An extensive study of the single-step replication of form-birefringent quarter-wave plates is presented. Using rigorous diffraction theory, the fabrication parameters and tolerances are carefully studied in order to obtain ideal conditions for successful replication. The design considerations are then applied to fabricate a master element by electron-beam lithography, and to replicate quarter-wave plates using the UV-moulding process. The measurements show that the replicas behave as high-performance quarter-wave plates for the design wavelength.
©2008 Optical Society of America
Elements that provide phase retardation are key components in a number of different optical systems. These phase retarders are usually made of materials that exhibit natural birefringence. However, it has been shown during the last few decades, that Subwavelength Period Gratings (SPGs) can also act as birefringent elements. In such a case, the period must be sufficiently small such that all diffracted orders, except for the zeroth, are evanescent. Thus, one-dimensional SPGs can be understood as artificial negative uniaxial materials whose optical axes are parallel to the grating vector . The phenomenon is widely known as form birefringence. This artificial birefringence can be much larger than the natural one and hence the elements can be as thin as several hundreds of nanometers, making them suitable for integration.
The first investigations of form-birefringent dielectric gratings for phase retardation were carried out in the 1980’s. Flanders  measured the phase retardation produced by binary silicon nitride gratings, while Enger et al.  and, some years later, Cescato et al.  fabricated gratings in SiO2 and in photoresist, respectively. Thanks to the high refractive index of silicon nitride, it was possible for Flanders  to achieve large retardation. However, the birefringence of gratings made in lower refractive index materials [3, 4] was small and, consequently, both Enger et al. and Cescato et al. proposed to fabricate elements whose retardation is equal to λ/8 and to cascade them. Thus, although the form birefringence can be much larger than the natural birefringence, use of high refractive indices is usually required if one desires to fabricate quarter-wave-plate-like or half-wave-plate-like elements  for visible wavelengths. When the refractive index is small, required aspect ratios (thickness-to-linewidth ratio) are high, leading to extremely challenging fabrication. In addition to visible light, grating-based retarders have been designed and tested also for infra-red frequencies, for which semiconductor materials with high refractive indices, such as GaAs, can be used. In the infra-red range, the required minimum features of the elements are larger and the aspect ratios are smaller, and hence the fabrication process is, in general, easier than in the visible wavelengths [6–8]. Another approach  is to employ dichromated gelatin emulsion in order to holographically record a deep (the birefringence of the emulsion being low) volume grating acting as a quarter wave plate (QWP).
It is obvious from the above-made discussion that, even if these elements have been extensively investigated, it is still very challenging to produce them easily in large quantities (because of required high-index material) and, consequently, at low cost. Yu et al.  investigated a multilayered element made by coating of a thin, high-index ZTO film onto a subwavelength structure fabricated on a low-index substrate that can be produced by replication techniques. However, weak directionality of film growth by sputtering can lead to a lack of accuracy in the retardation and the process still needs several steps. Nano-imprint lithography (usually along with Cr evaporation) can also be used to fabricate a mask before reactive ion etching [11, 12]. Nevertheless, in order to further reduce the costs, faster techniques involving fewer steps are absolutely required. Some potential techniques leading to low-cost fabrication are hot-embossing, injection moulding, and UV-moulding. However, most of them are limited to relatively small aspect ratios. Lately, methods to improve the ability of nanocasting lithography and UV-moulding in high-aspect-ratio replication have been proposed [13, 14]. These methods involve heat and solvent assisted processes or vacuum baking. Yoshikawa et al.  attempted to replicate, by nanocasting lithography, a quarter wave plate to polycarbonate from a quartz mold. The use of PC (n~1.55) compels to replicate high aspect ratio structure (period 400 nm, height 1900 nm) which can generate errors. For instance, the replicated element was actually 1/5 wave retarder (75° phase shift) instead of the targeted quarter-wave plate.
Recently, new UV-molding materials with high refractive index (n~1.7) have been developed. In this paper, we intend to show that they are suitable for low-cost replication of high aspect-ratio structures and in particular of form-birefringent quarter wave plates. Conditions to facilitate the replication are taken into account in the design. The paper is organized as follows: In Section 2, the design and the different requirements are considered, fabrication of the master and replication is presented in Section 3 while the optical measurements are reported in Section 4. Finally, in Section 5, we summarize our results.
2. Design considerations
Since our goal is to achieve high form-birefringence using high-refractive-index materials, the optimal grating period is very close to the threshold period d swl=λ/n (see, for example, Ref. ). In such a case, the well known first-order Effective Medium Theory (EMT)  is not accurate enough, since higher-than-zeroth grating modes have a significant effect on the behavior of the element. In fact, the first-order theory begins to work well only for periods d~λ/10, and hence it has usually only qualitative use within visible wavelengths . Further, also the second-order EMT is not accurate enough close to the threshold period, and hence one should employ rigorous diffraction theory that is nowadays very well known. In this work, we made the design using in-house-written rigorous Fourier Modal Method (FMM) , naturally with correct factorization rules  and stable solution of boundary conditions .
It is often the case that one desires to find a design for a structure with lowest possible aspect ratio, which is usually the most important single parameter to determine how difficult the direct replication will be . After fixing the refractive index to n=1.7042 (at λ=632.8 nm), that corresponds to the UV-moulding material available to us, and the period to d=360 nm, which leads to high form-birefringence, we found out that the lowest aspect ratio is achieved with thickness of 987.4 nm and with fill factor 0.532. The aspect ratio is thus equal to 5.2, which is remarkably lower than that can be obtained with, e.g. polycarbonate materials . With these parameters, not only the phase difference between the transmitted components is equal to π/2, but also the (intensity) transmittance coefficients T ⊥ and T ‖ perpendicular and parallel, respectively, to the grating lines are the same, as it can be seen from Fig. 1.
However, it is not obvious that most favorable conditions for replication are achieved with the above-mentioned condition. Namely, if the phase retardation is very sensitive to the parameters, small copying errors in the replica may lead to large deviations in the performance of the replicated element. Because of that, careful tolerance analysis is necessary before making the final decision of the desired parameters. Since we have fixed the period in order to achieve high form birefringence, only thickness and fill factor are adjusted in the tolerance analysis.
The results of the tolerance analysis are summarized in Figs. 1 and 2 that show the variation of the phase retardation depending on the parameters. From Fig. 2 (a) it can be seen that the dependence of the phase shift with the thickness is barely similar for two elements characterized by different fill factors (f=0.376 that leads to the smallest possible thickness or f=0.532 that leads to the smallest aspect ratio). If we set the acceptable limits for the phase retardation to 90°±2°, we find that the error in the depth of the grating must be no more than ±15 nm for f=0.376 and ±18 nm for f=0.532. Examining Fig. 2 (b), we find that the dependence of the phase retardation on the fill factor is much stronger than on the thickness: 90°±2° phase retardation leads to f=0.532±0.013 (191.5±4.7 nm for the linewidth) and to f=0.376±0.049 (135.4±17.6 nm for the linewidth). This is remarkable, as very-high-aspect-ratio structures are considered, and the fill factor is usually the most difficult parameter to control during the fabrication. For instance, slightly slanted walls because of overcutting and partial destruction of the mask during the etching process can lead to non-negligible errors in the fill factor. Thus, tolerances under ten nanometers for the linewidth are very challenging, especially since the thickness is close to one micron. It is thus quite obvious from the tolerance analysis that the fabrication parameters f=0.376 and h=842 nm are the most favorable one. Indeed, although the aspect ratio is high, the tolerances are larger, and thus the replication of the quarter wave plate should be considerably easier.
3. Fabrication and replication
We employed electron-beam lithography to fabricate a 5×5 mm QWP master in fused silica, as this method enables the fabrication of very accurate and high-quality gratings, with a rather good control of the fill factor. In the fabrication process, we used a fused silica mask plate substrate with a 35 nm chromium layer on top of it. We then spin-coated a high resolution ZEP 7000 resist layer onto the substrate, after which we exposed the linear grating with Vistec EBPG 5000+ES HR electron beam writer. After the exposure, we developed the sample in ethyl 3-ethoxypropionate for 60 seconds, and rinsed it in isopropanol for 30 seconds. We then used the attained grating profile in ZEP as an etching mask in the chlorine-based etching process, during which the profile was transferred to the chromium. We removed the remaining resist afterwards by O2 plasma ashing. It was then possible, with the fabricated Cr mask, to transfer the grating profile into the substrate material by trifluoromethane (CHF3) based etching process. Finally, after removing the extant chromium by wet etching, the grating profile in silicon dioxide was attained, as it can be seen in Fig. 3.
We prepared the master for replication by applying an anti-adhesive surface treatment. The performed treatment is based on liquid-phase deposition of alkyltrichlorosilane, which modifies the surface energy, making the quartz surface hydrophobic and therefore more suitable for copying . First, the master is immersed in the solution of HFE7100 solvent (3M) and tridecafluoro-1,1,2,2-tetrahydrooctyl-trichlorosilane (1000 ml/2 ml) for 15 min. Then it is rinsed in pure HFE7100 solvent for another 15 min and dried in a strong nitrogen flow. The whole process is performed under nitrogen atmosphere because of the high reactivity of the silane.
As mentioned in preceding section, the master structure is in the scale of hundred nanometers and the aspect ratio is relatively high (~6). These characteristics cause special challenges for the replication technique in filling of the structure and demoulding of the replica. Therefore, the chosen replication method is the UV-replication by liquid UV-curable prepolymers. In this study, the UV-moulding of QWP nano-structure is performed by EVG520 UV-embossing equipment from EV Group by using a novel optical polymer from Mitsubishi Gas Chemical. The replication polymer is a new Lumiplus material which has high optical clarity and high refractive index (n=1.7042 at λ=632.8 nm) in visible wavelength band and hence it is optimal for the class of components considered here . The UV-material is made of a mixture of three components (monomer, catalyte, and photo initiator) whose self-life in liquid-form is 6–10 hours, and therefore it needs to be mixed just before the replication process . In room temperature, the liquid Lumiplus UV-material has also optimal 20 cps viscosity that can be decreased by heating during the replication process in order to improve the filling of the structure. The substrates for the replicated component is made from similar Lumiplus material.
In the replication process, the liquid Lumiplus material is dispensed on the master and the Lumiplus substrate is laid on the top. The stack is heated in the embosser chamber at 40 °C temperature and pressed together with an uniform 3400 N pressing force for a 4”×4” substrate area by a wedge compensated piston. The pressure is applied for 10 seconds before the exposure when the dispensed droplet of UV-material is spread between the master and substrate and has filled the structure properly. Despite the low viscosity of the UV-material, the hydrophobic surface and nanostructure surface properties avoid a proper filling of the UV-material. Consequently, replication equipment with high pressing force is essential. The pressure is held until the hardening of the copy with 3700 mJ/cm2 UV-dose is done. The light source used in the process is a 400WMetal Halide Lamp with intensity >70 mW/cm2 for wavelengths 300–500 nm.
After the exposure cycle, substrate and replicated structure are peeled off from the master. Owing to the high aspect ratio, the demolding is very sensitive to the separation technique because of relatively high adhesion in the grating area despite the anti-adhesion layer on the master surface. Moreover, the adhesion difference between the structure area and the clear master surface is remarkable and hence the separation tends to be uneven. Consequently, without precautions, the replica and the master are separated with locally progressive boundary starting from the center to the border of the element [Fig. 4 (a)]. Moreover, if the direction of this boundary differs strongly from the direction of the grating lines, the replicated structures may suffer from mechanical stress which may cause breaking of the replicated grating lines [Fig. 4 (b)]. Figure 4 (c) shows SEM pictures of elements presenting such a behavior during the demolding process.
In order to avoid the aforementioned drawbacks, we performed demolding by applying the opening force locally to the grating area. At the same time, the surrounding area is pressed against the master until the grating area is separated simultaneously. With this technique, we obtained successful replicas. We inspected the quality of the replicated structures carefully by SEM, and found no defects in the 5×5mm surface area. Figure 5 shows examples of the results of successful replication.
4. Optical measurements
We performed the optical measurements of different replicas with a HeNe laser (λ=632.8 nm) using a quarter-wave-plate method: The incident linearly polarized electric field is input to the system formed by the element to be measured, followed by a quarter-wave plate and an analyzer. The grating vector of the element is set to 45° with respect to the plane of vibration of the input field, whereas the fast axis of the quarter-wave plate is set parallel to the input-field polarization. The rotation angle of the analyzer is denoted by θ. The Jones vector of the output
electric field thus assumes a form 
where t ⊥ and t ‖ denote the complex-amplitude transmittance coefficients in directions parallel and perpendicular to the grating vector, and we have normalized the amplitude of the incident field to unity. The output intensity thus assumes the form
where Δα=arg(t ‖)-arg(t ⊥) is the unknown value of the phase retardation. It can be thus determined very accurately by finding the value θ=θ min for which the intensity reaches its minimum value I min=(|t ⊥|-|t ‖|)2/4. Thus, the value of the intensity minimum also gives us the (relative) difference between the transmission coefficients.
We carried out the measurements for different elements characterized by slightly differing fill factors, as well as different replicas of the same master element. In fact, we varied the doses during the exposure step by step in order to investigate the behavior of the elements as a function of fill factor. The results are in excellent agreement with the theoretical predictions. The best element leads to 90° phase retardation with equal transmission coefficients in two directions. The measurement accuracy is estimated to be better than 1%. We also cut some of the replicated elements, and performed analysis of the actual structure shape by SEM. We found that the fill factor of the best element is around 0.38 that was also our target value (linewidth varies from 120 nm to 150 nm from up-part to bottom-part of the grating). In this case, the valued of phase retardation varied from 87° to 90° depending on the replica made from the same master element. For the other elements, we found that the phase retardation varied between 75° and 85°. For instance, one element whose fill factor was afterwards found to be equal to 0.42 led to 83–86° phase retardation, while another element whose fill factor was measured to be around 0.47 led to 75–80° phase retardation. The values of the phase retardation are slightly (few degrees) lower than what could be expected (Fig. 2), because few tens of nanometers are missing from the depth.
In addition to the measurements of the phase retardation, Fig. 6 (a) shows the transmission after the analyzer behind the elements as a function of the rotation angle of the analyzer. It is obvious that, along with a correct phase retardation (measured by the quarter-wave plate method described above), the third element produces a perfectly circularly polarized wave. With form-birefringent elements, the phase retardation is a crucial point but the transmission values for the different components are also very important. If the shape is not accurate, phase-shift variations are followed by variations in the transmission, which explains why the transmission after the analyzer varies quickly from one element to another even though the phase retardation does not vary remarkably.
Concerning the different replicated elements, we observed variations up to 5° between two replicas of the same master element. This happens when the fill factor is too high, since the phase retardation is very sensitive with the fill factor, as shown in Fig. 2. However, when the fill factor value allows to be in the “high-tolerance region”, variations up to only 3° [Fig. 6 (b)] have been measured, showing the importance of the replication considerations in the design of the elements. Indeed, in this case, small variations of the profile between the different replicas do not lead to intolerable variations in the phase retardation. It can also be noted that each element has been tested at different points of its surface and the same results were observed.
This study deals with straight replication, suitable for mass production, of form-birefringent quarter-wave plates by UV-moulding process. Because of high aspect ratios, correct replication of such elements is very challenging and, to the best of our knowledge, this paper reports the first successful demonstration of single-element quarter-wave plates by single-step replication technique. In this paper, new UV-curable replication material characterized by high refractive index n=1.704 (allowing significant reduction of the aspect ratio) is utilized to produce quarter-wave plate elements. Moreover, a design made using rigorous diffraction theory is presented which allows larger tolerances. The large tolerances also lead to good reproducibility of the replicated elements originating from the same master. The measurements show that the optical performance of the replicas is very high: the best replicas lead to 90° phase retardation and practically equal transmission coefficients along the axes of the element.
The work was supported by the Academy of Finland (grants 111701, 118951, and 207523). The authors acknowledge the support of the Network of Excellence in Micro-Optics (NEMO). The funding from the National Agency of Finland (TEKES) (project Hippo) as well as from the Ministry of education (The Research and Development Project on Nanophotonics) is gratefully appreciated. The authors wish also to thank Sami Hassinen and Victor Prokofiev for technical assistance.
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