METHOD FOR SYNTHESIS AND FORMATION OF A DIGITAL HOLOGRAM FOR USE IN MICROLITHOGRAPHY

摘要

The invention describes a method of manufacturing a holographic mask capable of producing an image pattern that contains elements of a sub-wavelength size along with decreased deviations from the original pattern. The original pattern is converted into a virtual electromagnetic field and is divided into a set of virtual cells with certain amplitudes and phases, which are mathematically processed for obtaining the virtual digital hologram. The calculation of the latter is based on parameters of the restoration wave, which is used to produce the image pattern from the mask, and on computer optimization by variation of amplitudes and phases of the set of virtual cells and/or parameters of the virtual digital hologram for reaching a satisfactory matching between the produced image pattern and the original pattern. The obtained virtual digital hologram provides physical parameters of the actual digital hologram that is to be manufactured.

主权项

1. A method for synthesis and formation of a digital hologram for use in microlithography comprising the following steps:
(a) introducing an orthogonal coordinate system x, y, z having three mutually perpendicular axes X-X, Y-Y, and Z-Z, choosing a point O on the axis Z-Z, and passing through this point a virtual digital hologram plane (VDHP), which is perpendicular to the axis Z-Z and which is to be used as a plane of a virtual digital hologram (VDH) for manufacturing the actual digital hologram; (b) selecting an orthogonal coordinate system x′, y′, z having three mutually perpendicular axes X′-X′, Y′-Y′, and Z-Z, choosing a point O′ on the axis Z-Z that is spaced from the virtual digital hologram plane (VDHP) at a certain distance “d” and passing through this point O′ a virtual original pattern plane (VOPP) that contains a virtual original pattern and is perpendicular to said arbitrary axis Z-Z, and wherein the virtual original pattern that contains image elements is to be used for subsequent synthesis of the virtual digital hologram; (c) selecting a nontransparent restricted area NTRA in the virtual original pattern plane (VOPP) and placing the virtual original pattern (VOP) in the nontransparent restricted area NTRA of the virtual original pattern plane (VOPP), the virtual original pattern (VOP) being formed by virtual image elements VIE; (d) applying onto the virtual original pattern plane (VOPP) a first virtual net FVN that divides the non-transparent restricted area (NTRA) into a plurality of first virtual unit cells; e) classifying the first virtual unit cells into white first virtual unit cells, black first virtual unit cells, and grey first virtual unit cells, wherein a white first virtual unit cell is obtained if a first virtual unit cell of the first net overlaps the virtual image elements of the virtual original pattern, a black first virtual unit cell is obtained if a first virtual unit cell of the first net overlaps only a space between the adjacent virtual image elements, and a grey virtual unit cell is obtained if a first virtual unit cell of the first net overlaps adjacent virtual image elements and a space between the adjacent virtual image elements; (f) presenting the virtual original pattern (VOP) in the form of a virtual digital amplitude-phase mask, wherein each first virtual unit cell is assigned a transmission value so that white first virtual unit cells are assigned a transmission value of 1.0, black first virtual unit cells are assigned a transmission value of 0.0, and grey first virtual unit cells are assigned a transmission value in the range of 0.0 to 1.0; all areas beyond the restricted area are assigned an amplitude value of 0.0; and wherein each first virtual unit cell has a function of a rotational phase shifter for shifting the phase in each respective first virtual unit cell when this first virtual unit cell passes the light of a first virtual light wave that has a given phase and amplitude, which are changed individually in each first virtual unit cell when the first virtual light wave FVLW passes through this cell, whereby a plurality of first individual virtual light sources selected from the group of point light sources and/or extended light sources is formed, and wherein each first individual virtual light source of said plurality acquires a precalculated phase and amplitude; (g) carrying out an auxiliary correction of said acquired precalculated phase and amplitude for each first individual virtual light source of said plurality for obtaining a post-calculated distribution of said phase and amplitude of the first individual virtual light sources of said plurality; (h) fixing the obtained post-calculated distribution of said phase and amplitude of the first individual virtual light sources of said plurality, said first individual virtual light sources generating a first electromagnetic field; (i) applying a second virtual net onto the plane of the virtual digital hologram, thus dividing the plane of the virtual digital hologram into a plurality of second virtual unit cells and generating with the first light sources of said plurality a second electromagnetic field in the second virtual unit cells of the virtual digital hologram plane; (j) calculating an amplitude and phase of the second electromagnetic field in the virtual digital hologram plane from the first light sources of said plurality; (k) providing a given virtual restoration wave that propagates from the virtual digital hologram plane to the virtual original pattern plane for subsequent restoration of the final virtual image and comprises a spherical or a non-spherical wave that converges to point O″, which may or may not coincide with point O′ on the virtual original pattern plane (VOPP); (I) inverting the given virtual restoration wave into a virtual reference wave to be used for calculating the virtual digital hologram; (m) adding the virtual reference wave to the second electromagnetic field obtained in the second virtual unit cells for calculating interference amplitudes and phases obtained as a result of interference of the second electromagnetic field obtained from the first virtual light sources with the virtual reference wave; (n) calculating the values of the virtual digital hologram in the second virtual unit cells based on the interference amplitudes and phases in each second virtual unit cell; (o) passing the given virtual restoration wave through the virtual digital hologram plane, thus forming a plurality of second individual virtual light sources in the second unit cells, the second individual virtual light generating a third electromagnetic field in the virtual digital hologram plane; (p) selecting a final virtual image plane for subsequent formation of the final virtual image, the final virtual image plane coinciding or not coinciding with the virtual original pattern plane (VOPP); (q) applying a third virtual net onto the final virtual image plane, thus forming a plurality of third virtual units, the second individual light sources generating a fourth electromagnetic field in the third virtual unit cells; (r) calculating amplitudes and phases of the fourth electromagnetic field; (s) calculating the values of the final virtual image in the third virtual unit cells based on amplitudes and phases of the fourth electromagnetic field (REF) calculated in step (r); (t) introducing a criterion of matching between the final virtual image and the virtual original pattern; (u) comparing the final virtual image with the virtual original pattern based on the criterion of matching if deviations are present; (v) minimizing the above deviation, if any, by repeating the steps (g), (h), (j), (m), (n), (o), (r), (s), and (u) until a satisfactory value of the criterion of matching is achieved and thus obtaining the final virtual digital hologram; and (w) manufacturing the actual digital hologram with use of the obtained final virtual digital hologram.