2.1.

Calibration

A calibration step is required to map the nonlinear (photoresist/processing dependent) correlation between UV exposure intensity and photoresist development depth. This information is crucial for correctly adjusting layer segmentation in the GSC process, a necessary step as most photoresists are not chemically engineered for grayscale lithography. The nonlinear relationship is assumed to vary depending on a given set of process variables—i.e., photoresist type, spin speed/time, soft bake time, LPG settings, and so on. Ideally, a multivariable analysis (using principal component analysis or similar technique) would provide a generalized model to identify the effect each physical process variable has on development depth. For the work presented in this manuscript, however, a simplified univariable mode of photoresist development depth was chosen. This simplified model was selected for clarity in presenting the conversion method and resulted in the calibration procedure described henceforth. As such, when using this method, the authors recommend a new calibration whenever there is a change in any aspect of the photoresist processing. If the only aspect changing is the CAD model, however, a new calibration is “not” required. Before evaluating nonlinearities in the photoresist, equipment and processing variables require evaluation. The thickness of the photoresist and maximum UV exposure intensity need to be balanced such that applied LPG beam intensity has the ability to expose both partially and fully through the photoresist. This is an equipment-based step involving LPG setup and photoresist deposition parameters. For example, if at the maximum UV exposure intensity development occurs only through a fraction of the total available photoresist thickness, problems in postprocessing may occur. If the structure is being used for mold transfer, however, this may be acceptable if total development depth is adequate. Likewise, if the entirety of the photoresist is developed before the maximum LPG exposure levels, then multiple layers will register as fully exposed in the fabricated device and a portion of the topography features will be lost.

The mapping process entails writing a standardized grayscale file (in this case, a ramp structure) on the LPG using the same photoresist, processing parameters (spin speed/time, soft bake, and so on), and optical setup as the planned device. Any calibration structure geometry can be used provided that it is sufficient to establish a relationship between desired and experimental development depth. A ramp-type structure, however, provides a natural means to obtain such a relationship. After fabricating the calibration structure, its development depth profile is measured to obtain the experimental exposure depth ($d_i$) versus exposure intensity relationship as $n_i$ ranges from $n_0$ to $n_{\max }$. The key in the calibration step is to first assume a “linear” (ideal) exposure/development depth profile. A calibration relationship is established by comparing differences in development depth of the $i$’th layer between the experimental data and linear (or “ideal”) profiles. Profile data from the fabricated calibration ramp structure should exhibit easily identifiable and distinct “steps” corresponding to each change in exposure intensity [Fig. 2(a)]. In reality, the authors experienced mixed success in this regard (mainly depending on type of photoresist used), and therefore, a generalized curve fitting process is later described that applies to all cases.

Fig. 2

Calibration detail for AZ4620 photoresist. (a) Profile of ideal (stepped) calibration structure. Note that for clarity, the number of layers ($n$) has been reduced and layer thicknesses ($t_i$) exaggerated. (b) Initial (uncalibrated) profilometer of actual ramp structure showing discrepancy between ideal and experimental development at higher UV exposure intensity. (c) Calibration plot showing normalized layer thicknesses.

Horizontal ramp length ($L$) is already known from the design of the calibration structure, and maximum photoresist development depth ($D$) can be obtained from a profilometer scan. Using these values, an ideal linear fit is determined [Eq. (1) and Fig. 2(a)] that provides the development depth profile that would result given the ideal initial assumptions stated previously—a linear photoresist exposure/development relationship, where $x$ equals distance from the start of the ramp [indicated by “structure start” on Fig. 2(a)]. Using MATLAB, an $n$’th order polynomial (in this case $n=5$) was fit to a single experimental profilometer scan ($2.7\times {10}^4$ data points, $R^2=0.975$) and shown plotted against the ideal case [Eq. (2) and Fig. 2(b)]. The horizontal ramp length is $10\mu \mathrm{m}$ and development depth is $4\mu \mathrm{m}$ (AZ4620 photoresist). Note that while the two curves agree relatively closely through the first half of the ramp structure, discrepancies become especially evident at higher UV intensities. Equation (3) gives the nonlinearity error ($ϵ$) in the experimental structure. While the calibration goal is to collapse $f{(x)}_{\exp }$ onto $f{(x)}_{\text{ideal}}$ such that the experimental profile emulates the ideal profile as close as possible, the challenge is that the LPG has a limited number of discrete UV exposure intensity settings (i.e., 128), where each results in a “layer” with a fixed development depth:

Therefore, the only means to modify $f{(x)}_{\exp }$ is through tuning layer thicknesses to collapse it onto the ideal, linear curve. The first step is determining actual experimental development depth ($d_i$) of each layer in the fabricated ramp structure. Equation (4) provides discrete values of $d_i$ by evaluating the experimental fit function at $x$ values corresponding to each layer of the fabricated test structure ($x_i$). Stated another way, $d_i$ is the “actual experimental” development depth of the $i$’th layer ($n_i$) for the real-world system. Furthermore, $d_i$ is a fixed value, and there is no way to alter it for a given setup. If a different depth profile is desired, some physical aspect of the grayscale writing process must be changed. Therefore, the only method to collapse the experimental data onto the ideal data is to adjust layers’ thicknesses during the conversion process. Instead of linear segmentation, which was assumed for the ideal structure, CAD model features should be “pushed” to a layer based on the $d_i$ array. Since the GSC process scales layers based on the maximum height of the microstructure (where $n_0$ represents the wafer surface and $n_{\max }$ the model’s peak), normalized layer thicknesses ($t_i$) are required [Eq. (5)]. The plot in Fig. 2(c) shows normalized “ideal” and “experimental” layer thicknesses versus layer number and normalized depth (note that the integral of each curve equals one).

There are several important consequences of the nonlinear exposure relationship demonstrated by the experimental structure. First and most obvious is the inconsistency of depth resolution of different layers. For example, this inconsistency is highlighted when comparing experimental and ideal profiles. While first-order derivatives for the ideal and experimental fit functions are “equal” [point 1 in Figs. 2(b) and 2(c)], experimental layer thickness is approximately “equal” to the ideal case. However, when the first-order derivative for experimental is “greater than” the ideal case, this relationship signifies that real-world resolution in this region is “coarser,” or worse than the ideal case. Likewise, when the first-order derivative for experimental is “less than” ideal, real-world resolution in this region is “finer,” or better than the ideal case. Taking the second-order derivative of the experimental fit function, the inflection point provides a local minimum that shows the region of highest $z$ resolution (Table 1 provides a summary). For example, in the ideal case, each layer has an identical thickness [horizontal line in Fig. 2(c)], meaning that the $z$ resolution of the structure is identical throughout. If this was reality, writing layer 64 out of 128 (50% UV intensity) would result in photoresist developing to half the total depth. Unfortunately, the experimental data confirm that this is not the case. Rather, in the initial 20 layers, resolution is much coarser as the thickness of the experimental layers exceeds that of the ideal. In the middle region (between layers 21 and 105), however, experimental layer thicknesses are much finer than the ideal, resulting in better resolution in this region. Finally, from layer 106 onward, each experimental layer becomes quite thick, indicating poor resolution and extremely coarse features. Overall, this means that when designing structures, engineers should be cognizant of this depth profile and if possible, try to concentrate key design features in regions with the best $z$ resolution. These calibration results should be valid for any grayscale lithography fabricated with identical processing variables as the calibration structure. When a parameter changes (for example, spin speed), however, it is prudent to perform a new calibration and re-verify.

Table 1

Depth resolution relationships between experimental and ideal exposures.

2.2.

Microstructure Design

While the GSC software presented here was written such that 3-D models (parts or assemblies) can be generated in any CAD software capable of exporting to the STL format, there are several design considerations necessary for proper process implementation. Starting off, a neutral plan (or simulated “wafer” substrate) is required [Fig. 3(a)] as the GSC software relies on this plane to define the conversion bounds. Since a 2-D integer array is utilized for writing the final DXF file, this substrate must be a square or rectangular shape with a footprint equal to or exceeding that of the desired microstructure. One necessary consideration needed if a substrate is added after the initial part design, such as in an assembly, is that the top plane of the substrate forms a lower boundary for the conversion process. Thus, any portion of the model coincident to or below top plane of the substrate (or for example, extending out the bottom) will not be “seen” by the GSC software. As such, thickness of the substrate modeled in the negative $z$ direction is irrelevant.

Fig. 3

Design considerations and conversion detail. (a) Initial sample structure designed with an enclosed/overhanging feature. (b) Top view of CAD model, simulating what is observed by the GSC software. (c) Modified model showing the more realistic version of the actual structure that will be fabricated. (d) Detail of integer array that will be created and list of the five parameters written to the mask file for each element. (e) Hemisphere array CAD sample (top), and models of default (middle) and inverted (bottom) photoresist conversion mask options in the GSC software.

Because of how the conversion software was written (and in order to mimic real-world LPG writing restrictions), the output grayscale file represents a topographical map of the model with relief contours resulting from layer segmentation. The repercussion with respect to part design is that only features visible from a “top view” of the model/assembly will be written to the grayscale file, meaning that features, such as undercuts or enclosed voids/cavities, will not be converted and all information regarding these elements lost. For example, Fig. 3(a) shows a sample part that features a void underneath a bridge-type structure. When viewing this part from a topographical view [Fig. 3(b)], this open-space feature is no longer visible and therefore during conversion will be “erased.” To illustrate this point, the structures shown in Figs. 3(a) and 3(c) will produce identical grayscale mask files using this GSC process.

Finally, since the STL file format strips all superfluous information about the model and only saves surface geometry, the units or scale used is irrelevant as long as consistency is maintained within the model in the $xy$ direction (scaling is set during the conversion process). For example, when designing a part in CAD, a square substrate of 100 in. per side will result in a model identical to one designed with 100 m per side and will be read by the GSC software utility as 100 “units” per side; final dimensions for conversion (in $\mu \mathrm{m}$) are set by the user. Furthermore, since the GSC process does not make any distinction regarding depth of the photoresist layer, scaling in the $z$ direction is somewhat arbitrary and does not necessarily need to correlate to the scale chosen for the $xy$ dimensions. Rather, the conversion process scales the $z$ direction such that the substrate surface is coincident with the first layer ($n_0$), and the maximum layer ($n_{\max }$) set to the highest point of the structure. Individual layer thicknesses are calculated based on the previously described calibration process. Therefore, it is merely the relative height of features with respect to one another that matters, and features in the $z$ direction can be exaggerated without consequence if this exaggeration aids in the design stage.

2.3.

Grayscale Conversion Software Utility

While the actual conversion process is fairly straightforward, the need to repeat an identical series of steps up to several million times necessitated writing a software utility to streamline the process. This GSC utility enables fast, automated generation of DXF files (suitable for a variety of LPGs) and is used in the follow-on experimental fabrications. Stated simply, the GSC software stores surface topology data from the 3-D CAD model in a 2-D integer array containing layer assignments. This integer array is then written to a mask file in a format suitable to a particular grayscale lithography device (typically DXF). The machine uses the mask data to essentially control relative UV laser exposure levels or values for the grayscale lithography device at a plurality of locations along the surface of a die, wafer, or other substrate.

Once layer thicknesses have been determined through calibration, actual model conversion to grayscale begins. Starting with the topographic view of Fig. 3(b), the GSC software first creates a 2-D plane above the CAD model with a footprint equal to the bounds of the wafer section. Next, an $N\times M$ integer array is placed coincident to the plane with the number of elements in the array governed by $N=sX/R$ and $M=sY/R$, where $X$ and $Y$ are the unitless dimensions of the wafer footprint (from the STL file), $R$ is the LPG address grid resolution, and $s$ is a user-provided scaling factor (such that $sX$ and $sY$ provide the desired structure footprint in microns). Although this process enables scaling to a particular microstructure size regardless of initial CAD model setup, consideration must be taken when exporting the STL file to ensure that the resolution adequately captures the features. By tying dimensions of the integer array to the LPG address grid size, each array cell can be thought of as a “pixel” with a height and width equal to the resolution value [Fig. 3(d)]. This relationship greatly simplifies calculation of element positions when writing the DXF file. For the example shown assuming a 250-nm LPG address grid and a square wafer substrate of $100\mu \mathrm{m}/\text{side}$, a $400\times 400$ integer array will be created with $1.6\times {10}^5$ elements. Square elements were chosen as they are most suitable toward writing various grayscale files types (DXF, bitmaps, and so on). Next, to convert the CAD model into a representative set of layer numbers, the 2-D array is indexed, first by column then by row, and height of the feature present within each element ($h_{j,k}$) measured. Equation (6) scales the elemental height as a function of the maximum feature height present in the CAD model ($h$) and assigns a layer number based on the calibration development depth profile. This process creates a default negative (inverse) of the original CAD model, with top of the photoresist equivalent to the simulated substrate [Fig. 3(e), assuming positive photoresist]. The option also exists to invert the layers in order to fabricate a microstructure similar to the original CAD design:

Table 2

Integer array element information.

While a grayscale mask file for a single dome is relatively straightforward, even with relatively simple surface topography [such as a hemisphere array of connected domes, Fig. 4(a)] manual creation is prohibitively complex. Figures 4(b) and 4(c) show the intricacy associated with even a small $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ structure. Note that since the number of integer array elements scales exponentially with the substrate size being converted, several considerations should be taken into account. First, the current iteration of the GSC software utility scales the array in a single operation. Excessively large array sizes may cause memory-dependent issues in the computer running the software. While not implemented in the software utility presented here, one such solution is to piecewise convert the structure—loading sections of the array, then clearing the buffer before proceeding to the next portion of the model. Second, regarding file compression, adjacent array elements on the same layer can be merged prior to writing the DXF file (this merging method was incorporated into the software utility), which can greatly reduce total number of elements written and hence final file size. For example, 20 adjacent array elements on the same layer can be reduced from 100 data points to just 5 required to define the combined larger element.

Fig. 4

Grayscale mask complexity detail. (a) Top view of hemisphere array CAD model. (b) Resulting grayscale mask after processing. (c) Detail of mask (250-nm address grid on a $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ die).

2.4.

Fabrication

This experiment was performed using a Heidelberg 66FS LPG. Traditionally, Heidelberg LPGs are suited only for binary exposures; but this machine has added functionality that allows for modulating laser intensity during the writing process. This feature enables use of the 66FS toward grayscale lithography to create more complex 3-D structures. The LPG employs either a diode laser ($\sim 405\mathrm{nm}$) or a HeCd laser (442 nm), and laser output power is between 20 and 180 mW, depending on specific design. This LPG system features a software package to import a variety of source files, such as Gerber, DXF, crystallographic information file, GDSII, Hewlett-Packard Graphics Language or structure format into the Software License File (LIC) format the machine needs as input.³⁹ During exposure, this LIC format data is converted in real time into the final pixel data. Theoretically, the original design data could be converted directly to the final pixel set, but the advantage of the LIC format is that its file size is much smaller due to a highly optimized compression, leading to a much faster data transfer from the workstation to the system.³⁹ Ultimately, resolution of the patterned grayscale design depends on the writing head used in the LPG. The University of Louisville MNTC currently has three different write heads in their inventory, where the heads are specified by the focal length (distance from the head when the beam is in ideal focus, shorter distances indicate a tighter beam). Table 3 presents minimum feature sizes. The 20-mm head writes faster than other heads, whereas the 2-mm head writes slower than other heads. The address grid defines the smallest feature that the LPG will even attempt to write, anything smaller is completely ignored when compiling the design.

Table 3

Heidelberg 66FS specifications.

For the examples presented in this work, two photoresists were used—Shipley 1827 and AZ4620 (both positive photoresists). Photoresists layers were spun onto cleaned 4′′ silicon wafers in accordance with manufacturers’ specifications, resulting in layer thicknesses of $\sim 2.7\mu \mathrm{m}$ and 4 to $20\mu \mathrm{m}$, respectively. A Veeco Dektak 8M Profilometer was used to scan the profile of the structures, and a Zygo Optical Interferometer was used to generate 3-D images of the fabricated structures. The GSC software utility was written and deployed as an executable using a combination of MATLAB and National Instruments LabVIEW Professional Development System.