1. Introduction

Recent progress in the fields of plasmonics [1,2], nanophotonics [3,4] and metamaterials [5–7] has attracted significant interest for a broad range of modern applications: in electronics, sensing, displays, lighting and more. Commercialisation of such devices requires a fast, flexible, high-resolution and large-scale nanopatterning technique so that the nanofabrication process is cost-effective. Meeting all these criteria in one tool is challenging whilst still producing the highest performance. State-of-the-art optical approaches like Deep-UV (DUV) immersion lithography (with or without resolution enhancement via multiple patterning) and Extreme-UV (EUV) lithography [8] allow the highest resolutions at a large scale but with little flexibility. Furthermore, the capital outlay can be unaffordable for devices produced at lower volume or for research. In contrast, direct-write methods with high resolution using an electron beam [9], or at lower resolution using a laser, allow high flexibility, but the length of time it takes to pattern large-areas makes them prohibitive for all but the smallest sample batch sizes. Whilst this could be mitigated by using multiple electron [10] or laser beams [11], they will nevertheless remain serial lithography approaches.

Nanoimprint Lithography (NIL) [12] is a promising high-throughput, high-resolution technique. However, it suffers a) from being a contact lithography process, limiting the life of the master, and b) from being very sensitive to particulates, affecting the fidelity of the pattern and the yield. Furthermore, each pattern design requires a separate master, at extremely high cost for the highest resolutions. Bottom-up technologies are also being developed with the potential for being large-scale, flexible and cheap. Colloidal lithography [13] promises feature resolutions down to tens of nanometres for ordered arrays, but is limited by defects leading to finite domain sizes and other array defects [14]. Directed self-assembly [15,16] offers a solution to achieving macroscopic order over large areas with high resolution features by using guiding patterns. However, the guiding patterns are typically created via lower resolution top-down lithography. For both these bottom-up technologies and numerous variations [17], the constraints of the process limit the complexity of the features that can be obtained.

Returning to non-contact optical lithography approaches, the pattern resolution is limited by not only the wavelength used but also the control of diffraction behind the mask. The latter issue is exploited in Laser Interference Lithography (LIL) and Talbot Lithography by using the constructive interference occurring between multiple periodic sources. Simple periodic patterns are achievable by LIL [18] and complex periodic patterns have been obtained by a combination of the Talbot effect and controlling the effective source shape [19]. However, the latter was achieved only in the micron-size regime and without the flexibility offered by direct-write tools. A key challenge for these techniques is the careful and reproducible positioning of the sample in the 3D interference pattern. This difficulty was solved by the technique of Displacement Talbot Lithography (DTL) [20] whereby the depth of focus is made effectively infinite.

In this paper, we describe a new direct-write lithography technique that builds on the simplicity and low-cost of DTL to allow the creation of complex periodic patterns. It can be considered as a direct-write technology with $\sim 10^{10}$ ‘beamlets’ or ‘pens’. Whilst the particular arrangement of the ‘beamlets’ is determined by a single photomask, thus placing a restriction on the periodicity on the sample, a wide range of different patterns of varying complexity can be realised thus achieving a significant cost-saving over other high-throughput techniques. Examples of applications that could benefit from such a technique include: negative index metamaterials [21], plasmonic absorbers [22,23] and SERs-active substrates [24] for biological and chemical sensors, and plasmonic colour filters [25].

2. Results

Our technique, which we refer to as ’Double Displacement Talbot Lithography’ (D$^2$TL), is based on combining lateral displacements either during single DTL exposures or in-between multiple exposures in order to draw arrays of complex features in resist over a large area (See schematic in Fig. 1(a)). The idea of lateral translation has been demonstrated using multiple-beam interference lithography (MBIL) [26] and EUV achromatic Talbot lithography (ATL) [27]. However, the very low depth of field in MBIL means that it is critical to control the sample position and parallelism with submicron accuracy, thus making it less transferable to large-scale fabrication than DTL, for which the depth of field is essentially infinite. In contrast, whilst the issue of the depth of field is addressed with achromatic Talbot lithography, the technique is currently limited to a few mm² with a single exposure, in contrast to the 30,000 mm² achievable with DTL.

 

Fig. 1. Dual DTL exposures with single lateral displacement. a) Schematic illustrating ‘double’ displacement Talbot lithography (D$^2$TL). b-d) Modelling of the aerial image and (f-h) SEM images of the developed photoresist for a single DTL exposure of 80 mJ/cm$^2$ using a 1.5 µm hexagonal period amplitude mask (f), and two exposure doses of 80 mJ/cm$^2$ with displacements of 400 nm (c, g) and 600 nm (d, h); and (j-l) metallic nanoparticle arrays after a lift-off process for a single exposure (j) and displacements of approx. 300 nm (k) and 400 nm (l) using a 1 µm hexagonal period mask, respectively. In (i, m) rotated higher magnification versions of (h, l) are shown, where the gap between nanoparticles in (m) is measured to be around 50 nm. (e) shows the aerial image for a 425 nm displacement for a 1 µm pitch corresponding to (m) where the elongation of the maxima can be seen.

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Figures 1(c)–1(i) show a simple double exposure with a lateral displacement along x, for a 375 nm laser source and a 1.5 µm hexagonal amplitude mask. The secondary-electron scanning electron microscope (SEM) images are shown below the results from computer simulations of the expected illumination pattern. The simulations are shown as normalised heat maps for which the exposure dose and development time determine the size of the resulting features. (Details of the experimental set-up and the computer model can be found in the ‘Experimental methods’ section). The feature sizes are relatively large at around 400 nm but they serve to illustrate the process. The ultimate resolution that could be achieved with DTL is a function of the mask parameters [28] and Fig. 1(f) shows the smallest features achievable with a 1.5 µm pitch amplitude mask with high homogeneity at around 280 nm. The features in Figs. 1(g) and  1(h) are larger since the proximity effect of the separate exposures was not taken into account in the determination of the optimum exposure dose. The lateral control of the feature positions is determined by the resolution of the nanopositioning stage, which is sub-nm in our case, and noise within the local environment. In these examples, separate features were obtained for displacements greater than 600 nm (Fig. 1(h)) and elongated dashes for less than 600 nm (Fig. 1(g)). Examining the corresponding simulation for separate features in Fig. 1(e) shows that the relative intensity in between the dots is approximately 50% for this threshold displacement; i.e. in order to get separate features, the relative intensity between them should drop below $\sim$50% to prevent the resist from being developed. Whilst the precise threshold value of the relative intensity will depend on the absolute exposure dose, we can use this 50% value to estimate from similar simulations the minimum lateral displacement required to get separate features for a lower 1-µm-pitch mask to be 400 nm. These patterns can be used in a lift-off process to create metallic nanodots with small nanogaps potentially over a full 50 mm wafer (For details see the section on Experimental methods). SEM images of such metal nanoparticle arrays are shown in Figs. 1(j)–1(m), where the nanogaps in Fig. 1(l) are measured to be around 50 nm. Further reduction of the gap is limited by the variability from feature to feature. The simulations of the 600 nm displacement in Fig. 1(e) show a deviation from ideal circles due to the proximity dose of the neighbouring exposures. Whilst these are not easily seen in the developed photoresist in Figs. 1(h)–1(i) with a 1.5 µm pitch, there is evidence of the deformed shape of the displaced nanoparticles when using a 1 µm pitch as shown in Figs. 1(l)–1(m). The manufacture of such structures over large areas is valuable for the exploitation of, for example, surface enhanced fluorescence spectroscopy and nanoplasmonic sensors [29,30].

Extending this idea to additional exposures allows us to circumvent one of the existing design constraints of DTL; the minimum period achievable on the sample for a hexagonal lattice. This is determined by the equation for the Talbot length: $Z_T=\lambda /(1-\sqrt {1-\lambda ^2/a^2 })$, where $a=p\sqrt {3}/2$ for a hexagonal lattice of period, $p$, and $\lambda$ is the incident wavelength [20]. Therefore, in our system that uses a 375 nm laser, the minimum periodicity for a hexagonal lattice is around 433 nm. Two displacement patterns have been considered in order to create finer-pitch hexagonal arrays and are shown in Fig. 2(d) on top of the single exposure DTL pattern. Three- and four-point exposures, respectively, enable the reduction of pitch from 600 nm to 346 nm, a reduction by a factor of $\sqrt {3}$ (Figs. 2(b) and 2(e)), and 300 nm, a reduction of 2 (Figs. 2(c) and (f)); both being below the conventional limit.

 

Fig. 2. Reduction in pitch to below the incident exposure wavelength. Simulated aerial images (a-c) and secondary-electron SEM images are shown for (d) a single exposure of 40 mJ/cm$^2$ using a 600 nm hexagonal period phase mask to give a 600-nm-period array of 250-nm-diameter holes in photoresist, (e) a series of three separate exposures each of 21 mJ/cm$^2$ to give a 346-nm-period array of 230-nm-diameter holes in photoresist, and (f) a series of four separate exposures to give a 300-nm-period array of holes in photoresist.

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The fidelity of the resulting pattern depends on a number of factors. Firstly, the original mask axes must be carefully aligned with those of the nanopositioning stage. Secondly, the exposure dose should be optimised for the smallest features. Thirdly, noise in the mechanical positioning system should be minimised. Finally, the relative intensity of the region between the features should be low enough to prevent over-exposure of the resist and thus the coalescence of neighbouring dots. Simulations, shown in Figs. 2(a)–2(c), indicate that the intensity between neighbouring maxima drops to 13% intensity for three exposures and 36% for four exposures for a wide range of mask periodicities; both values can successfully lead to a binary resist pattern. It is not possible to increase the number of exposures above four in order to achieve further reduction of pitch since the intensity between neighbouring maxima is not low enough.

The quality of the resulting pattern is better for the three exposures in Fig. 2(e) than the four exposures in Fig. 2(f) since the former overlays subsequent exposures on the secondary maxima, whereas the latter does not. (These secondary maxima can be seen in the aerial image in Fig. 2(a) in between the primary maxima.) This leads to poorer minimum intensity between features for the four exposures, further forcing the exposures to be closer to the exposure threshold in order to achieve the smallest features and reducing process latitude.

Further simulations of hexagonal phase masks with a smaller pitch, while keeping a laser wavelength of 375 nm, suggest that sufficient contrast could be maintained for four exposures to achieve $\sim$220 nm pitch hexagonal patterns on the sample, though this has not been experimentally verified. In practice, the quality of DTL masks below 600 nm, the illumination homogeneity, the control of positioning stage, and noise in the environment are likely to affect the ultimate limit achievable. Reducing the pitch below 220 nm would require decreasing the laser wavelength, for example, to 266 nm or 193 nm or exploiting soft lithography [31].

Square array phase masks behave differently to hexagonal arrays during simple DTL as the pitch on the sample is already reduced by a factor of $\sqrt {2}$. Simulations of two separate exposures allow a further reduction of pitch by a factor of $\sqrt {2}$, but with a moderately high relative intensity between neighbouring maxima of $\sim$55%, which is on the threshold of being achievable in practice (more exposures are beyond this threshold). Considering the different expression for the Talbot length for square arrays, the theoretical limit of the minimum pitch for a 375 nm source is $\sim$190 nm.

So far, we have only considered exposures during which the lateral position of the sample is stationary with respect to the mask. The sample, nevertheless, is still displaced an integer number of Talbot lengths in the perpendicular direction during each exposure in order to regularize the aerial image and make it insensitive to the starting position; one of the unique advantages of DTL. Whilst this method is good for small numbers of exposures to create simple patterns, it becomes more difficult to implement for patterns that are more complex where larger numbers of exposures are required. In this case, simultaneous lateral and perpendicular motions would be more suitable, if they do not jeopardise the aerial image integration that is essential for DTL. The easiest way to achieve this requirement is for the lateral displacements to occur with a much faster timescale as the perpendicular displacement. Each position on the sample that moves in and out of the lateral regions in space with high intensity sees many time slices of that high intensity, thus effectively averaging over the Talbot carpet, akin to digitally sampling an analogue waveform. This works if the Talbot carpet is a slowly varying function of position, and there will be a Nyquist-like limitation on the spatial frequencies that can be utilized in the Talbot carpet. The simplest motion that does not require specific attention to alignment and complex routing algorithms that also take into account the velocity and acceleration in the lateral direction are continuous circular displacements. Figure 3 shows computer simulations of the aerial image and SEM images from exposures through a 1.5-µm-period hexagonal mask for different radii of circular, relative, lateral displacements of the mask and sample. For each radius, the exposure dose was tuned and chosen to replicate the clearest features of the aerial image. Strikingly, different radii can be chosen to achieve almost perfect inverse structures; small holes with no displacement (Fig. 1(f)) versus small dots with a circular displacement of 1100 nm radius (Fig. 1(k)), large holes for 325 nm radius (Fig. 1(g)) versus large dots for a 750 nm radius (Fig. 1(j)). This shows another example of the flexibility that can be achieved with a single mask.

 

Fig. 3. Effect of continuous circular lateral displacements during DTL exposure. Simulations of the aerial image are shown alongside SEM images for circular displacements of radii (a, b) 0 nm, (c, d) 325 nm, (e, f) 450 nm, (g, h) 650 nm, (i, j) 750 nm, and (k, l) 1100 nm. A wide range of features can be observed with different radii, including several patterns and their inverses.

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Extending this idea allows an even greater range of patterns to be created from a single mask. Rather than the circular lateral displacements above, oscillating linear displacements can be used to create linear gratings from a hexagonal mask, with the final grating pitch determined by the direction of the linear displacement with respect to the mask axes. Figure 4 shows simulated aerial images and SEM images of an 866-nm-pitch grating alongside a 500-nm-pitch grating in photoresist created from a single 1-µm hexagonal patterned mask that correspond to displacements from one lattice point to its nearest and next-nearest neighbour, respectively. The simulations show the relative minimum illumination background to be around 0.4, and the experimental results validate that this contrast level is sufficient. We observe a degree of resist line edge roughness in the sample with translation to the nearest neighbour but not in the translation to the next-nearest neighbour. This could be due to the influence of the secondary pattern that coincides with the translation for the latter, and not for the former. Alternatively it is a feature of the displacement amplitude and could be removed by process optimisation. Whilst grating structures can easily be created using DTL without the complication of lateral displacements with a simple grating mask even with the benefit of a halving of the mask pitch and slightly improved contrast, these results, again, emphasise the versatility of the process with a single hexagonal mask.

 

Fig. 4. Creation of various grating patterns from a single hexagonal mask. Simulated aerial images (a-c) and secondary-electron SEM images of the resulting photoresist (d-f) from a 1-µm-pitch hexagonal mask for no lateral displacement (a, d), and an oscillating linear displacement along the direction to the first nearest neighbour (b, e) and the second nearest neighbour (c, f).

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The final variations of the lateral displacements are more complex. Figures 5(a)–5(c) show the simulation of the aerial image alongside SEM images from continuous, triangular displacements, where the two SEM images correspond to different exposure doses. Figures 5(d)–5(e) show similar results from continuous U-shapes. The width of the resist walls in Fig. 5(c) is $\sim$160 nm and the remaining resist inside the U-shape in Fig. 5(e) is $\sim$200 nm. In both cases the pitch of the features is 1 µm. We expect that more complex structures could be achieved by tuning the displacement path. By iterating the path through simulations, one could envisage sharpening features akin to proximity correction in other lithography techniques. The fundamental limit to the complexity of the features that can be achieved depends on the ratio of the resolution of a feature from a single exposure compared with the pitch of the pattern. A ratio of $\sim$20% can be deduced from Fig. 1(f) which can be compared with a value of $\sim$10% demonstrated by multiple-beam interference lithography [26]. Our previous publication discussed the impact of the mask design on the feature resolution as a function of pitch and highlighted a complex relationship [28]. Optimisation of the DTL mask should improve on this value of $\sim$20% but at the expense of exposure duration since the transmission of an amplitude mask will be reduced. In addition to the amount of space available for complex patterns, secondary features in the aerial image will also affect the feasibility of creating arbitrary shapes.

 

Fig. 5. Demonstration of complex features. Simulated aerial images (a, d) and secondary-electron SEM images of the resulting photoresist (b, c, e) from a 1-µm-pitch hexagonal mask for continuous triangular displacements (a-c), and U-shape displacements (d-e). The photoresist in (c) received a higher exposure dose than that in (b).

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All three processes of MBIL, ATL and DTL are based around the creation of diffracted beams from a periodic mask and the properties of the final patterns are critically dependent on the diffraction process; e.g. the size, periodicity and uniformity of features on the mask. All have subsequently been used to create complex structures via lateral displacements. Fundamentally, MBIL is limited by the very small depth of field, which makes it challenging to pattern large areas or non-flat samples. ATL and DTL solve this problem in two different ways; ATL by introducing a controlled wavelength spread in the incident light which blurs the intensity structure in the $z$-direction, and DTL by integrating over the periodic nature of the intensity variation. With a similar centre source wavelength and mask, one would expect similar performance from optimised systems. However, the exact sample positioning for MBIL and the stringent control of the achromatic source for ATL represent stricter requirements than the relatively simple $z$-motion for DTL. To date, DTL has demonstrated variations across a 50 mm wafer of metallic nanoparticles to be less than 5% [32]. Therefore, one would argue that D$^2$TL also has similar advantages over the use of ATL and MBIL for complex structures.

3. Conclusion

In conclusion, this paper concerns the high-throughput nanopatterning of surfaces with periodic features. We describe and demonstrate a new photolithography-based technique termed ‘Double Displacement Talbot Lithography’ for creating highly-controlled nanoscale patterns across large-area substrates, such as semiconductor wafers, that is superior to other state-of-the-art solutions. The flexibility of the process allows multiple different patterns to be created simply by varying the motion of the sample with respect to the mask during exposure, thus reducing the capital outlay of multiple masters that would be required to achieve the same with nanoimprint lithography. We demonstrate examples of various grating patterns, dots, circular, triangular and U-shaped holes in positive photoresist, and examples of pattern transfer via lift-off to metallic nanodots for plasmonic applications. Furthermore, the technique can reduce the pattern period by a factor of 2 when compared with simple ‘Displacement Talbot Lithography’; allowing hexagonal pitches between 100-200 nm with long range order to be potentially achieved for coherent excitation at 193 nm. As a result of its speed and flexibility of patterning at high resolution across full wafers with no contact between the sample and the mask, this technique can provide a route to accelerate the mass production of nanophotonic-enhanced devices, plasmonic structures and metamaterials.

4. Experimental methods

The experiments were performed on 50 mm silicon wafers onto which a bottom antireflective coating (BARC) (Wide 30W, Brewer Science) was initially spin-coated at 3000 rpm for 30 seconds and baked with a two-step process to give a thickness of 280 nm. The first step was at 80 °C for 1 minute followed by a second step at 150 °C or 200 °C for 3 minutes depending on the purpose of the sample. The lower temperature bake allows for the creation of an undercut via the dissolution of the BARC in developer for a metal deposition lift-off process, whereas the higher temperature prevents such dissolution. On top of the BARC a positive photoresist (Ultra i-123, diluted to obtain a 240 nm thickness resist) was spin-coated with the same conditions followed by a single softbake step at 90 °C for 90 seconds.

A modified DTL system (PhableR 100, Eulitha AG) was used to expose the photoresist with a laser power of 1 mW/cm$^2$. Three masks were principally used: a 1.5 µm and 1 µm amplitude mask with 800 nm and 550 nm openings respectively, and a 600 nm phase mask with the diameter of one phase equal to 380 nm. The system was modified by adding an XY nanopositioning stage (P-541.2DD, PI Ltd.) to the mask holding system, which has sub-nanometer resolution. A gaussian integration along the illumination axis in the Z direction was performed during the exposure over a distance of at least eight Talbot lengths and a maximum gap of 150 µm between the mask and the sample surface. The cycle time of this integration was targeted to be around 30 seconds. In the case of a continuous displacement with the nanopositionning stage, this time allows a large difference of frequencies between the XY & Z displacements.

After the whole illumination process, a post-exposure bake at 120 °C for 90 seconds was followed by 10 minutes resting time to allow for the rehydration of the photoresist. The photoresist development time in MF CD-26 developer was tuned depending on the function of the antireflective layer, the size of the features and the exposure dose. When the BARC is baked at a lower temperature a longer development time can create an undercut suitable for lift-off. In this case, an electron-beam evaporator was used to deposit first a 5-nm-thick adhesion layer of Ti and then 50 nm of Au. After the deposition, since the BARC is still soluble in the developer, the samples were re-introduced into a bath of developer to induce the lift-off of the remaining BARC, resist and unwanted metal within a few minutes.

Further details of the simulations can be found in our previous paper [28].