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Periodic nanopatterns can be generated using lithography based on the Talbot effect or optical interference. However, these techniques have restrictions that limit their performance. High resolution Talbot lithography is limited by the very small depth of focus and the demanding requirements in the fabrication of the master mask. Interference lithography, with large DOF and high resolution, is limited to simple periodic patterns. This paper describes a hybrid extreme ultraviolet lithography approach that combines Talbot lithography and interference lithography to render an interference pattern with a lattice determined by a Talbot image. As a result, the method enables filling the arbitrary shaped cells produced by the Talbot image with interference patterns. Detailed modeling, system design and experimental results using a tabletop EUV laser are presented.
© 2015 Optical Society of America
1. Introduction
Amongst the low volume nanopatterning techniques available nowadays, interference lithography (IL) or holographic lithography and Talbot lithography have attracted much attention because they are well suited to fabricate periodic structures like photonic crystals (PCs) [1], meta-materials [2], and biomedical nanosensors [3].
IL is achieved by combining multiple mutually coherent beams at the photoresist-coated wafer. The amplitudes and polarization of the individual beams can be selected in order to modify the absolute contrast and plane group symmetry of the structure while the configuration of the wave-vectors determines the lattice constant and the translational symmetry. IL has been used with a variety of lasers in different configurations to fabricate 1D gratings, 2D arrays [4], 3D photonics crystals [5, 6], and chiral metamaterials [7].
One strategy to reduce the minimum size of the printed feature is using illumination with shorter wavelengths since the pitch of the interference pattern is proportional to the wavelength. On this path synchrotron radiation has been used to push the limits of the attainable feature size by IL [8]. An alternative more convenient approach to achieve similar results is using compact extreme ultraviolet (EUV) lasers that were developed in the last two decades [9]. Nanopatterning with table top EUV lasers had been implemented at 46.9 nm and 18.9 nm [10,11], increasing the accessibility of EUV lithography beyond the utilization of large facilities like synchrotrons.
Interference lithography has the capability to create periodic structures with a period limited by the wavelength. Also it has the advantage of a relaxed depth of focus (DOF). IL provides a simple and robust nanofabrication method, but is limited to pure simple periodic patterns. To fabricate functional nano-devices like photonic crystal waveguides using IL, additional processes like multiple patterning techniques are needed to modify the periodic lattice. On the other hand, Talbot lithography [12–14], which supports arbitrary periodic patterns, liberates the lattice design so that a variety of features can be fabricated. However, the resolution of Talbot image is limited by the numerical aperture (NA) of the exposure system and the capability to fabricate a mask with enough contrast and resolution to produce a reliable print in the sample.
Lai et al. presented an interesting hybrid approach combined interference with mask-photolithography to produce periodic patterns by multiple beam interference and print “defects” in the periodic lattice by superimposing an aerial image [15]. Gaylord et al. improved this idea by introducing pattern-integrated interference (PII) [16]. PII is an imaging method superposing two identical and coherent aerial images to create custom designed periodic patterns. Advantages of this imaging method over traditional aerial image or interference image are obvious. It is simple, fast and robust with high resolution.
This paper will describe a technique combining EUV Talbot lithography and interference lithography to generate periodic nanostructures with an arbitrary lattice. At a common Talbot plane, two Talbot images generated by coherent EUV laser illumination are superimposed. In this way, the interference pattern is modified by a defined Talbot image. This method enables filling the arbitrary shaped cells produced by the Talbot effect with fine interference features, relaxing the fabrication constrains of the mask and extending the DOF of the exposure. With a simple experimental setup, Talbot interference lithography (TIL) can claim the advantages of both lithography methods, interference lithography and Talbot lithography, creating a pattern that neither of them can accomplish separately. We present a description of the system, a detailed modeling and experimental results using a tabletop EUV laser.
2. Talbot interference lithography
A conceptual diagram of the Talbot interference lithography is depicted in Fig. 1. Two mutually coherent beams impinging the mask with incidence angles ± θ illuminate a periodic semi-transparent Talbot mask. Each beam produces an image of the mask at the Talbot distances defined by zT = 2Na2/λ, with a the period of the structure in the mask, N the Talbot plane order and λ the wavelength of the illumination. At the common Talbot plane, the images produced by each one of the beams coincide producing interference. This interference pattern is used to print a sample located at this plane. The electric field in the plane of the sample can be calculated utilizing the diffraction formalism described in [17]. Assuming a Talbot mask placed in the plane (ξ,η), with a periodic transmission tA(ξ,η) illuminated by plane waves, the Fresnel propagator allows to compute the electric field of each one of the propagating beams as:
where Ti(ξ,η) = tA(ξ,η) × Xphase × Yphase takes into account the phase shift across the plane of the Talbot mask due to the angle of incidence:After a propagation distance equal to the Talbot distance zT, the Talbot images are formed. At this plane the total electric field is the interference of the two fields and the intensity is
where E2i(x,y,z) are the time-averaged intensity distribution of each beam and U12 = E1 × E2 is the correlation factor.
Figure 2 shows the results of this calculation. A binary Talbot mask, composed of an array of 20 × 20 square holes in a square matrix with a period of 12.5 µm, defines the transmission function tA(ξ,η). The mask was illuminated by two mutually coherent plane waves with λ = 46.9nm impinging at angles θ1 = 4° and θ2 = −4°. At the common second Talbot plane, the diffracted fields interfere generating a pattern defined by Eq. (3). Figure 2(a) is the binary Talbot mask design. Figure 2(b) shows the diffracted intensity in the first Talbot plane due to one of the illuminating waves, calculated using the Eq. (1). The superposition of both mutual coherent Talbot images creating a Talbot interference pattern is shown in Fig. 2(c). Figure 2(d) depicts the detail of a single cell. The Talbot mask design is combined with the interference produced by the two waves to generate a hybrid image of Talbot interference.
Fig. 2 Simulation results for Talbot interference image using Eq. (3). Figure 2(a) is the binary mask; Fig. 2 (b) is the traditional Talbot image generated by one beam at normal incidence; Fig. 2(c) is the TIL image generated by superposing two coherent Talbot images; Fig. 2(d) is a zoom of one cell in 2(c).
3. Experiment
A proof of principle TIL experiment was implemented using a EUV tabletop capillary discharge laser. Figure 3 schematically shows the experimental arrangement. The light source used in this experiment was a capillary discharge EUV laser which emits a highly spatially and temporal coherent beam at λ = 46.9nm [18–20]. The laser linewidth is Δλ/λ = 3-5 10−5yielding a coherence length Lc = 700μm. A Talbot mask was placed in front a Lloyd’s mirror arrangement. The binary Talbot mask was implemented with a commercially available TEM grid. The mask (grid) is composed of 7.5 × 7.5µm2 squares holes covering a circular area of 3 mm in diameter. After the mask, a flat mirror implemented with a gold-coated Si wafer was positioned at an angle of 4° relative to the incoming beam separating the diffracted light into two mutually coherent wavefronts. With a pitch of 12.5 µm the Talbot distance is 6663 µm. A Si wafer spin-coated with HSQ was placed at a distance of 33316 µm from the mask, in the position where the Talbot images produced by the two illuminated beams are rendered in the fifth Talbot plane. The sample was exposed with 12 shots of the EUV laser that approximately provides an exposure dose of 21.1 mJ/cm2 in the sample.
Figure 4 shows the experimental results obtained with this setup. The Talbot interference pattern obtained in the sample is shown in Fig. 4(a). The SEM image shows the lattice generated by the Talbot image superimposed with fringes generated by the interference between the two wavefronts. The pitch of the interference fringes (340 nm) is consistent with the angle of incidence in the Lloyd’s mirror. Figure 4(b) is a plot of a cross section of one cell in the direction perpendicular to the interference fringes (in dashed blue) superimposed with the expected print in the photoresist obtained with the two beams illumination (in solid red). The expected print was calculated using Eq. (3) with the parameters used in the experiment. An optimized sigmoid function was applied to the calculated intensity to represent the photoresist response. The agreement between the calculated period in the pattern and the experimental period is satisfactory. The results of this proof of principle experiment confirm the TIL method. It is not intended to reach the limit of the resolution.
Fig. 4 (a) SEM image of the print produced by Talbot interference. (b) Calculated and experimental profile in the photoresist. In dashed blue line the cross section of the experimental print. In solid red line the calculated print assuming a sigmoidal response for the photoresist. The periods of the calculated and experimental patterns are in good agreement.
The advantages of this approach as compared with standard Talbot lithography resides in that the minimum feature size is no longer determined by the Talbot mask, but depends on the wavelength of illumination as occurs in IL. Additionally the extended DOF inherent to IL facilitates the implementation of the TI lithography. To exemplify the potential of this approach, we performed a simulation to analyze the required conditions for printing a periodic structure composed of an array of squares sections 65 × 65 nm2, with a periodicity of 100nm, each square filled with lines with a periodicity of 13 nm utilizing both standard Talbot lithography and TIL. With these design constrains, the Talbot mask that would be necessary to fabricate should have an array of square sections each one of them with a grating with 13nm pitch. To achieve the necessary resolution to print the 13 nm period lines with Talbot lithography the required NA is 0.72, that is achieved for the 2nd Talbot plane. Assuming an illumination with a 13.9nm laser [21, 22], and a mask size of 6 × 6 μm2 yields a Talbot distance of 1439 nm with a DOF of 27 nm [12]. However, using the Talbot interference approach,satisfactory results are obtained with more relaxed design parameters. In this case the Talbot mask is just an array of square holes 65 × 65 nm2 while the 13nm pitch of the gratings inside the squares is obtaineded by the interference of two Talbot images. The DOF can be enlarged choosing a higher order Talbot plane (N). The restriction on the Talbot mask fabrication is relaxed because it requires a square matrix of larger dimension holes (65nm) as compared with the period of the gratings inside the squares in the first design (13nm). Performing a calculation of this alternative design confirm the advantages of the Talbot interference lithography: higher resolution with larger DOF.
Figure 5 shows the results of the calculation. Figure 5(a) is the design of a Talbot mask with 65 × 65 nm2 sectors with a period of 100nm filled with lines 13 nm pitch, arranged in a square array of 60 × 60 units. Figure 5(b) is the expected intensity distribution in the third Talbot plane located at 4.32 µm from the mask. As expected, the result shows that the Talbot image fails to replicate the fine periodic structure inside the square fields. The resolution of Talbot image will keep degrading at higher order of Talbot plane because the NA is further reduced. In contrast, Fig. 5(c) shows the design of an alternative Talbot mask with just 65 × 65 nm2 squares with 10nm radius of curvature corners arranged in an array of 60 × 60 units. This mask illuminated by two coherent beams of the same wavelength impinging at an angle of 32.32° would generate the intensity distribution at the 6th Talbot plane shown in Fig. 5(d). The interference fringes have enough contrast to print 13nm periodic lines. In this case the distance between the Talbot mask and the sample would be 8.64 µm and the DOF 135 nm, which is 5 times larger than the required positioning precision (DOF) in the standard Talbot lithography.
Fig. 5 Demonstration of the advantages of TI. Figure 5(a) is a Talbot mask composed of 6.5nm half pitch lines assembled in 65 × 65nm2 squares with 100nm periodicity; Fig. 5(b) is the calculated Talbot image at in th 3rd plane generated by one beam; Fig. 5(c) is the binary mask for TIL, composed of 65nm square holes with a period 100nm and 10nm radius of curvature corners; Fig. 5(d) is the TIL image at 6th Talbot plane, showing good contrast interference fringes with 13nm period.
4. Conclusion
We analyzed a hybrid lithography technique that combines Talbot lithography and interference lithography. In a single exposure step Talbot interference lithography is able to print custom defined periodic patterns with high resolution and generate nanopatterns that neither the Talbot nor interference lithography techniques can accomplish by itself. The resolution limit is set by the wavelength of illumination source as in IL while the arbitrary periodic pattern that modulates the interference pattern is obtained by Talbot imaging. The arbitrary shaped cells produced by the Talbot image can be filled with fine interference patterns (lines or dots) generated by interference of two or more coherent wavefronts. Additionally the TIL method relaxes the constrain in the mask fabrication and simultaneously expands the DOF of the exposure. The hybrid lithography technique described here adds flexibility to fabrication of more complex nanostructures.
Acknowledgments
This work was supported from the National Science Foundation by Grant No. ECCS 1507907.
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