCD exposure conditions such as the amount of accumulated ICCD gates per frame or increasing the binning to reduce the time it takes to read each frame.
One important aspect to keep in mind is that the optimum conditions for lateral resolution may not be the optimum conditions for depth resolution. Nevertheless, GDOES elemental mapping gives more flexibility in terms of depth resolution compared to the typical GDOES arrangement. In the latter, the emission is basically an average from the sputtered species that are excited in the plasma and as such a major emphasis has to be placed on having the very best crater shape (flat) over a very large area to prevent mixing of different layers from the sample. This is not the case with GDOES elemental mapping (within the limits of lateral resolution) where the laterally resolved information allows us to determine from which part of the crater the emission is coming. This concept, however, requires further study currently underway in our laboratory.
One last aspect to note is that the Cu pin/Ni substrate sample is a very simple model but it serves well the main objective here. Besides Cu, and Ni in this study, only emission from Ag containing samples has been reported in the literature of GDOES elemental mapping.3 It is clear that these elements have very strong emission lines and it remains to be seen how other samples behave in terms of sensitivity, which is also ongoing work in our laboratory. It is not straightforward to come up with an expected limit of detection because it depends on many things (operating conditions, type of imaging system and spatial resolution, elemental line, etc.) which still have to be optimized for the application. Keeping this in mind, one can compare the typical GDOES arrangement to the push-broom elemental mapping by keeping all experimental conditions the same except using a PMT detectorvs. a CCD. Thus, under the conditions used in this study the emission from the 7 mm anode is distributed vertically over ∼300 pixels along the slit while it would be collected by a single detector in the typical GDOES arrangement. In this case, the limits of detection would be expected to be about two orders of magnitude lower for the elemental mapping in the detector limited background case. Nevertheless, this is only the starting point in this discussion because one also has to consider that in typical GDOES depth profiling the experimental conditions are optimized for best crater shape not for best detection limits; likewise in elemental mapping the conditions would be optimized for best lateral resolution. Finally, it is worth noting that there are applications of GDOES elemental mapping where current limits of detection are already remarkable, for example it was shown that bovine serum albumin could be detected down to 1 fmol when blotted onto PVDF membranes and stained with silver enhanced colloidal gold by measuring the Ag emission with a monochromator-based staring imaging spectrometer.3
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