On the trends and application of pattern density dependent isofocal dose of positive resists for 100 keV electron beam lithography

Electron beam lithography (EBL) is still today an essential tool to pattern at the nanoscale for emerging technologies. In spite of all its complexity, an advanced high energy EBL system can be operated as a blackbox and through the process of trial-and-error and perhaps a little luck for the novice or much experience for the seasoned lithographer, simple isolated or repeating patterns can be printed by way of a dose matrix.¹ However, said strategy is resource intensive and time consuming for very complex structures with heterogeneous pattern density due to the ubiquitous challenge of the proximity effect. It is well known that complex designs patterned using EBL can have overexposed dense features and underexposed sparse features. To resolve these uniformity issues, proximity effect correction (PEC) is used. A modern PEC algorithm convolves the pattern with a point spread function (PSF) to evaluate the absorbed energy distribution and then physically fractures the pattern, assigning the shapes a dose factor to deposit the appropriate energy so they develop to size.² Recent work has attempted to model EBL processes to account for the impact of temperature³ and microloading.⁴ By applying PEC to maintain critical dimension (CD) uniformity across varying pattern density for a singly prescribed effective blur (⁠$blureff$⁠) and/or microloading for specific pattern densities, desired results were achieved. The $blureff$ is defined as a combination of resist processing and tool artifacts, such as beam focus, that contributes to the final resist image and can be mathematically represented as a full width half maximum blur whose Gaussian is convolved into the corresponding material stack’s PSF. The $blureff$ is only part of the story as the robustness of the prescribed process corrections with respect to changing $blureff$ is not inherently clear.^4,3

Process robustness in EBL is achievable by exposing with the isofocal dose (IFD), which is defined as the dose that results in the same feature size independent of $blureff$⁠.^5–7 An underlying assumption is that the $blureff$ is much smaller than the feature size and that the dominant component of the $blureff$ is the electron beam focus which directly impacts the beam spot size.

In Fig. 1, the illustration connects the isofocal behavior that stems from the $blureff$ [Fig. 1(a)] to the exposure latitude [Fig. 1(b)]. The exposure latitude [Fig. 1(b)] is defined as the change in CD with respect to dose (the solid blue and dashed red curves). In Fig. 1(b), as the dose increases [over dose in Fig. 1(a)], the CD also increases [oversize in Fig. 1(a)]. As the dose decreases [under dose in Fig. 1(a)], the CD decreases [undersize in Fig. 1(a)]. The edge slope of the blur in Fig. 1(a) directly impacts the slope of the exposure latitude and ultimately the process window for given CD tolerance, both of which are illustrated in Fig. 1(b). The CD tolerance, typically user defined, in Fig. 1(b) is directly related to the process window which is the dose range required to achieve said CD tolerance. A good $blureff$ with a steep edge slope at the resist threshold [the solid blue line in Fig. 1(a)] yields an exposure latitude curve with a shallow slope [the solid blue line in Fig. 1(b)]. A poor $blureff$ with a shallow edge slope at the resist threshold [the dashed red line in Fig. 1(a)] yields an exposure latitude curve with a steep slope [the dashed red line in Fig. 1(b)]. Notice in Fig. 1(b) that the process window for a good blur is much wider than the process with a poor blur. A wider process window indicates that a wider variation in dose can be used to achieve an acceptable CD tolerance. This is particularly useful to understand since achieving a prescribed CD tolerance requires PEC to modulate the base dose with relative precision to achieve the approximate CD target across a design with heterogenous pattern density.

As one can infer in Fig. 1(a), a good $blureff$ can imply a focused beam (small beam diameter), where a poor $blureff$ can imply a defocused beam (large beam diameter). The isofocal point is the intersection of said $blurseff$ for a target CD at the resist threshold as shown in Fig. 1(a). The same intersection corresponds to the intersection of the exposure latitude curves that result from exposing said $blurseff$ as shown in Fig. 1(b). It is at or near the isofocal point where e-beam lithographers would want to operate to ensure process robustness given the relatively flat response in CD. Coupled with a minimum $blureff$⁠, they would be able to operate in a wide process window.

Previous work has empirically shown that the EBL isofocal dose exists for various resists using 10 keV (Ref. 5) and 50 keV (Refs. 6 and 7) systems. These works demonstrated that the isofocal dose results in a flat response in terms of feature size (isofocal feature) independent of the $blureff$ and that the said feature is typically larger than the drawn target CD.⁵ The difference between the isofocal feature and the CD target defines the isofocal bias (⁠$IFΔ$⁠). To maintain the intended drawn target CD at isofocal, a pattern bias equal to $IFΔ$ can be applied to the data.

Isofocality, its pattern density dependency, and application to PEC have been explored in greater detail at 50 keV using ZEP520A.⁶ Figure 2 describes the general response of an exposure latitude slope with respect to pattern density (backscattered energy) and beam focus⁶ that resulted from this work. It was found that PEC superimposes the pattern density dependent exposure latitudes such that they intersect at a base dose that yields a tolerable operating point for the user. The intention of this work implies that if PEC can provide the correct isofocal dose with respect to a specific pattern density, a given resist process will exhibit a tolerance to a change in focus with the correct isofocal base dose (⁠$IFDB$⁠). This paper examines isofocality at 100 keV.

In the text that follows, we present a robust process characterization strategy to empirically identify the approximate pattern density dependent isofocal doses (⁠$IFDρ$⁠) and biases (⁠$IFΔρ$⁠) while sharing viable resist processes and PEC application of four positive resists. The resists are AR-P 6200 (commercially known as CSAR 62) by AllResist GmbH, ZEP520A by Zeon Corp., PMMA 950 A4 (polymethylmethacrylate with a 950k molecular weight in anisole) by MicroChem Corp., and mr-PosEBR 0.3 by Micro Resist Technology GmbH. The commercial names as suggested by the manufacturers will be used to reference their specific products. The goal of this paper is to reveal trends in isofocality while connecting the dots between the low level concepts (e.g., resist contrast analysis and exposure latitude) in EBL resist characterization to more highly applicable concepts that promote process robustness as they pertain to isofocality and PEC.

In Sec. II, the background on resist characterization and PEC is explained. Section III describes the experimental setup, while Sec. IV discusses the results. Finally, Sec. V summarizes our findings and ideas on future work.

For this paper, resist processes in Table I were evaluated using a Raith EBPG 5200 using the exposure parameters in Table II. Characterizing these resists requires knowledge of their spin curves, contrast, and exposure latitude. Application of this characterization to PEC and isofocality completes the characterization loop. This section reviews the steps in process characterization using a focused beam at 100 keV per Table II for the named resists and corresponding thicknesses in Table I.

The spin curve is a plot of the resist thickness versus spin speed. Said curve is typically provided by the vendor. However, if a desired thickness is out of specification for a standard dilution, one can formulate their own. As in our case, ZEP520A was diluted to spin at 1000 rpm for 60 s to yield a 200 nm thickness.⁸ The resists used in this study, their spin speeds, and resulting thicknesses are listed in Table I. The resist thicknesses were chosen on their capacity for optimal pattern transfer described in Table III.

High contrast resist processes have long been sought after by the EBL community.^9–12 A proper contrast curve pattern is generated by exposing squares that are 4$β$ by 4$β$ or greater in size in a dose matrix. Monte Carlo simulations using tracer (Ref. 13) show that backscattering length scale for Si, $βSi$⁠, is 30 $μ$m at 100 keV. Measurements can be performed with a thin film interferometer or step height profilometer. It is worth mentioning that the size of the measurable area of an interferometer should be considered when determining the final size of the contrast curve squares such that the area under test as seen by the interferometer is uniform in thickness. As shown in Fig. 3, normalized contrast curves developed per Table I directly compare the computed resist contrast¹² $γ$ between the four resists under test. CSAR 62 exhibits highest contrast where mr-PosEBR exhibits the lowest in the group. In addition to γ, the contrast curve also indicates the dose-to-clear (⁠$DC$⁠), which is at the 100% pattern density. Since dense features experience higher backscattered energy, they require less dose to develop. The $DC$ on a contrast curve is the lowest dose needed to develop a structure with heterogeneous pattern density. In other words, the $DC$ is the minimum operating dose for a resist process, which exists at the 100% pattern density. Any dose lower than $DC$ will simply not develop the resist to clear to the underlying substrate.

The exposure latitude can be extracted by exposing tower patterns in a dose matrix.⁶ A modified structure illustrated in Fig. 4 implements a test region in the center of each pattern density that contains line-space patterns with 100, 200, 300, and 400 nm features that sit atop the backscattered energy of their respective pattern density. An optical image of tower patterns exposed in a dose matrix for PMMA can be seen in Fig. 5. After resist development (Table I) and contrast curves measurements have been obtained, the pattern is transferred (Table III) into the Si substrate to mitigate charge effects during scanning electron microscopy. Any remaining resist after etch is ashed away in an O$2$ plasma.

As previously defined, the slope of the exposure latitude is correlated to the edge slope of the deposited energy density $blureff$ at the resist threshold. It is also correlated to the amount of backscattered energy, which is pattern density dependent, that is imposed on the region of interest as illustrated in Fig. 6. The exposure latitude of 100, 200, 300 and 400 nm lines for ZEP520A after etch is plotted versus dose per pattern density in (a), (b), (c), and (d) of Fig. 6. Isolated features at 0% pattern density exhibit the shallowest slope with virtually no influence of backscattered energy. As the pattern density increases, so does the backscattered energy and, consequently, the slope of the exposure latitude becomes steeper. As expected, the exposure latitude at 100% pattern density exhibits the steepest slope for all feature sizes in Fig. 6. Similar trends for slope are found for CSAR 62, PMMA, and mr-PosEBR.

This investigation explores the application of isofocality to long range PEC where the $blureff$ is smaller than the target CD as opposed to short range PEC where the $blureff$ is near to the size of the target CD. Proximity effect correction exists in modern EBL software such as beamer by GenISys, GmbH.² It operates by convolving the pattern with a PSF to evaluate the absorbed energy distribution and then physically fractures the pattern, assigning the shapes a dose factor to deposit the appropriate energy so they develop to size. As mentioned, Fig. 6 plots the CD-sensitivity versus absolute dose; however, the output for a PEC algorithm such as the one found in beamer (Ref. 2) exports only dose factors. The dose factors imply that a base dose (or a single dose issued at the time of an exposure job as known as a job dose) must be applied to the pattern during exposure that will be modulated with respect to the assigned values per shape. It can be shown for long range PEC that the dose factor D is a function of pattern density $ρ$ and $η$ as shown in Eq. (1), where $η$ is the ratio of the backscatter energy (⁠$β$⁠) to the forward scatter (⁠$α$⁠).⁴ 

For Si at 100 keV, $η$ = 0.6. With $η$ fixed, the dynamic dose range of Eq. (1) has a minimum of 0.7273 for dense features [Eq. (2)] and a maximum relative dose of 1.6 [Eq. (3)] for isolated features. According to Eq. (1), the base dose, $DB$ (⁠$D=1$⁠), can be found using a $ρ$ = 50% [Eq. (4)]; however, this was not the case in previous work at 50 keV.⁶ 

It will be shown in Sec. IV that the dynamic dose range is limited in capturing the scope of the empirically determined values of $IFDρ$’s especially for very dense features.

Thus far, we have discussed how one would characterize a typical resist process while providing some specific and general evaluation of the four positive resists along with the underlying principles of isofocality, exposure latitude, and PEC. To quickly summarize, the resist thicknesses in Table I were chosen based on the requirement for pattern transfer per Table III. Specifically, the contrast curves reveal a minimum operating dose (⁠$DC$⁠) required to clear dense features (Fig. 3). The exposure latitude analysis identified trends in the slope with respect to pattern density. In this section, we apply the theory of isofocality to empirically determine the $IFDρ$ and $IFΔρ$ by systematically manipulating the beam spot size. Using the contrast curve and tower pattern structures described in Sec. II, the impact of beam focus on the resist contrast and exposure latitude will be analyzed across all four resist processes. Table IV concisely describes the experimental scope for all four resists under test using multiple beam diameter values for various pattern densities and linewidths.

Using the Raith EBPG 5200, the beam spot size can be calibrated to an approximate diameter. The beam diameter is estimated by moving the electron beam over the edge of a high contrast metallic feature. The slope of this transition is a convolution of the edge profile of the feature and the beam profile. For small beam diameters, this will tend to be dominated by the slope of the edge, whereas for larger beam diameters, the measurement will become a more accurate reflection of the beam profile. The implication here is that the focused beam diameter measurement will have a larger error than the defocused spot sizes. Inputted beam diameter values versus measured spot sizes are shown in Table IV.

The beam spot sizes of 75 and 150 nm were arbitrarily chosen. In theory, the resulting exposure latitudes per pattern density should intersect to determine isofocality; however, it was not well known before conducting the experiment which defocus value would be the most adequate. For example, if two exposure latitudes from two different beam spots exhibited similar slopes for a given pattern density, isofocality could be difficult to ascertain especially when considering measurement error. As such, a false positive for isofocality would manifest itself. As Fig. 1 illustrates, it is important to have at least two extremes in beam spot size to determine isofocality given that both beam spot sizes are sufficiently smaller than the intended CD. We will expound more on this constraint through empirical evidence and discuss how to statistically determine isofocality in Sec. IV.

Four Si substrates measuring 2 cm by 2 cm in size were coated independently with CSAR 62, ZEP520A, PMMA 950 A4, and mr-PosEBR 0.3 per Table I. For exposure, the samples were mounted side-by-side as illustrated in Fig. 7(a). The job was prepared such that the focused beam exposed all the contrast curve and tower patterns on all four substrates. Upon completion, the beam was defocused to an approximate spot size of 75 nm and exposed the same patterns adjacent to the previous exposure. The third and final exposure defocused the beam to an approximate spot size 150 nm and exposed the same patterns adjacent to the previous exposure on all four substrates. Figure 7(b) illustrates this writing strategy.

After exposure, contrast curves were measured for all focus values for each resist process. The pattern was then transferred via etch per Table III. Images were taken with an FEI Strata DB235 FIB and postprocessed with prosem.¹⁴ According to Table V, over 99% of the line measurements exhibited a standard error (SE) of the mean to be 2 nm or less. Exposure latitude curves were then plotted and compared. Using tracer, the $blureff$ for each resist and beam spot size was calculated¹³ and tabulated in Table VI. In Sec. IV, we will discuss the results and identify trends in the data.

In this section, measurements and trends in the data are discussed. More importantly, a connection between the initial data from the contrast and exposure latitude curves to EBL isofocality and PEC will be established.

Upon optical inspection, the contrast curve patterns exposed using three different beam diameters appear unremarkable to one another as shown in Fig. 8 for CSAR 62. Similar observations can be made for ZEP520A, PMMA, and mr-PosEBR. A plot of the resist contrast curves is illustrated in Fig. 9 for all resists for all focus values. The $DC$ values provided by the contrast curves for the four positive resist processes are listed in Fig. 3 and Table VII for quick reference. These values are the physical lower limit of the resist process which is at 100% pattern density. Any dose value lower will not fully develop the resist to the substrate especially for dense features.

The exposure latitude for each resist at every pattern density and feature size was plotted and analyzed. Similar plots as in Fig. 10 for CSAR 62 were generated for ZEP520A, PMMA, and mr-PosEBR. In all the plots, the general trend as described in Fig. 2 was found. Both the impact of backscattered energy and beam focus are effectively illustrated in Fig. 10. Exposure latitude curves for 200, 300, and 400 nm features bear similar slopes per pattern density.

Upon further analysis, subtracting the target CD from the respective data results in a bias versus dose plot as in Fig. 11 for PMMA. It is immediately apparent that the 200, 300, and 400 nm test patterns exhibit the same bias response with respect to dose for a focused beam and beam spot size of 75 nm. This is probably due to the target CD being more than twice the $blureff$ as reported in Table VI. For the 150 nm beam spot size, data for 300 and 400 nm maintained similar magnitudes in bias versus dose also due to the target CD being roughly twice that of the $blureff$⁠. Similar trends were found for the other resists under test, empirically showing that a target CD that is roughly twice as large than the $blureff$  especially 300 or 400 nm features, would have been adequate for this study.

Figure 12 plots the process bias versus dose for all three beam spot sizes that are fit to a second order polynomial. The plotted values are the average bias values obtained from the 300 and 400 nm test patterns. The theory of isofocality dictates that all isofocality curves intersect at one point (the isofocal point). However, as with any experiment, there is the presence of measurement error and uncertainty. For example, if the slopes of the curves are nearly identical (which could be true for a focused beam versus a defocused beam spot size of 75 nm), there is increasing uncertainty of the intersection coordinate (the isofocal point). Therefore, a methodology to isolate the approximate isofocal points was implemented, producing Fig. 13.

1. The mean process bias values are computed by averaging the bias values for each beam spot size corresponding to each pattern density. As a rule, there should be a corresponding bias value per dose for each beam spot size to properly compute the average. For this work, this meant at a given dose, three bias values corresponding to each spot size must be present to compute the mean.

2. For every mean, the SE of the mean is computed, which is the population standard deviation divided by $n$⁠, where n is the number of observation in the sample. For this work, $n=3$⁠.

3. The isofocal point can now be identified as the mean with the minimum SE that was computed in step one, which is the IFΔ_ρ and its corresponding IFD_ρ.

Figure 13 plots the mean of the process bias response from the three beam spot sizes per pattern density in Fig. 12 versus dose as well as the SE of the mean as error bars. The minimum SE for each pattern density was used to determine the $IFDρ$ in Fig. 12. In Table VII, the approximate $IFDρ$’s are listed per resist along with the $DC$ values and their relative value with respect to 0% pattern density.

Based on the empirical evidence, some general rules and trends in isofocality are summarized below and in Table VIII:

1. It is important to use $blurseff$ that are less than half the size of the target CD.

   • The response to the $blureff$ for isofocality in Table VIII is true as long as the target CD is roughly 2X or greater than the $blureff$⁠. A $blureff$ that is equal to or greater than the target CD will not help ascertain a reliable isofocal point.

   • The process bias response to dose will remain unchanged for a fixed $blureff$ so long as the target CD is roughly twice or greater than the $blureff$⁠. Figure 11 best illustrates this trend.

2. The $IFDρ=100%$ is $∼$20% larger than the $DC$ (Table VII).

3. The $IFDρ=0%$ is roughly twice the $DC$ (Table VII).

As expected, isolated features require the highest dose when examining the $IFDρ$’s in Table VII. Using the isofocal dose at 0% pattern density as a reference, according to PEC, the assigned dose factor should be 1.6 for Si. The remaining $IFDρ$’s are converted in the same manner to their normalized pattern density dependent isofocal dose factors, $NIFDρ$⁠, using Eq. (5) to yield Table IX. The dynamic dose range described by Eq. (1) indicates that the lowest dose factor is given by Eq. (2). However, according to Fig. 3, the minimum operating dose for the resist processes described in Table I at 100 keV when normalized to the isofocal dose for isolated features is generally higher than the minimum dose factor in Eq. (2). Figure 14 plots the dynamic dose range from Eq. (1). It also illustrates how the dose factor for 100% pattern densities generally falls below $DC$ listed in Fig. 3. In fact, when plotting the relative values from Table IX, the curve of the former dynamic dose model in Eq. (1) falls short of landing on the empirically determined $IFDρ$’s.

Adjusting Eq. (1) to Eq. (6), where $ψ$ is an arbitrary dynamic dose range optimizer whose value can range from 0 to 100, where 100 yields Eq. (1), the dynamic dose range for PEC can be modified to fit the empirical $IFDρ$ data.

The empirically determined normalized pattern density dependent isofocal dose (⁠$NIFDρ$⁠) for the highest pattern density that is evaluated should be used to determine $ψ$⁠. By setting Eq. (6) equal to an empirically determined $NIFDρ$ for $ρ>0%$ and solving for $ψ$ yields

Since dense features (⁠$ρ$ = 100%) determine the lowest limit of the PEC dynamic dose range, Eq. (7) reduces to

In Fig. 14 with $ψ=34$⁠, the new dynamic model [Eq. (6)] describes the isofocal behavior for CSAR 62, ZEP520A, and PMMA 950 A4. A similar finding for mr-PosEBR can be made when setting $ψ=5$⁠. Since isolated features can be approximated to $1+η$⁠, the isofocal base dose, $IFDB$⁠, for the process can be defined as shown in Eq. (9). The $IFDB$ values are listed in Table IX. For completeness and quick reference, the entire resist process and exposure parameters along with the $IFDB$ and $ψ$ values are found in Table I.

Based on this study, a positive resist process characterization to enable isofocal proximity effect correction could resemble the following:

1. Expose and develop a contrast curve to identify $DC$⁠.

2. Expose a dose matrix of isolated (⁠$ρ=0%$⁠) to dense (⁠$ρ=100%$⁠) features that are at least $2×$ the size of the $blureff$ using a focused and highly defocused beam. A feature size of 300 or 400 nm is recommended. Expose the isolated features with a job dose that is centered about roughly twice the $DC$ and the dense features with a job dose that is centered about $∼$20% higher than the $DC$⁠. Exposing additional pattern densities (e.g., 25%, 50%, and 75%) will produce more data points to ensure behavioral accuracy.

3. Plot the exposure latitudes. Confirm their behavior follows the general trends as described in Fig. 2 and Table VIII. Ensure $IFDρ=100%$ $>$ $DC$⁠.

4. Using the plots, identify the $IFDρ=0%$ and calculate $IFDB$ using Eq. (9). Next, compute the $NIFDρ=100%$ using Eq. (5). Finally, note the corresponding $IFΔρ$ for each $ρ$⁠.

5. Using $NIFDρ=100%$⁠, compute $ψ$ using Eq. (8) to adjust the PEC dynamic dose range accordingly for subsequent exposures using the same resist process that was just characterized while applying the noted $IFΔρ$ from the previous step. Modern PEC software such as beamer can support this level of correction.² 

As a final test, test patterns with L-gratings and dot arrays atop backscattered energy from various pattern densities were exposed using PEC with $ψ=34$⁠. In this application, the CSAR 62 protocol went under test. Despite the varying focus values, the images in Fig. 15 bear a striking resemblance to one another with the exception of corner rounding due to a changing $blureff$⁠.

Isofocality has been demonstrated for commercially available resists at 100 keV. Aside from determining resist contrast, contrast curves provide the minimum operating dose as the $DC$⁠. Based on empirical evidence, a test pattern feature size at approximately twice the size of the $blureff$ is enough to extract the trends in isofocal dose and bias across the pattern density spectrum. A modified dynamic dose equation for PEC was introduced and optimized to match the empirically determined isofocal dose range. As a result, an EBL resist characterization method has been proposed and was partially demonstrated on a test pattern at 100 keV with varying beam spot sizes. This investigation explored the application of isofocality to long range PEC. Future work could be performed to investigate trends with respect to negative resist, short range PEC, resist thickness, and resist development rate.

This work was performed in part at the University of Pennsylvania Singh Center for Nanotechnology, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (Grant No. ECCS-1542153). A special thanks goes to both the staff at the University of Delaware and the Pennsylvania State University for their time and efforts to further enable this research. The authors are also especially grateful for the generous advisement of Leonidas Ocola.