1. Introduction

Nanoscale patterns are demanded urgently for the rapid development of the nanoscale science and technology, especially for the semiconductor fabrication industry. Interference lithography is a powerful technique for high resolution patterning for its low cost and mass-fabrication. However, the traditional photolithography techniques suffer the resolution barrier due to the diffraction limit, which limits the spatial resolution to about half of the illumination wavelength. To improve the interference lithography resolution, one straightforward way is to using shorter wavelength light such as the deep ultraviolet light (DUV) [1] or extreme ultraviolet light (EUV) [2], and immersing in a higher refractive index material and fluid. Now the 22 nm half pitch gratings have been patterned by immersion interference lithography with 157 nm light [3]. But the main disadvantages of this technique are complicated system and the corresponding cost. Based on the concept of using shorter wavelength light as illumination source, surface plasmons (SPs) [4] is a good candidate for the interference lithography for its wavelength is smaller than that of light in free space at the same frequency. In the past decade, due to the surface plasmons having the extraordinary transmission behavior through the metal film, more and more efforts based on the SPs technique are interesting to extend the resolution of photolithography beyond the diffraction limits [5–8]. Ref. 7 and 8 demonstrate a photolithography scheme that determines the period ratio between the mask and the photolithography pattern by designing a flat metamaterial superlens, and pattern feature periods down to 50 nm [8]. V. M. Murukeshan recently reported the sub-30 nm plasmonic lithography using the exciting of gap modes in a metal particle-surface system [9]. The next effort focuses on breaking the 22 nm node even to 16 nm. In this letter, a dielectric-metal multilayer (DMM) is designed as a filter only allows a part range of enhanced evanescent waves transmitted through it [10]. Considering modern lithographic fabrication processes with positive photoresist at contrast about 0.4, we use the DMM structure patterning the feature size down to 21.5 nm at 193 nm with p-polarization. Further more, if common negative photoresist is used at laboratory condition [11], it can help people pattern the feature size down to 16.5 nm at contrast about 0.2. It can be used to achieve deep subwavelength feature size pattern with fewer layers (i.e. 4 pairs DMM structure) for positive photoresist, so it can dramatically reduce the unavoidable experimental error as possible. And more exciting point is that the 22 nm node can be broken with the DMM structure we proposed.

2. Principle

For a periodic chromium mask with period Λ, the waves generating from the mask can be decomposed a series of diffracted plane waves. We define x as the grating direction of the mask and z as the wavevector direction of the illumination light [see Fig. 1 ]. The diffraction wavevector follows the grating function,

 

Fig. 1 Schematic of the plasmonic interference lithography with dielectric-metal multilayer.

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In our interference lithography approach in this letter, we need a special device that only allows a part range of evanescent waves transmitted through it. However, the special device does not exist in the real world. It can be realized by an artificial metamaterial for its extraordinary properties that are not observed in the nature [10,12–14]. The dielectric-metal multilayer, which has been proposed for various applications as a special metamaterial [10,15], can be designed to meet the need we expected in this letter. In addition, the choosing of the metal is also a key to design the metamaterial for different wavelength range. Generally, Au is not appropriate for plasmonic lithography purposes because its plasmonic frequency ${\omega }_{\text{sp}}$ locates at visible range. Ag and Al are good material candidates for plasmonic lithography for their plasmonic frequency locates at UV range. In this letter, Al is chosen as an example in this letter because of its relatively lower energy loss at 193 nm.

The DMM structure designed in this paper is an 8 pairs of GaN(10 nm) and aluminum(12 nm) multilayer. We used rigorous-coupled wave analysis method [16] to calculate the transmission as a function of transverse k [see Fig. 2 ] for the proposed DMM at a wavelength of 193 nm with p-polarization. The Drude model, ε_r(ω) = ε _∞ - ω_p ² [ω (ω + iV_c)]⁻¹, was used to describe the permittivity of Al, where the parameters, ε _∞ = 1.0, ω_p = 2.4 × 10¹⁶ rad/s, V_c = 3.8 × 10¹⁵ rad/s, are obtained by fitting the model to the experimental data taken from the literature [17]. The permittivity of GaN is 1.295 [18]. The permittivity of the photoresist below the multilayer is 2.89. From this transfer function of the dielectric-metal multilayer, only a part of high wavevector k (evanescent waves) can pass through for interference lithography we expected.

 

Fig. 2 The transmitted amplitude VS the transverse wavenumber for an 8 pairs of 10 nm GaN and 12 nm Al multilayer at a wavelength of 193 nm with p-polarization.

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3. Numerical Simulation and Discussion

Here we discuss the first order diffracted waves pass through the filter. From the Fig. 2, a period of mask is about 86 nm corresponds to a high transmission. The finite-difference time-domain method is then performed for numerical analysis. The x directional boundary condition is perfect electrical conductor (PEC) and the z directional one is perfect matched layer (PML). The two dimensions with a grid size of 0.2 nm and the input light intensity is set as 1. The mask is 43 nm half-pitch and 40 nm thickness Cr grating, only the ± 1 order pass through the proposed DMM structure for interference, the simulated total electric field intensity (E² = E_x ² + E_z ²) distribution in the photoresist zone is shown in Fig. 3(a) . Clearly the feature size of the formed pattern is down to 21.5 nm. For photolithography purpose, the normalized total electric field intensity distribution at planes 0(red), 10(blue), and 20(black) nm below the DMM/photoresist interface is also shown in Fig. 3(b). The intensity visibility (or contrast) V = (I _max-I _min)/(I _max + I _min) ≈0.4, which satisfy the minimum contrast (~0.4) for positive photoresist in modern lithographic fabrication processes.

 

Fig. 3 The distribution of simulated electric-field intensities for the mask with periods of (a) 86 nm, and (c) 66 nm. The zero value along the vertical axis corresponds to the multilayer/ photoresist interface. The corresponding electric-field intensities at the planes 0 (red), 10 nm (blue), and 20 nm (black) are shown in (b) and (d), respectively.

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Because there exists a π phase shift between the interference fringes of E_x and E_z components for p-polarized wave, the ratio of E_z/ E_x must be high (or low) enough to provide sufficient intensity contrast. The ratio of $E_z/E_x=-k_x/k_z$. For larger values of the transverse wave vector (evanescent waves),$k_z=i\sqrt{k_x^2-{\epsilon }_{\text{PR}}{k}_0^2}$. Then V can be deduced as,

From Fig. 2 and Eq. (2), we can conclude that within the range of the periodic of the mask from 110 nm to 66 nm, corresponding to the first diffracted order transverse k band from 1.755 k ₀ to 2.9242 k ₀, feature sizes using the proposed DMM structure could be formed from 27.5nm to 16.5 nm. Figure 4 shows the feature sizes versus the visibility and the normalized electric field intensity, respectively, with the proposed dielectric-metal multilayer. The black square and the red solid circle represent visibility with theoretical and simulation results, respectively. The blue triangle represents the average normalized intensity at the plane of 5 nm below the interface of multilayer/photoresist. From Fig. 4, the simulation visibilities agree with the theoretical ones from Eq. (2). And the normalized electric field intensity can be explained by the transmission from Fig. 2.

 

Fig. 4 The feature sizes VS the visibility and the normalized electric field intensity, respectively, with the proposed dielectric-metal multilayer. The black square and the red solid circle represent visibility with theoretical and simulation results, respectively. The blue triangle represents the average normalized intensity 5 nm below the interface of multilayer/photoresist.

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Combined with the number of proposed DMM structure and its corresponding transmitted amplitude distribution, we can forecast that with increased number layer of the DMM structure, the zeroth order diffracted wave will be further filtered, the simulation visibility will approach to the theoretical results, and the normalized electric intensity will be strongly decreased for additional metallic absorption. In order to validity it, we here demonstrate two examples with two other different number of the DMM layers. One is 4 pairs and the other is 12 pairs of the GaN(10 nm)/Al(12 nm) multilayer. In Fig. 5 , the feature sizes versus the visibility and the normalized electric field intensity (at the plane of 5 nm below the interface of multilayer/photoresist) are shown for (a) 4 pairs and (b) 12 pairs of the DMM layers, respectively. The two structures transmitted amplitude distribution is also presented (see inset). For 4 pairs DMM layers, the simulation visibility has some divergence to theoretical results due to the impact of the zeroth order which cannot be filtered completely. For 12 pairs one, the zeroth order diffracted wave was well filtered, the simulation visibilities agree well with theoretical results for the mask whose period less than 84 nm, but for bigger period of mask, the more divergence between them, this can be well explained by the transmitted amplitude of the structure. The distinct difference between the Fig. 4 and Fig. 5 is that with more normalized electric field intensity endowed the fewer number of DMM layers and this can also be easily understood through the transmitted amplitude of the DMM layers. Considering today’s fabrication facilities in modern lithographic fabrication processes with positive photoresist, 4 pairs of the proposed multilayer can be competent for pattern the minimal feature size with 21.5 nm at the visibility about 0.4 (see Fig. 5(a)). This would drastically reduce the difficulty of the multilayer fabrication and the corresponding experimental errors. Lower than 4 pairs DMM layers, the zeroth order wave transmitted through it can strongly impact the contrast of the pattern.

 

Fig. 5 The feature sizes VS the visibility and the normalized electric field intensity with (a) 4 pairs and (b) 12 pairs of the GaN(10 nm)/Al(12 nm) DMM layers, respectively. The black square and the red solid circle represent visibility with theoretical and simulation results, respectively. The blue triangle represents the average normalized intensity 5 nm below the interface of multilayer/photoresist. The transmitted amplitude of the two structures at the wavelength of 193 nm is also presented (see inset).

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The potential to fabricate the Cr, DMM and photoresist structure is discussed here. The Cr mask can be well fabricated by electron-beam lithography and liftoff process. Deposition of nanometer-thick thin film is sufficiently feasible with conventional techniques. In 1999, a spin-valve multilayers consisting of NiFe(10 nm)/Co(1 nm)/Cu(13 nm)/Co(10 nm)/NiFe(2 nm) but with only a width as small as 70 nm were deposited using direct current sputtering [19]. In 2006, a dielectric core was fabricated as thin as 3 nm but with only 55 nm long [20]. The dimensions of that previous structure are smaller than the dimensions we proposed. However, actual implementation will be a challenge since the proposed structure has several layers and large areas. The quality features of films like smoothness, hardness, and stickiness should be fully considered in experiments and a compromise state between them is expected. For instance, some issues like surface tension could be strong for so many layers of alternatively stack films. Further analyzed the transmitted amplitude function of the proposed DMM layers, it indicates that 1~2 nm tolerance is allowable in film thickness which is sufficiently feasible with conventional techniques. The thickness and layer number of DMM structure should be optimized to yield a tradeoff between them.

4. Conclusion

In conclusion, we have developed and numerically illustrated the plasmonic interference lithography technique to obtain the feature sizes down to sub-22 nm for today’s fabrication facilities with positive photoresist with a 4 pairs of proposed dielectric-metal multilayer at the wavelength 193 nm with p-polarized. If common negative photoresist can be possibly used, the feature size would down to 16.5 nm through increasing the number of the DMM layer to 8 pairs. The dielectric-metal multilayer was designed as a filter which makes only a narrow evanescent waves band pass through for interference lithography. The influence by the number of the DMM layer was also analyzed in detail. Finite-difference time-domain method is used for confirming the validity of this technique. For the 22 nm half pitch mask can be mass fabricated, we believe that this technique has an exciting potential to print pattern with half pitch 16 nm and below.