Supplementary Information. Resolution limits of electron-beam lithography towards the atomic scale

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1 Supplementary Information Resolution limits of electron-beam lithography towards the atomic scale Vitor R. Manfrinato a, Lihua Zhang b, Dong Su b, Huigao Duan c, Richard G. Hobbs a, Eric A. Stach b, and Karl K. Berggren a,* a Electrical Engineering and Computer Science Department, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA; b Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA; c Micro Nano Technologies Research Center, Hunan University, Changsha , China * Corresponding author: berggren@mit.edu Table of Contents 1. Sample Processing 2. STEM Lithography 3. TEM Metrology 4. Image Processing 5. 1-nm Features 6. Dose Latitude 7. Throughput Considerations 8. Lithographic PSF: dot-exposure method 9. Calculated PSF 10. HSQ contrast for PSF calculation 11. Energy Density Contrast Calculation 12. EELS 13. Stopping Power and Bulk Plasmon Peak 14. Percentage of Energy Loss in HSQ and in SiN x 15. References 1

2 1. Sample processing The samples were prepared by spin-coating HSQ (1% solids XR-1541, Dow Corning) on 10- or 50-nm-thick Si 3 N 4 membranes (purchased at Ted Pella or TEMwindows.com) at a spin-speed of 8 krpm. The resulting thickness was 10 nm, measured by fallen over structures on TEM. To avoid thermally-induced cross-linking of HSQ, which might lead to a loss in resolution, no preexposure bake was performed 1. After exposure, samples were immersed in salty developer (1% weight NaOH + 4% weight NaCl) 1 for 4 min at 24 C, rinsed under deionized water for 2 min, rinsed in isopropyl alcohol for 15 s, and gently blown dry with nitrogen gas for 1 minute. The typical total processing period from spin coating to development was about 4-5 days. 2. STEM lithography The exposures were carried on a Hitachi HD 2700C dedicated aberration-corrected scanning transmission electron microscope (STEM) with a cold-field-emitter source (~ 0.3 ev energy spread), 0.15 nm spot size 2, and a beam current of pa. We loaded our samples overnight, 15h before exposure, to remove contaminants from the chamber. We avoid using any artificial structures (e.g., colloidal particles) for focusing the electron beam in the sample, thus reducing electron-beam-induced contamination. We used the Ronchigram method to focus the electron beam in the sample 3. Briefly, this method consists of adjusting the focus, stigmation, and aberration corrections by monitoring the electron beam diffraction, as shown in Figure S1. For example, Figure S1A presents the electron beam in focus but stigmatic. Figure S1B shows the electron beam in focus and not stigmatic, presenting a smooth Plato in the back focal plane, indicating a focused electron beam. Typically, we focused the electron beam 5 to 10 µm away from the exposure area. 2

3 Figure S1. Ronchigram image (from the diffraction camera) while adjusting focus, stigmation, and aberration correction. (A) Shows a focused and stigmatic electron beam while (B) shows a focused and non-stigmatic electron beam, ready for exposure. We did our exposures by imaging the resist with a Digiscan Control Unit, embedded within the Digital Micrograph Suite (Gatan, Inc.) choosing: (1) the desired dwell time; (2) microscope magnification; (3) number of pixels; and (4) beam current. These parameters define the area and pitch of interest. No pattern generator was used. We investigated the minimum fabricated pitch (or highest pattern density) by exposing dot arrays with varying pitch at 4 µm 4 µm area. To investigate the minimum feature size, we used a different design because posts smaller than 4 nm usually collapsed, thus resulting in small contrast when imaged in the TEM. We decided to expose square-like gratings or network structures that would give robust mechanical support for linear structures, increasing resist adhesion and avoiding feature collapse during development. The exposures were carried out without a pattern generator, so the pattern geometries were limited. Therefore, we used a design depicted in Figure S2 that roughly approximates a squarelike grating. 3

4 Figure S2. TEM micrograph of square-like grid or network structure exposed to give support for small width lines. Wider lines (coming from the rightmost circle) gave mechanical support for finer lines. This pattern also inhibits feature collapse during the solvent drying of the development step. 3. TEM Metrology We chose to do TEM instead of SEM metrology because TEM enables higher spatial resolution and TEM metrology enables visualization of sub-5-nm resist residues between fabricated structures, which is important to define the minimum pitch, as demonstrated in Ref. 4. The TEM metrology was done on JEOL JEM 2010F transmission electron microscope at 200 kev. The images were taken slightly defocused in order to provide a slight Fresnel fringe to enhance edge contrast. This has a small to negligible effect on the measured resolution. 4. Image processing The feature size variation was calculated using TEM micrographs and imaging processing with ImageJ. Specifically for post diameter deviation, we transformed the TEM micrographs in black 4

5 and white, for a given pixel threshold that would not dramatically change the post size. Then, we used analyze particles on ImageJ to calculate the area of all posts in each picture shown in Figure 1B and 1C in the main text. We calculated the diameter of each post based on its area, considering that the posts are circular. Then, the standard deviation of all diameters was obtained. For feature size analysis, we converted the TEM micrograph (Figure 1D) in black and white, for a given pixel threshold that would keep the same FWHM. Then, we used find edges on ImageJ to obtain the contour of the feature size. We obtained the standard deviation of all measured line widths, sampled with 0.3 nm spacing and 250 nm long nm features The minimum feature size attainable with HSQ at 200 kev was also investigated. The main results of this investigation are discussed in the main text. However, here we show a structure that had poor uniformity but with even smaller feature size. We fabricated a dot array with 15 nm pitch, but slightly overdosed. Figure S3 shows the resultant array with HSQ structures down to 1 nm. This result gave the smallest resist structure ever written by EBL in conventional resists. This pattern had poor uniformity and due to limited control of the electron beam in the STEM we could not fabricate a network pattern to support these 1-nm features without affecting resolution. Nevertheless, this shows that HSQ could achieve 1 nm feature size, but with poor reproducibility to date. 5

6 Figure S3. Bright field transmission electron micrograph of HSQ structures exposed by the STEM at 200 kev. The HSQ thickness was 20 nm and it was on top of a 50-nm-thick Si 3 N 4 membrane. The lines had a pitch of 15 nm, with feature size variation from 1 to 6 nm. The feature variation was due to different dwell times (electron dose) between dot and inter-dot exposures of the scanning beam (a beam blanker was not available). The HSQ structures appear to be fully developed, with some fallen-over posts indicated by slightly darker areas than the background. 6. Dose Latitude Figure S4 presents two measured PSFs at 200 kev. We fitted both PSFs and obtained the deviation ( Radius) and the relative deviation ( Radius/Radius) between the two fits for all radii. We obtained an average deviation of 1 nm and relative deviation of 13% for all radii. 6

7 normalized PSF (1/nm2) 1.E+00 1.E-01 1.E-02 PSF 200keV 1st experiment PSF 200keV 2nd experiment 1.E radial distance (nm) Figure S4. Two measurements of the point-spread function (PSF) for 10-nm-thick HSQ at 200 kev on SiN x membrane substrate. 7. Throughput Considerations Aberration-corrected STEM lithography has also a throughput advantage due to reduced spot size and increased beam current. The STEM system has 0.15 nm spot size at 100 pa. In principle, one could design an aberration-corrected EBL system with 2 nm spot size and beam current of 18 na, i.e. with ~ 4 higher beam current than state of the art EBL tools. 8. Lithographic PSF: dot-exposure method 7

8 Isolated posts were patterned with single-pixel exposures with doses ranging from 1 to 10 3 fc/dot, followed by salty development 1. The reciprocal dot dose was then plotted versus the dot radius, as described in Ref. 5, given the functional form of the point-spread function (PSF). We normalized the PSFs at 30 and 200 kev by setting the same intensity of each PSF at 2 nm radius: 2 (1) This normalization was used to compare the PSFs without the effect of different resist sensitivities at these beam energies. We should note that the differences in PSF curvature are the important factors to calculate energy density contrast and compare resolution capabilities. 9. Calculated PSF In order to calculate the PSF for sub-2 nm radius, we used one H -shaped structure with 2-nm minimum feature size. The H -shaped structure is shown on the leftmost inset of Figure 2B. The 200 kev PSF was fitted with two functions with the form a/(1+x/b) c (one analytical approximation for electron beam current density). However, representing the PSF with two of these fitting functions was not sufficient to generate the energy density contour that approximates the H-shaped structure. So, we added another function with the form a/(1+x/b) c for the sub-2nm radius. We chose to set the function power, c, as 4.2 for keeping the same drop off from the experimental PSF data. So, we optimized a and b (for c= 4.2) to obtain a dose contour (righmost inset of Figure 2B) that matches the H -shaped structure (leftmost inset of Figure 2B). The fitted PSF and the calculated PSF are given below:... (2). 8

9 ..... (3). These PSFs were normalized to have intensity equal to unity for radius equal to zero. See section 10 to compare dose density contours in the resist into fabricated structures. 10. HSQ contrast for PSF calculation One remaining issue to compare energy density contours from section 9 to a fabricated structure is to consider the resist contrast. The resist contrast translates dose density to resist thickness, i.e., translates deposited energy into topographical shape in the resist. The resist contrast for sub-10- nm isolated lines is close to infinity, as shown in Figure S5. So, we can consider that the red energy density contour (the one defining the 2 nm feature in the H -shaped structure) depicted in the inset of Figure 2B closely matches the fabricated structure dose (nc/cm) Figure S5. Contrast measurement for isolated HSQ lines. Left: bright-view TEM images of isolated lines exposed at different doses, from which we were able to obtain the thickness remaining of HSQ lines at different exposure doses. Due to high aspect ratio, all isolated HSQ lines collapsed, translating the thickness measurement to be width measurement. The original thickness of HSQ spin-coated for EBL was 100 nm, and the exposure was done at 100 kev. The development was done in 1% NaOH + 4% NaCl for 4 min at 24 C. Right: the contrast curve (thickness normalized thickness remaining (%)

10 remaining vs. dose) of the isolated HSQ lines, showing an almost ideal development contrast, i.e. there was no gradual thickness transition when changing the dose. 11. Energy density contrast calculation Quantifying resist exposure and the resolution limit translates into calculating the energy density (ev/nm 3 ) deposited in the resist. We usually assume a uniform energy distribution through resist depth once the thickness (10 nm) is much smaller than the mean free path (272 nm), which is the case here. Then, PSF gives the areal energy density (ev/nm 2 ). To evaluate how close we could expose and develop two adjacent structures with distance d, we need to calculate the energy density contrast: (4) where is the maximum energy density and is the minimum energy density (ev/nm 2 ) in the resist, for a given pattern. Calculating K as a function of distance d, we obtain the Figure 2C in the main text. A contrast curve measured for 30 kev electrons and extrapolated for HSQ thickness of 10 nm (with same development as done here) 6 shows that K 0.25 for a resolvable pattern. 12. EELS Electron energy loss spectroscopy (EELS) was done on Hitachi 2700C dedicated aberrationcorrected STEM with a cold-field-emitter source (~ 0.3 ev energy spread) at 200 kev. The beam current was ~20 pa, 0.3eV/channel dispersion. The electron beam convergence semi-angle was 28 mrad. The spectrum was taken with 0.06s dwell time with 12s of integration time, over an area of nm. 10

11 13. Stopping power and bulk plasmon peak To verify if the electron dose agreed with the stopping power at 200 kev, we measured and calculated the mean energy loss in the HSQ + SiN x membrane as shown in the table below. We measured the mean energy loss by computing a weighted sum of energy loss from 1 to 370 ev using the EELS spectrum in Figure 3. We calculated the energy loss by using the tabulated stopping powers 7 and using stoichiometric proportions of HSQ (H 1 S 1 O 1.5 ) and SiN x (Si 3 N 4 ), with 2.654g/cm 3 mass density for HSQ 8 and 3.44g/cm 3 mass density for Si 3 N 4. As tabulated, the measured and calculated mean energy loss are in close agreement. We also measured and calculated the bulk plasmon peak in HSQ. The measured bulk plasmon peak was the maximum energy loss in the low-loss EELS spectrum in Figure 3, which was 22.5 ev. However, the peak at 22.5 ev could be composed of other excited states, as measured in Ref. 9, 10. To calculate the bulk plasmon energy we used the free-electron gas model 11 : ħ Ɛ (5) where n is the electron density, e is the elementary charge, m 0 is the rest electron mass, Ɛ 0 is the vacuum permittivity, and ħ is the Plank s constant. The HSQ electron density may vary during exposure. So, considering the HSQ with mass density of g/cm 3, 8 the calculated bulk plasmon peak is 24 ev. However, considering the HSQ with mass density of 1.4 g/cm 3, the calculated bulk plasmon peak is 17.5 ev. Therefore, this range of plasmon energies (17.5 to 24 ev) reasonably agrees with the measurement of 22.5 ev. In addition, the HSQ bulk plasmon energy is similar to the 22.7 ev plasmon energy of SiO

12 Sample 20nmHSQ/10nmSiN x Bethe energy loss (ev) 20.8 EELS mean energy loss from 1 to 370 ev (ev) 19.9 Plasmon peak calculated (ev) Plasmon peak measured (ev) Percentage of Energy loss in HSQ and in SiN x To calculate the percentage of energy loss per unit thickness in HSQ and in the SiN x membrane, we obtained the percentage of energy loss of samples with varying HSQ thicknesses and SiN x thicknesses, as shown in table below. SiN x thickness (nm) Measured energy loss/ total energy % 6.1% % 8.3% % 10.5% % 34.9% HSQ thickness (nm) Mean least square of energy loss/ total energy We determined a mean least square fitting of this tabulated data by using the equation:.. (6) For the sample of 20 nm thick HSQ on top of 10 nm SiN x, we estimated an energy loss of 42% in HSQ and 58% in SiN x. We note that some errors would come from the surface plasmons formed at the lower energy side of the bulk plasmon peak. 11 However, the formation of surface plasmon would cost a reduction of bulk plasmon (Begrenzungseffekt effect) which therefore compensates the errors. Totally, we believe the above formula would give a meaningful distribution of energy loss between HSQ and SiN x. 15. References 12

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