1.1.

Motivation

Wire EDM is a common method of fabricating spectrograph slits. This is an electrothermal production process where a thin single strand metal wire cuts through metal by the use of heat from electrical sparks. This method has been one of the most consistent, precise, and cost effective methods of machining slits.⁴ Despite this, there is still room for improving the consistency and uniformity of these slits. The slit edge roughness of the wire EDM slits from DIS (Fig. 1) is visually apparent, especially upon comparison to the chemically etched slits in Fig. 11. Typical roughness as a result of wire EDM is on the order of micron scales,⁵ whereas typical roughness from wet-etching is on the scale of nanometers.⁶ With nanofabrication facilities available at many research universities (including the University of Washington), we wanted to test the feasibility of the semiconductor device fabrication methods for producing ultra-flat reflective slits as demonstrated in Ref. ⁷ and compare their uniformity and performance. Many of these fabrication processes and their benefits and constraints as applied to astronomical instruments are not well-documented. As these techniques have become more widely available, in this paper, we attempt to better constrain requirements, make measurements, and document their impact on astronomical data.

Fig. 1

Example reflective slits fabricated via wire EDM for DIS at the ARC 3.5m.³

Below we present the manufacturing and characterization of chemically etched reflective slits, a required upgrade to accommodate the new slitviewing capability of KOSMOS at APO. In Sec. 2, we discuss the design approach for the new slits. In Sec. 3, we discuss the manufacturing process for the nanofabricated slits. In Sec. 4, we discuss the acquisition and processing of data taken via microscope and in lab with KOSMOS. In Sec. 5, we present the slit edge roughness and width results of the matte and reflective slits and their impact on the data.

3.1.

Photolithography and Pattern Transfer

The processing begins with $525\text{-}\mu \mathrm{m}$ thick, 100-mm diameter silicon wafers coated with $25\text{-}\mu \mathrm{m}$ LPCVD silicon nitride on both sides by Rogue Valley Microdevices (for more information, please refer to Ref. 16) [Fig. 4(a)]. The nitride acts as a mask to protect the silicon from dissolving in the KOH bath, as silicon nitride etching by KOH is negligible ($<1\mathrm{nm}/\mathrm{h}$) if etched at all. To etch the nitride such that the silicon beneath it can be exposed, we used photolithography to create a nitride mask on one side of the wafer for etching the silicon. First, we coated the top of the wafer with $1.5\mu \mathrm{m}$ of AZ 1512 photoresist [Fig. 4(b)]. We then used a 175W 405-nm laser with a 20-mm write head (Ref. ¹⁷ DWL 66+ laser lithography tool) with edge roughness of $0.11\mu \mathrm{m}$¹⁷ to expose the photoresist [Fig. 4(c)] with the pattern in Fig. 2. We chose the 20-mm write head due to its faster write speed and because the resulting edge roughness is small compared to the width of the slit.

Fig. 4

Schematic of fabrication process steps. Thicknesses not to scale. (a) Starting silicon wafer, coated on both sides with silicon nitride. (b) Coated with photoresist. (c) Photoresist written with 405-nm laser. (d) Photoresist developed. (e) ICP-F etches the exposed silicon nitride. (f) EKC bath to remove photoresist. (g) Pattern from photoresist transferred onto the nitride. (h) KOH bath to etch exposed silicon. (i) Slit and dicing lanes etched into silicon wafer. (j) Nitride at the bottom of wafer etched off. (k) Aluminum evaporated onto wafer. (l) Silicon dioxide deposited onto aluminum. (m) Light can now go through the slit and have whatever light that doesn’t go through reflected back. (n) Dicing the extra parts of the wafer off. (o) Now completed slit ready for mounting. Silicon in gray; nitride in blue; Silicon dioxide in teal; Photoresist in dark orange; Aluminum in orange; Developer in light blue. Note—steps (j) to (l) were switched in the initial testing of this process such that the reflective side was the wider side. After testing at APO, future slits will be manufactured as described in this diagram.

Then we developed the photoresist with AD10, vacuum baked at 100°C for 60 s [Fig. 4(d)]. This developed photoresist acts as a mask, allowing us to etch the nitride off where the slit will be. We use ICP (inductively coupled plasma) to remove the nitride with a ${\mathrm{CHF}}_3\text{-}{\mathrm{O}}_2$ plasma at 20°C [Fig. 4(e)]. Bare silicon is thus exposed where the slit and dicing lanes will be. We removed the photoresist in an EKC bath [Fig. 4(f)].

3.2.

KOH Etching and Plasma Etching

With a nitride mask protecting the parts of the silicon wafer we do not want removed [Fig. 4(g)], we used the KOH to etch the silicon to create the slit [Fig. 4(h)]. In our process, this took between 5 and 14 h (further discussed in Sec. 5.4). In ideal conditions, a 35% KOH solution at 100°C should etch this in 2 h.^12,18 The remaining nitride on the back of the wafer is removed via the reactive ion etcher [Fig. 4(j)].

3.3.

Metallization and Assembly

We then evaporated (through physical vapor deposition) $1\mu \mathrm{m}$ on aluminum onto the side of the wafer with the narrow end of the slit to make it more reflective [Fig. 4(k)]. To protect the aluminum from oxidation (which causes the aluminum to become dull and less reflective), we used plasma-enhanced vapor deposition to deposit 100 nm of silicon dioxide onto the wafer [Fig. 4(l)]. Lastly, we diced the wafers into rectangles for the mounts using a Disco diamond dicing saw [Fig. 4(n) and Fig. 2]. Three of each size slit were mounted for use, and the remaining are kept as extras.

4.1.

Acquisition—Microscopic Data

For each slit, 10 sections along the slit were imaged randomly [Fig. 5(a)], taken on an optical Leica DM compound microscope, with the slit being illuminated from below with the light pointing through the slit toward the camera. For chemically etched slits with slit widths between 60 and $400\mu \mathrm{m}$, images were taken at magnifications of $5\times$, $10\times$, and $20\times$. Images were taken with the light illuminating through the narrow side of the slits and the wide side of the slits to test whether there is a measurable difference in the widths of the slit. However, as the narrow side of the slit, which is its targeted width, sets the amount of light coming into the slit, the measured slit widths ended up being the same on both sides. For etched slits with slit widths larger than 1 mm, images were taken at $5\times$, as the slit is too wide for imaging at higher magnifications. For wire EDM slits, data were taken with the $10\times$ objective to allow for standardized comparisons between all slits.

Fig. 5

Sample of data taken on the microscope at various stages of metrology, specifically a 5 arcsec reflective slit at $20\times$ magnification with light coming through the reflective side of the slit and hitting the eye piece and detector (backlit). (a) Data taken with microscope in uncompressed.tiff file format. The yellow is a result of the scaling of the intensity of the image. (b) Data after unsharp masking. (c) Edges detected by Canny edge detection in OpenCV. (d) Straight lines (in red) detected in data using probabilistic Hough transform with residuals calculated by taking the separation between the detected edge (in white) and the detected line (in red). The text on the image is the width and roughness output for just this image. Note: The detected edges and lines are exaggerated in (c) and (d) to improve readability. The $50\mu \mathrm{m}$ scale bar was added retroactively for sense of scale.

Using numerical apertures and and estimated peak wavelength to be at 550 nm, we obtain the resolution of images at each objective. We also imaged a reticle at $5\times$, $10\times$, and $20\times$ magnifications to find the conversion of pixels to microns Table 1. Due to the low spatial resolution of the optical microscope and unresolved structure, these measurements set upper limits on the roughness of the slits and high errors on the measured width.

Table 1

Spatial resolution of each microscope objective.

4.2.

Data Analysis—Microscopic Data

Images were sharpened using Gaussian unsharp masking [Fig. 5(b)], a common digital signal processing technique used to enhance the intensity at the edges.¹⁹ First, we smooth [Eq. (1)] the original image by convolving a Gaussian kernel [Eq. (2)], which is a discretized approximation of a two-dimensional (2D) Gaussian—in this case in a $5\times 5$ matrix, which acts as a highpass filter, with the original image. Because the smoothing is done at a smaller spatial scale than the rough features (more than $5\times 5\text{pixels}$), resolution of the slit edges are not impacted

Fig. 6

Cross-sections of edges in the process of unsharp masking (a) idealized edge; (b) observed edge; (c) smoothed version of (b) [see Eq. (1)]; (d) sharpened edge as a result of subtracting a proportion of (c) from (b) [see Eq. (3)].

Then one subtracts a blurred or smoothed image [Eq. (1)] from the original image resulting in a sharpened image with reduced Gaussian noise [Fig. 6(d); Fig. 5(b); and Eq. (3)].²⁰

This is a vital step for allowing Canny, the edge detection algorithm used and described below, to properly detect the edges of the slit.

Images were then analyzed with algorithms from OpenCV, an open-source computer vision and machine learning software library. The edges of the slit were detected with OpenCV’s implementation of the Canny edge detector, a widely used edge detection algorithm²¹ [Fig. 5(c)]. After Gaussian unsharp masking, the algorithm finds the intensity gradient at each pixel in the image by filtering with a Sobel kernel, outputting the first derivative of intensity in both horizontal and vertical directions. With the vertical and horizontal first derivatives, it computes magnitude and direction of the gradient at each pixel location. It then searches for potential edges by looking for high gradients in brightness. Then, it applies an upper and lower threshold, where it rejects all potential edges below the lower gradient threshold, accepts all strong edges above the upper threshold, and tentatively accepts weak edges in between the upper and lower thresholds. Lower thresholds were determined by testing various input values to check whether Canny would successfully detect the edges of the slit without detecting any background Poisson noise or non-existent structure as edges. Finally, using hysteresis, any strong edge with weak edges in between are connected together to be one edge, and all weak edges not connected to strong edges are suppressed, shown in Fig. 7. With a picture of what the edges of the slit looks such as from Canny [Fig. 5(c)], we then use Hough transforms to fit a line to the edge.

Fig. 7

One-dimensional example of how Canny detects strong edges above the upper threshold and connects the weak edges between the strong edges to make one detected edge. Any pixels with intensity gradient below the lower threshold is not detected as an edge.

Straight lines were fit to the detected edges using OpenCVs probabilistic Hough transform algorithm (HoughLinesP) [Fig. 5(d)]. The probabilistic or randomized Hough transform²² is a modification of the Hough transform.^23–25 This allows us to fit straight lines to those detected edges to understand how far the deviation of the slit is from an idealized straight edge. HoughLinesP randomly picks some number of points and maps it in the Hough parameter space, $\theta$ and $\rho$, where $\theta$ is an alternative way to measure the slope of a line and $\rho$ measures the distance of the line to the origin (Fig. 8). HoughLinesP then searches a grid of $\rho$ and $\theta$ to find the best-fit line, given by the line with $\rho$ and $\theta$ that has the most votes or points that fall in that line.

Fig. 8

(a) Representation of a line in $xy$-space where $m_0$ is the slope and $b_0$ is the y-intercept. (b) Representation of a line in mb-space, which is a point where lines $(x_0,y_0)$ and $(x_1,y_1)$ intersect. (c) Representation of a line $xy$-space where ${\rho }_0$ is the distance between the origin and the line and ${\theta }_0$ is the angle between the orthogonal to the line and $x$-axis. (d) Representation of a line in Hough space—looks like a point where waves $(x_0,y_0)$ and $(x_1,y_1)$ intersect.

The roughness is determined by the mean residual (absolute value of the difference) between the edge detected and the best-fit line determined by HoughTransformP along the sampled image. The slit width is the average distance between the two lines detected. Due to the reflective slits being angled at 15 deg for the slitviewer, the effective slit width is slightly smaller [by cos(15 deg)] than the measured width. The width uniformity is the standard deviation of the measured width along the length of the slit. These roughness and width measurements for both matte and reflective slits and the effective width for the reflective slits are described in Sec. 5.

4.3.

Acquisition—KOSMOS Data, In Lab

For each mounted slit, both chemically etched and wire EDM, spectra were taken using the krypton, neon, and argon internal calibration lamps on simultaneously, alternating between red and blue grisms. By having all internal calibration lamps on, more emission lines were present across the entire optical bandpass and minimized the need to wait for warm up times of the individual calibration lamps for each set of observations. Both red and blue grisms were separately used in observations to gauge impacts on throughput throughout the entire bandpass. Darks, or images taken without opening the shutter, were taken to characterize the thermal noise of the detector. Flats, which characterize the individual pixel response of the KOSMOS charge coupled device detector, were not taken. The spectra for wire EDM and chemically etched slits of the same size and position fell in roughly the same place on the detector, which was sufficient for sample data to compare between the machined and chemically etched slits. For specific details on KOSMOS as an instrument, see Kadlec et al., in prep.

4.4.

Data Analysis—KOSMOS Data, In Lab

Data were reduced by subtracting a median-combined master dark, where all the darks taken were median-combined, from spectral data. From this reduced data, we divided by exposure time to convert the measured counts in analog-digital units (ADU) to flux, in units of ADU/s/pixel. The background, both background from outside of the slit and spectral background, was then averaged in each frame. The background light through the slits provides an analog for scattering, though not absolute, is sufficient for comparisons of scattering in the matte and reflective slits. Since data were taken with both the red and blue dispersers for each mounted slit, the background and slit widths obtained from the separate red and blue disperser frames were averaged (Fig. 9).

Fig. 9

Top left: Example spectra taken using the chemically etched, reflective slit; Top right: Example slit cross section, reflective slit; Bottom left: Example spectra taken using the wire EDM, matte slit; Bottom right: Example slit cross section, matte slit.

5.1.

Slit Results—Width Uniformity and Maximum Roughness

By comparing the results given in Tables 2 and 3, the reflective wet-etched slits are less rough, with smaller residuals than the matte machined slits, throughout the various target sizes of slits. The overall average roughness of chemically etched slits across all slit widths is $0.42\pm 0.03\mu \mathrm{m}$. The average variation across etched slits (average of the standard deviation of each slit), excluding the widest slits, which could only be taken at $5\times$, setting errors at 20%) is $6\pm 3\mu \mathrm{m}$. The overall average roughness of machined slits is $1.06\pm 0.04\mu \mathrm{m}$. The average variation across machined slits is $10\pm 6\mu \mathrm{m}$. This makes the etched slits on average $2.5\times$ smoother than the machined slits on average. Due to the low resolution of the optical microscope used for measurements, and subsequent error propagation in the measured width, the comparison of width uniformity between the two types of slits is inconclusive.

Table 2

Average reflective slits roughness/residuals.

Table 3

Average matte slits roughness/residuals.

To examine the roughness as a function of width for both methods of fabrication, we fit roughness versus width in Fig. 10. The roughness of the slits do not depend on widths in both the machined and etched slits. Additionally, the wire EDM slits are consistently rougher than chemically etched slits, no matter the slit width.

Fig. 10

Plot of average roughness as a function of average width with error bars from the standard deviation of both. The roughness of the machined slits is consistently higher than that of the etched slits. Both have no width dependence.

In comparing Tables 4 and 5, the chemically etched slits also are more uniform in width throughout the individual slits, as the error is more consistent and generally smaller than machined slit width error. This is due to the $0.11\text{-}\mu \mathrm{m}$ precision of the laser lithography tool, which sets the shape of the slit. Under ideal conditions, the KOH etching sets the size of the slits and will etch a smooth edge in the silicon. However, due to the remaining nitride on the slit (Fig. 11) as well as residue from the dicing tape being removed with acetone seen when visually inspected, the slits are rougher than expected. The reactive ion etching (RIE) etcher responsible for removing the remainder of the nitride on the slit did not appear to remove all of it.

Table 4

Individual reflective slit widths.

Table 5

Individual matte slit width.

Fig. 11

Imaged slit, where the nitride is the glittery gold and the slit is in the middle. The red box highlights a bit of remaining nitride on the slit. For scale, a $20\text{-}\mu \mathrm{m}$ scale bar was added.

In the testing of this process, we found a large disparity between the targeted slit width and the measured slit width of the chemically etched slits. This comes from the unpredictability of our wet-etching process, which was missing a step of removing silicon dioxide prior to the KOH etch, discussed in Sec. 5.4. Instead of grouping them by targeted slit width, we chose to demarcate the slits by their functional measured slit width for practical purposes in Table 4.

5.2.

Slit Results—Scattering

In examining Tables 6 and 7, the scattering of the chemically etched slits is higher on average than that of the machined slits. Since the etched slits are smoother than the machined slits, the reflectivity, not the roughness, is the major contributor to the observed scattering. The scattering increases as slit width increases for both matte and reflective slits and is greater for reflective slits (Fig. 12). To normalize the scatter by slit width and compare the impact of reflectivity, the scatter was divided by the width, giving units of $\mathrm{ADU}/\mathrm{pix}/\mathrm{s}/\mu \mathrm{m}$. The scatter/width for matte slits including continuum is $0.09\pm 0.5\mathrm{ADU}/\mathrm{pix}/\mathrm{s}/\mu \mathrm{m}$ and $0.13\pm 0.3\mathrm{ADU}/\mathrm{pix}/\mathrm{s}/\mu \mathrm{m}$ for reflective slits. For light outside the slit, the scatter/width for matte slits is $-0.0004\pm 0.03\mathrm{ADU}/\mathrm{pix}/\mathrm{s}/\mu \mathrm{m}$ and $0.04\pm 0.02\mathrm{ADU}/\mathrm{pix}/\mathrm{s}/\mu \mathrm{m}$ for reflective slits. In both scenarios, the scatter using the reflective slits is higher, but with proper background subtraction, the impacts of the scatter can be minimized.

Table 6

Average reflective slit scatter.

Table 7

Average matte slits scattering.

Fig. 12

Plot of average scattering vs average width with standard deviations of both as error bars. Scattering was measured with two methods, with the solid line fit representing scatter measured in the spectra and the dotted line fit representing scattered light outside the slit. Scattering increases linearly as a function of width for both wire EDM and chemically etched slits with both methods.

5.3.

Potential Biases and Shortcomings of Measurement Technique

The measurements for roughness and width were made using an optical microscope with low resolution. Due to this, the measurements made in this paper are upper limits and only meant to be used as a comparison between the two types of slits presented, taken with the same optical microscope. As discussed in Sec. 6, measurements of future slits will be made with a scanning electron microscope to better characterize the roughness.

5.4.

Advantages and Disadvantages of Wet Chemical Etching for Slit Fabrication

The primary advantages of using wet chemical etching to make slits are that they are less rough than that of wire EDM slits. There are many academic labs with nanofabrication tools available, making this fabrication method fairly available. The process for setting the widths and features of the slits is also easy, as it just requires editing a CAD file. In addition, as mentioned in Ref. 7, these slits are ultra-flat, which makes them more ideal mirrors for the purposes of the slitviewer and minimizes any distortions due to warping or uneven polishing.

The disadvantage for this specific project was the unpredictability in the etching process. The etch rate was inconsistent across wafers in the bath due to native oxide on the silicon slowing down the KOH etch. A way to mitigate these inconsistencies in future work would be to use BOE (buffered oxide etchant) to etch away the silicon oxide that grew after etching the nitride off, as done in Ref. 26. This is expected to constrain the etch times to be closer to the theoretical through etch time of 2 h at 35% KOH at 100°C,¹⁸ as opposed to the 5 to 14 h that it took for this project. Another factor that contributed to the difficulties of this process were that labels with the different slit sizes in the etch process would etch away, making distinguishing different slits difficult. A suggested alternative method of labeling would be making multiple marks in the etching process that do not blend together. Lastly, the dicing lanes would not always fully etch through, though ultimately with the way the dicing saw was set up, it did not matter too much.

Overall, this is an effective method for those who need reflective, highly uniform, and flat slits with multiple custom sizes provided that there is the addition of the step of a BOE etch to remove the silicon dioxide prior to the KOH etch to reduce unpredictability in sizing. The lead time is longer, as the uniqueness of each project in these academic labs make the process look vastly different for each user and there are a large number of tools to learn to use. It is possible for this process to be outsourced to contractors at facilities with equipment to handle different sized wafers, though this has not been considered at this point due to the process still being tested. Fortunately many of these steps can be done in batches, cutting some of the time it takes for processing. Most of the uncertainty in etch time can be minimized by doing a quick BOE dip prior to the KOH etch, as well as considering the amount of silicon that will be exposed and etched at a time.