2.2.1.

EUV exposure

The sample preparation for EUV exposure was done by spin coating the desired underlayer (SOG or UL) on top of a silicon wafer. This layer was subsequently baked at the vendor recommended setting. On top of this underlayer, a state-of-the-art CAR was spin coated at the desired nominal FT (10, 15, 20, 25, or 30 nm) and baked at vendor recommended settings (130°C 60 s). An FT check was performed using ellipsometry to confirm these nominal values. The wafers were subsequently exposed in an ASML full-field NXE:3400 scanner with a custom X-dipole illumination to print vertical 1:1 lines and spaces at a pitch of 32 nm. Subsequently, the wafers received a postexposure bake of 90°C for 60 s and were developed with a 2.38% tetramethyl-ammonium hydroxide solution.

2.2.2.

CDSEM and power spectral density

Patterning images were taken with a Hitachi CG-6300 CDSEM. The wafer dies with the selected conditions were investigated by taking 50 images per die. For the CDSEM images, we used the following best-known imec settings: using 500-V acceleration voltage, 8.0-pA probe current, $1638\mathrm{nm}\times 1638\mathrm{nm}$ images at $2048\times 2048\text{pixels}$, 83K magnification, 0.8-nm pixel size, for a total area of $128\mu {\mathrm{m}}^2$, according to imec protocol.⁶ These images were then used to obtain unbiased line-width roughness (uLWR) and critical dimension (CD) values through the Fractilia MetroLER software version 2.3.0.⁷ In addition to the unbiased roughness value, the software also gives access to the full power spectral density (PSD) averaged over 50 images, which provides additional information on the size-scale distribution of the roughness.⁸

2.2.3.

Atomic force microscopy

Resist array height measurements were conducted using a Park systems NX3DM atomic force microscope (AFM) utilizing a high aspect-ratio probe, over a $2000\times 500{\mathrm{nm}}^2$ area at 2048 pixels (resist line length) and 32 resist lines at $\sim 12\text{pixels}$ (resist line width). A blanket (unexposed) area was used for Z-drift correction as this area was nearby and wide enough for our purpose. The bottom of a completely exposed and developed dummy structure was used as the zero resist FT reference. Since a single AFM cut line is affected by roughness, averaged sections (16 lines) were acquired to improve statistics. The final AFM resist array height measurement was obtained from the averaged results. The AFM line top roughness (LTR) measurements were obtained over a $1000\times 1000{\mathrm{nm}}^2$ area at 2048 pixels (resist line length) and 256 resist lines at $\sim 12\text{pixels}$ (resist line width).

3.1.1.

CDSEM image contrast and AFM resist array height

An initial CDSEM image comparison of the patterned resist at different nominal resist FTs on both underlayers is shown in Fig. 1. In this figure, two basic observations can be made: (1) a reduction in resist FT leads to a reduction in CDSEM image contrast, to such an extent that it is difficult to confirm a line-space pattern for 10 nm resist on SOG, and (2) the different underlayers provide a different CDSEM image contrast.

Fig. 1

CDSEM images of resist FT variation (30, 25, 20, 15, and 10 nm) on an SOG UL and an organic UL.

The observed contrast difference can have two possible origins. It could be induced by a patterning effect, meaning that the same nominal resist FT would lead to a different effective resist FT after exposure and development depending on the underlayer. However, the underlayers could also exhibit a discrepancy in electron yield (CDSEM response) causing the contrast difference, indicating a metrology effect. To this end, AFM measurements were done to determine the resist array height. Figure 2 shows the AFM line-space patterns for the various resist FTs on both underlayers. The average resist array height of five different dies (through dose) for the different underlayers is shown in Fig. 3(a). This shows that the average resist FT shrinkage follows a linear trend and that the resist array height is $\sim 70\%$ of the nominal coated resist FT value. This empirical value in resist FT reduction can be attributed to both the development process (as you will always lose a portion of unexposed resist) and the dark erosion effect. It also reveals a small height difference between both underlayers, as the resist array height on the UL is 10% lower compared to the SOG. This difference can be explained when looking at the influence of exposure dose on the resist array height in Fig. 3(b). A higher exposure dose results in a lower resist array height, explaining the lower resist FT on the UL because a resist typically requires a 10% higher dose to obtain a similar CD compared to the SOG. Since these results show that the UL provides a better CDSEM contrast, despite having a slightly lower resist array height, we can conclude that the contrast discrepancy between SOG and UL is a metrology effect. In addition, the results confirm that the line-space pattern for 10 nm resist FT on SOG is indeed present, confirming successful patterning and indicating a metrology issue.

Fig. 2

AFM images of resist FT variation (30, 25, 20, 15, and 10 nm) on an SOG UL and an organic UL.

Fig. 3

(a) Average AFM resist array height for five different dies through dose, and (b) the single AFM resist array height measurements for those dies plotted versus their respective exposure dose.

Having qualitatively confirmed that the UL provides a higher CDSEM image contrast, despite the slightly lower resist array height, a further investigation aimed to quantify this effect is necessary. The contrast of a CDSEM image can be calculated by looking at the minimum and maximum grayscale values of the CDSEM image signal and calculated with the following equation:

However, the contrast of a CDSEM image is not the best choice to assess image quality, as the images are often subjected to contrast stretching or normalization. A better way to quantify the quality of a CDSEM image is the linescan signal-to-noise ratio (SNR), as both signal and noise levels are considered. For lines and spaces, this SNR is calculated per feature based on the average linescan as a function of the minimum and maximum grayscale value, and grayscale noise ($1\sigma$) that is measured as the standard deviation of the image grayscale values. For the minimum and maximum grayscale value the average linescan is considered, meaning that the CDSEM image is collapsed into a single line grayscale value. For the grayscale noise, each column of pixels can be assessed so an average value of the noise can be obtained. Both the line and space area of the CDSEM image is considered while staying away from the line edges since that would correlate with measuring roughness and not grayscale noise.

For a given resist-underlayer combination, a trend is observed between the SNR and AFM resist array height, as shown in Fig. 4. These results quantitatively confirm that the UL provides better CDSEM images, as the UL SNR is higher for the same FT compared to the SOG. A plausible explanation is that the UL mostly contains carbon–carbon bonds, whereas the SOG contains more oxygen-rich chemical species (i.e., the silicon–oxygen bonds), which leads to an increase in electron yield for the SOG material. A higher electron yield in the underlayer will cause a higher background (noise) signal during CDSEM image collection, and thus lower SNR.

Fig. 4

AFM resist array height versus SNR for five dies per resist FT for both SOG and UL.

3.1.2.

CDSEM image SNR and CD precision

A point of concern related to the SNR reduction is that it could influence the precision of resist performance parameters, such as the CD and LWR. The static CD precision from a CDSEM image can be determined by taking one CDSEM image of the desired features (i.e., line-space) and performing a static repeat of the same feature at the exact same location. This ensures that the resist lines in both images are the same. The reason for choosing a static repeat, rather than a dynamic one, is solely due to the lack of a good SEM alignment target nearby the measured features. On a mask with a more suitable SEM alignment, we expect the dynamic precision to be similar to the static one. In each investigated die, 50 CDSEM images (at a different location within the die) plus a static repeat image per CDSEM image were taken at 49 lines per image. The CDs of the 49 lines in the CDSEM image were then compared to the corresponding CDs of the static repeat image in the following way, to calculate the static precision: (1) the average CD difference between the 50 images and its repeat is calculated (shrinkage), (2) the CDs of the 49 lines of the 50 repeat images are corrected for the shrinkage, and (3) the variance of the CDs of the image and the corrected repeat CDs is calculated for all pairs. The square root of the average of this variance multiplied by three gives the single line CD precision of the CDSEM image. To calculate the CD precision of a full image, this value must be divided by the square root of 49 (the number of lines in the CDSEM image). Figure 5 shows the full image CD precision versus SNR. For the SOG, the full image CD precision error stays below 0.15 nm (for the resist FT indicated). For the UL, the full image CD precision error stays below 0.09 nm for the same FT range (down to 15 nm resist FT) but increases to 0.19 nm for the 10 nm resist FT (not measurable for SOG). This CD precision value can be further lowered by taking additional images. The required CD precision depends on the technology node and feature type. Taking a desired CD precision of 10% of the required CD control is a good rule of thumb, resulting in a required CD precision of $\le 0.1\mathrm{nm}$.⁹

Fig. 5

Full image (49 lines) CD $3\sigma$ precision versus linescan SNR.

3.1.3.

Unbiased roughness trends

Since the metrology challenges were addressed, also the patterning performance will be investigated through the comparison of roughness. The unbiased roughness is determined through an unbiasing procedure in which a PSD plot is used to determine the SEM noise floor.^7,8 This noise floor is subsequently subtracted from the PSD to obtain the unbiased PSD and the associated uLWR value. Figure 6 shows the outcome of the unbiasing procedure for the SOG and UL. Each datapoint represents the averaged results of 50 images taken at different locations within the same die. From these results, two observations can be made: (1) the error on uLWR increases with reduced resist FT and (2) the uLWR seems to scale inversely to a reduction in resist FT (i.e., a lower resist FT leads to a higher uLWR) in agreement with previous reported observations.^4,5 In addition, the uLWR scales differently on the two underlayers. On the SOG, the uLWR increase originating from a reduced resist FT remains limited, whereas it increases dramatically for the UL. Considering the CDSEM image differences between the SOG and UL, this indicates either an effect of the SNR on the uLWR (metrology effect) or an effect of underlayer-resist interaction that becomes more pronounced as the resist FT is reduced (patterning effect).

Fig. 6

Unbiased LWR $3\sigma$ with associated $3\sigma$ standard deviation error bars determined from 50 images.

3.1.4.

SNR and frame variation

To further elucidate the effect of the SNR on the uLWR determination observed in the previous section, a set of CDSEM images with a different number of frames (1, 2, 4, 8, 16, 32, and 64) was collected on both underlayers. The different number of frames were used to modulate the SNR of the CDSEM images, thus providing further information to understand the origin of the uLWR behavior. Figure 7 shows the uLWR versus the number of frames for both the SOG and UL.

Fig. 7

Unbiased LWR $3\sigma$ versus a different number of frames (1, 2, 4, 8, 16, 32, and 64) for different resist FT variations with associated $3\sigma$ standard deviation error bars determined from 50 images.

For 30- and 25-nm FT, we observe that the uLWR differs slightly for the SOG and UL at a lower number of frames but converges at the highest number of frames (64). The 20- and 15-nm FT show a larger difference between the SOG and UL but still show a tendency to converge toward a similar uLWR value at higher number of frames. This is a first indication that SNR differences play a role in uLWR determination on both underlayers. Stronger evidence of this correlation can be found by combining all frame variation plots in a single master plot, by plotting the uLWR values versus SNR for the different number of frames, as reported in Fig. 8.

Fig. 8

Unbiased LWR $3\sigma$ versus SNR for different number of frames (4, 8, 16, 32, and 64) for different resist FT variations on SOG and UL with associated $3\sigma$ standard deviation error bars determined from 50 images. An example for the different number of frames is given for 30 nm (UL).

In this unified graph, each datapoint represents the averaged results of 50 images with the different number of frames (4, 8, 16, 32, and 64) for both the SOG and UL. In this graph, we observe two effects: (1) an increased dependence of uLWR on SNR when reducing the resist FT and (2) a characteristic response curve for each resist FT, where uLWR increases when reducing the resist FT.

The first effect where a uLWR dependency on SNR is observed can be addressed as a metrology effect: at conventional resist FT (30 nm), the SNR differences do not cause large changes in uLWR on both SOG and UL, as the curvature of the response curve is relatively small. However, moving down in resist FT results in an increase of the steepness of the response curves and thus also a larger discrepancy between uLWR for SOG and UL. We thus interpret the trend of the UL characteristic response curves with SNR as a metrology artifact, suggesting that the real uLWR value is potentially linked to the plateau value in each response curve.

The second effect where an increase in uLWR is observed for a lower resist FT can be addressed as a patterning effect. Since reducing the resist FT lowers SNR, this may also be the cause of an uLWR change. However, we argue that it is not a metrology effect, because (I) in the first effect a lower SNR is directly correlated to a lower uLWR value. This would mean a lower uLWR should be obtained for a lower resist FT, which is not the case. (II) If the uLWR differences between the different resist FTs would be solely due to a metrology effect, a single uLWR-vs-SNR master curve should be observed for all resist FTs. However, we observe a distinct response curve for each resist FT. Labeling this observation as a patterning effect can be intuitively explained by considering that a lower resist FT requires a lower dose to print and, as such, increase the resist stochastics, which negatively impact the roughness. In addition, when reducing the resist FT, the resist–underlayer interaction becomes more dominant, which may affect resist roughness as well.¹⁰

These observations suggest that a threshold SNR should be defined above which the real uLWR value is given, and below which the uLWR value is not reliable anymore. This also implies that the resist patterning performance on two different underlayers is best compared when estimated at the same SNR rather than the same number of frames as is standard. An important note to make here is that the unbiasing procedure works perfectly for high SNR values. This means that at high resist FT the LWR can be considered unbiased regardless of SNR value. However, at lower resist FT a dependency on SNR is observed below a certain SNR threshold value. Thus, the use of the term unbiased LWR is only valid above this threshold value.

3.1.5.

SNR modulation by simulation

To further confirm our interpretation, some basic concerns need to be addressed. In particular, the physical impact of the frame variation used to modulate the SNR needs to be understood. In fact, a higher number of frames may cause physical changes in the resist line, which could artificially create a trend. To this end, the AFM LTR was measured for the 15-nm resist FT lines exposed to different number of frames on both SOG and UL, shown in Fig. 9. This reveals that the LTR does not change drastically with increased number of frames and even has the tendency to smoothen the line. Hence, we can conclude that the SNR trends obtained in Fig. 8 are not caused by CDSEM e-beam interaction.

Fig. 9

AFM LTR $3\sigma$ RMS versus different number of frames (0, 4, 8, 16, 32, and 64).

Following these results, some simulations were performed to better understand the reliability of uLWR at low SNR. MetroLER was used to create synthetic SEM images ($2048\times 2048\text{pixels}$ at 0.8 nm pixel size) of various SNR ratios (various amounts of added grayscale noise), with a fixed uLWR of 2.5 nm. When generating synthetic SEM images, MetroLER includes a sophisticated noise model that includes non-Gaussian added pixel noise and image contrast stretching, validated with experimental images.^11,12 These synthetic images were then analyzed to determine the uLWR and corresponding SNR values, as shown in Fig. 10(a).

Fig. 10

(a) Unbiased LWR $3\sigma$ with associated $3\sigma$ standard deviation bars versus SNR and (b) uLWR percent deviation versus SNR of the synthetic SEM images.

Figure 10(a) shows that the synthetic MetroLER SEM images exhibit a similar behavior to the experimental data; the uLWR increases for higher SNR values, reaching a plateau near the input uLWR value, confirming our conclusions based on Fig. 8. Furthermore, the simulated data help to define a quantitative SNR threshold value, based on the percent deviation from the nominal uLWR value, shown in Fig. 10(b). In this case, an SNR threshold value of 2 is estimated for a 5% uncertainty on the uLWR value.

While these guidelines are useful, they do not provide the full picture. Several factors can influence the SNR threshold value to obtain a reliable uLWR. For instance, as seen in the experimental data, the SNR threshold will be pushed to a lower value when the resist is thicker. Vice versa, this is pushed to a higher threshold value when the resist is thinner. Moreover, additional simulation results, shown in Fig. 11(a), indicate the importance of pixel size in determining the SNR threshold value. A larger pixel size will require a higher SNR threshold value, whereas a smaller pixel size allows for a more lenient, lower threshold value. It is thus important to note that the SNR threshold value depends on the pixel size used and moving to a smaller pixel size will shift these thresholds to lower SNR values, potentially enabling more accurate uLWR determination for thinner resists films, as shown in Fig. 11(b).

Fig. 11

(a) Simulated unbiased LWR $3\sigma$ for different pixel size with associated $3\sigma$ standard deviation bars versus SNR and (b) uLWR percent deviation versus SNR of the synthetic SEM images.