2.1.

Principles of Grayscale Lithography

There are two key elements that are required for grayscale photolithography: (1) a nonideal resist and (2) subresolution mask features. Unlike ideal resists with infinite contrast, practical photoresists have large yet finite values for contrast (Fig. 1). These finite values imply that there will be a range of exposure doses when the resist is partially exposed. This leads to partially developed resist with final thickness ranging between the initial (unexposed) value and zero.

Fig. 1

Contrast curves of an ideal resist and real resist. The remaining resist thickness of a positive-tone resist after development is plotted as a function of exposure dose. The contrast is defined as the slope of the curve between the highest dose when the remaining resist retains its undeveloped thickness ($D_0$) and the dose when the resist is fully developed ($D_1$). The ideal resist in microelectronics has an essentially infinite contrast; real resists may have high but finite contrast, where $D_0$ may be significantly smaller than $D_1$. Grayscaling will occur within this dose range between $D_0$ and $D_1$.

The second component in grayscaling is the use of subresolution features on the photomask, which control the effective dose and its spatial distribution at the resist. As shown in Fig. 2, the aerial dose modulation increases from uniform exposure when the features are much smaller than the resolution limit of the optics ($<450\mathrm{nm}$ lines and spaces) to slight modulation (between 500 and 900 nm lines and spaces) to fully resolved features (2000 nm lines and spaces and above). We note that the trend shown in Fig. 2 is universal, although the numerical values of the nominal lines and spaces are specific to the optical system under consideration. In the case of Fig. 2, we simulated the aerial image obtained with our i-line stepper (see below). In conventional optical lithography, the emphasis is on patterns that result in some degree of intensity modulation, and the goal of the high-contrast resist is to degrade this modulation as little as possible. In contrast, for the purpose of grayscale lithography we explicitly utilize feature sizes that result in minimal aerial image modulation and prefer to employ resists with low contrast to “wash out” the little image modulation that may still be present.

Fig. 2

The average intensity distribution at the wafer plane of the light projected through a mask for various line/space dimensions. In all cases shown, the line/space ratio is $1:1$. The simulations were performed with PROLITH and used the optical system of the current work: an i-line stepper (365-nm wavelength), with NA of 0.24 and a partial coherence of 0.70 (see also text). The resolution limit [Eq. (1) in the text] is $\sim 450\text{-}\mathrm{nm}$ lines and spaces. In grayscale lithography, subresolution features of less than $\sim 450\mathrm{nm}$ were employed.

In this version of grayscale lithography, the information content of the photomask is not the smallest possible printable resolution. Instead, it is on a larger spatial scale: the average dose at the resist plane is determined by the relative area of the transmissive parts of the mask versus the absorptive (or reflective) parts. While Fig. 2 simulates only lines and spaces with a $1:1$ ratio and the resultant relative intensity is always $\sim 0.25$, Fig. 3 shows that in the subresolution regime the average intensity can be adjusted by changing the line-to-space ratio: the higher the ratio, the higher the exposure dose and the thinner the postdevelopment resist thickness.

Fig. 3

Diagram showing the pattern at the photomask and the postdevelopment resist profile when the features to be patterned are much larger than the resolution of the optical system and the features are below the resolution limit.

The key to using grayscale photolithography to make arbitrary shapes in the resist is to modulate the aerial intensity with a series of subresolution masking features. By tuning the density and location of subresolution features, the effective exposure dose can be modulated to control resist thickness and therefore be used to make arbitrary 3-D shapes.

2.2.

Resists and Exposure Tool

SPR518 and SPR220 resists were used for grayscaling with an i-line exposure tool on a 200-mm platform. We used a Canon FPA-3000 iW stepper, which has a 50-mm field size, $2\times$ reduction, an exposure wavelength ($\lambda$) of 365 nm, a partial coherence ($\sigma$) of 0.70, and a numerical aperture (NA) of 0.24. For the thinner resist processing, SPR518 was spun to a thickness of $\sim 1180\mathrm{nm}$ and soft-baked at 95°C for 60 s, followed by a postexposure bake at 110°C for 80 s, and a postdevelopment bake at 115°C for 60 s. For the thicker resist processing, SPR220 was spun to a thickness of $\sim 5000\mathrm{nm}$ and soft-baked at 115°C for 90 s, with a postexposure bake at 115°C for 90 s, and developed in MF-24 for 60 s.

2.3.

Create Resist Models in PROLITH

Grayscale lithography requires resist processing in the exposure range between fully exposed and unexposed, $D_1$ and $D_0$ in Fig. 1. A contrast curve for a particular resist is required to determine the range of exposure doses that will enable grayscaling. The contrast curves for SPR518 and SPR220 were determined without a mask by performing an exposure matrix on $1\mathrm{cm}\times 1\mathrm{cm}$ open frames on the Canon FPA-3000 iW. The resist thickness was determined by ellipsometry. The contrast curves for SPR518 and SPR220 are shown in Fig. 4, with extracted dose-to-clear $D_1$ values of $\sim 930$ and $\sim 2400{\mathrm{J}/\mathrm{m}}^2$ for SPR518 and SPR220, respectively.

Fig. 4

Contrast curves for (a) SPR518 and (b) SPR220 as measured experimentally (actual) and simulated with PROLITH. By iterating model elements with known model parameters, a good fit to the experimental data can be obtained, especially in the highlighted dose ranges.

Next, a model for simulation must be created and calibrated for good agreement with the experimentally measured contrast curves. A simulation software that models the optical response, chemical behavior, and physical geometries of photolithographic processes, PROLITH,^13,14 was used to calculate contrasts curves. The simulated curves were then compared to curves that were measured experimentally. This requires the specification of the parameters listed in Table 1. A summary of the PROLITH model parameters is tabulated in Appendix A.

Table 1

Model inputs for PROLITH.

For this work, the lumped parameter model (LPM) type was sufficient. The resist thicknesses were input from measurements made with ellipsometry. The absorption coefficients for each resist can be calculated for an unexposed resist using the Dill parameters that are frequently listed in the resist datasheets. The indices of refraction and resist tones were taken from the resist datasheets as well. The minimum development rate, or Development $R_{\min }$, is a parameter in the LPM and can be determined by measuring the unexposed resist thickness after develop and bake. The imaging method is determined by the exposure tool configuration. The three parameters, image diffusion length, dose to clear, and resist contrast were iterated independently to achieve acceptable agreement between experimental and simulated contrast curves. In this work, five to ten iterations of each parameter were found to be sufficient.

Using the above model parameters, the experimentally determined resist thicknesses were fit to simulated contrast curves. Figure 4 shows the PROLITH-simulated contrast curves, as well the dose ranges over which the fit was best: 575 to $850{\mathrm{J}/\mathrm{m}}^2$ for SPR518 and 1000 to $1700{\mathrm{J}/\mathrm{m}}^2$ for SPR220. These dose ranges are also highlighted in Fig. 4 for the two resists.

2.4.

Estimating Tool Resolution

The resolution limit is a function of the exposure and development processes. The resolution limit ($R$), defined as the pitch at which the aerial image modulation approaches zero, is determined by the optical performance of the stepper. Assuming aberration-free imaging, $R$ can be estimated using Eq. (1), if the wavelength ($\lambda$), partial coherence ($\sigma$), and NA of the source are known.

Using the optical parameters of the Canon FPA-3000 iW, the resolution limit is $\sim 900\mathrm{nm}$. Thus, the smallest features one can expect to resolve with this stepper are $R/2$, which is $\sim 450\mathrm{nm}$. This value can be obtained only with an ideal photoresist. In practice, the resist response and its processing conditions may further degrade the achievable resolution. While this effect is a drawback in high-resolution lithography, it is a desired feature of grayscale lithography.

2.5.

Correlating Resist Thickness and Average Intensity with Aerial Density

Using PROLITH, the average intensity at the wafer plane and the postdevelopment resist thickness can be determined as a function of aerial density (AD) at the photomask for a range of incident doses. To determine dependence of resist thickness and average intensity on the AD, a series of test designs that utilize subresolution features, as prescribed by the lithography tool, can be input into PROLITH. The photomask AD of a test design is determined by the amount of open space, by calculating the percentage area coverage of what would be nontransmissive features on a mask. For a simple test mask, lines and spaces are suitable. For this work, the pitch between lines was set to be 895 to 900nm in wafer units and the width of the line will determine the AD of the feature. Figure 5(a) and Eq. (2) show how to determine the AD. The output from PROLITH, regarding average intensity at the wafer plane as a function of AD at the photomask, is shown in Fig. 5(b).

Fig. 5

(a) Examples of the photomask test design used for correlating resist thickness with an AD. (b) Average relative intensity at the wafer plane as a function of AD as calculated by PROLITH.

In Fig. 5, the transmissive “slits” in the photomask cover a fractional area that is (1-AD). Note that in this subresolution regime, when the pitch is less than the resolution limit $R$ [Eq. (1)], the transmitted light is proportional to the square of the slit area¹⁵ and not to the area itself. This regime is also sometimes referred to as the “Rayleigh limit” in scattering theory. Indeed, as Fig. 2 shows, the relative intensity at the wafer plane is $0.25={(1-\mathrm{AD})}^2$, where $AD=0.5$ and $R$ is $<900\mathrm{nm}$ or below.

As resist exposure dose and intensity at the wafer plane are directly proportional, with exposure time as the proportionality factor, reducing the AD increases the relative intensity, which in turn increases the effective dose for a given exposure time. Using the upper and lower limits of the doses that showed a good fit between experimental and PROLITH-determined contrast curves, process windows can be defined for a given AD. Such process windows for SPR518 and SPR220 are shown in Fig. 6. For example, in designs with the SPR518 resist process, exposure conditions should range between 2000 and $3000{\mathrm{J}/\mathrm{m}}^2$ around the photomask features with an AD of 45%, which corresponds to 400-nm lines on an 895-nm pitch. For the SPR220 resist process, exposure conditions should range between 2200 and $4000{\mathrm{J}/\mathrm{m}}^2$ around the features with an AD of 35%, which is a 315-nm line width at a 900-nm pitch. It should be noted in Fig. 6 that the $y$ axis is on a logarithmic scale, which indicates a wider process window with higher ADs.

Fig. 6

Process windows for (a) SPR518 and (b) SPR220. Calibrated PROLITH models will match well with designs and exposure conditions in the process window (blue region).

To validate the estimated process windows, contrast curves with various ADs were measured experimentally and compared with those generated with PROLITH. These contrast curves are shown in Fig. 7 and agree with the predicted process windows in Fig. 6.

Fig. 7

Contrast curves for various ADs for SPR518 and SPR220.

4.1.

Blazed Gratings for Chrisp Compact Visible, Near-Infrared/Shortwave-Infrared Imaging Spectrometer

Visible through infrared (IR) spectrometers are of use for capturing images that contain not only spatial but also compositional and thermal information. This renders them desirable for a host of science and exploration applications. However, even the state-of-the-art imaging spectrometers are quite large. While they can serve a satellite payload, there is a growing need to deploy such imagers on smaller platforms, such as unmanned aerial vehicles and small satellites. While compact forms of IR spectrometers have been demonstrated by Van Gorp et al.²⁰ at the Jet Propulsion Laboratory (JPL), these are too large for many drones or small satellites.

A key element that drives the size of modern spectrometers is the diffraction grating: larger area diffraction gratings can enable smaller distances between optics and therefore smaller volumes of the overall optical system. Further, the use of an appropriately blazed grating improves the efficiency, which in turn improves resolution and speed of sampling, as shown by JPL.²⁰ As shown in Fig. 9, Chrisp et al.²² have proposed an IR imaging spectrometer, the Chrisp Compact visible, near-infrared/shortwave-infrared Imaging Spectrometer (CCVIS), which occupies $11\times$ less volume than the state-of-the-art imaging spectrometers with similar optical performance.²⁰ The key to this new capability is the requirement for a large area grating with multivalued blaze angles.

Fig. 9

The CCVIS optical form.²¹

The existing methods of fabricating blazed gratings are challenging. Employing diamond turning for blazed gratings is expensive and scanning electron beam lithography is limited to areas much smaller than that required for the CCVIS. Using grayscale photolithography, we show that large areas of multiangle blazed grating are achievable and have comparable performance to those fabricated with scanning electron beam lithography.

Three different blazed grating designs were fabricated using PROLITH-guided grayscale lithography. One design has a single blaze, and the two other designs feature multiple blaze angles. These are shown in Fig. 10. These designs are particularly challenging as the blaze angles are very shallow. The gratings were fabricated using the SPR518 resist process, which was discussed in Sec. 2. Following grayscale lithography, the patterned resists were coated with 50 nm of aluminum to make them reflective throughout the visible and near-infrared. A 3-D profile was captured using a Zygo Nexview NX2, as shown in Fig. 11. There is excellent agreement between the designs, simulated profiles from PROLITH, and the measured data, as shown in Fig. 12. The relative scatter, and therefore signal to noise, of the blazed gratings is shown in Fig. 13. It should be noted that the measured signal-to-noise ratio of 4 to 5 orders of magnitude is comparable to that of the blazed grating fabricated by scanning electron beam lithography.^23,24 These results clearly indicate that grayscale photolithography is a lower-cost, higher-throughput alternative for fabricating blazed gratings for high performance optical components.

Fig. 10

Three designs feature various blaze angles.

Fig. 11

The 3-D resist profiles of completed blazed gratings using a Zygo Nexview NX2.

Fig. 12

Comparing the design, PROLITH simulations, and measured profiles of the blazed gratings for the CCVIS.

Fig. 13

Relative scatter measurements as a function of the angle of incident light.

4.2.

Solid Emitters for Highly Integrated and Miniaturized Electrospray

Electrospray is the electrostatic atomization of a conductive liquid with an applied voltage. Generally, this process requires a very high electric field at the liquid surface, necessitating the use of sharpened structures that concentrate the electric field. This process is illustrated in Fig. 14, where a voltage is applied between an extractor plate (blue) and an array of emitter tips that are covered in a conductive fluid (red). When the applied voltage exceeds some threshold, ions or fluid droplets will be pulled from the emitter tips toward the extractor plate.^25,26

Fig. 14

An illustration of the electrospray process.

Electrospray has utility in applications such as sources for mass spectrometry,²⁷ ink jet printers,²⁸ thrusters for electric propulsion for satellites,²⁹ and air purification.³⁰ If the key components (emitters, extractors, fluids management, and power supply) of electrospray could be miniaturized, this would open the door for new capabilities, such as ubiquitous chemical monitoring through small-scale mass spectrometers and propulsion for ultraminiature (femtoscale) satellites.³¹ Silicon-based microfabrication is a promising approach for miniaturized electrospray systems.^32–35 While silicon microfabrication is often restricted in terms of the ability to make 3D structures, grayscale lithography offers sufficient control over the emitter shape to tune electrospray performance.

Different emitter architectures were fabricated using PROLITH-guided grayscale lithography, with varying emitter height, base width, and tip radius of curvature. These designs are challenging, as relatively tall structures are needed compared with the resist thickness, leading to very steep angles in contrast with the shallow angles of the blazed gratings in the CCVIS. The emitters were etched into Si using a Bosch deep-Si etch process with a silicon-to-resist selectivity of $40:1$, whereby the silicon etches 40 times faster than the resist. (see Sec. 2). The resulting emitters are shown in Fig. 15.

Fig. 15

The 3-D resist profiles of electrospray emitters taken with an optical profiler (Zygo Nexview NX2) and matching scanning electron micrographs (SEMs) of the resulting electrospray emitters after the Si etch process.

Defining features in a process regime where there are instabilities will result in poor pattern transfer fidelity. There tends to be more process instabilities at the start of many dry-etch processes. As patterns with thinner resist will transfer earlier in the Si etch process, these areas will not transfer patterns well. This is evident in Fig. 15 as the base of each fully formed emitter in Si is $\sim 25\mu \mathrm{m}$ smaller than that defined by its resist feature. Further, the shortest emitter, which has the thinnest resist ($1.2\mu \mathrm{m}$), forms in the shortest amount of time and has a rougher surface compared with those emitters that take longer to fully form (taller emitters, thicker resist).

To test the performance of the emitters, the ionic liquid EMI-BF4 was applied to the surface of an array of emitters. The surfaces of the emitters were roughened to facilitate wetting of the entire surface with EMI-BF4, as shown in Fig. 16. A grounded plate was positioned over the array to measure the current generated by the spray as voltage was applied to the emitter array. The current measured in response to the applied voltage is shown in Fig. 17. When the voltage exceeds 1 kV, the electrospray is initiated, as evidenced by the measured current of $\sim 1$ to $2.5\mu \mathrm{A}$.

Fig. 16

SEMs of an array of emitter tips. (a) An overly wet emitter tip b) A tip that is almost fully wet.

Fig. 17

Sampling of ion current from the electrospray while increasing the magnitude of the extraction voltage.

4.3.

Liquid Microlenses with Adjustable Focusing and Beam Steering

Electrically controlled micron-scale liquid lenses are being developed that combine both adjustable focusing and beam steering in a single optical element with the goal of applying them to optogenetics^36,37 for in-vivo mapping of brain activity with a single cell resolution. The liquid microlens is formed by the interface shape between two immiscible liquids having different refractive indices, which are contained in a conically tapered lens cavity etched into a fused silica substrate, as shown in Fig. 18. Interdigitated electrodes are patterned along the sidewall of the taper to control the liquid lens curvature and tilt through electrowetting.³⁸ In electrowetting, the surface energy between a conductive liquid in contact with a hydrophobic solid substrate is modified by the application of voltage, changing it from hydrophobic to hydrophilic in prescribed regions via suitably designed electrodes covered by a hydrophobic film. The observed result is a change in the contact angle between the liquid–liquid interface and the solid substrate.

Fig. 18

(a) Liquid microlens design that combines both active focusing and steering by controlling the interface formed between two immiscible liquids. $D_o$ is the lens diameter and $D_{\mathrm{ca}}$ is the clear aperture diameter. The liquid interface is contained within a 45-deg-tapered conical region. Reprinted with permission from Ref. 38. Copyright 2017 Optical Society of America.

In this work, four different microlens cavity sizes were fabricated with an outside diameter, $D_o$ of 50, 60, 75, and $100\mu \mathrm{m}$. Based on numerical simulations,³⁹ the taper angle and taper depth that would provide the best dynamic range of the liquid lens were found to be 45 deg and $15\mu \mathrm{m}$, respectively. To form the sloping sidewall of the conical taper, grayscale lithography was used.

To form the conical taper, subresolution annular lines with radially varying linewidths were used between the outside diameter and the inside diameter of the taper on the mask. Setting the pitch $P$ between subresolution features equal to $R$ the resolution limit of the exposure system (from Eq. 1), which was 895 nm (Sec. 2 above), the number of subresolution features between the inside and outside diameters was determined as

Fig. 19

Example of a grayscale mask used for a liquid lens cavity having a $50\text{-}\mu \mathrm{m}$ OD and a $25\text{-}\mu \mathrm{m}$ ID. Linewidths vary radially in size from 340 nm in the inner diameter to 550 nm in the outer diameter and are equally spaced at a pitch $P$ equal to 895 nm.

PROLITH was used to predict the resist profile for the four different microlens designs based on the mask design shown in Fig. 19. The predicted profiles are shown in Fig. 20 for $5\text{-}\mu \mathrm{m}$-thick Shipley SPR220 photoresist, with an exposure dose of $4900{\mathrm{J}/\mathrm{m}}^2$.

Fig. 20

Resist profiles predicted from PROLITH. (a) For lens design 1: $50\mu \mathrm{m}\mathrm{OD}\times 25\mu \mathrm{m}\mathrm{ID}$. (b) For lens design 2: $60\mu \mathrm{m}\mathrm{OD}\times 35\mu \mathrm{m}\mathrm{ID}$. (c) For lens design 3: $75\mu \mathrm{m}\mathrm{OD}\times 52\mu \mathrm{m}\mathrm{ID}$. (d) For lens design 4: $100\mu \mathrm{m}\mathrm{OD}\times 75\mu \mathrm{m}\mathrm{ID}$.

Figure 21(a) compares the measured resist profile after exposure and development with the predicted profile from PROLITH for the $50\text{-}\mu \mathrm{m}$ lens design. The agreement between simulation and experiment is remarkably good. It is important to note, however, that with these photomasks the profiles do not have a linear slope. This is mainly a result of not being able to have enough graduated subresolution features between the inner and the outer diameters of the lens for this pitch and radial distance, with the correct linewidth variation. As a result, a second processing step, thermal reflow, was required to transform the nonlinear profile into one that is more linear. It was found, through experimentation, that baking at 150°C for 5 min was sufficient for smoothing the resist profile, especially near the transition at the inner and outer taper diameters, as shown in Fig. 21(b).

Fig. 21

(a) Comparing the actual resist profile after exposure and development with the predicted profile from PROLITH for the $50\mu \mathrm{m}\mathrm{OD}\times 25\mu \mathrm{m}\mathrm{ID}$ lens. (b) Comparing the resist profiles after exposure and after reflow at 150°C for 5 min.

The next step was to transfer the resist profile [Fig. 22(a)] into a fused silica substrate. An optimized RIE process that created a $12\text{-}\mu \mathrm{m}$-deep conical taper with a 45-deg sloping sidewall was developed [Fig. 22(b)]. Once an optimized etch was developed, additional processing steps were required to turn the structure into a functional electrowetting lens, including metallizing and patterning electrodes on the side walls and the taper, as well as patterning a hydrophobic film just within the lens cavity. The results from these processing steps are shown in Fig. 22. Details of the liquid lens fabrication, packaging, and testing can be found in the report from Berry et al.³⁸

Fig. 22

(a) Measured resist profile after reflow at 150°C, for a $50\text{-}\mu \mathrm{m}$ outside diameter and $28\text{-}\mu \mathrm{m}$ clear aperture lens design. Image captured from a 3-D microscope (Keyence). (b) Measured etch profile in fused silica. Final lens cavity dimensions: $55\text{-}\mu \mathrm{m}$ outside diameter, $32\text{-}\mu \mathrm{m}$ clear aperture, $12\text{-}\mu \mathrm{m}$ etch depth, and 43-deg taper angle. Image captured from a 3-D microscope. (c) Top-down microscopic image of quadrupole electrode design after metal patterning and etch. (d) SEM image of quadrupole electrode design after depositing 500 nm of PECVD oxide. (e) SEM image after CYTOP processing. Reprinted with permission from Ref. 38. Copyright 2017 Optical Society of America.