Dynamic Imaging of Periodic Structures using Extreme Ultraviolet Scatterometry

TL;DR

Dynamic Imaging of Periodic Structures using Extreme Ultraviolet Scatterometry (DIPS) tackles the challenge of rapidly imaging nanoscale dynamics in periodic systems by exploiting EUV scatterometry. The authors derive a linear mapping between changes in the $l$-th diffracted order and the corresponding Fourier component of the dynamic perturbation, achieving diagonal reconstruction under specific conditions ($\epsilon_n$ purely imaginary and $\gamma_{\ell}$ terms with identical phase) and validate it with RCWA simulations. They apply the method to an EUV pump–probe experiment on 1D nickel gratings on diamond, reconstructing time-resolved unit-cell deformations that agree with finite-element models. The work offers a fast, low-data-volume metrology approach for nanoscale energy transport and surface dynamics, with guidelines for experimental optimization and potential extension to higher-dimensional periodic systems.

Abstract

Dynamic scattering and imaging with coherent, ultrafast, extreme ultraviolet (EUV) light sources can resolve charge, phonon and spin processes on their intrinsic length and time scales. However, full field coherent diffraction imaging requires scanning of the sample combined with computational phase retrieval, making it challenging to quickly acquire a large series of dynamic frames. In this work, we demonstrate a technique for extracting dynamic 1D images of the average unit cell in a periodic sample from traditional EUV scatterometry data by analyzing the changing intensities of the far field diffracted orders. Starting from a system of equations relating small changes in far field diffraction to phase and amplitude perturbations at the sample plane, it is shown that under certain conditions, changes to the $n$th diffracted order map exclusively onto the $n$th Fourier component of the perturbation via a closed-form relation. We show through rigorous coupled-wave analysis simulations that our method can provide a good approximation even outside the scalar diffraction theory framework in which it is derived. Finally, we experimentally demonstrate this reconstruction method by exiting 1D nickel nanowires on a diamond substrate using an infrared laser pump pulse, and measuring their relaxation using a time-delayed EUV probe pulse, to visualize nanoscale phonon dynamics.

Figures (5)

• Figure 1: Dynamic imaging of periodic structures. In the sample plane, light diffracts from a periodic profile subject to a small time-dependent perturbation, creating a dynamic diffraction pattern on the detector. Under certain conditions, the change in each far field diffracted order, $\Delta \tilde{I}_{\ell}(\tau)$, can be related to the corresponding Fourier component of the perturbation, $\epsilon_{\ell}(\tau)$.
• Figure 2: Reconstruction of a dynamic phase perturbation to a square grating (a) The static grating geometry consists of a 1D array of rectangular structures of linewidth $L$, height $H$ and period $P$ on a substrate (see Eq. \ref{['eq:fieldgtg']}). The complex EUV reflectivities of the grating and substrate are $r_g$ and $r_s$, respectively. The transmittance function for the static grating (blue) is multiplied by a small dynamic phase perturbation (red), which is exaggerated here. (b) The Fourier components $\epsilon_{\ell}$ of the perturbation (red) and their reconstructions (green) from a Fresnel simulation of the far field diffraction pattern. Each Fourier component of the perturbation is reconstructed using the corresponding far field diffracted order. (c) By including an increasingly large number of diffracted orders in the reconstruction (labeled numerically) and Fourier transforming back into real space, one approaches the original dynamic perturbation.
• Figure 3: Simultaneous treatment of an amplitude and phase perturbation in the square grating geometry (a) Finite element calculation of the temperature $T(x,z,\tau)$ and displacement $\vec{u}(x,z,\tau)$ fields in a unit cell of the square nickel grating geometry one nanosecond after the nickel structure is excited by an ultrafast pulse. (b) EUV reflectivity across one unit cell before (blue) and after (orange) the excitation. The change in reflectivity is exaggerated for visibility. While the change in silicon substrate reflectivity is assumed to be negligible due to its low temperature rise, the change in nickel reflectivity varies laterally as a function of density. (c) Fourier components $\epsilon_{\ell}$ of the phase perturbation calculated directly from the simulated vertical displacement using Eq. \ref{['eq:phasetoheight']} (red) and their reconstruction from a Fresnel simulation of the far field diffraction pattern under two scenarios. The reconstruction performs reasonably well when using Eq. \ref{['eq:gtgreconstructionamp']} to account for the change in reflectivity (orange). If the reflectivity is assumed to be static, as in Eq. \ref{['eq:gtgreconstruction']}, the reconstruction fails (gray).
• Figure 4: Simulated reconstruction method robustness (a) Average error in the reconstructed Fourier coefficients $\epsilon_1$ to $\epsilon_3$ of the transmittance function perturbation $\Delta t_A(x,\tau)$ as a function of perturbation size. The simulation considers $\lambda$ = 30 nm EUV light normally incident on a square silicon grating of $H = 3\lambda/8$, $L$ = 500 nm and $P$ = 2000 nm (inset) and computes random surface deformations of the form in Eq. \ref{['eq:randompert']} with Fourier coefficients chosen from a uniform distribution over [-$a_n$,$a_n$]. The corresponding transmittance function perturbations are directly computed using Eq. \ref{['eq:phasetoheight']} and compared to the results of a Fraunhofer diffraction simulation and subsequent reconstruction. The error grows as a function of perturbation size because Eq. \ref{['eq:linearphasediagonal']} neglects terms of second order in the $\epsilon_{\ell}$. The error here and in subsequent panels is defined as the percentage difference between the reconstructed and directly computed Fourier coefficients of the transmittance function perturbation averaged over many random trials. (b) Average reconstruction error vs. Fourier coefficient for a small perturbation to the geometry in panel (a). The random surface deformations are computed as before, but now the object plane transmittance function and far field diffraction pattern are computed using an RCWA simulation, which introduces small off-diagonal terms neglected in scalar diffraction theory. When the static diffraction efficiency is also small, which for a square grating is the case when $\ell L/P$ is an integer, the reconstruction error is large. (c) Average error in reconstructed Fourier coefficients as a function of $R_s/R_g$. To isolate the effects of reflectivity, the simulation considers 25 nm EUV light normally incident on a square ruthenium (Ru) grating of $H = 5 \lambda / 8$, $L$ = 200 nm and $P$ = 2000 nm and twice the nominal density, so that the structure transmits no light, on a Ru substrate of variable density and reflectivity. The same RCWA simulation is used as in panel (b) and the error grows as $R_s/R_g$ decreases, because this causes the size of the on-diagonal term in Eq. \ref{['eq:linear']} to decrease. (d) Average error in the reconstructed Fourier coefficients $\epsilon_1$ and $\epsilon_2$ as a function of grating size using the method of generating random surface deformations described in panel (a). The simulation considers $\lambda$ = 30 nm EUV light incident normally on a silicon grating of $H = 3\lambda/8$ and variable period $P$, with $L = 0.3P$. As in panels (b) and (c), the reconstruction is performed on an RCWA simulation of the far field diffraction. For the solid red curves, the $\gamma_{\ell}$ used in the reconstruction and the perturbed transmittance function to which to compare the reconstruction results are calculated directly using RCWA. For the dashed green curves the $\gamma_{\ell}$ are computed using Eq. \ref{['eq:gtgfouriercomponents']} and the reconstruction is compared to the perturbed transmittance function calculated from the vertical surface displacements using Eq. \ref{['eq:phasetoheight']}.
• Figure 5: Experimental reconstruction of unit cell dynamics for a nickel grating on diamond (a) Schematic of the dynamic EUV scatterometry experiment and one unit cell of the nickel grating on the diamond substrate with oxide and amorphous carbon interlayer. (b) Vertically binned EUV diffraction pattern on the CCD camera with the pump blocked (blue). Difference in counts with the pump unblocked versus blocked (green) 100 ps after the excitation. (c) Example AFM scans for the nominal $L$=500 nm, $P$=2000 nm and $L$=200 nm, $P$=2000 nm gratings used to extract linewidth, height and surface roughness. (d) Reconstructed $\epsilon_{\ell}$ as a function of pump-probe time delay for both gratings. Each curve shows a different $\epsilon_{\ell}$ from low (bright) to high (dark). The positive and negative diffracted orders are averaged in the reconstruction. The insets show the vertical surface displacement ($u_z$) calculated using Eq. \ref{['eq:phasetoheight']} at a 100 ps delay. (e) The corresponding finite element calculation of $\epsilon_{\ell}$ using Eq. \ref{['eq:phasetoheight']}, normalized to the same average value as the experimental reconstruction. The insets show the vertical surface displacement at 100 ps. Gray curves show the full finite element simulation, while red and purple curves show the result of a low pass spatial filter capturing only those Fourier components which can be reconstructed experimentally.