Zone-Plate-Array Lithography (ZPAL):Simulations for System DesignRajesh Menon*, D. J. D. Carter+, Dario Gil*, and Henry I. Smith**Department of Electrical Engineering and Computer Science, Massachusetts Institute of technology,Cambridge, MA 02139.+Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139.Abstract. We present a simulation study which examines the use of zone plates for lithography.Zone-Plate-Array Lithography (ZPAL) is a maskless lithography scheme that uses an array ofshuttered zone plates to print arbitrary patterns in resist on a substrate. We have demonstrated aworking ZPAL system in the UV regime, and are pursuing further experiments with the 4.5 nmX-ray to obtain smaller feature sizes. A general numerical simulation tool, based on the Fresnel-Kirchhoff diffraction theory, has been developed. A pattern will consist of many pixels exposedindependently in the resist. Various zone plate and system parameters will affect the intensitydistribution at the focal plane. We present simulation results which show the effect of theseparameters on both the individual spots and exposed patterns.INTRODUCTIONZone-plate-array lithography (ZPAL) is a maskless lithography scheme thatemploys an array of shuttered zone plates to expose patterns of arbitrary geometry ona resist-coated substrate [1-4]. It is illustrated schematically in Fig. 1. By using anarray of zone plates, and independently controlling their illumination while movingthe substrate, one can achieve parallel writing in a dot-matrix fashion.ZPAL borrows heavily from the field of X-ray microscopy, which over the last twodecades has greatly advanced the technology of fabricating zone plates. Zone plateswith minimum outer zone widths of sub-25 nm have been fabricated [5], and it is notunreasonable to expect that this will be further reduced in the future. Because the focalspot or point-spread-function of a zone plate is approximately equal to the width of theoutermost zone, we believe that ZPAL can approach the limits of the lithographicprocess. For the lithography application we believe the optimal wavelength is 4.5 nm,i.e. just beyond the carbon-K edge. The 4.5 nm photon can be used to expose thickfilms of carbonaceous resist, while minimizing the proximity effects due tophotoelectrons [6,7]. In fact, back in the late 1970’s D. C. Flanders demonstrated thatlines and spaces of 18 nm can be exposed in PMMA using CK X-ray lithography in acontact mode [8]. Similar results have been obtained in the intervening years [9-12].The main disadvantage of ZPAL at 4.5 nm wavelength is the necessity of using anundulator or similar collimated source of narrow-band radiation. However, suchsources are clearly feasible [13]. The main challenges to developing ZPAL are themultiplexed shuttering of the illumination to individual zone plates, and the problemof matching the efficiencies of all the zone plates of a large array. To address thisproblem of multiplexing, and our inaccessibility to an undulator, we have insteadpursued ZPAL at UV wavelengths. In addition, we have developed ZPAL simulationtools which enable us to evaluate a variety of tradeoffs among such system and zoneplate parameters as: source bandwidth, number of zones, fabrication errors, effects oforder-sorting apertures, and number of zones per array vs. multiplexing rate.FocusedBeamletZonePlateWaferWafer Scane.e. moonResistUpstream micromechanics (not shown)FIGURE 1. Schematic of zone-plate-array lithography (ZPAL). An array of zone plates focusesradiation beamlets onto a substrate. The individual beamlets are turned on and off by upstreammicromechanics as the substrate is scanned under the array. In this way, patterns of arbitrary geometrycan be created with a minimum linewidth equal to the minimum width of the outermost zone of thezone plates. Using 4.5 nm radiation, we estimate that lines and spaces of 20 nm should be achievable,provided that the zone plates can be fabricated.THEORYFresnel-Kirchhoff diffraction theory [14-16] is used to calculate the point-spread-function of a zone plate. Scalar theory is suitable at the 4.5 nm wavelength since zonewidths are much larger than the wavelength. However, at UV wavelengths, where wehave done most of our experiments, the use of scalar theory is subject to question.Because the exposure of any arbitrary pattern is made up of separately exposed focalspots (pixels), we calculate the intensity distribution for any given pattern by addingthe intensities of point-spread-functions. For simplicity, a binary clipping level wasused to model the resist development.The solution of the exposure/development simulation was implemented on an IBM-SP2 with 10 parallel processors. A Single Instruction Multiple Data (SIMD) model ofparallelization was utilized in these simulations [17]. We can break up the problemspatially into numerous points, which are divided up among the available processors.Each processor then computes the phase and amplitude of the diffracted wave at itsassigned group of points. In this scalar model, the field at each point is independent ofits neighbours and hence, inter-processor message passing is not necessary. Thus ourproblem is an obvious candidate for the SIMD parallel-processing model.SIMULATONSFig. 2 compares a simulated spot compared to spots exposed in resist. Phase zoneplates, with an outer zone width of 331 nm were used at an exposure wavelength of λ= 442 nm. The simulation tools took into account a 10% measured phase-shift errordue to over-etching of the quartz during fabricaton. Despite the well- knowninadequacy of scalar diffraction theory when wavelengths are comparable to orsmaller than zone widths, our simulations come quite close to experimental results.This may reflect the fact that line-to-space ratios are close to unity near the outer zones[18].354 nm800 400 0 400 80000.20.40.60.81Radial distance (nm)Intensity (arb.) Spot Size = 354 nm @ clipping level = 0.42(a) (b)FIGURE 2. (a) Focal spots exposed and developed in photoresist, using the 442 nmwavelength HeCd laser, and zone plates fabricated in fused silica using direct-write e-beamlithography and reactive-ion etching. Zone plates of the array have 76 zones. They wereetched within 10% of the π-phase depth. (b) Simulated point-spread-function for these zoneplates, illustrating that a clipping level of 0.42 would produce the 354 nm diameter spot. Thezone plates have a numerical aperture of