Photolithography experiments using forced Rayleigh scattering M. D. Levenson Citation: Journal of Applied Physics 54, 4305 (1983); doi: 10.1063/1.332665 View online: http://dx.doi.org/10.1063/1.332665 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/54/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Study of thermal transport in nanoparticle suspensions using forced Rayleigh scattering J. Appl. Phys. 100, 094310 (2006); 10.1063/1.2360378 Measurement of mass diffusion coefficients using nonexponential forced Rayleigh scattering signals J. Chem. Phys. 109, 267 (1998); 10.1063/1.476560 Thermodiffusion in polymer solutions as observed by forced Rayleigh scattering J. Chem. Phys. 98, 660 (1993); 10.1063/1.464610 Measurement of the thermal diffusivity of liquids by the forced Rayleigh scattering method: Theory and experiment Rev. Sci. Instrum. 59, 1156 (1988); 10.1063/1.1139743 Dye diffusion in swollen gels by forced Rayleigh scattering J. Appl. Phys. 53, 6513 (1982); 10.1063/1.330077 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.209.6.50 On: Mon, 22 Dec 2014 18:47:21 Photolithography experiments using forced Rayleigh scattering M. D. Levenson IBM Research Laboratory, San Jose, California 95193 (Received 31 January 1983; accepted for publication 13 April 1983) Phase conjugate wavefront generation by degenerate four-wave mixing has been used to project images with spatial resolution greater than 500 line pairs per millimeter. The nonlinear medium, a solution of rhodamine 6G in acetone, produced the images by forced Rayleigh scattering. These images were bright enough to expose photoresist in 30 sec and their quality was adequate for fineline lithography and consistent with theoretical expectations. PACS numbers: 42.65.Cq, 42.30. - d, 85.40.Mt INTRODUCTION In previous experiments, we showed that the images projected by phase conjugate wavefront generation by degenerate four-wave mixing have resolution sufficient for fine-line lithography. 1.2 Those experiments employed cw ion lasers with high quality TEMoo output beams but relatively low average power. The conjugator materials available in large optical quality samples could not project bright images in configurations compatible with high resolution when pumped with such lasers. Literally hours were required to project each l-cm2 chip image. Other experiments showed that forced Rayleigh scattering could produce conjugate beams with reflection efficiency up to 300% at the pump intensity levels characteristic of unfocused rare gas halide laser beams. 3•4 We found that reflection efficiencies of several percent could be obtained in a geometry theoretically consistent with high resolution. 5 The purpose of the experiments reported here was to verify that images ofsufficient quality and brightness for line lithography could, in fact, be projected by forced Rayleigh scattering. The light source employed was the l-W average power third harmonic of an available Nd:YAG laser. Average power levels two orders of magnitude greater are possible with specially engineered ultraviolet sources. The conjugator medium was an absorbing liquid solution of rhodamine 6G dissolved in acetone. The geometry as shown in Fig. 1 was very similar to that employed in the cw laser experiments. 2 We found image resolution in one dimension up to 800 lines per millimeter and verified this by scanning electron microscope inspection of developed photoresist films. Image brightness was sufficient to properly expose 1cm2 images in 2-12 min. The high peak powers characteristic of our pulsed laser source led to various difficulties, including damage to the mask and beam splitter cube, but no unexpected degradation of the image was detected. With higher pump power and more refined optical engineering, lithographic exposure by conjugate wavefront generation could be made practical. In the second section of this paper, we describe the desing ofour prototype exposure system and the considerations that lead to the final design. The third section describes the operation of this system along with the photoresist coating and developing procedures. The fourth section discusses our experimental results and difficulties. The final section delineates our proposals for a practical production camera. APPARATUS The laser in our experimental image projection system was a Quanta-Ray DCR-IA Nd:YAG unstable resonator system equipped with "filled-in" beam optics and an electronically controlled Q-switch. This laser had a cavity length of 120 cm and operated with several axial modes but gave adequate coherence length when the electronically controlled Q-switch was used without an intracavity etalon. The amplified output was converted to the third harmonic at 355 nm in the standard way with two KD*P crystals, and the horizontally polarized third harmonic beam was separated from the fundamental and second harmonic with two equilateral prisms. The average power of the third harmonic at the prisms was typically 1.2 W at 10 pps; a lO-ns pulse width implied a peak power of 12 MW. While the third harmonic beam did not have the dark hole characteristic of diffraction coupled resonators, it did develop an intense central spot downstream which was capable of damaging optics. To smooth the beam profile, the third harmonic was focused with a 50-cm focal length lens into an evacuated cell containing a 150-,um-diam tungsten carbide aperture. The transmitted portion (typically 60%) was recollimated by a second 50-cm focal length lens and Flow cell mirror Compensator plate k-----,n~~wafer - _-. "Exposure v- meter Optically contacted beam splitter cube i Illuminating beam FIG. I. Schematic of the forced Rayleigh scattering projection lithography apparatus. The faces of the beam splitter cube were 20 mm square, and the compensator plate was roughly 0.6 mm in thickness. Otherwise, the figure is roughly to scale. Not shown are the laser source and optics necessary to reshape and direct the beams. 4305 J. Appl. Phys. 54 (8), August 1983 0021-8979/83/084305-09$02.40 © 1983 American Institute of Physics 4305 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.209.6.50 On: Mon, 22 Dec 2014 18:47:21 split into pump and illuminating beams. The pump was compressed in the horizontal plane with two 45° prisms oriented away from the angle of minimum deviation. The pump beam was reflected into the conjugator medium, as shown in Fig. 1, entering at about Brewster's angle. The illuminating beam was directed onto the mask and hence through a beam splitter onto the conjugator cell. At the cell, the pump beam was rectangular in cross section with dimensions 3.3 and 3.9 mm in the horizontal and vertical directions and had average power of 280 mW. At the mask the illuminating beam dimensions were 7.5 X 4.0 mm with average power of 58 mW. The pump beam traversed the 2-cm-thick conjugator cell at an angle of roughly 35° from the normal and was reflected back through the cell by a retromirror mounted on an NRC precision differential mount. The direction of the retroreflected pump beam was exceedingly critical; a deviation of a few microradians in the horizontal plane reduced the phase conjugate reflectivity essentially to zero. The Brewster's angle pump geometry was chosen over a 90· geometry in which the pump and object beams would enter through different faces of a rectangular conjugator cell because of the greater toleration of the Brewster's angle geometry for pump beam misalignment. The mask consisted ofa pattern ofapertures etched into 700 A of bright chrome deposited on a UV grade quartz substrate. Similar chrome-on-glass films without etched apertures had shown damage thresholds well above the intensity levels produced in these experiments. Nevertheless, mask damage continued to be a serious issue throughout the program. The diffraction pattern produced by the mask was directed into a quartz beam splitter cube. Since the open area of the mask was at most a few percent of the total area, and since the widest apertures were 10 f-l or so across, the power and intensity at the reflective beam splitter surface were much lower than at the mask. Even so, we found that the nominally transparent cements used to hold the two prisms forming the beam splitter tended to damage. Damage to the beam splitter could be avoided by eliminating the optical cement and substituting an optically contacted beam splitter for the cemented cube. The technology of optical contacting does not permit precision assembly, and the optically contacted beam splitters that we were able to obtain were hardly cubes. The two prisms that had been contacted along their hypotenuses were found to have been translated along the diagonal making the beam splitter more a rectangular parallelepiped than a cube (see Fig. 1). This asymmetry of the beam splitter is serious, because wavefront conjugation cancels all optical aberrations except those introduced by the beam splitter. The different ray paths for object waves reflected by the beam splitter and conjugate image waves transmitted through the partially reflecting surface introduces an uncompensated spherical aberration. Figure 2 shows how this aberration arises. The diagram at the top shows the input surface of the beam splitter cube and the rays emanating from an object point. The phase conjugator reverses these rays to form the image, but if the actuallocation of the output face of the beam splitter is as shown by the lower diagram, the Snell's law refraction at the surface Object rays Input face of beam splitter Object plane n=l Conjugate rays Output face : Image I plane I I I Spherical I aberration I White light fringe plane FIG. 2. Ray traces showing the effects of asymmetry in the beam splitter. Rays originating at an object on the mask are shown at top. The effect of the partially reflecting surface of the beam splitter have been omitted from the drawing, and the only influence of the beam splitter is to refract the rays at the surface. Conjugate wavefront generation produces rays inside the beam splitter that propagate along paths near the output face that are identical to those near the input face. Displacement of the output face from a position symmetric with the input introduces unwanted optical effects. The displacement.1Z shifts the plane of best focus and the white light fringe plane used as a focusing reference, as well as creating spherical aberration and magnification error. prevents the image rays converging to a point. In addition, the image point location is translated from the phase conjugate point, thereby introducing a magnification error. The plane of white light fringes (which we have used as a reference plane to facilitate focusing) is also deviated from the image plane. Ray tracing calculations show that, if the difference in perpendicular distances from a point on the hypotenuse to the two surfaces is ..1Z, the translation of the paraxial focus position is ..1 ZnB'sl, where nBS is the index of refraction of the beam splitter cube, and the longitudinal spherical aberration for a ray at N.A. = 0.2 is 7.6X 10-3 ..1z. The white light fringe plane is translated by (nBS - nssl)..1Z from the actual paraxial focus and the magnification error is..1Z (nBS t )-1 where t is the total optical length between the object plane and the conjugator medium. The beam splitters that we had obtained had an asymmetry of ..1Z = 610 f-l, which implied unacceptable values for the spherical aberration, magnification and paraxial focus displacement. To correct the aberration as much as possible, we added a fused silica compensator plate of thickness 595 f-l between the wafer and beam splitter, as shown in Fig. 1. With this compensator, we found that the white light fringe plane was deviated by 34 f-l from the focal plane, which implies that the remaining optical asymmetry is ..::1Z = 40 f-l. The uncorrected longitudinal spherical aberration at N.A. = 0.2 is then 0.3 f-l, the magnification error expected is ..::1M = 4 X 10-4 , and the transverse spherical aberration (which might limit the resolution) is 0.05 f-l. The medium producing the conjugate wave was a solu- tion of Rhodamine 6G perchlorate in acetone. This medium shows virtually no saturation of the absorption at the wave- 4306 J. Appl. Phys., Vol. 54, No.8, August 1983 M. D. Levenson 4306 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.209.6.50 On: Mon, 22 Dec 2014 18:47:21 length and intensity levels of this experiment and produces the conjugate wavefront by means of forced Rayleigh scattering. 5 The low thermal conductivity of acetone and the large thermal coefficient of the refractive index make this solvent ideal for image protection experiments. Rhodamine was chosen as the absorber, because it proved photochemically stable and does not fluoresce at a wavelength that exposes photoresist. The concentration was chosen to attenuate the forward pump beam by a factor of 2, near the optimum for this sort of wavefront conjugation. The dye solution was flowed through the 1.8 cmXO.9 cm cross-section cell at 2 gallons per min in order to suppress long-lived thermal gradients which are detrimental to image quality. Mie scattering from suspended particulates could potentially cause unwanted exposure of the resist. Mie scattering was suppressed by carefully filtering the fresh solution through filters with 0.2-Ji pore size and by incorporating a cartridge filter in the dye flow circuit. Ethylene propylene and teflon seals were required throughout the flow system to avoid chemical attack which could liberate particulates. The conjugate wave transmitted through the beam splitter and compensator plate, focusing to an image on a photoresist film coated on a I-in. diam borosilicate glass substrate. The substrate was positioned less than 1 mm from the compensator plate and could be tilted and translated in two directions. Rough focusing was accomplished by observing the white light fringes formed in the interferometer consisting of the mask and substrate wafer and the beam splitter cube. 2 The substrate was then translated 35 Ji away from the beam splitter by means of a differential micrometer to the plane of best focus. Light passing through the resist and substrate was collected by an optical system, which separated the ultraviolet conjugate beam from the visible fluorescence produced by the Rhodamine dye. Part of the conjugate beam was reimaged upon a PIN photodiode, the pulses from which were integrated and their areas summed digitally to yield a measure of total resist exposure. Another portion was imaged upon a fluorescence converter consisting of thin layer of sodium fluorescein dissolved in glycerol and gelatine. 6 The fluorescent image, thus produced, could be viewed through a magnifier for real-time diagnostics on image brightness and illumination uniformity. The complex geometry of this system makes it difficult to exactly calculate the expected resolution. The ray diagram in Fig. 3 illustrates the difficulties, as well as techniques yielding approximate estimates. The central ray of the diffraction pattern from the mask is shown as line OBL. The region of the cell illuminated by the pump beam is shown as white, while the unpumped regions of the cell are gray. The image of the object point 0 is formed at point I. In the cell, ray B-L traverses an unpumped region between the cell wall and point C. In this region, the intensity is attenuat- ed by an amount e - PI. where f3 is the Beers law absorption constant, and lu is the arc length through unpumped dye. The ray crosses the pump region between points C and C', and it is in this region that the conjugate wave is generated. The intensity of the conjugate ray at point C can be calculat- K L M Beam Splitter FIG. 3. Ray diagram for estimating the resolution of the projection apparatus. Point 0 is an object point on the mask which is managed by the apparatus at point I. Ray OBL corresponds to the central ray from point 0 while rays OK and OM define the effective numerical aperture. The unshaded region of the cell is illuminated strongly by the counterpropagating pump beams and is thus the active region for wavefront conjugation. The line segment C-C' of the central ray interacts with the pump beams and the brightness of the returning ray is proportional to the square of the length of this segment. ed by solving the appropriate differential equation,8 but since the length of the segment C-C' is less thanf3 -1, it is not too bad an approximation to ignore absorption. In the absence of absorption, the intensity of the conjugate ray at point C is proportional to the square of the length of the segment. The conjugate ray must then traverse an unpumped region of the cell where it is attenuated as was the object beam. The result of these calculations is that the intensity of the conjugate ray corresponding to any of rays in the initial diffraction pattern is proportional to I a: e - 2PI·1; where lp is the length ofthe ray segment crossing the pump beam, and Iu is the length of the ray through unpumped dye. Using the diagram in Fig. 3, we were able to plot the intensities of the conjugate rays as a function of diffraction angle e. The three rays indicated in Fig. 3 are highlighted in the result of this calcultion in Fig. 4. Following Hubbard, 7 we can estimate the effective numerical aperture of this system by noting the angle where the intensity of the returning ray falls to 1/4 of that of the central ray. The corresponding amplitude of the conjugate wave is 1/2 of the initial amplitUde. For a sinusoidal input intensity pattern with 100% contrast and spatial frequency at this cutoff, this image would show 60% contrast. As can be seen from Fig. 4, the cutoff angle defined in this way is sin - 10.19 = 110, implying an effective numerical aperture of N.A. = 0.19 and a maximum useful spatial frequency ofN.A.!A. = 535liter/mm for normal illumination. Ifthe illumination were altered so that the central ray grazed the edge of the effective aperture, the maximum spatial frequency would increase to roughly 1070 liter/mm. The situation is simpler in the vertical plane. The pump beam then subtends an angle of 7.80 at the image point, im- 4307 J. Appl. Phys., Vol. 54, No.8, August 1983 M. D. Levenson 4307 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.209.6.50 On: Mon, 22 Dec 2014 18:47:21 L 1.0 .~ U> C ~ c K 0.5 '0 ~ ''''c""" M u 0 -0.2 -0.1 o 0.1 0.2 0.3 FIG. 4. Calculated relative brightnes~ of returning phase conjugate rays as a function ofthe diffraction angle at the mask. Zero angle corresponds to the central ray OBL-LBI, while the extreme rays OK-KI and OM-MI are also indicated. The effective numerical aperture of this device is estimated as the arc sine of the angle at which the relative conjugation efficiency falls to 0.25. plying an effective numerical aperture of 0.068 and a cutoff spatial frequency of 1911ine/mm. This limited resolution in the vertical direction is a direct result of the low power ofour laser source. Had we stretched the pump beam vertically to improve resolution, we would have sacrificed image brightness (which is proportional to the square ofthe pump intensity) and unduly lengthened the exposure time necessary to pattern photoresist. The pulse lengths and beam angles in this experiment allow the expected brightness of the image formed by conjugate wavefront generation to be estimated by the thermal diffusion model of forced Rayleigh scattering.4 The relevant parameters appear in Table 1. The path length through pumped dye is assumed equal to that of the central ray OBL in Fig. 3. After accounting for the reflection loss in the beam splitter the estimate average image intensity is 52 mW/cm2• The photoresists employed require a nominal energy deposition of 100 mJ/cm2 for optimal development. Thus, our esti- TABLE I. Parameters of acetone-rhodamine 6G conjugator experiment. Heat capacity pCp Thermal conductivity K Index of refraction n Temperature dependence of n (anlaT)p Absorption constant (3 Scattering wave vector q Grating decay time 7. 1.71 J/cm3 'C 1.79 X 10- 3 W/cmoC 1.36 - 53 X 10- 5 (oq-' 0.39 cm-' 1.5 Xla' cm-' 2.4 X 10- 7 sec mated image brightness would imply an exposure time of 1.9 sec. The theoretical image brightness cannot be achieved in these experiments, because the strict phase matching condition makes it impossible to utilize all of the pump laser power. The theoretical calcualtion assumes that the pump laser beams are plane waves, or at worst, TEMoo laser modes. Our beams were well collimated, but showed intensity variations across their profiles in the near field, as well as subsidiary maxima of intensity in the far field. Only 60% of the laser harmonic could be focused through at 150-fL-diam spatial filter while the expected diameter of a focused TEMoo with the same diameter at the lens was 32fl. This fact implied that a significant fraction of the spatially filtered beam propagated at angles larger than the diffraction limit with respect to the beam axis. Two problems introduced by these aberrant rays are illustrated in the wave-vector matching diagrams in Fig. 5. The upper diagram shows the wave-vector q of the transient thermal grating formed by the object beam ko and forward pump k]. If the wave vector of the backwards propagating pump k2 deviates by an amount I) k from the correct phase matching direction in the horizontal plane, a wave-vector mismatch .1K = I)k sin

11'/2 the image brightness is strongly suppressed. A large proportion of the power in the pump beams corresponded to rays that -ko Or;) + k, -ko ~q, k, \ ---. ..Ik