Lost Mold-Rapid Infiltration Forming of Mesoscale Ceramics: Part 2, Geometry and Strength Improvements

Abstract

Iterative process improvements have been used to eliminate strength-limiting geometric flaws in mesoscale bend bars composed of yttria-tetragonal zirconia polycrystals (Y-TZP). These improvements led to large quantities of high bend strength material. The metrology of Y-TZP mesoscale bend bars produced using a novel lost mold-rapid infiltration-forming process (LM-RIF) is characterized over several process improvements. These improvements eliminate trapezoidal cross sections in the parts, reduce concave upper surfaces in cross section, and minimize warping along the long axis of 332 × 26 × 17 μm mesoscale bend bars. The trapezoidal cross sections of earlier, first-generation parts were due to the absorption of high-energy ultraviolet (UV) light during the photolithographic mold-forming process, which produced nonvertical mold walls that the parts mirrored. The concave upper surfaces in cross section were eliminated by implementing a RIF-buffing process. Warping during sintering was attributed to impurities in the substrate, which creates localized grain growth and warping as the tetragonal phase becomes destabilized. Precision in the part dimensions is demonstrated using optical profilometry on bend bars and a triangular test component. The bend bar dimensions have a 95% confidence interval of < ±1 μm, and the tip radius of the triangular test component is 3 μm, consistent with the UV-photolithographic process used to form the mold cavities. The average bend strength of the mesoscale Y-TZP bend exceeds 2 GPa with a Weibull modulus equal to 6.3.

I. Introduction

Microfabrication holds much promise in manufacturing for a variety of applications including microelectrical mechanical systems (MEMS), microbiology, miniature sensors and actuators, and mechatronics.^1–4 In particular, free-standing mesoscale components are being codeveloped for the next generation of surgical instruments.^5,6 Ceramics, particularly yttria-tetragonal zirconia polycrystals (Y-TZP), have the high fracture strength and elastic modulus required for mesoscale surgical instruments.⁵ In the first part of this series on mesoscale (i.e., sub-millimeter) manufacturing, we reported a new microfabrication approach based on Y-TZP nanoparticulate processing, lost mold-rapid infiltration forming (LM-RIF).⁷ The generation 1 (Gen1) mechanical test bend bars had a relatively high aspect ratio (15:1) and high resolution edges (<1 μm), and were manufactured in large numbers on refractory substrates (up to 200 000 bend bars per 10 cm × 10 cm refractory substrate). The mesoscale (340 μm × 30 μm × 20 μm) bend bars had reasonable bend strength, with a mean strength between 829 and 913 MPa and a Weibull modulus of 6.8. The range in bend strengths reported for the Gen1 materials was created by uncertainty in the orientation of the trapezoidal cross sections of the small bend bars. In addition to the trapezoidal cross sections, dishing or concave upper surfaces in cross section and warping along the length of the bend bars are present in most of the Gen1 bend bars.

Lange⁸ showed that systematic processing changes to remove strength-limiting flaws can lead to significant strength improvement. An average bend strength of 1340 MPa for Y-TZP was achieved with at least one specimen having a strength >2210 MPa.⁹ In the current study, the mesoscale Y-TZP bend bars provide an excellent model for iterative process improvements to eliminate the strength-limiting geometric flaws that specifically occur in mesoscale ceramics. In addition, the mechanical strength determined for the mesoscale bend bars is used in the finite-element design for mesoscale applications such as surgical instruments.⁵ Although there are numerous forming processes for micro or mesoscale ceramics,⁴ the metrology of the parts produced is often left uncharacterized. The goals of this paper are to address the processing variables that lead to the geometric defects, characterize the metrology of specimens produced with the LM-RIF process, and determine the strength distributions in the third-generation (Gen3) materials in which the geometric defects have been eliminated or minimized.

The LM-RIF process is described in detail in Part 1 of this series.⁷ LM-RIF processing is an integration between semiconductor manufacturing based on ultraviolet (UV)-photolithography and ceramic powder processing first pioneered by Gauckler and colleagues, who patterned ceramic colloids on substrates.^10–13 Photolithography is used to produce the mold cavities and ceramic powder processing is used to fill the molds and produce a dense, submicrometer microstructure. In the LM-RIF process, hundreds to hundreds of thousands of free-standing parts are produced simultaneously on a 10 cm × 10 cm refractory substrate, which eliminates handling or manipulating the parts in the fragile green state.

The first dimensional defect that will be addressed is the trapezoidal cross section of the first-generation (Gen1) bend bars that was described in Part 1 of the series.⁷ Preliminary scanning electron microscopy (SEM) examination of the mold cavities revealed that the photolithographic process was producing trapezoidal molds that were reproduced in the parts by the ceramic forming process. The trapezoidal sidewall profile of thick photoresists, such as SU-8, in silicon MEMS processing has been well documented.^14–17 Nonvertical mold walls in SU-8 are caused by absorption of low wavelength light in the top portion of the photoresist, creating a gradient in the photoinitiator concentration, cross-link density, and chemical resistance to the developer. The solution used by Reznikova et al.¹⁵ was used for the current process. This solution uses a 100 μm layer of SU-8 as a high-pass filter for wavelengths below the absorption edge of the photoresist and the ideal 365 nm i-line. The high-pass frequency is tunable by controlling the thickness of the photoresist.¹⁵ This solution has proven effective in standard photolithographic processes and also works with the current LM-RIF process. The elimination of trapezoidal cross sections led to generation 2 (Gen2) bend bar specimen with 90° sidewalls.

The dishing geometric defect was observed in the Gen2 parts during optical profilometry thickness measurements. Dishing produces a bend bar that is thinner in the center of the cross section compared with the sides or ends. The dishing defect compromises mechanical strength as well as mechanical testing because the raised edges of the test specimen contact the testing apparatus and increase the stress intensity at these points. Preliminary analyses revealed that distortion of the polymer squeegee at the edges of the mold cavity during the RIF process causes dishing. Mannan et al.¹⁸ have analyzed a similar geometric defect called scooping, in stencil printing of solder pastes that have been deposited through brass apertures or stencils. Although Mannan et al. show how scooping can be reduced, their processing solutions are not useful to the RIF process because the reduction is not great enough to limit dishing to even <10% of the mold thickness or <2.5 μm. This is a consequence of the thin (25 μm) molds being manufactured. Therefore, a different method to prevent dishing is reported in which an overcoat of ceramic suspension is deposited during RIF, followed by a planarization and buffing process after drying and gelcasting.

The third geometric defect is warping along the length of the bar. Warping is a chronic problem in particulate-forming processes¹⁹ and can manifest itself in the green state or after sintering. In the present case, two types of warping are observed: one after mold removal by reactive ion etching (RIE) and one after sintering. Curvature in the green state is often related to drying.²⁰ However, the bend bar warping after sintering was greater than the curvature in the green state and was accompanied by optically darker regions near the center of curvature. Preliminary analyses identified the warping in the Gen1 and Gen2 materials as localized transformation of tetragonal zirconia (t-ZrO₂) to monoclinic zirconia (m-ZrO₂) in the mesoscale bend bars. This is attributed to chemical interaction with the glass-bonded 96 wt% alumina substrate used for Gen1 and Gen2 materials. Attempts to minimize curvature in the green state are ongoing, but warping during sintering has been minimized by using higher purity α-alumina substrates in the Gen3 materials. This has improved the yield of straight bars from 60 to over 90%.

The metrology and processing iterations will be presented relative to the mechanical strength of each mesoscale material generation. The strength of the Gen1 material with trapezoidal cross section, dishing, and warping was reported previously.⁷ The mechanical strengths of the Gen2 material with rectangular and nontrapezoidal cross sections but with dishing and warping present and the Gen3 material with a rectangular cross section, minimal dishing, and minimal warping are reported in this study.

II. Materials and Methods

The LM-RIF manufacturing process is described in detail in Part 1 of the series,⁷ but will be summarized here. A high aspect ratio, epoxy-based photoresist, SU-8, is spin coated in two layers on an alumina substrate with an antireflective coating (Barli-II 90, Clariant Corp., Charlotte, NC) to form the mold. The first layer is a 25 μm thick solid SU-8 underlayer (Microchem Corp., Newton, MA), while the second layer is a 25-μm-thick patterned mold layer. Dispersion of 43–45 vol% commercial Y-TZP (TZ-3Y, Tosoh Corp., Tokyo, Japan) is obtained by chemically aided attrition milling at pH 9 in the presence of 1.5% dry weight basis (DWB) of ammonium polyacrylate (NH₄-PAA) (Darvan 821A, RT Vanderbuilt, Norwalk, CT) to achieve a particle size D50 by dynamic light scattering of 215 nm by volume (114 nm by number).^7,21,22 The molds are then filled by the RIF process, which uses a squeegee to shear and fluidize the pseudoplastic (Bingham yield point of 160 Pa, high shear viscosity of 0.65 Pa · s), well-dispersed, highly loaded (43–45 vol%) ceramic suspension. Green strength is provided by gelcasting a 5 wt% (DWB) combination (6:1 mass ratio) of methacrylamide/methylene-bisacrylamide initiated (2.5% by mass of the total monomer content) with ammonium peroxydisulfate and N′, N′, N′, N′–tetramethylethylenediamine (Sigma-Aldrich, St. Louis, MO).²³ The green parts are allowed to gel in a humid, nitrogen environment, and then slowly dried by exposure to lab air overnight. The mold is either removed thermally as described in Part 1 of the series⁷ or via RIE that will be demonstrated in the current work. The parts are sintered on the substrate and washed off in an ethanol ultrasonic bath to be characterized by confocal optical microscopy, SEM, optical profilometry, and three-point bend testing. Several improvements have been made to enhance the geometric tolerance of the parts in the current work. These improvements include adopting RIE to remove the mold, filtering the wavelength of the UV light used to expose the photoresist, modifying the RIF process to limit the effect of dishing, and using only high-purity α-Al₂O₃ substrates.

RIE is a common process in semiconductor manufacturing that is used to remove photoresist from the surfaces of silicon. Because oxygen is primarily used as the reactive species, the etch rate for the polymeric photoresist is much higher than that of oxide ceramics such as 3Y-TZP. The RIE (PT720, Plasma-Therm Inc., St. Petersburg, FL) settings were 350 W at 200 mTorr with 50 sccm of O₂ and 5 sccm of SF₆. These settings were modified from the work of Hong et al.,²⁴ and found to work best on the PT720 system. An etch time of 50 min was used to remove 50 μm (underlayer and mold layer) of SU-8 for an etch rate of 1 μm/min.

To make a high-pass UV filter, a 100 μm layer of SU-8 100 photoresist (Microchem Corp., Newton, MA) was spin coated onto a blank soda lime silicate glass mask using the manufacturers' recommended spin cycle and exposure parameters. The transmittance of the filter was measured using a UV-Vis Spectrophotometer (Lambda 950, PerkinElmer, Waltham, MA). The spectral intensity of the MA6 mask aligner used to expose the photoresist was transcribed from the MA6 spectral data by Reznikova et al.¹⁵ and normalized to the 365 nm peak. The spectral intensity with the SU-8 100 filter and a blank glass mask was calculated by multiplying the spectral intensity of the MA6 by the percent transmittance through the filter and glass mask at each wavelength. To compensate for reduced intensity at 365 nm, the exposure time was increased from 10 s at 12 mW/cm² to 120 s at 8 mW/cm².

The modification to the RIF process was slight, but significantly reduced the amount of dishing. Rather than removing the slurry deposited on top of the mold surface using a squeegee, a blanket layer of slurry is left on the entire mold surface and the monomer and crosslinker are allowed to gel. After gelling and drying, the blanket layer of slurry is gently buffed away by hand using a class-10 cleanroom wipe (Polywipe C, Contec Inc., Spartanburg, SC) dampened with ethanol. Polishing cloths used in the diamond polishing of metallographic samples were also tried in an automated process, but the cloths left fibrous debris on the sample and pulled some of the bend bars out of the mold cavities.

Substrate purity was found to have an effect on warping. Two α-Al₂O₃ substrates of different purities (Kyocera Industrial Ceramics Inc., Somerset, NJ), 96 and 99 wt%, were tested. The substrate purity was verified by X-ray fluorescence (The Mineral Lab, Lakewood, CO). The firing cycle was then changed from a soak temperature of 1300°C for 2 h to 1400°C for 1 h because the parts became translucent, signifying a microstructure with less residual porosity at a comparable grain size. However, the 96 wt% pure substrate caused the parts to warp. Confocal Raman spectroscopy (Alpha300, Witec Instruments Corp., Savoy, IL) was used to identify the amount of t-ZrO₂ and m-ZrO₂ at various locations on a bend bar. Spectral excitation was achieved using a 5 mW argon laser at 488 nm through a × 100 objective with a spot size under 2 μm. The spectrum was collected on a 1024 × 127 pixel CCD camera using an 1800 line/mm grading. An integration time of 50 s was used over two hardware accumulations for the single-spot spectra, while a 15s integration time over two hardware accumulations was used for the line-scan spectra. The monoclinic phase content was analyzed using the calibration curve provided by Kim et al.²⁵ because a calibration using X-ray diffraction could not be made due to the small sample size. Because the 180 and 192 cm⁻¹ monoclinic peaks could not be resolved on the spectra, a deconvolution was performed using the PeakFit^® program (PeakFit ver.4.12, SeaSolve Software Inc., San Jose, CA). The peak intensities were found by fitting the background to a linear baseline with endpoints at 120 and 205 cm⁻¹ and deconvoluting the peaks with a Gaussian plus Lorentzian peak shape. Initial peaks were placed at 148, 180, and 192 cm⁻¹ and refined using the software until the r² value was at least above 0.990 or typically 0.997.

The parts were imaged using a SEM (S-3000H, Hitachi, Tokyo, Japan). Physical dimensions were measured with an optical profilometer (Wyko NT1100, Veeco Instruments Inc., Plainview, NY). The optical profilometer was fitted with a × 20 objective and a × 0.5 FOV lens. At this magnification, the lateral sampling interval is 0.82 μm. The dimensions of three-point bend test bars were measured while in the mold, after RIE, and after sintering. The in-mold thickness was calculated by subtracting the difference in height between the part and the top surface of the mold from the mold thickness measured before casting. All of the other measurements were made directly.

Gen3 bend bars were tested in three-point bending with a lower span of 114 μm. Before testing, intact bars were selected from the sintered specimen using a stainless-steel microprobe and placed onto a glass slide. The dimensions of each bend test bar were measured using optical profilometry. Only the strength data for the bars lying face up as molded were included because the minimum and maximum height could be measured only for these bars. Each bar was then manipulated with tungsten microprobes onto the edge of a TEM grid, and then onto the lower span of the test apparatus. Several modifications were made to the apparatus before testing the new generation of materials. Forces were applied to the bars using a piezoelectric actuator at a constant displacement rate of 1 μm/s and measured using a 50 g load cell. The testing span was mounted on a three-axis manipulation stage, samples were preloaded to approximately 0.01 N to ensure placement during testing, and then loaded until failure. The time and applied force were recorded at a rate of 100 samples/s. The force–displacement curves show linear elastic behavior, followed by catastrophic, brittle failure. Because we were unable to collect the specimens after fracture, the calculation of strength was made using the average height measured by optical profilometry for each individual bar. The strength data were evaluated using a two-parameter Weibull distribution, which used a maximum likelihood standard regression method, calculated using Weibull+ +7 by ReliaSoft Publishing: Tuscon, AR.

III. Results and Discussion

An important modification to the photolithographic process enables vertical sidewalls in the SU-8 photoresist by filtering the sub-365 nm wavelength light during the exposure. Figure 1 shows a comparison between the mold walls for an unfiltered exposure (a) and a filtered exposure (b). The high aspect ratio capability of SU-8 is enabled by its high transmittance at 365 nm (i-line). The absorption edge (50% transmittance) of a comparable 10 μm thick, unexposed SU-8 layer is 350 nm.¹⁷ However, the emission of the mercury lamp below 350 nm can be as high as 15% of the peak value as shown in Fig. 1(c).¹⁵ This shorter wavelength light is absorbed in the upper portion of the SU-8 layer, resulting in a higher local concentration of photoacid and a more crosslinked structure in the upper region. This results in wider mold walls at the top of the mold and the trapezoidal mold cross section after development in Fig. 1(a). A high-pass filter made of SU-8 100 eliminates the sub-350 nm wavelength light shown in the inset of Fig. 1(c) and uniformly crosslinks the photoresist, creating the vertical sidewalls in Fig. 1(b). Using the 100 μm SU-8 filter, a sidewall angle of 90.2° ± 0.2° (±95% confidence interval) was achieved in Gen2 molds versus 82.9° ± 0.9° for the unfiltered exposure in the Gen1 molds as shown in Table I. By measurement of SEM images of Gen1 sintered test bars, the top width of the trapezoidal cross section was 20 ± 0.3 μm and the bottom width was 28.7 ± 0.6 μm.⁷ Assuming a thickness of 20 μm, the sidewall angle is 78.2°, which is similar to the Gen1 mold wall angle of 82.9°, verifying that the forming process reproduces the trapezoidal mold. A difference in the top and bottom width of Gen2 bend bars could not be distinguished in either the SEM or the optical profilometer, which means any difference is <1 μm.

Fig. 1.

(a) The mold produced without filtering the exposure light has a trapezoidal cross section. (b) Using an SU-8 100 filter to remove the sub-365 nm light, the mold walls are vertical. (c) The emission of the MA6 aligner below 365 nm¹⁵ is substantial even through a soda lime silicate glass mask. This light is absorbed in the upper portion of the photoresist and creates a crosslink gradient, which after developing, results in the angled mold walls shown in (a). By filtering out the light below the absorption edge of the photoresist, the photoresist is uniformly crosslinked through the thickness and the vertical mold walls in (b) are achieved.

Table I. Improvements in the Geometry of the Bend Bars were Made in Each Successive Material Generation, Resulting in Strength Improvement.

			Sidewall Profile		Dishing		Warping		Strength
Generation	Major Defects	Process Change	Trapezoidal Angle (θ)	±95% Conf.	Max. Height Difference (ρ) (μm)	±95% Conf. (μm)	Deflection Over Length (d/l) (%)	±95% Conf. (%)	Average (Std. Dev.) (Mpa)
Gen1	Trapezoidal x-section, Warping, Dishing	Filter UV exposure	mold: 82.9°	0.9°	Not measured		Not measured		821 (142) to 913 (157)
			part: 78.2°	0.5°
Gen2	Warping, Dishing	Substrate purity, Buffing	mold:90.2°	0.2°	4	2	∼8%	-	1191 (675)
			part: ∼90°	NA			Rcurv=500 μm
Gen3	Warping, Grain Size	Heat Treatment	mold:90.2°	0.2°	0.9	0.2	1.5%	0.3%	2236 (376)
			part: ∼90°	NA			Rcurv=2,758 μm

In the first generation (Gen1), the largest defect was the trapezoidal cross section, which was eliminated in the second generation (Gen2) bend bars by filtering the wavelength of the exposure light in photolithography. However, the Gen2 bars had both dishing (see Fig. 2) and warping (see Fig. 4). This led to Gen3 bend bars with an average strength of 2.2 GPa as warping and dishing were minimized by the use of a higher purity substrate and incorporation of the buffing planarization technique. Warping is defined as the maximum height difference along the length of the bar divided by the length (d/l). The radius of curvature is also given, which is calculated assuming the geometry shown in cartoon (a) below the warping data.

The mold cavities for mesoscale bend bars have five sides, including the bottom, with the topside left open to fill the mold. An effect called dishing can occur on the top side of the bend bars, which results in a thickness gradient in the part. Distortion of the polymer squeegee as it passes over the mold cavity causes dishing. Figure 2 shows a thickness variation of 3 μm over the 18 μm thickness of a representative Gen2 bend bar. The average amount of dishing in sintered Gen2 samples was 4 ± 2 μm over a thickness of 15 ± 3 μm. A stiffer squeegee would alleviate dishing,¹⁸ but the slight variations in mold height and the presence of an edge bead on the outer edge of the substrate cause the suspension to spread unevenly over the mold when using a stiff squeegee. Squeegees of varying stiffness (60, 90, 100 Shore A) at different qualitative pressures were tried, but 4 μm was the minimum amount of dishing that was achieved while still maintaining uniform mold filling across the entire substrate. However, dishing was minimized by casting a layer of suspension over the entire substrate and allowing the layer to gel and dry before buffing away. The amount of dishing is decreased to an average of 0.9 ± 0.2 μm or 5% of the thickness using this buffing process. Although the dishing is reduced, the buffing results in a higher surface roughness compared with the bend bar surfaces in contact with the mold walls and bottom. This is a result of the debris that is removed from the edges of the parts and deposited over the surface. The average root-mean squared roughness (R_g) on the buffed surface is 0.4 ± 0.1 μm, whereas the R_g of a surface cast against the mold walls is 0.2 ± 0.1 μm. A roughness of 400 nm is considered tolerable because it is not significantly larger than the grain size.

Fig. 2.

A concave top surface or dishing is caused by the polymer squeegee deforming into the mold cavity. The profile of a representative, sintered Gen2 bend bar shows a height difference of 3 μm, whereas the Gen3 bend bar has a height difference of 1 μm. The profiles were taken in the center of the bars shown above the graph. On average, the dishing in Gen2 bend bars was 4 ± 2 μm, while the dishing in Gen3 bars was 0.9 ± 0.2 μm (Table I). The bend bar at the top of the Gen3 3D image is lying on its side and thus appears thicker than the bend bar in the foreground.

Warping is curvature along the length of the bend test bars. Two types of warping are observed: the first type is characterized by as-sintered out-of-plane curvature; the second type is characterized by as-molded out-of-plane curvature. The as-sintered out-of-plane curvature means the bars curve away from whichever side they are resting on as they are fired. Thus, both thickness/height curvature and width/height curvature are possible because the bend bars can lay on either the as-molded bottom or the as-molded side. Figure 3(a) shows an optical image in transmission of a Gen2 bend bar that was fired lying on its side with a radius of curvature of 502 μm or 8% deflection. Deflection is defined as the maximum difference in height divided by the length of the bend bar and is illustrated in Table I. Figure 3(b) shows an optical image in transmission of a straight Gen3 bend bar whose particular radius of curvature is 8.2 mm. Curvature at a radius of 8.2 mm over the bend bar length is negligible relative to the bend bar length of 332 μm, and results in a deflection of only 0.5%. Figure 3(c) shows a backscattered electron (BSE) image of the more opaque (darker) area in Fig. 3(a). From Figs. 3(a) and (c), the area in contact with the 96% pure alumina substrate during firing is optically opaque and composed of larger grains. Energy-dispersive spectroscopy (EDS) was insensitive to the concentration of any possible diffused species because the spectra in the curved region and at the tip of the bend bar were identical (not shown). Therefore, any difference in local chemistry was below the detection limit of EDS or a few atomic percent. While transmission electron microscopy combined with electron energy loss spectroscopy can potentially verify the elemental contamination, such a program of study is beyond the scope of the current work. Confocal Raman spectroscopy was used to compare the crystalline phase of the coarse grains (optically dark region) with the crystalline phase of the fine grains (optically light region). The spectra in Fig. 3(d) show that the coarse grains near the contact area with the substrate are primarily monoclinic, whereas the fine grains near the end of the bar are primarily tetragonal.²⁶ SEM BSE diffraction verified the phase composition from the Raman spectra, but the Kikuchi lines were too diffuse for publication due to the unpolished nature of the sample. Figure 3(e) shows the intensity ratio (X_M) as a function of distance along a line extending from the coarse grain region to the fine grain region. The intensity ratio is the sum of the monoclinic 180 and 192 cm⁻¹ peak intensities divided by the sum of the monoclinic peak intensities plus the 148 cm⁻¹ tetragonal peak intensity.²⁵ The fraction of monoclinic phase (f_M)²⁵ is also given as a function of distance from the coarse grains (distance = 0 μm) into the interior of the bend bar (distance = 20 μm). The f_M data appear scattered at high monoclinic concentrations because the calibration curve²⁵ is nonlinear and highly sensitive to X_M at high monoclinic concentrations and is an extrapolation above the 30 wt% monoclinic phase. The dip in intensity ratio for 8.5 μm data point is likely due to the depression running along the middle of the bar in Fig. 3c, which stems from a mold defect in this particular bend bar. Additionally, the number of grains sampled decreases over the line scan as the grain size increases because the spot size remains constant. This sensitizes the data to the structure of a single grain. Although the grain size changes over the course of the line scan, the spectra are not expected to change significantly due to grain size alone. Siu et al.²⁷ and Fangxin et al.²⁸ show a grain size dependence in the Raman spectra of m-ZrO₂ only below 80 nm, which is significantly below the minimum grain size in the bend bars (∼200 nm). Therefore, the spectral changes are likely from phase content alone. The amount of monoclinic phase decreases rapidly at about 14 μm away from the initial region of the line scan. A 10 grain average of the grain diameter near the 14 μm mark indicates that the decrease in the monoclinic phase occurs at a grain size of 540 ± 70 nm. A grain size of 540 nm roughly correlates to the grain size above which the tetragonal phase is no longer stable for 3 mol% yttria in the zirconia alloy.²⁹ Therefore, the curvature occurring during firing is likely due to localized compositional variations leading to grain coarsening and subsequent tetragonal phase destabilization, producing a ∼3–5 vol% expansion³⁰ on the side of the bend bar in contact with the 96 wt% alumina substrate. This volume expansion on the side of the bend bar contacting the substrate causes the bars to warp with the concave side facing away from the substrate.

Fig. 3.

The source of warping in the Gen2 bend bars when fired on a 96 wt% pure alumina substrate is a result of localized destabilization of the tetragonal phase. (a) The transmitted light image of a Gen2 bend bar reveals that this bar was fired on its side and warped with the concave side facing away from the substrate. The radius of curvature is 502 μm. The more opaque or darker region in this transmitted light image corresponds to larger grain sizes shown in (d), and primarily monoclinic zirconia (m-ZrO₂) shown in (d) and (e). (b) This transmitted light image shows a straight Gen3 bend bar that was fired on a 99 wt% pure alumina substrate. There is no localized decrease in transmitted light in Gen3 bend bars verifying the uniform, fine-grained microstructure. (c) The backscattered electron SEM images of the opaque region of the bar in part (a) reveal that the dark region is composed of coarse grains. The approximate location of the line scan in (e) is shown. The depression in the center of the bar is a mold defect in this particular mold (incomplete photoresist development) and not a crack. The depression is probably the cause of the dip in the monoclinic intensity ratio at 8.5 μm in (e). (d) Confocal Raman spectra for the two points labeled in part (a) reveals that the curved region is composed of 58% m-ZrO₂, while at the fine-grained end of the bar the phase composition is 98 % tetragonal zirconia (2% m-ZrO₂). (e) The confocal Raman line scan whose location is shown in (a) and (c) reveals that the fraction of monoclinic phase decreases as a function of distance away from the area of contact with the substrate (defined as distance = 0 μm). The abrupt decrease in m-ZrO₂ content beginning at a distance of 14 μm corresponds to an approximate grain size of 540 nm.

The cause of the localized grain growth is indicated by the composition of the 96% pure alumina substrate based on X-ray fluorescence analysis. The substrate contained 0.11% Na₂O, 1.24% MgO, and 2.43% SiO₂ by mass. An Al₂O₃–SiO₂–Y₂O₃ eutectic occurs between 1300° and 1400°C, and can cause liquid-phase sintering of 3Y-TZP when Al₂O₃ and SiO₂ are present as impurities.³¹ In the present case, localized liquid-phase sintering due to contact with the impurities in the substrate likely causes grain growth at the primary point of contact between the 3Y-TZP bend bars and the alumina substrate. The decrease in translucency in the curvature region may be due to grain-boundary scattering in the birefringent monoclinic phase³² and/or scattering due to microcracking³³ from the phase transformation. Warping during sintering was eliminated by switching to a higher purity 99 wt% α-Al₂O₃ substrate (0.08% Na₂O, 0.27% MgO, and 0.18% SiO₂), but maintaining the same 1400°C firing temperature. Minimization of warping from a deflection of 8%–1.5% using a higher purity substrate is consistent with the hypothesis that the impurities in the 96 wt% substrate were responsible for this type of warping.

The second type of warping is characterized by out-of-plane curvature in the as-molded orientation only. This type of warping occurs in the green state and persists through sintering as shown in Fig. 4; however, it only appears after RIE and not when the test bars are still in the mold. The line-scan data in Fig. 4 can be fit to a circle and the radius of curvature obtained. The radius of curvature of the green specimen is roughly twice that of the corresponding fired specimen. The most plausible explanation is that of residual drying stress. If this hypothesis is correct, then the mold constrains the dried green body and prevents warping until the mold is removed by RIE. Warping can occur by either a moisture gradient through the thickness of the green body²⁰ or by capillary tension.³⁴ The short transport distance in the 20.8-μm-thick green bodies makes a through thickness moisture gradient less likely. As-molded warping is most likely due to the capillary tension that develops during drying as the body is constrained by the mold but released when the mold is removed by RIE. Residual warping away from the substrate has been noted by several authors in ceramic thick films dried on substrates.^34–36 The small 0.6% differential strain needed to produce the 1.79 mm radius of curvature in the green bend bar in Fig. 4 is similar to the small shrinkage strains associated with the collapse of the repulsive dispersion layer as the body moves from a saturated state to a dry state.^34,37

Fig. 4.

The height profile along the length of a Gen3 bend bar shows modest warping after reactive ion etching (RIE) and after sintering. The upper chart shows warping on a magnified height axis, while the lower chart shows warping on a 1:1 height to length scale. The dotted lines represent the fitted curves used to calculate the radii of curvature. The radius of curvature after RIE is 1.7 mm, and the radius of curvature after firing was 3.6 mm for this particular bend bar.

Overall, the warping is reduced from a deflection of 8% for the Gen2 specimen to 1.5% for the Gen3 specimen. A deflection of 1.5% is tolerable in the mesoscale bend bars, which have an aspect ratio of 19:1, meaning the bars have an average maximum height difference of 5 μm. Although the deflection is small in Gen3 bend bars, it will not be acceptable for higher aspect ratio parts⁵ for which the manufacturing process is ultimately intended. Efforts to further reduce the warping and accompanying drying cracks in the higher aspect ratio parts will be addressed in a later report.

Accurate dimensional measurements are required in most ceramic manufacturing processes to verify the final part dimensions and to account for shrinkage in the design specifications for near-net shape forming because machining fired ceramics is impractical especially at the mesoscale. Table II summarizes the dimensions and percent dimensional change of the Gen3 bend test bars from the mask design through firing. The mold dimensions are slightly smaller than the design dimensions, but are within 2 μm. The as-molded bend test bars are 2.5 μm thinner than the mold due to the buffing process. After RIE, the test bars appear to grow in length and thickness, but shrink in width. The apparent growth in the thickness is due to a small amount of photoresist under the parts that is not totally removed in the RIE process. The growth in the length may be due to the RIE process itself or warping along the length. The sintering process results in the largest dimensional change. Isotropic sintering would result in a linear shrinkage of 24.5%, assuming a green density of 43% of theoretical density (suspension solid concentration). If the post-RIE dimensions are used as the green size, isotropic shrinkage in sintering is verified. If the as-molded dimensions are used as the green size, the thickness shrinks less than the width or the length during sintering. The likely explanation is that the body consolidated more in the thickness before sintering. This is expected to occur in one-sided drying during the constant rate period,³⁸ which consolidates the thickness, but not the width or the length.

Table II. Dimensional Measurements of Three-Point Bend Test Bars.

	Process Step	Width (μm)	±95% Conf.	Thickness (μm)	±95% Conf.	Length (μm)	±95% Conf.
	Design	33.3	NA	25.0	NA	416.7	NA
	Mold	32.4 (12)	0.5	23.3 (12)	0.5	414.7 (12)	0.7
	Green Part in Mold	34.8 (17)	0.2	20.8 (17)	0.6	415.6 (17)	0.5
	Post-RIE	33 (17)	1	23.0 (17)	0.7	423 (17)	2
	Sintered	25.8 (65)	0.5	17.4 (37)	0.3	332.1 (65)	0.6
% Change	In mold to sintered	-26%	2%	−16%	3%	−20.1%	0.2%
	Post-RIE to sintered	-23%	4%	−24%	3%	−21.5%	0.5%
	Design to sintered	-23.0%	0.7%	−30.5%	0.7%	−20.29%	0.05%

The percent change between the design, as-molded, and post-RIE dimensions versus the sintered dimensions. The number of samples measured is given inside the parentheses. RIE, reactive ion etching.

The edge resolution of the parts is limited by the resolution of the mold, which is formed by UV photolithography. Therefore, the resolution is on the order of a few microns depending on the exposure parameters.³⁹ However, the resolution at the edge corresponding to the interface between the suspension, mold, and atmosphere on the top side of the part may be on the order of a grain size as was shown in Part 1 of the series.⁷ In order to better determine the lateral resolution of the process, triangular shapes with a 30° pointed tip were made on the mask. By measuring the tip radius, the lateral resolution limitations imposed by the LM-RIF process can be assessed. Figure 5 shows an image of a triangular mold tip (a) and a triangular part tip (b). The tip radius of the mold is 3.3 μm, whereas the radius of the part is 3.0 μm. This is the effective lateral resolution of the LM-RIF process for a 24-μm-thick photoresist and is consistent with the diffraction limitations imposed by UV photolithography.³⁹ A finer resolution (sub-50 nm) may be achieved by using a higher resolution exposure technique such as electron beam exposure,⁴⁰ but this more expensive technique is not required for the current work. Through the use of optical profilometry, the 3D quantification of many mesoscale parts is possible, for example the bend bars shown in Fig. 5(c). This has enabled geometric deviations to be identified and eliminated through process improvements. Additionally, accurate strength measurements can be made at the mesoscale because the test bar geometry can be accurately measured.

Fig. 5.

(a) The radius of curvature of a 24-μm-thick triangular mold cavity is 3.3 μm with resolution limited by the UV-photolithography. (b) The 3.0 μm tip radius of a part produced in the triangular mold cavity is nearly identical to the mold cavity radius. Therefore, the resolution of the LM-RIF process is limited by the mold-forming process and not the ceramic powder processing. (c) A 3D optical profilometer image representing the height of Gen3 parts. Once the data set is collected, many different measurements can be made yielding reliable mesoscale dimensional data. The scale on the right is slightly misleading because there is a high point at the very top of the scan. For reference, the maximum height difference in the bar marked (1) is 8.5 μm, whereas the maximum height difference of the lower bar marked (2) is 2.4 μm.

With each successive generation, the elimination of geometric irregularities resulted in a strength improvement as given in Table I and graphically as the inset of Fig. 6. The average strength increases from 829–913 MPa in Gen1 (the range is due to trapezoidal cross section) to 2.24 GPa in Gen3. The Weibull modulus (m) is roughly equal for both the Gen1 (m = 6.8) and the Gen3 (m = 6.3) specimens, but the characteristic strength (σ_o) increases from 888–978 MPa to 2.39 GPa as shown in Fig. 6. A Weibull plot is not available for Gen2 material because only five specimens were tested. The Gen2 specimen was the first to be measured for dishing with the optical profilometer and the 4 μm average difference in height resulted in a large uncertainty in the stress calculation. An average bend strength of 2.24 GPa for the Gen3 bars is relatively high, but consistent with the expectations based on the specimen size scale. If Lange's average strength of 1340 MPa (σ_{4−pt, Lange}) for 2.3Y-TZP⁹ is used for comparison and the loading factors (four-point versus three-point) and specimen surface areas (S) (1.5 cm² vs 2900 μm²) are taken into account, a mesoscale bend bar with the size of a Gen3 specimen and a Weibull modulus (m) of 6.3 should have a strength (σ_{3−pt, meso}) of 9.4 GPa according to Davies⁴¹

Fig. 6.

Third generation (Gen3) bend bars without trapezoidal cross sections, minimal dishing and warping are significantly stronger than (Gen1) bend bars with the three geometric irregularities. The two parameter Weibull curve fit to the strength data gives σ_o = 888−930 MPa, m = 6.8 and σ_o = 2.39 GPa, m = 6.3 for Gen1 and Gen3 specimens, respectively. The two sets of data for the Gen1 bars represent the geometric uncertainty based on the trapezoidal cross section, while the Gen3 data is represented using the average height of each bar and ignores the uncertainty due to the dishing (0.9 μm on average). Uncertainty due to dishing also applies to Gen1 specimen, but was not characterized at the time of testing. The inset shows the strength increase with each material generation that has occurred with the systematic elimination of geometric defects.

$${\sigma }_{3‐\text{pt},\text{meso}}={\sigma }_{4‐\text{pt},\text{Lange}}{\left(\frac{m+2}{2}\right)}^{1/m}{\left(\frac{S_{\text{Lange}}}{S_{\text{meso}}}\right)}^{1/m}$$

assuming surface flaws are strength limiting. It is not likely mesoscale bend bars will reach strengths as high as 9.4 GPa due to limits imposed by surface roughness. In addition, the grain size in Gen3 bend bars is approximately 300–600 nm, which is likely too fine for transformation toughening in the 3 mol% Y₂O₃–TZP,^42,43 making the specimen less resistant to defects. A strength as high as 3–4 GPa is thought possible with further surface and microstructure refinements. Future experiments will examine the effect of these refinements.

IV. Summary

Several modifications to the original LM-RIF process have eliminated the trapezoidal cross sections characteristic of Gen1 parts, reduced the amount of dishing in Gen2 parts, and eliminated warping that occurred during firing. The current Gen3 parts are orthogonal with uniform rectangular cross sections and have dimensional tolerances from 1 to 3 μm and a tip resolution of 3 μm, which is characteristic of the UV-photolithographic process that forms the mold cavities. RIE has replaced thermolysis as the method of mold removal, and a buffing process has been added to eliminate dishing. The warping during sintering was due to grain growth likely from liquid-phase sintering enabled by contact with the impurities in a 96 wt% pure alumina substrate. The localized grain growth destabilized the tetragonal phase, causing a localized volume increase that subsequently warped the bend bar. The use of a 99 wt% pure substrate eliminated this type of warping. The second type of warping occurs in the green state and is hypothesized to be drying related, but the amount of warping is small enough to neglect in the Gen3 bend bars. These process improvements have increased the average bend strength from 829 to 2236 MPa.