A theoretical model is introduced to evaluate the ultimate resolution of plasmonic lithography using a ridge aperture. The calculated and experimental results of the line array pattern depth are compared for various half pitches. The theoretical analysis predicts that the resolution of plasmonic lithography strongly depends on the ridge gap, achieving values under 1x nm with a ridge gap smaller than 10 nm. A micrometer-scale circular contact probe is fabricated for high speed patterning with high positioning accuracy, which can be extended to a high-density probe array. Using the circular contact probe, high-density line array patterns are recorded with a half pitch up to 22 nm and good agreement is obtained between the theoretical model and experiment. To record the high density line array patterns, the line edge roughness (LER) is reduced to ≈17 nm from 29 nm using a well-controlled developing process with a smaller molecular weight KOH-based developer at a temperature below 10°C.
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The reduction of feature sizes in nanometer-scale devices is a key issue in nanotechnology for industrial applications. Because of its noncompetitive throughput, over the past several decades, optical lithography has been a main production technique of nanodevices. In the production process of nanodevices, the first step is to optically transfer the pattern of the device to a substrate coated with a photoresist using a high-precision optical instrument to create an image. The resolution of optical lithography is limited by the intrinsic property of light diffraction, which has been enhanced either using a shorter wavelength light for exposure or using larger numerical aperture optics. As an alternative to the conventional optical lithography using imaging optics, various optical near-field lithographic techniques have been developed to overcome the diffraction limit of light.1–12 Since the optical resolution of a pattern depends on the size of the light spot used for exposure, a subwavelength size aperture has been adopted to form a small light spot. This spot is generated in the near-field region at a size that approximately matches the physical dimension of the aperture.4, 6, 10–14 Optical near-field lithography has advantages not only because of its high resolution beyond the restriction of the diffraction limit, but also for its applicability to conventional light sources and resist materials.3
Plasmonic lithography offers new possibilities for optical lithography. Its uses a high-intensity nanometer-scale light spot induced by a localized surface plasmon polariton underneath metal nano-apertures, which enhances the transmission of the light.4–6, 9–12 Intensive studies have aimed to enhance its resolution and productivity and increase its potential for practical application. Because of the rapid decay of the high spatial frequency component of an evanescent field beyond the far-field cutoff, the optical probe must be in the near-field region with an accurate distance between the probe and substrate to be patterned. In recent reports, a plasmonic lens array attached to a hard-disk head aerodynamically floated 5–20 nm above the rotating disk has been adopted to improve the throughput, and demonstrated to have an extremely high patterning speed.5, 10 However, the floating method is still impeded by the need for accurate distance control using a larger area head to extend to a high-density probe array system. To study the feasibility of plasmonic lithography with a high-density probe array, an optical contact probe with an additional solid thin film layer and a lubricant layer underneath the aperture has been demonstrated; this probe scans without an external distance control device during high-speed recording.6
To extend the scope of practical applications for plasmonic lithography, a patterning process needs to be rigorously analyzed in terms of its ultimate resolution, pattern depth, overlay, and throughput to ensure it satisfies the demands of the semiconductor industry. The resolution of plasmonic lithography is generally given by the spot size (FWHM; full width at half maximum) of light to be used for recording.4, 10, 12 Thus, the spot size is an important parameter for determining the resolution of near-field lithography.
Plasmonic lenses having additional circular grooves around the nano-aperture have been designed to enhance the light transmission and beaming in the near-field region.10, 15 At theoretical analysis of the exposure model of the near-field indicates that the resolution of near-field lithography also depends on several process parameters, such as the distance between the aperture and the photoresist, the distribution of the near-field, and the exposure dose and time.16 An accurate near-field lithography model has been proposed which is capable of measuring the distribution of the near-field formed by the aperture.17 In order to analyze the ultimate resolution of plasmonic lithography and the depth profile of the near-field recording, we need to investigate a theoretical near-field exposure model, which to date has not been intensively studied for evaluating the resolution as function of pattern density in plasmonic lithography. In terms of the throughput of plasmonic lithography, it is necessary to develop a parallel patterning process with a reliable high-density optical probe array. However, it is difficult in practice to implement an array with a large number of elements for near-field recording, since the distance between each probe and the substrate to be patterned must be accurately maintained within a few nanometers to use the evanescent field of the probe.
In the present work, we introduce a theoretical model to analyze the resolution of plasmonic lithography. We fabricate a micrometer-sized circular contact probe for high positioning accuracy which can be extended into a high density probe array for a parallel patterning process. By comparing the theoretical model with the experimental results from the high density line array patterns, we estimate the ultimate resolution of plasmonic lithography using a ridge aperture.
2. Results and Discussion
2.1. Theoretical Analysis of the Resolution Limit in Plasmonic Lithography
2.1.1. Dose Modulation Function (DMF)
The photoresist profile created by the near-field of a nano- aperture is quite different than that formed by the propagating electric field of a conventional optical image, since the near-field around the aperture sharply decays instead of propagates. To evaluate the resolution limit of near-field lithography using an optical scanning probe, we extend the near-field exposure model by combining it with decaying near-field characteristics. The resolution limit is evaluated by calculating the line array pattern to determine whether the line patterns remain separated when their spacing is reduced.
We calculate an exposure dose distribution for the line array pattern which superposes the dose exposed to draw adjacent line patterns with a ridge aperture. A finite differential time domain (FDTD, commercial software XFDTD 7.0) calculation is performed to obtain the exposure dose distributions of various apertures with ridge gaps of 10, 20, and 30 nm after x-direction line scanning. The intensity distribution can be assumed to be the exposure dose distribution, since the exposure time is maintained uniformly during line array patterning. The geometry of the bowtie aperture in an aluminum film is assumed to have outline dimensions of 150 nm × 165 nm. The film thickness is 150 nm in order to match the Fabry-Pérot resonance of the aperture to the exposure wavelength of 405 nm with x-direction polarization. The transmitted field is calculated in the x–y plane on the photoresist (n = 1.7) surface in a calculation volume of 700 nm × 700 nm × 500 nm with a 2 nm mesh size. The sizes of the beam spots determined by the FWHM of the intensity distribution in y-direction at the photoresist surface are 19, 37, and 48 nm for a ridge gap of 10, 20, and 30 nm, respectively. The calculated exposure dose on the surface of the photoresist for a line array pattern recorded by a bowtie aperture is schematically illustrated on a vertical axis in Figure1a. On the horizontal plane, the calculated line array pattern is displayed simultaneously with the intensity distribution. We define the dose modulation function (DMF = (Emax–Emin)/(Emax + Emin)) where Emax and Emin are the maximum and minimum values of the exposure dose, respectively, as indicated in Figure 1a. The calculated DMF for the bowtie apertures at the photoresist surface with a ridge gap of bowtie apertures of 10, 20, and 30 nm is depicted in Figure 1b. The higher DMF can be obtained with a smaller ridge gap and the DMF decreases gradually as the half pitch decreases from 45 to 5 nm.
2.1.2. Critical Modulation Transfer Function (CMTF)
The optical modulation transfer function is an important parameter for evaluating the resolution of conventional optics, as defined by the intensity modulation of an optical image. In general, the obtained pattern profile is not the same as the exposure dose distribution on the photoresist surface; however, the dose distribution in the depth direction of the photoresist plays an important role in determining the pattern profile. The profile also depends on the parameters of the photoresist, such as the sensitivity, the threshold dose Eth, and the clearing dose Ec. Eth and Ec are defined as the minimum exposure doses required for the photoresist to react to light and for clearly removing the photoresist, respectively.18 In conventional lithography, the critical modulation transfer function (CMTF) is defined using the photoresist contrast γ as follows,19, 20
where γ (=[ln(Ec/Eth)]−1) is the photoresist contrast. As shown in Equation (1), the CMTF becomes a constant determined by a photoresist contrast γ. To obtain a pattern for a given feature size, DMF generated by the exposure dose distribution of an optical image must be larger than or equal to the CMTF. Thus, we can determine the resolution criterion of the photolithography system by comparing the DMF with the CMTF. In near-field lithography, however, the contrast γ is not the same as that in conventional lithography, since the exposure light does not propagate in the photoresist but exists only in the near-field region. Therefore, we need to rewrite the CMTF with the photoresist constant γ reflecting the decay property of the exposure light.
2.1.3. Decay of Near-Field Intensity Generated by a Nano-Aperture
Since the propagation vector k becomes imaginary due to the high spatial frequency components of a subwavelength-sized near-field spot,21 the intensity of the near-field spot decays rapidly with distance z from the aperture exit; then the near-field lithography exhibits a shallow depth profile. Assuming a decay length β(z), we can describe the intensity of the near-field from the aperture as
where β(z) = a + bz + cz2 +···; a, b, and c are constants, and Ii is the intensity at z = 0. To obtain a simple analytic decay function for the near-field intensity, we assume β(z) is approximated by a linear function,
where a is the decay length at z = 0, and b is a dimensionless parameter which determines the decay characteristic of the near-field. Then, I(z) can be easily solved as a hyperbola curve:22
According to Equation (4), the intensity decreases by a simple exponential decay function in the short range of z, while it decreases by a power law over a sufficiently long range of z. The constants a and b depend on the geometry of the near-field distribution and are determined by fitting the peak intensity decay of the near-field distribution obtained by the FDTD calculation. The constants (a, b) are (3.295 nm, 0.457), (8.970 nm, 0.440), and (13.435 nm, 0.432) for the bowtie apertures with ridge gaps of 10, 20, and 30 nm, respectively.
2.1.4. Dose Distribution in a Photoresist and Resolution Limit
The dose distribution in the photoresist exposed by the near-field spot generated by a nano-aperture is described by
where ti is the exposure time, Ei = Iiti is the exposed dose on the photoresist surface at z = 0, and α is the absorption coefficient of the photoresist material itself.20, 23 In this study, α is assumed to be 1.151 μm−1 for the photoresist (Dongjin Semichem, DPR i-7200P) at 405 nm wavelength.23 In previous work, it was proved theoretically that the lithography profile exposed by the near-field quantitatively agrees with its distribution that matches a threshold dose under proper development process conditions, i.e., E(z) = Eth.17 Then, we have the photoresist contrast γ for near-field lithography,
Substituting Equation (6) into Equation (1), we can calculate the CMTF for near-field lithography for a given near-field distribution of a bowtie aperture. To record a pattern with a certain depth on a photoresist, the DMF needs to be larger than or equal to the CMTF. Thus, we theoretically can calculate the maximum depth to be obtained for various half pitches of line and space patterns by comparing the CMTF to the DMF for the near-field distribution.
The calculated CMTF curves for several bowtie apertures with ridge gaps of 10, 20, and 30 nm are plotted in Figure2a. To evaluate the resolution of plasmonic lithography, we calculate the maximum depth of the photoresist profile by comparing CMTF in Figure 2a with DMF shown in Figure 1b. The results are depicted in Figure 2b. It is generally accepted that the spot size of the near-field distribution is the most important feature of plasmonic lithography, as it indicates the capability of high density patterning.4, 10, 12 We estimate resolution limits of plasmonic lithography with a half pitch where the depth is 0 nm. The resolution limits are 7, 15, and 19 nm for the bowtie aperture with ridge gaps of 10, 20, and 30 nm, respectively. It is found that the resolution is ≈60% smaller than the spot sizes of the recording beams used for patterning in comparison with the spot sizes 19, 37, and 48 nm for ridge gaps of 10, 20, and 30 nm, respectively.
2.2. Circular Contact Probe for High-Positioning Accuracy and High-Throughput Plasmonic Lithography
2.2.1. Fabrication of Circular Contact Probe
One of the main challenges in this research is the fabrication of an optical contact probe for near-field recording at high speed. The design of a circular-structure optical contact probe has been previously proposed to obtain high positioning accuracy in plasmonic lithography using optical contact probes.24 According to this design, high positioning accuracy is obtained for the vertical translation of the optical probe by using a fixed-fixed instead of a fixed-free beam structure for a cantilever-type probe. The probe also has a flat tip structure instead of a sharp tip in order to remove the rotational moment induced by lateral friction on the tip apex. The positioning accuracy for vertical translation and the rotational movement due to lateral friction become important issues in the use of an array of probes to increase patterning throughput.
The design parameters for a circular probe are illustrated in a schematic view in Figure3a. Based on the design, we fabricated the optical contact probe with conventional silicon processes (see the Experimental Section). The scanning electron microscope image of the fabricated circular probe is illustrated in Figure 3b, which shows the circular spring structure and a prominent probe tip at the center of the spring. The base material is a low-stressed silicon nitride (Si3N4, n = 2.07), which has good mechanical hardness, optical transparency, and compatibility to the wet etching process. A diamond-like carbon (DLC, n = 1.9) film was coated on the tip apex with a thickness around 4–5 nm using the plasma enhanced chemical vapor deposition (PECVD) method for protection, and a lubricant layer between the probe and the photoresist.25–28 We also applied a hexamethyldisilazane (HMDS) self-assembled monolayer (SAMs) to reduce the friction on the photoresist surface,29, 30 so we could achieve high speed scanning faster than 1 mm/s without any surface damage of the photoresist and the optical contact probe.
2.2.2. Measurement of Positioning Accuracy
We can easily expect that the vertical translation (Δd) of a cantilever-type probe will cause a large positioning error (Δp), as schematically illustrated in Figure4a. To evaluate the performance of the circular probe, we compare the positioning error of the circular contact probe and that of a cantilever-type probe for vertical translation after the optical probe contacts the photoresist. The cantilever-type probe (Nanosensors, SNOM-CONT-B) is made of silicon with a length of 470 μm, a width of 150 μm, a thickness of 1.8 μm, and a tip height of 16 μm. It has a rectangular silicon cantilever with an integrated hollow, pyramidal silicon oxide tip of thickness 250 nm. A bowtie aperture same as that in the circular-type probe is fabricated on the aluminum metal-coated pyramidal tip. We set the vertical translation Δd = 0 where the optical probe just contacts the surface of the photoresist. As the probe system moves down, Δd increases. The probe system is deformed with higher contact pressure.
The direct patterning system with an optical contact probe was described in our previous work.31 We illuminated the x-polarized 405 nm wavelength laser light (CrystaLaser, BCL 025 405S) at the optical probe with an objective lens (numerical aperture 0.8, Nikon CFI LU Plan Epi ELWD 100×). Dot patterns were recorded by increasing and decreasing Δd over a range of 0–2 μm in steps of 0.5 μm with a piezoelectric translation stage (Thorlabs, NF5DP20). The recorded dot patterns on the photoresist are measured by atomic force microscopy (AFM, Park system, XE-100) with a high resolution sharp silicon tip (Nanosensors, SSS-NCHR, typical tip radius ≈2 nm with an aspect ratio ≈ 4) in tapping mode and are illustrated in Figure 4b. We determined the positioning error Δp of an optical probe by measuring the lateral displacement of the dot pattern in the AFM image. The results of the measured positioning errors of the circular-type and the cantilever-type probes are plotted together in Figure 4c. At the maximum vertical translation Δd = 2 μm, the measured positioning error of the cantilever-type probe becomes ≈295 nm, while that of the circular-type probe is less than ≈10 nm in the overall vertical translation range. The randomness of Δp for the circular probe may be caused by the positioning error and the measurement error (<2 nm) of the AFM.17 Since the vertical translation Δd can be in the range of ±0.5 μm during the scanning for patterning, we estimate that the positioning error of the circular probe is less than 3 nm from the scattering of the positioning error. In the parallel patterning process with a high-density probe array, the positioning error for each optical probe needs to be less than the resolution of the plasmonic lithography for the stitching and overlay of patterns. Therefore, the positioning accuracy of the circular probe presented in this work is reasonably high for high-throughput plasmonic lithography using a high-density optical contact probe array.
When we used a cantilever-type probe, we faced another practical problem, i.e., there was a large change in the transmission of the aperture coupled with the positioning error. As shown in Figure 4b, the deformation of the cantilever induces a position shift in the optical probe, leading to a misalignment of the incident beam on the ridge aperture and subsequently a large change in the transmission of the optical probe. We evaluated the transmission of the optical probes using the size of the recorded patterns in Figure 4b.4, 32 The change of transmission in the cantilever-type and the circular-type probes for the vertical translation is plotted in Figure 4c. The transmission of the optical probe is evaluated by measuring the recorded resist volume divided by the input laser energy, and is normalized with respect to the minimum transmission. The results show that the transmission of the cantilever-type probe becomes smaller by a factor of 7.3 for a variation in the vertical translation Δd from 0 to 2 μm, while that of the circular-type probe is changed within ≈28%.
2.3. High Density Line Array Patterning
It is well known that the line edge roughness (LER) of a nanometer-scale pattern caused by the grain size of a photoresist is a critical barrier to enhancing the resolution of the patterning.33 By changing the developer solution with a smaller molecule and optimizing the developing process,34, 35 we reduced LER from ≈30 to ≈17 nm, since the patterning of the line array with a line width smaller than LER is technically impossible. Using the plasmonic direct writing system with the circular contact probe, we recorded dense line array patterns with half pitches of 27, 32, 37, and 42 nm. The circular contact probe scans at a speed of 1 mm/s without an external control device. Based on the calculated spring constant of 15.1 N/m24 and the small tilting angle (<0.014°) of the substrate, we estimate the vertical load for maintaining conformal contact between the optical contact probe and the photoresist to be 1.51 ± 0.75 μN in the scanning area of 100 μm × 100 μm. The AFM images of the patterning results are shown in Figure5a–d. As shown in Figure 5d, the line array patterns exhibit quite good contrast. The contrast worsens due to lower DMF and LER as the half pitch decreases, but the line array pattern with 27-nm half pitch is still distinguishable.
To evaluate the ultimate resolution of the plasmonic direct writing system with the circular contact probe, we record the line array pattern with a feature size of 22-nm half pitch. The AFM image of the 22-nm half pitch line array pattern is shown in Figure6a. The cross-sectional view of the line array patterns is enlarged in Figure 6b, showing separated line patterns with a FWHM of 22-nm and ≈ 2-nm depth.
We also plot the maximum pattern depth for various half pitches in Figure7 to compare the theoretical model with the experiment. The experimental results of the depth-pitch relation reasonably agree with the calculation in the case of the 30-nm ridge gap. The results clearly show that, as was predicted in the theoretical model, a line array pattern with a half pitch less than the calculated spot size of 48 nm can be recorded with plasmonic lithography.
We have introduced a theoretical model to analyze the ultimate resolution of plasmonic lithography using a bowtie ridge aperture in a metal film. The theoretical analysis showed that resolutions of plasmonic lithography using the ridge apertures can reach 7, 15, and 19 nm for the bowtie aperture with ridge gaps of 10, 20, and 30 nm, respectively. These are a factor of ≈2.5 smaller than the size of a near-field spot generated by the aperture. We fabricated a micrometer-scale high-positioning circular contact probe for plasmonic lithography, which can be extended to a high-density probe array. It was found that the positioning accuracy of the circular probe was less than 3 nm, which is reasonably small for the stitching and overlay of patterns in plasmonic lithography. Using a plasmonic direct writing system that uses the contact probe, we recorded high-density line array patterns with a half pitch up to 22 nm. It was found that the theoretical model fits well with the experimental results of the maximum pattern depth for various half pitches. In practice, however, the LER associated with the grain size of a photoresist is an important issue for enhancing the pattern resolution. We can record the 22-nm half pitch line array pattern by reducing the grain size by ≈40% due to the use of a well-controlled developing process with a smaller molecular weight KOH-based developer at a temperature below 10 °C. By recording high density line array patterns with the circular contact probe, we demonstrated remarkable progress toward the practical realization of plasmonic lithography using a high density array of contact optical probes for high throughput. Further work for parallel patterning with plasmonic lithography using the array probe should progress in the near future.
4. Experimental Section
Fabrication of the Circular Contact Probe: The fabrication flow of the circular probe is schematically shown in Figure S1 (Supporting Information). Native oxide layers on both surfaces of a double polished 4-inch <100> silicon wafer were removed by a buffered hydrofluoric acid (BHF) solution, and then 100-nm-thick silicon nitride films were coated on both sides of the wafer using the PECVD method. A mask layer was patterned on the silicon nitride layer to define the contact area of the probe tip before a dry etching process, as shown in Figure S1a. After piranha cleaning and BHF cleaning to remove organics and native oxide, respectively, the wafer was anisotropically etched in a potassium hydroxide (KOH)-isopropyl alcohol (IPA) solution at 55 °C for 30 min to produce a probe tip with a flat tip structure, shown in Figure S1b. After removing the PECVD nitride mask using the BHF solution, a 400-nm-thick low-stress silicon nitride layer was deposited with the low-pressure chemical vapor deposition (LPCVD) method at 850 °C to produce a fundamental material for the probe tip and spring. The probe spring structure was defined by photolithography as shown in Figure S1c, and the wafer was deep dry etched on the frontside, shown in Figure S1d. Afterwards, the wafer was coated with 100-nm low-stress LPCVD silicon nitride to protect the sidewall of silicon in the subsequent wet etching process. A probe holder formation was defined by photolithography in Figure S1e. A wet etching process in 45% KOH solution at 90 °C for 10 h released the probe tip and spring structure, shown in Figure S1f. Finally, the extra silicon nitride film was removed by a H3PO4solution.
Fabrication of the Bowtie Aperture: The 300-nm-thick silicon nitride film coated with 2-nm-thick platinum (Pt) for precise milling of the 2 μm × 2 μm area was removed by a focused ion beam (FIB, SII SMI3050). A bowtie aperture was fabricated with FIB using the through-the-membrane milling method to improve the ridge sharpness of the bowtie aperture.36 A bowtie-shaped aperture having a 150 nm × 165 nm outline and a 30-nm ridge gap was milled through the two layers of 100-nm-thick Si3N4and 150-nm-thick aluminum films, under the condition of a FIB, 30 kV acceleration voltage, 1 pA current, and 5 μs dwell time. The surface of the tip apex was smoothed to a surface roughness <0.3 nm (RMS) to minimize the surface damage of the photoresist during the high-speed scanning of the probe.
Development and Surface Treatment of the Photoresist: The LER strongly depends on the size of the grain, which is a polymer aggregation structure in the photoresist. Since it is well known that the LER due to the polymer aggregation structure can be reduced using a proper developer solution with a small-size molecule,34, 35 we applied a potassium hydroxide (KOH)-based developer solution (AZ 400K) instead of a tetramethylammonium hydroxide (TMAH)-based solution (AZ MIF 300) to the photoresist (Dongjin Semichem, DPR i-7200P), exposed at a wavelength of 405 nm. Additionally, the development rate and the contrast curves of the developed resist are largely affected by the developing temperature.37–39 In general, it is known that the resolution can be enhanced using a photoresist with higher resist contrast.40 It was found that the photoresist contrast γ is increased by factor of ≈2–3 at a developing temperature below 10 °C compared with room temperature. To optimize the developing process, we measured the resist contrast curves at different developing temperatures, and then we set the temperature of the solution to 10 ± 1 °C with a developing time of 120 s. The AFM images of the line array patterns developed with TMAH and KOH-based solutions are shown in Figure S2a,b, respectively (see the Supporting Information). To calculate the LER of the line patterning, the measured AFM images were analyzed in Matlab. The LER values represent the 3σ value, where σ is the standard deviation. It was found that the LER of KOH-developed patterning is ≈17.07 nm, while the TMAH-developed patterning has a LER of ≈29.15 nm. To reduce the friction coefficient and the damage of the resist by a lateral force during the scanning motion, we coated a HMDS SAMs layer on the top surface of the resist as the lubricant layer. By measuring the lateral force microscope mode of AFM, we confirmed that the friction coefficient is reduced by a factor of ≈2.5 with a HMDS SAMs layer coated on the resist.
Supporting Information is available from the Wiley Online Library or from the author.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.2012-0008867). We thank Insung Kim at Samsung Electronics Co., Ltd. for fruitful discussion and technical assistance to measure the LER.