Toward Practical, Subwavelength, Visible-Light Photolithography with

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Toward Practical, Subwavelength, VisibleLight Photolithography with Hyperlens Jingbo Sun, and Natalia M. Litchinitser ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b07185 • Publication Date (Web): 27 Dec 2017 Downloaded from http://pubs.acs.org on December 28, 2017

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Toward Practical, Subwavelength, Visible-Light Photolithography with Hyperlens Jingbo Sun, Natalia M. Litchinitser*

Electrical Engineering Department, University at Buffalo, The State University of New York, Buffalo, NY 14260. Corresponding Author: [email protected] KEYWORDS: hyperlens, hyperbolic metamaterial, multi-layer, photolithography, diffraction limit, demagnification ABSTRACT: The future success of semiconductor technology relies on the continuing reduction of the feature size, allowing more components per chip and higher speed. Optical metamaterials-based hyperlens exhibit its ability for spatial pattern compression from the microto nano-scale, potentially addressing the ever-increasing demand of photolithograpy for inexpensive, all-optical nanoscale pattern recoding. Here, we demonstrate a photolithography system enabling a feature size of 80nm using a 405nm laser source. To realize such a system, we developed a fabrication method to obtain very thick hyperbolic metamaterial enabling a hyperlens with a very large demagnification rate of 3.75. Finally, we discuss several steps necessary to transform the proposed technique into a practical solution for the visible light-based

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nanolithography. These include flattening of the inner surface of the hyperlens to increase the working area and integrating the proposed device into a conventional stepper system. Optical lithography is a powerful method for patterning large areas with high throughput essential for the future progress in semiconductor industry.1 However, as any optical technique, the resolution of optical lithography is in the order of half the wavelength of illuminating light due to the well-known diffraction limit. Resolution is a key parameter for photolithography, which is determined by wavelength of the imaging light and numerical aperture of the projection lens. Resolution can be improved by decreasing the depth of focus, since according the Rayleigh criterion, the depth of focus for small features should decrease as the feature size squared. In recent years, several non-conventional lithography techniques aiming at overcoming the limits of conventional photolithography have been introduced. These include nanoimprint lithography,2, 3 nanosphere lithography,4, 5 laser interference lithography,6 stencil lithography,7 and dip-pen lithography.8 These techniques have several advantages and disadvantages. On the one hand, direct ways of increasing the resolution include decreasing the process parameter k, although it has an absolute lower limit of 0.25; increasing the numerical aperture of the lens, using, for example, an immersion liquid; or decreasing the wavelength of radiation used for patterning.9-11 However, several issues related to immersion liquids include the formation of micro- or nanosize bubbles, which scatter light and affect the image quality; contamination of the immersion liquid by the resist; and fluid heating changing the refractive index of the media during exposure.10 On the other hand, one of the most efficient and direct ways of improving the resolution is to use shorter illumination wavelengths. In the early days of lithography, light of the visible g-line (436 nm) and the ultraviolet i-line (365 nm) was used. Later, with the reduction of integrated circuits’ feature size, deep ultraviolet 248 nm KrF and 193 nm ArF excimer lasers


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were introduced, followed by deep-ultra-violet (UV) light (157 nm) and extreme-UV light (13.5 nm) . 12-17

Figure 1. Future visible light based optical lithography system. (a) A schematics and (b) numerical simulations of the system with 405nm enabled by a combination of diffraction-limited conventional lens and the proposed demagnifying hyperlens facilitating subwavelength patterning. There are two gaps with widths of 1.5µm and 1µm and a separated distance of 2.75µm, which can be treated as a macro size pattern. After the focusing of the conventional lens and the hyperlens, we can achieve the line width of 43nm and 30nm for the two gaps. The distance between the two gaps at the output surface is 80nm, which means that the whole system has a demagnification rate of 34. Despite the continuous success in mitigating the diffraction limit by changing the illumination source and, in many cases, different optical materials, the above described approach is evolutionary. Here, on the contrary we propose and demonstrate a practical implementation of the optical lithography system using a visible wavelength source operating at 405 nm capable of fundamentally overcoming the diffraction limit and enabling a feature size of 80 nm in its current


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implementation. These improvements are enabled by a combination of fundamentally different light-matter interactions in hyperbolic metamaterials and the proposed fabrication approach allowing for high-quality, up to 65 layers of hyperbolic metamaterial fabrication. Figure 1 shows a schematics and numerical simulations of a future ideal optical lithography system enabled by a combination of the diffraction-limited conventional lens with the proposed hyperbolic metamaterial-based structure facilitating subwavelength patterning. Despite the fact that the feature size demonstrated in this work is still one order of magnitude away from the current industrial record of 5 nm feature size achieved using 13.5 nm extreme-UV illumination, the proposed approach is only limited by the fabrication challenges. Results and discussion The enabling technology for the proposed visible-light subwavelength photolithography is a hyperlens.18-25 which is a cylindrically or spherically shaped hyperbolic metamaterial, as shown in Figure 2a. The dielectric permittivity of the hyperbolic metamaterial is described by the following tensor:26-28 ε ε% =  r

0 , ε r < 0, ε θ > 0, εθ 

0

(1)

where εr is the permittivity component in the radial direction, which in our case corresponds to the direction perpendicular to the layers, and εθ is the azimuthal component of the dielectric permittivity. Therefore, the equi-frequency contour (EFC) of such a structure in the r-θ plane can be described by

kr2

εθ

+

kθ2

εr

=

ω2 c2

.

(2)


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In eq. 2, kr, and kθ are the wave vector components along the radial and azimuthal directions, respectively; c is the speed of light, and ω is the frequency of the incident wave. Assuming

εr0 in eq. 1, the dispersion relation described by eq.2 possesses a hyperbolic shape, ensuring the propagation of evanescent waves that carry the subwavelength information. On the contrary, in a conventional lens with isotropic positive permittivity, evanescent waves decay and, therefore, subwavelength information is lost.

Figure 2. High demagnification hyperlens system. (a) The hyperlens of a cylindrical shape with Rout=1.2 µm has anisotropic permittivities of εr0 along the radial and tangential directions, respectively. Since |εr| >> εθ, the hyperbolic EFC is very flat, as shown in the inset. The incident beam propagates upwards with the electric field polarized perpendicular to the axis of the cylinder. (b) The intensity distributions at the outer surface right after the mask (red) and inner surface inside the photoresist (blue) obtained in numerical simulations. Sharp peaks in the intensity profile on the outer surface originate from the plasmonic enhancement at the edges of the Cr mask. The proposed system in Figure 2 is realized by alternating layers of alternating silver (Ag) and titanium oxide (Ti3O5), operating at 405 nm. Based on the theoretical calculations and the fabrication considerations, layer thickness of each Ag and Ti3O5 layer are set to 30nm [see supporting information]. The permittivities of the Ti3O5 and Ag at the wavelength of 405 nm are


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5.85 and -4.84+0.22i, respectively. According to the Maxwell-Garnett theory, dielectric permittivity tensor components of the multilayered structure can be determined by the following:

εθ = ε d f + ε m (1 − f ) ,

ε

r

=

ε dε ε

m

f + ε

d

m

(1

− f

(3a)

)

.

(3b)

Using eq. 3, we find that the permittivity component along the layers is εθ =0.51+0.11i and the permittivity component perpendicular to the layers is εr=−53+14.1i, which makes the hyperbolic EFC very flat, as shown in the inset of Figure 2a. In this case, inside the hyperlens light propagates along the radial direction. Therefore, the magnification/demagnification ratio of the hyperlens m is directly determined by the ratio between its outer and inner radius:

m=

Rout R t = out = 1 + Rin Rout − t Rout − t

(4)

in which t is the thickness of the hyperbolic metamaterial that forms the hyperlens. In order to maximize m, one can either decrease Rout (assuming t is fixed) or increase the thickness t. In this work, we focus on the later approach. In order to achieve the desired demagnification ratio, we cascaded two sets of l3 layers of hyperlens separated by a 60 nm thick polymethyl methacrylate (PMMA) layer, introduced in order to minimize the accumulation of surface roughness unavoidable in thick multilayers otherwise. Another PMMA layer is introduced on top of the mask on the bottom of the hyperlens in order to fill the air gaps in between the features of the pattern on the mask. As a result, the total thickness of the hyperlens t is 900 nm, corresponding to m ≈ 4. In our proof-of-principle demonstration, the mask is incorporated on the outer (curved) surface of the hyperlens in order to


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simplify the alignment of the mask. Detailed numerical studies have been performed to simulate the system shown in Figure 2b. In these studies, 405 nm incident light was used to illuminate a 50 nm thick Cr mask with a recorded U-shape pattern having a 300 nm feature size (the object) that was subsequently demagnified by the hyperlens to form an image on the inner surface of the hyperlens. These simulations confirm that the inserted PMMA layers do not affect the overall performance. The inset shows the intensity distributions right after the mask and inside the photoresist. The FWHM of the intensity distribution in the photoresist is around 70 nm, which is about 1/4 of the feature size on the mask as shown by the red curve and almost 1/6 of the illumination wavelength. In this section, we show the challenges associated with realization of high-magnification hyperlens and other thick hyperbolic structures in general. Figure 3a shows the scanning electron microscope (SEM) image of 27-layer-based structure consisting of alternating 30 nm Ag and 30 nm Ti3O5 layers. The colored lines depict the profile of the upper surface of the corresponding Ag layer, which shows accumulation of defects in each layer. These defects cause changes in the local effective material properties, result in cracks and bubbles in the top layer, decreases resolution and increases losses. The average surface roughness (Ra) of this kind of structure is always above 15nm. In our earlier work, we found that continuous deposition of 13 alternating layers of Ag (30 nm) and Ti3O5 (30 nm) results in acceptable multilayer quality.18 However, as the number of layers increases, the defects are accumulated and amplified. In this work, we proposed and realized a reliable procedure to overcome this challenge by developing a multiplestep deposition method to fabricate the hyperlens. This procedure is not limited to the hyperlens fabrication but may contribute to the realization of bulk metamaterials in general.


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In the first step, we deposited 13 layers of Ag/Ti3O5 and then spin coated a very thin layer of PMMA on top of this multilayer. As shown in Figure 3b, all the imperfections accumulated on the top Ag layer are smoothed out by the PMMA, completely eliminating the surface roughness accumulated from multiple layer deposition. In the second step, another 13 layers of Ag/Ti3O5 were deposited on top of the intermediate PMMA layer. The average surface roughness (Ra, AFM Dimension 3100) of the final structure is 5.5 nm. This two-step approach can readily be extended to a more general multi-step approach by introducing more intermediate PMMA layers after each of the 13 layers of Ag/Ti3O5. Figure 3c shows a 2.35 µm thick hyperbolic metamaterial fabricated by a five-step deposition method. This is the thickest metamaterials (5.8λ) structure demonstrated today at visible wavelengths.

Figure 3. Multi-step deposition for ultra-thick hyperbolic metamaterials. (a) Deposition of 27 layers Ag/Ti3O5 with no intermediate PMMA layer; (b) Two-step deposition of 26 layers Ag/Ti3O5 with a PMMA layer separating two 13-layered structures. The colored lines in the insets depict the profile of the upper surface of each Ag layer; (c) Five-step deposition of 65 layers of Ag/Ti3O5 with 4 intermediate PMMA layers separating every 13 layers.


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In experiment, we realized a cylindrical hyperlens-based nano-patterning system that enables demagnification in one direction while preserving the features of the object in the orthogonal direction. The cylindrical grooves were made by the standard buffered oxide etch (BOE) method. In the first example, a layer of 50 nm Cr was deposited on glass substrate, and relatively simple patterns (masks) consisting of a single line, double lines and a letter “U” with a feature size of 300 nm were milled using the focused ion beam (FIB) method employing a Zeiss AURIGA CrossBeam Workstation, as shown in Figure 4a. The distance between the two arms of the U shape on the mask is 700nm. Note that the hyperlens was designed to operate at 405 nm illumination, and the feature size of initial patterns on the Cr mask is above the diffraction limit for this incident light wavelength. Next, a 60 nm layer of PMMA was spin coated on the masks to form a smooth surface for the hyperlens deposition. Following the approach described in the previous section, 26 layers of Ag/Ti3O5 structure were deposited using the two-step method with 13 layers deposited continuously in each step separated by a 60 nm PMMA layer. The total transmittance of the entire structure is approximately 0.5% due to the high material's loss. Following the multilayer deposition, a 50 nm photoresist layer (diluted S1805) was deposited on the inner surface of the hyperlens to record the de-magnified pattern obtained using the realized hyperlens. The sample was illuminated from the glass substrate/Cr mask side with a 405 nm laser (150mW) for 3 minutes. Next, it was immersed in the developer solution MF-26A for 40 s to develop the pattern on the photoresist.


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Figure 4. Hyperlens structures and demagnification results. (a) Masks with single line, double line and U-shape patterns on the curved surface. (b) Demagnified single line on the photoresist. The widest part is around 130nm and the narrowest part is around 90nm; (c) Demagnified Ushape on the photoresist, the distance between the two arms of the U-shape indicated by the yellow scale bar is 190nm; (d) Cross section of the hyperlens with double lines pattern on the mask. Figure 4b shows the SEM image of the compressed (sub-wavelength) single line appearing on the photoresist layer. The width of this line is around 90 nm, confirming that the original pattern was demagnified by approximately 3.3 times. In Figure 4c, the developed pattern shows a Ushape with a feature size of 80 nm, and the center-center distance between the two arms of the Ushape is 190nm, corresponding to the demagnification up to 3.75. Figure 4d shows a crosssection of the hyperlens with the double-line pattern. The apparent nonuniformity of the PMMA layer thickness is due to the deformation of the fluidic PMMA right after the spin coating. This deviation from the designed PMMA thickness leads to some flattening of the hyperlens curvature and, as a result, a slight decrease in predicted demagnification.


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In the second example, we used a more complex image of an "Airedale Terrier" dog as a pattern on a mask (Figure 5a-b). The original pattern is 2.2 µm in height and width. After the exposure and development steps, the image of the dog reduced in height was recorded on the inner surface of the hyperlens. The height is around 0.8 µm, implying the demagnification factor of 2.75. Note that some details of the complex pattern that are below diffraction limit even on the mask (such as ears, mustache, neck and tail) are preserved in the final demagnified image recorded on the resist. However, the contrast for these features is not as high as for the larger ones, due to the relatively weak light intensity transmitted through the mask and the losses of the hyperlens. Larger details (such as the legs) are fully resolved but shortened, as expected, due to the demagnification property of the system. On the other hand, the largest features (such as the body) are also demagnified but overexposed on the photoresist. These results suggest that a trade-off between the longer exposure time required for the smallest features and reduced exposure time for the largest features has to be further optimized. Once again, since the cylindrical hyperlens only demagnifies the pattern in one direction (the height of the dog in this case), the features along the hyperlens are preserved to be the same as those on the mask. As a result, the proposed photolithography system transformed the original "Airedale Terrier" on the mask into a "Dachshund" on the photoresist (Figure 5c-f). To make a comparison, numerical simulations were also performed with Comsol 5.2. Figure 5g shows the dog pattern on the Cr mask. The demagnified pattern on the output surface is shown in Figure 5h. Detailed simulation results can be found in Supporting Information.


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Figure 5. Anisotropic demagnification of complex patterns combining different scales (above and below the diffraction limit). (a) Original pattern of an Airedale Terrier dog; (b) Airedale Terrier pattern on the mask; (c) original pattern on the photoresist after the development; (d) Outline of the pattern on the photoresist; (e) Pseudo color image of (c); (f) Comparison between the demagnified pattern and the directly compressed original pattern in (a); (g) Dog pattern on the mask drew in numerical simulation and (h) Simulation result after the demagnification.


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Comparing to the current state-of-the art techniques used in industry that rely on reducing the wavelength of the exposing light and re-designing the entire system for a new wavelength, the proposed hyperlens-based photolithography allows to overcome the diffraction limit and using visible wavelength light. While the results of our study brought the hyperlens-based pattering close to its practical application in modern photolithography, several practical challenges need to be further addressed: (i) In its current implementation, the hyperlens possesses a curved output surface that limits its applications. (ii) It has limited size of the working area. (iii) High losses of currently used materials’ combination. These challenges can be addresses as follows: 1) Several theoretical proposals to achieve flat output surface hyperlens have been reported in the prior publications.21-24 As discussed above, in our current work, additional PMMA layers have been used in the multi-step deposition process. In addition to smoothing the surface of the hyperlens, these additional PMMA layers also decrease the curvature of the hyperlens. This observation supplies a viable solution for further optimization (flattening) of the output surface of the lens. Figure 6a shows a cross-section of a 1.4 µm-thick hyperlens fabricated using a 3-step method. The magnified inset shows that the top surface is indeed significantly flattened. Figure 6b shows the results of numerical simulations, suggesting that the flattening effect does not deteriorate the overall demagnification performance of the lens. However, an additional (3rd) group of 13 metal/dielectric layers adds more losses to the system. This is why this design was not used in our experiments and requires further optimization.


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Figure 6. Toward a flat-output hyperlens. (a) A cross-section of a 1.4 µm-thick hyperlens fabricated using a 3-step method. (b) Intensity (in logarithm) distributions in the hyperlens. The inset shows the intensity distribution along the red curve at the output surface. 2) The limited working area of the hyperlens restricts its applications in both the microscopy and lithography. It was recently proposed that the hyperlenses can be arranged in an array.29, 30 In our work (as shown in Figure 3a), we have demonstrated an array of hyperlenses, although the spacing between them was rather large. 3) Finally, the material loss in the current hyperlens system originates from the losses of silver. Possible solutions include exploring other materials' system with lower losses31 or alternative designs32-34. On the other hand, we can also use high power laser to overcome the loss of the hyperlens in its current implementation.


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Although significant developments are necessary in order to transfer the proposed technique to the real-world industrial applications, hyperlens-assisted lithography offers an effective and feasible way to overcome the diffraction limit in the conventional photolithography, and is potentially promising nanofabrication tool of high resolution, efficient, large area and low-cost.

Conclusions In summary, we demonstrated a high demagnification ratio hyperlens as a step toward the nondiffraction-limited visible-light-based photolithography technology. The demagnification ratio of 3.75 enabled by thick hyperbolic metamaterials was demonstrated. This result surpasses previously reported magnification/demagnification ratios (Rout Rin ) by a factor of 2.18, 19, 25-29 In our experiments, complex patterns with feature size ranging from above to below the diffraction limit on the mask have been demagnified to a minimum line width of 80 nm using a 405 nm laser light. The proposed and demonstrated multi-step deposition method enabled the further increase of the thickness as well as the demagnification ratio of the hyperlens, supplying a route to practical applications of bulk hyperbolic metamaterials in modern photolithography and beyond.

Methods The hyperlens fabrication was started from the glass substrate with half cylindrical grooves. A 100nm Cr was first deposited to a flat glass substrate and then FIB was used to mill an array of 50nm wide slits on the Cr film. A cylindrical grooves array was obtained through using the Cr film as a mask as well as isotropic wet etching in a buffered oxide etch (in a 6:1 ratio). In the next step, Cr film was removed using CR-7 Cr etchant, and then a 50 nm Cr was deposited by electron beam evaporation as the photomask. Different patterns shown in Figure 4a were made with FIB on the Cr film. Subsequently, the Cr mask was covered by 60 nm-thick PMMA


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A2 (MicroChem) with spin-coating, on top of which the Ag/Ti3O5 multilayered structures were deposited using 2-step method. All the film depositions in this work were done by SEMICORE e-beam evaporation system. AUTHOR INFORMATION

Corresponding Author * To whom correspondence should be addressed: [email protected]

Author Contributions J. S and N. M. L. proposed the idea developed in this work. J. S. made the design and did the simulation. J. S. did the fabrication and the characterization of the sample. N. M. L. and J. S. wrote the paper. N. M. L. supervised this work.

Associated Content The authors declare no competing financial interest. Funding Sources: Army Research Office [W911NF-15-1-0146]. ACKNOWLEDGMENT The author would like to thank Dr. X. Zeng from the ASML for detailed discussions on the current status and requirements of modern photolithography. We would like to thank Dr. B Liu from the Materials Research Institute at Pennsylvania State University helping with the materials deposition.

Supporting Information Available: Simulations of materials' loss and demagnification performance. This material is available free of charge via the Internet at http://pubs.acs.org.


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