2.1.

Sample Fabrication

To systematically study the latent images with CD-RSoXS, a commercial Zeon Electron beam Positive-tone resist (ZEP) was employed as the initial testing sample in this paper. E-beam can serve as a reliable proxy for EUV due to their similar resist interaction mechanisms. Both techniques generate secondary electrons that initiate chemical reactions in the resist, making the E-beam a valuable tool for studying resist performance. In addition, E-beam lithography offers a greater flexibility in achieving uniform features, facilitating quantitative analysis and the construction of initial models. Samples were fabricated with various line pitches, ranging from 100 to 40 nm. The fabrication began with dehydrating the substrate, featuring freestanding 100-nm-thick silicon nitride (${\mathrm{SiN}}_x$) membrane windows, on a hotplate at 110°C for 90 s. Following cooling, hexamethyldisilazane was spin-coated onto the substrate, which was then baked at 110°C for 2 min. Subsequently, the resist was spin-coated onto a standard ${\mathrm{SiN}}_x$ window on Si wafers to create a film $\sim 40\mathrm{nm}$ thick. A post-application bake was then conducted for 5 min at 170°C. Line grating patterns, with a line width of 16 nm narrower than the designed half pitch values (50, 40, 30, 20 nm), were exposed on membrane windows using a 100-keV Raith EBPG5200 tool at Molecular Foundry, Lawrence Berkeley National Laboratory (LBNL). The exposed area covered the entire ${\mathrm{SiN}}_x$ window, measuring $0.5\mathrm{mm}\times 0.5\mathrm{mm}$, as illustrated in Fig. 1(a). Subsequently, latent images were acquired post-exposure, whereas the developed samples underwent processing through a dissolution procedure. The substrate was developed in hexyl acetate for 30 s, dipped in pentane for 5 s, and then blow-dried with nitrogen. Different line pitches were exposed with varying dosages. Specifically, 100 and 80 nm line gratings were exposed at $1.5\mathrm{mC}/{\mathrm{cm}}^2$, whereas dosages of 1.7 and $4.5\mathrm{mC}/{\mathrm{cm}}^2$ were used for the 60- and 40-nm pitches, respectively.

Fig. 1

(a) Illustration of the latent image and developed sample on ${\mathrm{SiN}}_x$ windows. (b) Illustration of CD-RSoXS with the beam path in transmission geometry.

2.2.

CD-RSoXS Measurement

CD-RSoXS experiments were performed at beamline 11.0.1.2 of the Advanced Light Source (ALS), LBNL.²⁰ The X-ray beam has an elliptical shape with approximate diameters of 400 and $200\mu \mathrm{m}$. The dose we used for CD-RSoXS measurement is around $0.35\mathrm{mJ}/{\mathrm{cm}}^2·\mathrm{s}$. The charge-coupled device (CCD) camera was positioned at varying distances, depending upon the line pitch of the samples. Measurements were conducted at the carbon K-edge, specifically within the energy range of 280 to 300 eV. The line grating samples were manually aligned, ensuring the diffraction peaks to be captured by the CCD, as illustrated in Fig. 1(b). In our experiments, we used the normal incident angle. The exposure time was optimized to balance signal-to-noise ratio, avoid detector saturation, and minimize radiation dose to prevent beam damage. The exposure time ranges from 1 ms up to 2 s. It is crucial to consider the X-ray probe beam damage, particularly for latent images, during prolonged exposure times. The minimum exposure time (1 ms) was achieved using a piezo shutter. Radiation dose can be further adjusted by tuning the incident beam intensity.

2.3.

Atomic Force Microscopy

The topographic imaging of the fabricated samples was captured using AFM. AFM images were acquired using the Bruker Dimension Icon3 in ScanAsyst mode at the Molecular Foundry, LBNL. The ScanAsyst probe was paired with a sharp tip ranging from 2 to 12 nm in radius. The thickness and cross-section profile were extracted from the AFM images.

3.1.

Near-Edge X-ray Absorption Fine Structure

To investigate the chemical alterations occurring in a resist during the exposure process, we conducted near-edge X-ray absorption fine structure (NEXAFS) spectroscopy separately on the uniform pristine and exposed resist films at ALS beamline 11.0.1.2. This established technique leverages the photoexcitation of electrons from a core level to unoccupied molecular orbitals, providing detailed insights into the precise chemical surroundings of a particular element. NEXAFS at the carbon edge is particularly suitable to analyze the chemical environment of the resists.^21,22 As shown in Fig. 2(a), NEXAFS reveals two primary peaks changed after exposure. The peak at 285.2 eV may belong to the ${\pi }^{*}$ $\mathrm{C}═\mathrm{C}$ resonance of the carbon–carbon double bonds.²³ The sharp peak at 288.6 eV may be attributed to C═O double bonds in the methacrylate group.²³ These two resonant energies will be used for CD-RSoXS measurement.

Fig. 2

(a) NEXAFS spectra for unexposed and exposed resists. Optical constants delta (b) and beta (c) as a function of energy for unexposed and exposed resists.

Furthermore, optical constant, delta ($\delta$) and beta ($\beta$) in the complex index of refraction $n(E)=1-\delta (E)+i\beta (E)$ can be determined from NEXAFS spectra, which was measured at ALS beamline 11.0.1.2 with total electron yield (TEY) mode. The absorption part of the index of refraction $\beta$ can be indirectly extracted by TEY measurements²⁴ and then scaled to the Henke atomic scattering factor database.²⁵ The dispersion part of the index of refraction $\delta$ can be determined with the Kramers–Kronig relations.^26,27 The energy dependence of delta and beta are shown in Figs. 2(b) and 2(c), respectively.

3.2.

CD-RSoXS Results

CD-RSoXS measurements were performed at the ALS beamline 11.0.1.2 using incident energies of 280, 285.2, and 288.6 eV. The incident angle was constant normal incidence. Scattering intensity was captured on a CCD detector featuring a pixel size of $27\mu \mathrm{m}$ and a sample-to-detector distance of 70 mm. The exposure times are 2 s for the latent image and 1 ms for the developed sample, respectively.

The CD-RSoXS scattering patterns of latent image and developed samples with different line pitches are illustrated in Figs. 3(a) and 3(b), respectively. The spacing between adjacent diffraction orders corresponds to the line pitch number. It is apparent that varying intensities are observed among different diffraction orders in latent images. Specifically, in the developed sample, the intensity of the second order is lower than that of the third order. However, in the latent image [as depicted in Fig. 3(a)], the intensity of the second order surpasses that of the third order. The one-dimensional (1D) q-space lineouts of the scattering intensity at 280 eV clearly delineate the distinction between latent image and developed sample with varying line pitches [Fig. 3(c)].

Fig. 3

CD-RSoXS scattering patterns of (a) latent image and (b) developed sample in transmission geometry. (c) 1D plots of the scattering intensity at 280 eV of latent image and developed sample with varying line pitches (40, 60, 80, and 100 nm).

To unveil the origin of such differences in scattering intensity, we conducted AFM to examine the structural differences between the latent image and the developed sample. AFM images reveal distinct structural features of the latent image [Fig. 4(a)] and the developed sample [Fig. 4(b)]. Notably, a reduction in thickness within the exposed area is observed in the latent image. Upon closer examination of the cross-sectional profile [Fig. 4(c)], it becomes apparent that the line width with reduced thickness measures less than half the pitch. In contrast, in the developed sample, the width of the lines nearly matches the width of the spaces (or trenches) between them, as illustrated in Fig. 4(d). Such measured topography of the developed sample approaches the shape of a square wave, which explains why the even-order diffraction peaks are significantly smaller than the odd-order peaks in the corresponding scattering patterns of the developed samples.

Fig. 4

AFM images of (a) latent image and (b) developed sample with 100-nm pitch. Cross-section profiles of (c) latent image and (d) developed sample.

3.3.

Finite Element Method Maxwell Solver

The AFM and CD-RSoXS measurements of the gratings reveal a transformation in shape from latent image to developed gratings. This combination has been demonstrated in the characterization of directed self-assembly polymers using hard X-ray scattering.²⁸ It is noted that the AFM tip size ($2\sim 12\mathrm{nm}$) is in the same order of magnitude as the grating, making it difficult to get the exact shape of the grating. As a result, AFM measurements primarily allow for the retrieval of the grating’s height. In the latent sample, a chemical distinction exists between the exposed and unexposed regions. However, AFM is limited to surface analysis and cannot capture this chemical difference. For a deeper understanding of the cross-sections in both latent and developed samples, as well as their variations, we numerically solve Maxwell’s equations using finite element method (FEM) to simulate the CD-RSoXS results. This simulation is capable of calculating the scattered intensity for complex shape.²⁹ To conduct the Maxwell solver simulation accurately, knowledge of the optical constants of the materials involved is essential. In the calculations presented here, the optical constants of the photoresist were derived from NEXAFS measurements (Fig. 2). Previous studies³⁰ have demonstrated that near an absorption edge, the optical constants deviate from database values when the corresponding element is present in the material.

Figures 5(a) and 5(c) present the reconstructed cross-sections of the latent and developed gratings, respectively. The blue section represents the ${\mathrm{SiN}}_x$ window, the grey portion indicates the unexposed area, and the green segment denotes the exposed resist. The triangulation represents the FEM mesh we used in this calculation. In our calculations, we employ periodic boundary conditions. On the right side, a comparison is made between the simulated and the measured scattering intensities [Figs. 5(b) and 5(d)]. The grating parameters of latent image and developed sample extracted from simulation are summarized in Table 1.

Fig. 5

Cross-section of the grating used for the FEM Maxwell solver calculation for latent (a) and developed (c) grating with the corresponding calculated scattering intensities (b) and (d) for different incident energies compared with the experimental values.

Table 1

Grating parameters extracted from simulation.

The initial shape of the latent grating used in the simulations was derived from the AFM measurements [Fig. 5(a)]. The height of the resist, measured at 41.8 nm, was obtained from the AFM analysis of the developed sample. A width of 60 nm was selected for the unexposed part (grey) to best represent the scattering data in first and second orders. It is worth noting that the calculated values for the third and fourth orders are presented, despite these orders not being observed in the experimental measurements of the latent image [Fig. 5(b)]. The calculation intensity was normalized to the first order, but the actual intensity of 280 eV was much lower for those of 285.2 and 288 eV due to the reduced incident beam intensity (potentially due to carbon contamination). According to the calculations, at an incident energy of 280 eV, the third and fourth orders approach the detection limit in magnitude. This energy falls below the absorption edge, where no distinction exists among the optical constants of the exposed and unexposed resist. Furthermore, the calculated intensities of the third and fourth orders at resonant energies are slightly lower than that of the second order. Therefore, the detection limit is unlikely to be the reason, pointing to a potential model issue. We will delve into this issue in the next chapter.

For the developed sample, the high scattering intensity and contrast enable us to observe orders from the first to the fifth. We use the shape derived from the AFM measurements as an initial approximation for calculating the scattering intensities [depicted as stars in Fig. 5(d)]. Although they exhibit a similar trend to the measured values, discrepancies arise, particularly for the second and third orders. AFM struggles to capture the exact profile due to the tip’s shape being comparable in magnitude to the critical dimension of the grating, complicating the determination of the grating’s sidewall angle. To obtain a more detailed shape, Bayesian optimization³¹ is employed to reconstruct the sidewall angle and width. The results are depicted in Fig. 5(d) (points) and align well with the measured intensities. In Fig. 5(c), the reconstructed shape is juxtaposed with the AFM-derived shape. Notably, the reconstructed shape appears smaller and has a steeper sidewall angle compared with the AFM measurement. From the reconstruction results, it is evident that the unexposed portion of the developed grating cross-section is smaller than that of the latent image, suggesting that some of the materials at the exposed gradient dissolved during the development process. These findings align with the AFM measurements and the presence of the unsuppressed second order in the CD-RSoXS measurements of the latent images.

Last, we proceed to the reconstruction of the developed sample with pitches of 60 and 80 nm (Fig. 6). For gratings of this size, obtaining shape information from AFM measurements is more challenging. The height of the gratings was fixed to the height obtained from the AFM measurement of the 100-nm pitch sample. As shown in Fig. 6, there is a good agreement between the measurements and the reconstructed diffraction order. The corresponding shapes are displayed as insets in Fig. 6. The reconstructed sidewall angle is closer to 90 deg compared with the 100-nm pitch sample. These differences may be clearer in the reconstruction of the latent image, which requires further study. Due to the limited number of available diffraction orders and no variation in the angle of incidence (normal incidence for all measurements), the number of model parameters is comparable to the number of available measurement points. This situation may result in overfitting and a model with high uncertainties due to the low number of degrees of freedom.

Fig. 6

Cross-section of the grating used for the FEM Maxwell solver calculation for pitch 60 nm (developed) (a) and pitch 80 nm (developed) grating with the corresponding calculated scattering intensities for different incident energies compared with the experimental values.