The Talbot effect is utilized for micro-fabrication of periodic microstructures via proximity lithography in a mask aligner. A novel illumination system, referred to as MO Exposure Optics, allows to control the effective source shape and accordingly the angular spectrum of the illumination light. Pinhole array photomasks are employed to generate periodic high-resolution diffraction patterns by means of self-imaging. They create a demagnified image of the effective source geometry in their diffraction pattern which is printed to photoresist. The proposed method comprises high flexibility and sub-micron resolution at large proximity gaps. Various periodic structures have been generated and are presented.
©2010 Optical Society of America
Every light distribution which is periodic in one plane gives rise to a periodicity in space. More precisely, an arbitrary one- or two-dimensional periodic structure will reproduce its geometry via diffraction in a certain plain behind it, if it is transilluminated by a plane wave. This circumstance was pointed out frist by H. F. Talbot in 1836  and is referred to as self-imaging or Talbot effect. In the special case of a periodic pinhole array, an array of bright spots will be created in a characteristic distance behind the structure. Since a self-image is obtained, the spot size equals the pinhole size in the array. Investigations by Kolodziejczyk  show, that the optical function of pinhole arrays can be compared to a set of lenses. This point of view highlights a second imaging property: In analogy to a lens array, a periodic pinhole array is able to generate multiple images of extended objects. This is true for both, spatially coherent and incoherent illumination [3,4]. To sum up, the diffraction pattern of a pinhole array can easily be predicted and provides high resolution. By imaging of extended objects, various periodic diffraction patterns can by created by on and the same pinhole array. Due to these interesting properties, diffraction effects on periodic geometries (and especially on pinhole arrays) are well suited to find application in the fabrication of periodic microstructures.
Jaroszewicz et al. fabricated 200µm pitched microlens arrays by imaging a grayscale picture which defines the lens shape with a pinhole array . Suleski et al. reported the possibility to copy gratings with 400µm period by means of self-imaging . In the current paper we present an application of pinhole arrays in mask aligner lithography where they can be used for large-gap high-resolution printing of periodic structures. Our approach is similar to the work of Jaroszewicz and Suleski. The advantage of our proposed method is the use of a well-established technology which includes the described techniques but can be extended down to small pitched structures and sub-micron resolution in an industrial fabrication environment.
Proximity lithography in a mask aligner is a cost-efficient and widely used technology suitable for the manufacturing of microstructures on wafers. In mask aligner lithography, the mask pattern is transferred by shadow printing. In order to avoid mask damage and to increase the processing speed, photomask and wafer are aligned using a gap of 30µm to 200µm. In this regime, diffraction effects during the free space propagation from mask to wafer can result in a significant derivation between mask pattern and aerial image. However, the occurring diffraction effects do not necessarily lead to information loss and can be used via adapted mask features in a well-directed way. To do so, it is required to understand the aerial image as a diffraction pattern which is influenced by mask features, the angular spectrum of illumination and the coherence properties of the light source. A straightforward approach in this consideration is the use of a periodic pinhole array photomask which is generating a predictable diffraction pattern of bright spots by means of self-imaging under plain incidence. By use of an extended source, the intensity profile within one period is determined by the source geometry.
In conventional mask aligners, the geometry of the effective light source which corresponds to the angular spectrum of illumination is defined by the geometry of its macroscopic optical set-up and cannot be changed. Recently, a novel illumination system, referred to as “MO Exposure Optics” [7,8], was introduced for SUSS MicroTec mask aligners. Besides improved homogeneity and telecentricity of the mask illumination, MO Exposure Optics provides the opportunity to determine the effective source shape by mechanical filter plates. This additional degree of freedom is the key for the use of the Talbot effect by means of pinhole arrays in mask aligner lithography.
In the presented work, we use periodic pinhole arrays in order to prove that periodic structures with an arbitrary unit cell can be created with high-resolution in large proximity gaps. At first, the modeling of the mask aligner set-up is described and basic equations are given. Subsequently, experimental results are discussed in detail.
This publication is part of a series on advanced mask aligner lithography using “MO Exposure Optics”. Another issue describes the novel illumination system in detail .
2. Model of the lithography set-up
The optical model of a mask aligner exposure set-up based on MO Exposure Optics consists of three planes  and is depicted in Fig. 1 . A metallic aperture, referred to as Illumination Filter Plate (IFP), which is transilluminated by secondary point sources is located in the aperture plane. It forms an effective light source of variable geometry. The distribution of secondary point sources is created by a preliminary optical system. It consists of a Mercury-vapor lamp, an elliptical mirror which redirects the light, a micro-optics based Köhler-integrator which homogenizes the light and a second double sided microlens array which generates a distribution equal to secondary point sources out of it. The functionality of the illumination system is described in detail by Voelkel et al. . Due to the large extension of the real source and the actual system geometry, virtually no spatial coherence is created by the preliminary optical system. In conclusion, the secondary point sources can be modeled to be totally incoherent. Behind the aperture plane, a system of two lenses with equal focal length f (approx. 500mm to 1000mm depending on the system) is situated. The second lens is located in the focal plane of the first lens. Such a system performs an optical Fourier transform of the field in the principle plane of the first lens to the principle plane of the second lens. The first lens is located in close proximity to the aperture plane and the second lens just in front of the mask plane. Accordingly, the mask is illuminated by the optical Fourier transform of the effective source geometry. Since the secondary point sources are considered to be incoherent to each other, the Fourier transform can be evaluated independently for every point source. Each secondary point source is characterized by its distance to the principal axis of the system. The Fourier image of a point-like source which is displaced from the principal axis corresponds to a tilted plane wave. The more the source is off-axis, the more the tilt of the plane wave increases. By adding up the contributions from all source points, an angular spectrum of plane waves is created in the mask plane. Each component of this spectrum corresponds to a position in the effective source. Hence, the aperture geometry determines the composition of the angular spectrum of illumination. Since all generating source points are incoherent to each other, the same is true for the corresponding plane waves. To sum up, the described mask aligner illumination set-up can be considered to be a device which creates a set of non-interacting plane waves. The composition of angular components is selected by the shape of a metallic aperture (IFP).
In the mask plane, a periodic array of square pinholes with pitch p and feature size w is placed. An air gap separates the photomask and the resist coated wafer. The size of this gap is typically called proximity distance d. Being modulated by the mask pattern, the light propagates in free space until the photo resist is reached. Thereby, diffraction phenomena occur. If the special case of normal monochromatic incidence with wavelengthλ is considered and the Talbot distance10]. Figure 2 provides a simulation of the described situation.
In the next step, an angular spectrum of plane waves, which illuminates the mask, is considered. Due to the design of the mask aligner illumination system, only small angles of tilt are created in the mask plane (up to 3°). Hence, each plane wave component generates a similar diffraction pattern after free space propagation. However, due to the oblique incidence, every diffraction pattern will exhibit a lateral shift which corresponds to the actual angle and that way to the position of the generating coherent area in the aperture plane. Since only small angles are involved in the mask aligner set-up, the shift relation shows a linear behavior. Beyond that, different angular components are not coherent to each other, which implicates that the associated diffraction patterns add up in terms of intensity. The incoherent superposition of a linear shifted basic pattern leads to a scaled replication of the aperture (IFP) geometry in the overall intensity distribution. In other words, multiple images of the effective source geometry are created in the resist plane. This result has already been indicated in Fig. 1. By simple geometrical considerations, the scaling of the aperture geometry obeys the relation
In the following paragraph, the theoretical and practical limitations of the method will be discussed. The resolution limit for the source geometry replication is given by the width of the diffraction pattern which the pinhole array creates under normal incidence. Due to the self-imaging property, it is approximately equal to the mask feature w. However, this is only valid for pinholes which have apertures larger than the exposure wavelength. Further shrinking will reduce the intensity in the diffraction pattern but will not result in a higher resolution. Consequently, to obtain the best resolution, pinhole apertures with a size in the order of the wavelength are most desirable. However, the intensity in the diffraction pattern will also scale with the pinhole size. A combination of a large pitch and small pinholes will lead to long exposure times. In praxis, a trade-off between space bandwidth product (resolution per pitch) and exposure time has to be made. Periodic phase elements can provide a loophole for this limitation. They are discussed in the outlook section.
Besides resolution, the depth of focus (DOF) is an important parameter for photolithography. The depth of focus in air, which can be assigned to a self-image of a pinhole array, can be roughly estimated to be equal to the array pitch p. Sub-micron pinhole apertures give rise to a slightly lower DOF, large apertures increase it. Since the refractive index of photoresist is comparably large (a typical value is 1.8), the depth of focus is reduced by this factor in praxis. The stated estimation leads to a general tread-off between resist thickness and mask pitch. Furthermore, it has to be considered, that vacuum-chuck, wafer and resist film are not perfectly flat in general. Hence, there is a minimum of DOF (or pitch respectively) which can be used in a reproducible process over large areas. Experiments show, that a pitch of 5µm is uncritical in praxis. Prints with 2µm pitch are still challenging. However, besides the described limitations, the proposed method features significant benefits compared to conventional proximity lithography. One advantage of the method is the great flexibility. Using a single pinhole photomask and a set of different apertures (IFPs) numerous periodic structures can be created. Thereby, the costs for a new aperture are due to the low demands on resolution significantly smaller than the costs of a new photomask. However, the main advantage of the proposed method is its high obtainable resolution, which is approximately on order of magnitude better than in conventional proximity lithography. In the later case, the resolution in dependence on the gap can be approximately calculated by 
Accordingly, a 60µm gap corresponds to a resolution of approximately 4.5µm and 100µm to 6µm respectively (i-line illumination, 365nm assumed). The resolution in the case of a pinhole array is virtually independent on the gap size as discussed above. A resolution of 600nm in conjunction with 66µm gap and 5µm pitch as well as 800nm in conjunction with 98µm gap and 6µm pitch has been demonstrated experimentally.
3. Experimental results
Based on the described concept, different periodic patterns have been evaluated and realized in praxis. The experiments were carried out on SUSS MicroTec mask aligners of type MA8 and MA6 equipped with “MO Exposure Optics” . For alignment and exposure, the proximity mode in combination with three-point wedge error compensation was used. As the Talbot distance is depending on the wavelength, self-images without distortions can only be generated via monochromatic illumination. Due to this fact, the illumination was restricted to the Hg i-line (365nm). The used pinhole arrays were realized by electron beam written chromium masks based on 5” fused silica substrates. The structures have been generated on 4” Silicon wafers spin-coated with different kinds of AZ photoresists (Clariant).
In addition to the description in section 2, fractions or multiples of the Talbot distance can be used for the exposure gap, as well. In rectangular symmetry, half the Talbot distance is generating an identical self-image, shifted by half the pitch of the pinhole array on the mask. If this circumstance is regarded in mask design, such gaps can be used without restrictions. Increasing the gap by adding multiples of the Talbot distance will cause a slight resolution loss but reproduces the same diffraction pattern. However, the scaling of the aperture replication is depending on the gap size in a linear way. Thus, it will change for different multiples or fractions of the Talbot distance. Using the Eqs. (1) and (2), an adequate combination of mask pitch, aperture size, and proximity distance can be obtained. To generate the structures described below, the parameters have been selected in order to compromise a preferably large aperture (IFP) in combination with a proximity distance in the range of 60µm to 100µm.
According to the basic example stated in Fig. 1 a periodic arrangement of a “F” pattern with 5µm pitch has been generated in 66µm proximity distance. Figure 3(a) shows the macroscopic metal aperture which defines the F-shaped angular spectrum of illumination. The photomask layout which consists of a pinhole array with 5µm pitch and 600nm width square features is shown in Fig. 3(b). A scanning electron micrograph of the generated pattern in photoresist is presented in Fig. 3(c). Half of the Talbot distance was selected for the proximity gap in this exposure. The scale of the pictures in Fig. 3 illustrates the large demagnification of the IFP geometry (approximately 7500X in the given configuration) which is performed by the set-up. The minimum feature size of the resist pattern is in the range of 600nm which matches the theoretical expectations since 600nm pinholes have been used. By reactive ion etching (Bosch process) the resist pattern has been transferred into the silicon substrate. A scanning electron micrograph of the structured silicon surface is shown in Fig. 3(d).
A significant corner rounding is noticeable in Figs. 3(c) and 3(d) respectively. This circumstance is not caused by diffraction effects but rather by insufficient light homogeneity in the plane of the secondary point sources in Fig. 1. Measurements show, that the intensity distribution in the aperture plane dips significantly in the boundary area. Hence, features in this area give rise to a lower intensity on the photoresist and lead to a rounding effect. This can potentially be compensated by assist features (referred to as Optical Proximity Correction OPC). However, the smarter way of correction would be an improved light homogeneity in the plane of the secondary point sources. In the case of a totally homogenous illumination level, a corner rounding which corresponds to the exposure wavelength would remain. This is a physical limit.
Similar exposures have been carried out with a star shaped IFP in combination with a pinhole array of 6µm pitch. Figure 4 shows the aperture geometry and the corresponding pattern etched into silicon. To generate the pattern shown in Figs. 3 and 4 different mask aligners have been used. A larger focal length of the Fourier lens is causing a stronger demagnification in the case of Fig. 4. Due to the strong downscaling in combination with comparably large mask features of 800nm the aperture geometry is not fully resolved in Fig. 4(b).
The described way of periodic pattern generation is not only working for masks with rectangular symmetry. Hexagonal layouts  or grating structures  can be used in analogy. This way, a periodic arrangement of 800nm lines with 6µm pitch has been realized in 98µm proximity distance. Figure 5 shows the IFP, the mask layout and the scanning electron micrograph of the lines etched into silicon.
Mask aligner based proximity lithography is a well-engineered technology which is widely-used by research and industry. A new illumination system for mask aligners, referred to as “MO Exposure Optics”, now provides excellent uniformity of the illumination light and allows at the same time shaping the angular spectrum of illumination. The Talbot effect describes a classical diffraction phenomenon and the corresponding imaging properties of pinhole arrays have been investigated in the past. By combining these two fields of technology and research, it was possible to develop a new method for periodic pattern generation which comprises convenient processing conditions, a high obtainable resolution, and great flexibility.
We have presented a theoretical description which reduces the optical functionality of the considered mask aligners to incoherent plane wave set generation. Under plain incidence, periodic pinhole arrays are generating spot arrays in characteristic distances. Expanding the illumination to an incoherent plane wave set which corresponds to an extended effective source, every angular component is generating such a spot array. Due to the difference in incidence angle, the diffraction pattern of different angular components will be shifted laterally. That way, multiple images of the effective source geometry are formed which are strongly demagnified. In consequence, periodic light distributions with arbitrary unit cell shape can be created. Compared to conventional proximity lithography, the proposed method provides significant benefits. The obtainable resolution is increased by approximately on order of magnitude and due to the pattern definition via effective source geometry numerous periodic structures with equal pitch but different unit cell can be created with a single pinhole photomask.
Applying the proposed method, various binary periodic structures with 5µm and 6µm pitch have been generated using pinhole array photomasks. Depending on the actual design, the obtained resolution was in the range of 600nm to 800nm in proximity distances of 60µm to 100µm. An excellent conformity between modeling predictions and experimental results has been achieved.
The presented work should be considered as prove of principle that diffraction driven mask aligner lithography works well and offers high resolution in convenient processing conditions.
Concerning periodic pattern generation, the application of the Talbot effect is probably the best way to obtain high-resolution diffraction patterns and the unit cell control via multiple source imaging offers great flexibility in terms of mask reutilization. In this sense, the use of pinhole arrays is only a first step. Periodic phase structures referred to as Talbot Array Illuminators (TAILs)  are able to generate similar self-images like pinhole arrays with much better efficiency. However, these devices have been originally designed for applications in optical communication and are not able to create a very high opening ratio (ratio of pitch divided by spot diameter, corresponds to space bandwidth product) with a single phase level. An obtainable ratio of five to one with a single phase level has been reported . For high resolution printing the use of multilevel [15–17] or continuous [18,19] phase profiles seems to be more promising.
So far, only binary periodic structure fabrication has been discussed. Following the work of Jaroszewicz et al. , the described method can probably be extended to the generation of periodic grayscale structures like blazed gratings or lenses. In the diffraction pattern, a strongly demagnified image of the aperture geometry is created. That way, it will likely be possible to encode half tone gray levels similar to the work of Reimer et al.  in the aperture plane which will not be resolved in the diffraction pattern. Generating one dimensional grayscale structures is even simpler since a grey level coding can be utilized in the direction of the grating lines. This direction will be averaged in the diffraction pattern.
In any case, not only periodic structures are important in praxis. Simulations and theoretical considerations related to this work show that a dedicated shaping of the angular spectrum of illumination is important in every proximity exposure. By combination of diffractive masks in conjunction with an adapted illumination, it will likely be possible to push the mask aligner based proximity lithography far beyond its classical limits.
The authors would like to thank Martin Eisner, Giovanni Bergonzi and Thomas Käsebier for performing the reactive ion etching and resist stripping as well as Tino Benkenstein for designing some of the mask aligner IFPs. Furthermore, the authors are grateful to the anonymous reviewers for there useful advices.
References and links
1. H. F. Talbot, “Facts Relating to Optical Science, No. IV,” Philos. Mag. 9, 401–407 (1836).
2. A. Kolcodziejczyk, “Lensless multiple image formation by using a sampling filter,” Opt. Commun. 59(2), 97–102 (1986). [CrossRef]
3. O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am. 63(4), 416–419 (1973). [CrossRef]
4. A. Kolodziejczyk, Z. Jaroszewicz, R. Henao, and O. Quintero, “The Talbot array illuminator: imaging properties and a new interpretation,” J. Opt. A, Pure Appl. Opt. 6(6), 651–657 (2004). [CrossRef]
5. Z. Jaroszewicz, A. Kolodziejczyk, and M. Sypek, “Microlens array produced with the help of the sampling filter,” Opt. Eng. 37(11), 3002–3006 (1998). [CrossRef]
6. T. J. Suleski, Y.-C. Chuang, P. C. Deguzman, and R. A. Barton, “Fabrication of optical microstructures through fractional Talbot imaging,” Proc. SPIE 5720, 86–93 (2005). [CrossRef]
7. R. Voelkel et al.., “Advanced mask aligner lithography: New illumination system,” Opt. Express (to be published). [PubMed]
8. R. Voelkel, U. Vogler, A. Bich, K. J. Weible, M. Eisner, M. Hornung, P. Kaiser, R. Zoberbier, E. Cullmann, “Illumination system for a microlithographic contact and proximity exposure apparatus,” EP 09169158.4, (2009).
9. T. Harzendorf, L. Stuerzebecher, U. Vogler, U. D. Zeitner, and R. Voelkel, “Half-tone proximity lithography,” Proc. SPIE 7716, (2010).
10. J. T. Winthrop and C. R. Worthington, “Theory of Fresnel Images. I. Plane Periodic Objects in Monochromatic Light,” J. Opt. Soc. Am. 55(4), 373–381 (1965). [CrossRef]
11. C. Mack, Fundamental principles of optical lithography (John Wiley & Sons, 2007), Chap. 1.
12. W. Wang, and H. Zhu, “Near-field diffraction of a hexagonal array at fractional Talbot planes,” Proc. SPIE 7506, (2009).
14. V. Arrizón and J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112(5-6), 271–277 (1994). [CrossRef]
16. H. Hamam, “Design of Talbot array illuminators,” Opt. Commun. 131(4-6), 359–370 (1996). [CrossRef]
17. A. Kolodziejczyk, Z. Jaroszewicz, A. Kowalik, and O. Quintero, “Kinoform sampling filter,” Opt. Commun. 200(1-6), 35–42 (2001). [CrossRef]
18. E. Bonet, P. Andrés, J. C. Barreio, and A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106(1-3), 39–44 (1994). [CrossRef]
19. B. Besold and N. Lindlein, “Fractional Talbot effect for periodic microlens arrays,” Opt. Eng. 36(4), 1099–1105 (1997). [CrossRef]
20. K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, “Micro-optic fabrication using one-level gray-tone lithography,” Proc. SPIE 3008, 279–288 (1997). [CrossRef]