Using numerical simulations, we report an observation of a novel tunable ultra-deep subwavelength nanolithography technique using a surface plasmon resonant cavity formed by a metallic grating and a metallic thin-film layer separated by a photoresist layer. The tuning capability is implemented by varying the cavity length, from which surface plasmon interferometric patterns with inherently higher optical resolution than that of conventional surface plasmon techniques are generated in the cavity of photoresist layer. The physical origin of the tunability is analytically confirmed by the dispersion relation derived from the cavity system.
©2011 Optical Society of America
With the developments of the nanoscale science and technology, the demand for fabrication of nanoscale patterns has been significantly increased. Photolithography has still been the most widely used microfabrication technique because of its ease of repetition, effective cost and suitability for large-area fabrication. The diffraction limit, however, restricts single-exposure resolution to features with periods no smaller than half wavelength of the illuminating sources. To achieve nanometer feature sizes within the regime of diffraction physics, one straightforward method is to reduce the working wavelength by employing light sources of higher photon energy such as extreme ultraviolet light (EUV), soft X-rays or atomic wavepacket [1–4]. The main drawbacks, however, are the drastic increase of complexity and cost for instrumentation and processing, including the developments of new sources, photoresist and the optical components. Several alternative techniques, such as electron-beam lithography , focused ion-beam lithography , dip-pen lithography , and nanoimprint lithography , can also achieve nanoscale feature sizes, however, these methods require the introduction of a new infrastructure of tools, materials, and processing technologies, which costs huge expenses.
Recently, a new photolithographic scheme, which is based on the unique properties of surface evanescent waves  or surface plasmon polaritons (SPPs) induced at the interface between a metal and a dielectric material, to achieve sub-diffraction limit nanopatterning was proposed and demonstrated [9–18]. The wave vector of SPPs can be significantly larger than that of the free space illuminating light at the same frequency, which results in extraordinary “optical frequency but X-ray wavelength” property . As a result, the resolution of this surface plasmon nanolithography can go far beyond the free-space diffraction limit of the light. It was demonstrated that the use of SPP waves in the optical near field of a metallic mask can produce fine patterns with a subwavelength resolution [9–13]. Specifically, using a silver one-dimensional(1-D) grating mask or a silver two-dimensional (2-D)perforated hole arrays mask, lithography with 100 nm pitch or sub-100nm dot array patterns(~1/4 illumination wavelength) has been demonstrated, respectively, with 300 nm mask periodicity at 436 nm illumination wavelength , and 200 nm mask periodicity at 365 nm wavelength [11,13] based on the SPP waves within the mask area. Liu et al further proposed a nanophotolithography technique based on the interference of surface plasmon waves in which 1-D and 2-D periodical structures of 40-100 nm features can be patterned with a 266nm exposing light within an area of ~1μm × 1μm using 1-D gratings of different orientations . Very recently, they experimentally demonstrated that plasmonic interference patterns can be formed when multiple surface plasmon waves overlap coherently by utilizing edge coupling mechanism . Other alternative techniques of generating deep subwavelength patterns using multilayer metamaterial structures which require precise nano-scale manipulation of multilayer thin film stack, were also proposed by different groups [16–18]. Xiong et al numerically demonstrated pattern periods down to 50 nm under 405 nm light illumination with a 12 pairs of 35 nm Ag and 21 nm fused silica multilayer , while Xu et al proposed a structure with 30 pairs of silver-fused silica thin slices with thicknesses of 20nm and 30nm, respectively, to achieve 40nm feature size patterns at 442nm wavelength . Especially, Yang et al achieved the feature sizes theoretically down to ~20nm at the wavelength of 193 nm by using the dielectric-metal multilayer structure .
To improve the quality of the near-field lithography, Blaikie et al first proposed a surface plasmon enhanced contact lithography (SPECL) technique to improve process latitude and depth of field . They found that, by placing a 40-nm thick silver layer beneath the mask separated by a 50nm-thick photoresist, much enhanced contrast and improved depth of field without image reversal can be obtained throughout the entire resist layer. This improvement was attributed to the generation of surface plasmons on the underlying silver layer, which illuminate from beneath in addition to the incident illumination from above. The SPECL technique was further experimentally demonstrated and theoretically analyzed by Shao [20,21] and Blaikie  in 2005 and 2007, respectively, in which one-to-one pattern transfer(i.e., the periods of the mask and the exposed patterns are the same) of subwavelength resolution has been achieved with a mask of array of line (100 nm in width) made on titanium film deposited on a quartz substrate using a 355nm laser beam as the light source. More recently, different versions of the SPECL technique have been numerically studied by Xu  and Yang , in which either a metal-cladding superlens  with mismatch permittivities between the metal slab and surrounding dielectric medium was used to realize sub-diffraction-limit optical imaging and improve the intensity contrast of the interference pattern due to the reflection effect on the metal-cladding interface, or a hetero-structure was used to generate subwavelength patterns with high contrast. All these studies were focused on the quality improvement of the near-field one-to-one pattern transfer, such as intensity and/or contrast by the introduced metallic layer between the photoresist and the substrate.
In this paper, using numerical simulations, we report a new phenomenon that happens in a photoresist cavity with two cavity walls being a metallic grating mask and a metallic thin film deposited on a dielectric substrate, respectively. The layout of the cavity structure is similar to that in SPECL technique, but the periods of the metallic grating mask is much larger than those used in the conventional SPECLs which require subwavelength periods in order to achieve subwavelength patterns due to one-to-one projection pattern transfer mechanism used in the conventional SPECL. It is found that the resolution of the generated deep-subwavelength pattern in the photoresist can be tuned by varying the cavity length, i.e. either thickness of the photoresist or the thickness of the fillings (e.g., fluids) in the cavity, although the periods of the metallic mask is fixed and much larger than the illumination wavelength. The tuning capability is implemented from which surface plasmon interferometric patterns with inherently higher optical resolution than that of conventional surface plasmon techniques are generated in the cavity of photoresist layer. The physical origin of the resolution tunability is interpreted as the surface plasmon interferometry in the cavity of photoresist layer and is analytically confirmed by the dispersion relation derived from the cavity system. The new phenomenon opens a new way to generate tunable ultra-deep subwavelength patterns by using a fixed diffraction-limited mask with capability of large area, deep exposure depth and flexibility of arbitrary 2D patterns.
2. Principle of a tunable surface plasmon resonant cavity
The schematic of the tunable surface plasmon resonant cavity is presented in Fig. 1 . A SPP cavity is formed by an upper diffraction-limited metallic grating mask and a lower backing metallic thin film deposited on a fused silica substrate(usually SiO2), separated by a photoresist(PR) layer or a combination of photoresist and index-matching fluids. In this paper, the upper metallic grating and the lower metallic thin film are assumed to be the same silver material. The illumination is incident from the top with a wavelength of 436nm and p-polarization. The refractive indices of SiO2 and the PR are 1.5 and 1.7, respectively, and the permittivity of Ag is εAg = −6.489 + 0.064i . All the components in Fig. 1 are treated as semi-infinite in y direction. Numerical simulations are performed using the FDTD Solutions (Lumerical of Canada)
Figure 2 (a) and (b) shows, respectively, the electric field distribution of the cavity structure (Fig. 1) and a conventional open structure with metallic grating/PR/SiO2 substrate(no surface plasmon resonant cavity) as a comparison. In both Figs. 2(a) and (b), the period and thickness of the upper Ag grating is assumed to be 600nm(much larger than the illumination wavelength) and 50nm, respectively, the slit width (open section) of the grating is fixed at 60nm, and the thickness of PR is 50nm. The Ag thin film layer deposited on the lower SiO2 substrate in Fig. 1(a) is assumed to be 50nm. It is seen that the nano patterns generated in the PR layer in Fig. 2(a) and (b) show different behaviors in terms of resolution and the exposure depth. With the cavity structure, 8 pairs of the plasmonic interference patterns are observed within two adjacent open slits of the metallic grating, while only 6 pairs of patterns are observed in the conventional SPP open structure under the exact same conditions. It is also seen that the exposure depth in the PR layer with the cavity structure is much higher than that of the conventional open structure.
Figure 3 shows the electric field distributions of the cavity structure with different PR thicknesses. The period and the thickness of the Ag grating are 600nm and 50nm, respectively. The slit width (open section) of the grating is fixed at 60nm, and the thickness of Ag layer on the lower substrate is 50nm. The thickness of PR layer is 50nm, 30nm, 20nm, 10nm, respectively in Fig. 3(a), (b), (c), and (d). We can see that the number of patterns in the PR between the adjacent slits increases with the decrease of thickness of the PR layer. The number of pattern pairs increases from 8 in Fig. 3(a), to 10 in Fig. 3(b), 12 in Fig. 3(c) and 16 in Fig. 3(d) when the thickness of the PR layer decreases from 50nm, to 30nm, 20nm, and 10nm, respectively.
This is a new phenomenon and represents a significant progress in generating tunable ultra-deep subwavelength patterns using a simple and practical technique when compared with the conventional open SPP structure as witnessed by Fig. 2(b). With the cavity technique, the optical resolution can be enhanced about 3 times that of the conventional open structure, down to about 16.5nm feature size with a wavelength of 436nm illumination and a diffraction-limit mask (period = 600nm). This is comparable to that of using a complicated 30-pair metamaterial structure and 193nm illumination . Furthermore, the optical resolution can be easily tuned by changing the PR thickness without the need of changing the metallic grating mask. This behavior is totally different from that of the conventional SPP structure in which the optical resolution is solely determined by the thickness of the metallic grating . It can further be shown that the resolution tunability with the SPP cavity length (i.e., PR thickness) is much more sensitive than that with thickness of the metallic gratings. This new findings can be used to guide the future design and experiments because the resolution is very sensitive to the PR thickness.
3. Theoretical analysis and comparison with numerical studies
The optical resolution of the cavity structure based on the interference of the surface plasmonic waves within the cavity is inherently higher than that conventional open SPP structure. The physical origin of the observed phenomenon can be explained by the dispersion relation derived from the cavity system. As shown in Fig. 1, the SPP cavity is formed by the upper metallic grating with thickness d2 and dielectric constant ε2 and the lower metallic film with thickness d4 and dielectric constant ε4, the cavity is filled with a PR layer with thickness (cavity length) d3 and dielectric constant ε3. Both upper metallic grating and lower metallic thin film are interfaced with dielectric substrates (assumed to be the same fused silica in this paper) with dielectric constant ε1. Under p-polarization illumination, in the region x<-d3, the EM fields have the form:
By applying electromagnetic boundary conditions at the interfaces of quartz/metallic grating/PR/metallic layer with continuity of electric field in tangential direction and magnetic field in normal direction, the dispersion relation of the SPP cavity system can be derived as follows:Equation (1) gives the explicit relations of the SPP wave vector with the geometric dimensions and the properties of the materials involved in the structure. Solving Eq. (13), we can obtain the dispersion relation between k sp and λ (wavelength of the illumination light) with different structural parameters.
Figure 4 shows the dispersion relations between the wave vector of SPPs and the wavelength of illumination light for structures with and without SPP cavity. The material of metallic grating and the metallic thin film layer is assumed to be silver (Ag), other parameters are the same as those used in Fig. 2. In the case of open SPP structure (no cavity), the lower metallic thin film is replaced by a SiO2 layer. From Fig. 4, we can see that the SPP wave vector of the cavity structure is always larger than that with the conventional open SPP structure, which implies inherently the shorter SPP wavelength, and hence the higher optical resolution in the cavity structure than that in the open structure. At the illumination wavelength 436nm, the wave vector is 0.0434 nm−1 and 0.0335 nm−1, respectively, which means the periods of the nano-patterns are 73nm and 94nm, respectively if we translate the SPP wave vector to the possible pattern period according to the definition of Λ(period of pattern) = λsp/2 = π/ksp. From the numerical results shown in Fig. 2, we can obtain that the periods of the patterns are 75nm and 100nm, respectively for the two structures, which are in excellent agreement with the analytical results from the theory in Fig. 4.
Figure 5 shows the dispersion relation between the SPP wave vector and the illumination wavelength with different cavity lengths. The parameters used in the calculation are the same as those used in Fig. 3, and the thicknesses of PR are 50nm, 30nm, 20nm, and 10nm, respectively. From Fig. 5(a), it is seen that the SPP wave vector is a very sensitive function of the PR cavity length. The wave vectors at 436nm wavelength are measured as 0.0434nm−1, 0.0533nm−1, 0.0663nm−1 and 0.108nm−1, respectively for the cavity lengths of 50nm, 30nm, 20nm and 10nm. The corresponding pattern periods are then calculated as 73nm, 59nm, 48nm and 30nm, respectively. The pattern periods measured directly from numerical results shown in Fig. 3 are 75nm, 60nm, 50nm and 33nm, respectively, which exhibit again the excellent agreement between the theoretical prediction and the direct numerical results. The detailed comparison of numerical results and analytical results is shown in Fig. 5(b).
To further show the characteristics of the cavity structure, Fig. 6 shows the dispersion relation between the SPP wave vector and the illumination wavelength for cavity structure with different thicknesses of metallic gratings. The parameters used in the calculation are the same as those used in Fig. 3, and the thicknesses of PR are fixed at 50nm. From Fig. 6, it is seen that the SPP wave vector is also sensitive to the metallic grating thickness, especially within the thickness range of smaller than 30nm. This behavior is the same as that in the conventional open SPP structures . However, it is clearly seen from Fig. 5 and Fig. 6 that the sensitivity of the SPP wave vector to the PR thickness is much higher than that to the metallic grating thickness. The dynamic range of the sensitivity of the SPP wave vector to the metallic grating thickness is very limited within the range of <30nm only, which drastically reduces the practical significance when compared with the large dynamic range using SPP cavity tuning.
The optical resolution of the subwavelength pattern is solely determined by the thicknesses of the cavity length(PR thickness) and the metallic grating, independent of periods of the metallic mask grating. Figure 7 shows the electric fields of the cavity structures with different mask periods. With the same material and the same thickness of the PR and the metallic grating, the optical resolution of the patterns remains unchanged at ~75nm for the mask periods of 310nm, 600nm and 890nm, respectively. It can be further shown that the slit width(i.e., the open section of the metallic grating) does not affect the pattern resolution but the pattern quality.
It should be emphasized that the cavity structure and the physical phenomena presented in this paper is different from that of the superlens structure . In a superlens structure, the thin metallic film acts as a natural optical lens, the grating mask (or arbitrary objective) is imaged on the other side of the thin-film lens with one-to-one pattern transfer, which represents a significant progress in terms of pattern quality when compared with conventional projection photolithography technique. In the structure of this paper, the grating mask and the backing metallic film forms a cavity, and the subwavelength patterns are formed in the cavity. The optical resolution of the formed pattern is tunable and determined by the thicknesses of the metallic grating and the cavity length with the physical mechanism of the interference of the plasmonic waves induced at both cavity walls/photoresist boundaries. It is not a one-to-one pattern transfer process as that in superlens technique. With the periods of the metallic grating mask much larger than the illumination wavelength, an ultra-deep subwavelength patterns can be obtained using the proposed cavity structure.
The key factor in the experimental implementation of the tunable nanolithography using the SPP cavity is the precise control of the cavity length. Figure 8 shows the typical sensitivity of the pattern quality on the cavity length when the cavity length is 42nm (Fig. 8(a)), 50nm (Fig. 8(b)) and 60nm (Fig. 8(c)), respectively. It is seen that the pattern resolution can be well maintained at 75nm when the cavity length varies in a range of 18nm from 42nm to 60nm, although the pattern quality in terms of uniformity and intensity degrades gradually when the cavity length deviates from the optimal length of 50nm. It is believed that the tolerance of the cavity length for a specified pattern resolution can be of at least several nanometers without significant degradation in pattern quality. With the current nano-scale control technology, in which the resolution of the motion control can be as small as sub-nanometers, it is thus assured that the control precision of the cavity length in experiments can be well within the tolerance.
In conclusion, we present a numerical observation of a tunable ultra-deep subwavelength photonanolithography technique based on a simple cavity structure. With the technique, it is found that the optical resolution is inherently higher than that of the conventional open SPP technique. Feature size down to ~16.5nm can be obtained with a wavelength of 436nm illumination and a diffraction-limit mask of 600nm period, which is comparable to that of using a complicated 30-pair metamaterial structure and 193nm illumination. Furthermore, the optical resolution of the structure is tunable with the cavity length without the need of changing the metallic grating, and more importantly, the dynamic range of the resolution tunability with the cavity length is much larger than that with the metallic grating thickness, which breaks the conventional concept in that the pattern optical resolution is solely determined by the thickness of the metallic grating. The generated nano-patterns with the cavity technique are of much improved uniformity, contrast and deep exposure depth compared to the open SPP technique. The superior characteristics of the cavity technique is confirmed and compared with a theoretical model derived from the SPP cavity system. The new phenomenon opens a new way to generate tunable ultra-deep subwavelength patterns by using a fixed diffraction-limited mask with capability of large area, deep exposure depth and flexibility of arbitrary 2D patterns.
The work is supported in part by University Scientific Research Foundation of Jiangsu Province (09KJA140004), the National Scientific Foundation of China (60776065), Suzhou High-Tech Research Program (ZXG0712), and the project of the Priority Academic Program Development (PAPD)of Jiangsu Higher Education Institutions.
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