We propose and demonstrate a self-referencing alignment technique to conveniently enlarge fabricated grating area. The latent image gratings are used as the reference objects to align (adjust and lock) the attitude and position of the substrate relative to the exposure beams between and during consecutive exposures. The adjustment system and the fringe-locking system are combined into the exposure system, eliminating the drift errors between them and making the whole system low-cost and compact. For the fabricated 1 × 4 mosaics of 50 × (30 + 30 + 30 + 30) mm2 area and 1 × 2 mosaics of 90 × (80 + 80) mm2 area, the typical peak-valley −1st-order wavefront errors measured by a 100-mm-diameter interferometer are not more than 0.06 λ and 0.09 λ, respectively.
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Large-area gratings play key roles in high-power chirped-pulse amplification laser systems for inertial confinement fusion , high-resolution spectral analysis for astronomical telescopes , long-range metrology for interferometers , high-throughput molds for nanoimprint lithography , etc. Holographic exposure, as a classic and rapid method, could fabricate meter-size gratings , but it is limited by the aperture size of the exposure system. The scanning beam interference lithography , incorporating many high-accuracy control techniques, uses two millimeter-diameter-size beams to make large gratings in a scan mode.
As an extension of single exposure and an alternative to scanning exposure, a technique called optical mosaic, which uses multiple exposures, has been proposed to enlarge grating size [7–9]. It is a convenient and low-cost approach dedicated to cross-scale fabrication of various gratings (including their overlay). To make high-quality mosaic gratings with diffraction wavefront aberration as low as possible, the mosaic conditions should be met: between exposures the attitude and position of the substrate relative to the exposure fringes (interference fringes of the exposure beams) must be adjusted well to reduce the mosaic errors; during an exposure the error-minimized relative attitude and position should be locked persistently.
In lithographic process, the latent image in the photoresist layer atop the substrate is an invisible image produced by exposure (through or without a mask) and to form specific pattern after development . As one of its representatives, the latent grating (exposed but undeveloped volume grating)  is the ideal and essential object for precise alignments by integrating the nano-fabrication and -metrology [12,13]. Other latent images also have been used for alignments in kinds of nanofabrication [14,15].
In our previously presented optical mosaic technique [8,9], the adjustment was done by employing the exposure beams and the latent grating. However, the phase of the exposure fringes was locked to a reference grating, which was a separate piece of optical element, thus giving room to possible drift errors between the reference grating and the substrate. These errors might be due to the deformation of optical table caused by moving the substrate from one exposure position to the next, for instance.
Here we present a method that abandons the reference grating and locks the exposure fringes to the latent grating to eliminate the above drift errors. The same latent grating and exposure fringes are also used for adjustment, completing a self-referenced alignment method to maintain the mosaic conditions.
2. Mosaic method
2.1 System setup
Figure 1(a) shows the mosaic system that consists of a conventional exposure system together with an alignment system. The x, y, and z axes are along the directions of grating vector (lateral direction), grating groove (vertical direction) and normal of grating surface, respectively. The alignment (adjustment and locking) of phase and attitude of the substrate relative to the exposure fringes will be done by employing the latent grating and the exposure beams as the measurement tools. A vertically polarized 413.1 nm Kr+ ion laser is used for the two-beam exposure system. The expanded and collimated exposure beams B1 and B2 are projected symmetrically onto the substrate G that is mounted on a translation stage.
After an exposure the latent grating is formed in photoresist, with extremely low diffraction efficiency in the order of 10−5. Then we insert specially designed wedged attenuators A1 and A2 into B1 and B2, respectively, to monitor the interference fringes formed by the diffractions from the latent grating. A1 and A2 are coated with Cr-Ni films, and their wedge angles are in the planes that are defined by their normal directions and the y axis [the illustration of Fig. 1(a)]. The −1st-order diffraction of the attenuated and tilted part of B1 from the latent grating is reflected by A1 to a high-sensitivity Electron-Multiplying CCD (EMCCD); so is the 0th-order of the corresponding part of B2. EMCCD is equipped with a 300 mm/F2.8 lens. Its sensor plate is a little out of focus and serves as the screen to receive the horizontal interference fringes of the two diffraction beams, namely the L fringes [Figs. 1(b) and 2(c) ]. In some later step, we will use the half-image pair [Fig. 2(d)] to compare the real-time L fringes with the recorded reference L fringes for aligning them to meet the mosaic conditions.
The tiny difference between the wedge angles of A1 and A2 is ~18”, to make a convenient L fringe width for the following alignment. The transmittivities of A1 and A2 are 10−2 and 10−6, respectively, for protecting the latent grating from excessive exposure. Their ratio (104) is close to the ratio of the 0th- and −1st-order diffraction efficiencies from the latent grating. In this way we can get two diffraction beams with similar intensities and then the L fringes with a high contrast. Thanks to the capacity of detecting single-photon events of EMCCD, the weak L fringes (in the order of 0.1 nw/cm2) are well captured.
2.2 Alignment of L fringes
The mosaic conditions tell that the in-plane rotation (about the z axis) and the lateral position (along the x axis) of the substrate relative to the exposure fringes must be controlled well so that the latent grating fringes and the exposure fringes are parallel and their lateral spacing is an integer multiple of the grating period . Errors in these two degrees of freedom are characterized by the width and phase errors of the L fringes, respectively.
As shown in Fig. 2(d), we align the real-time L fringes to the reference L fringes so that the uppermost fringe of former and the uppermost fringe of the latter are matched to each other and simultaneously so are their lowermost fringes. We control the tilt of B2 by driving the spatial filter F vertically via the piezoelectric transducer PZTa and the phase of B1 by driving the reflector R along its normal via PZTp to align the width and phase of the L fringes, respectively. Adjusting the exposure beams is equivalent to adjusting the substrate, but swifter and more convenient. By fringe-locking the typical misalignments of the uppermost and lowermost fringes are less than one pixel of EMCCD. That means the achieved phase and attitude accuracy are lower than dozens of nanometers and tenths of micro-radians, respectively. Besides, each time after moving the substrate, the up-down and left-right boundaries of the whole L fringe pattern may be misaligned, which would bring errors to the fringe-locking. Therefore, we must adjust the attitude of the substrate to align the boundaries before locking the L fringes. By visual judgment the residual misalignments of the boundaries are also lower than one pixel.
2.3 Denotations and definitions
After A1 and A2 are inserted, the exposure beam is divided into the monitoring region for generating L fringes, denoted as Region M, and the exposure region, denoted as Region E [Figs. 1(a) and 2]. Due to the high-accuracy requirement of attitude alignment, Region M is vertically as long as the exposure beams and could be laterally very narrow. Thus the total width w of the exposure beams is divided into a very small width w' of the Region M and a large width Δx of the Region E. Their heights are just the beam height h. We denote the first, second… exposure areas of the substrate as Areas 1, 2…, respectively. In Step j (j = I, II…) of the mosaic procedure, the set of L fringes generated from Area i (i = 1, 2…) is denoted as Li j fringes, whose phase is denoted as P Li j. The phase of the exposure fringes relative to the latent grating of Area i is denoted as P Ei j. In Step j for the being exposed Area i, the photoresist layer there is written by the exposure fringes to generate the latent grating. Therefore the exposure fringes and the latent grating are perfectly aligned to each other, i.e.
2.4 Mosaic procedure
The self-referencing alignment technique is to give up the reference grating, and to employ only the latent grating for eliminating the mosaic errors generated from the relative drifts between the fringe-locking, adjustment, and exposure systems. In brief, first we make a process edge on the substrate. Then we lock the exposure fringes to the latent grating there for the first official exposure. By substituting the latent grating for the independent reference grating, the random mosaic error from system drifts is eliminated. Note that there is an inevitable drift error between the exposure to the process edge and the recording of the L fringes from it. If we use this set of L fringes for the subsequent exposures, there would be an accumulative mosaic error. However, we can lock to this set of L fringes and simultaneously record the L fringes from the first official exposure area. Thus during this recording of the L fringes and the first official exposure, the exposure fringes are always locked to the latent grating of the process edge, i.e. there is not any drift error between the exposure beams and the substrate. Therefore the L fringes from the first official exposure area can be used for the subsequent exposures and will not cause any accumulative error. The key point of the self-referencing method is the transfer of the recorded L fringes for fringe-locking, i.e. from recorded in the process edge to recorded in the official exposure area.
Now we give the specific procedure to make a 1 × 2 mosaic (Fig. 2 and Table 1 ) under the assumption of having aberration-free exposure beams. To facilitate the following description, the phase error will be analyzed, but the attitude error will be omitted. This omission does not affect the error elimination with this mosaic method, because attitude error is essentially the relative phase error over the vertical direction.
Step I is the exposure to Area 1 [Fig. 2(a)]. Area 1 is just the process edge for the following steps, but does not belong to the official mosaic area. The width of it is w'. From the E condition, P E1 I ≡ 0.
Step II is the recording of the reference L1 II fringes [Fig. 2(b)]. After A1 and A2 are inserted, we record the real-time L1 II fringes as the reference L1 II fringes [Fig. 2(c)]. There is an inevitable phase difference Δβ = P E1 II − P E1 I, due to the drift of the exposure system (e.g. phase variation of exposure fringes by air turbulence). From the L formula, P L1 II = P E1 II + C = Δβ + C. For reducing the influence of acquisition noise of EMCCD, we continuously save many frames of the real-time L1 II fringes (~10 s × 50 fps), and record the mean frame calculated by pixel as the reference L1 II fringes.
Step III is the exposure to Area 2 with the fringe-locking enabled [Fig. 2(d)]. We lock the real-time L1 III fringes to the reference L1 II fringes, so that P L1 III = P L1 II, and simultaneously make the exposure to Area 2. Area 2 is the starting area of the mosaic and the width of it is Δx. From the L formula and the locking, P E1 III = P L1 III − C = P L1 II − C = Δβ; from the E condition, P E2 III ≡ 0. Consequently, the generated phase difference between the latent gratings of Areas 2 and 1 is P E1 III − P E2 III = Δβ. Because Region M is sharply attenuated, there is no overexposure to the already produced latent grating. Here we realize the scheme of strong exposure and weak locking, the ratio of whose intensities is ~107.
Step IV is the transfer of the fringe-locking [Fig. 2(e)]. After moving the substrate laterally for ~w'/2 to the position for monitoring the L1 IV and L2 IV fringes simultaneously, we adjust and lock the real-time L1 IV fringes to the reference L1 II fringes, so that P L1 IV = P L1 II. Then we keep on locking and simultaneously record the real-time L2 IV fringes as the reference L2 IV fringes [Fig. 2(f)]. From the L formula and the locking, P E1 IV = P L1 IV − C = P L1 II − C = Δβ; the phase difference between the latent gratings of Areas 2 and 1 is P E1 IV − P E2 IV = P E1 III − P E2 III = Δβ. Consequently, P E2 IV = 0. Then from the L formula, P L2 IV = P E2 IV + C = C. The reference L2 IV fringes is also a mean frame of continuously saved many frames, but the saving time should be longer (~60 s) to match the long-time locking during the following exposure.
Step V is the exposure to Area 3 with the fringe-locking enabled [Fig. 2(g)]. After laterally moving G for a distance Δx from the initial position, we adjust and lock the real-time L2 V fringes to the reference L2 IV fringes, so that P L2 V = P L2 IV. Then we keep on locking and simultaneously make the exposure to Area 3 whose width is also Δx. From the L formula and the locking, P E2 V = P L2 V − C = P L2 IV − C = 0; from the E condition, P E3 V ≡ 0. Consequently, the generated phase difference between the latent gratings of Areas 3 and 2 is P E2 V − P E3 V = 0, i.e. not any phase difference. So far the error-free 1 × 2 mosaic of Areas 2 and 3 are completed [Fig. 2(h)].
For more mosaics, continue stepwise moving G for the distance Δx and then using the reference L2 IV fringes for locking the real-time L3 VI, L4 VII… fringes to expose Areas 4, 5…, respectively. In a similar way, there is not any error between those adjacent areas, hence improving the self-referencing alignment method to be error-free. In the whole mosaic procedure, the latent grating areas for generating L fringes is always protected well by A1 and A2 under the exposure beams, and the other areas are covered by beam blocks BD1 and BD2 [Figs. 1(a) and 2] if unwanted to be exposed. For reducing stray light into EMCCD, we also use beam blocks BA1 and BA2 to keep the side walls of A1 and A2 out of exposure beams.
If the transfer of fringe-locking was not implemented at Step IV, we would use the reference L1 II fringes for locking the real-time L2 IV, L3 V… fringes to expose Areas 3, 4…, respectively. According to the E condition and the L formula (similar to Step III), the phase difference Δβ would be held between the latent gratings of Areas 3 and 2, 4 and 3..., i.e. the accumulative error.
According to the above self-referencing method, a 1 × 2 mosaic includes three times of locking the L fringes (during the second exposure, the transfer of the fringe-locking, and the third exposure) and two times of adjusting the boundaries of the L fringe pattern (before the transfer of the fringe-locking and the third exposure). Therefore the achieved phase and attitude accuracies are
3. Experimental results
3.1 Mosaic results
We made several 1740 l/mm mosaic gratings on 100 × 200 mm2 quartz substrates, on which are coated a chromium film and a photoresist layer both of 100 nm thick, and used a 100-mm-diameter interferometer to measure their −1st-order diffraction wavefronts.
Figure 3(a) shows a large-aperture 1 × 2 mosaic grating of 90 × (80 + 80) mm2 in area, with the exposure intensity of 1.6 lx and the single exposure time of 20 min for simulation of making meter-size gratings. The PV and RMS (root-mean-square) errors of the −1st-order diffraction wavefront around the seam are 0.087 λ and 0.018 λ, respectively. Besides, the PV errors for the +1st- and 0th-order are 0.072 λ and 0.059 λ, respectively. This large-aperture, long-time and weak-intensity mosaic result verified the accuracy and stability of the method.
Figure 3(b) shows a small-aperture 1 × 4 mosaic grating of 50 × (30 + 30 + 30 + 30) mm2 in area, with the exposure intensity of 24 lx and the single exposure time of 1 min. The PV and RMS errors of the overall −1st-order diffraction wavefront are 0.060 λ and 0.012 λ, respectively, and all fringes in the interferogram are in phase. This 1 × 4 mosaic result confirmed the remarkable reduction of accumulative error.
For these mosaic results, considering that the wavefront error consists of the exposure aberration, the substrate flatness error and the mosaic error, the last one is hardly perceived. In accordance with the above mosaic sizes, we have made two 1 × 4 and twelve 1 × 2 small-aperture mosaics and five 1 × 2 large-aperture mosaics. The −1st-order PV errors are not more than 0.06 λ for all the small-aperture mosaics and less than 0.1 λ for all the large-aperture mosaics, and are subequal to the ones of single exposed gratings.
3.2 Protection to the latent grating
Between different exposure areas, there are vertical narrow seams, typically less than 0.5 mm. In addition to this, owing to the good protection by the wedged attenuators, the areas for generating L fringes could not be distinguished from the rest uniform mosaic area (ordinary area). This is confirmed by SEM results (Fig. 4 and Table 2 ) showing uniform groove shapes from these two kinds of areas. These SEM samples are made on slides. The transmittivity of A1 is larger than that used for mosaic.
We propose and demonstrate a self-referencing alignment technique to conveniently make large-area mosaic gratings by combining the exposure, adjustment and fringe-locking functions into a compact system. The adjustment and locking of the exposure beams relative to the latent grating eliminates the random attitude and phase errors caused by different drifts between the reference grating and the substrate, and unpredictable errors generated from other indirect measuring and controlling techniques. The transfer of fringe-locking eliminates the accumulative attitude and phase errors produced by the drift of the exposure system between the first exposure and the following exposures. The protection of the latent grating is done well by employing two wedged attenuators and EMCCD, achieving the adjustment and even locking of the exposure fringes to the latent grating.
This low-cost cross-scale interference lithography technique is expected to be used for fabricating many kinds of periodic structures and generalized into other nanofabrication methods. Currently we are investigating one-dimensional gratings for pulse compression and two-dimensional gratings for length metrology. For other periodic structures such as two-dimensional photonic crystals, if the diffraction from the latent image is strong enough to be detected by EMCCD, this technique can be applied to enlarge the fabricated area. The way to increase the diffraction efficiency includes thickening photoresist and employing material with higher refractive-index contrast after exposure. Besides, the orders other than the −1st- and 0th could also generate interference fringes for alignment, e.g. the (−1,1)th and (0,1)th orders for two-dimensional gratings.
The work was supported by the National High Technology Research and Development Program of China, and the National Natural Science Foundation of China under Project No. 90923034.
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