A computer program has been developed for the analysis and design of electron guns. The program uses second-order, curved, isoparametric finite elements to obtain very accurate potential and field computation. Special features of the program include fast solution of the second-order finite element equations with a specially written incomplete Choleski conjugate gradient (ICCG) algorithm, accurate field computation using biquartic interpolation, and direct ray tracing with a third-order power series method. Space charge effects are taken into account, with an iterative solution of Poisson’s equation. The brightness is also computed. The second-order finite elements permit accurate simulation of curved cathodes and very large changes in geometrical scale factor. This allows the program to handle all types of electron guns, ranging from field emission guns with submicron radius cathodes, to high current Pierce-type guns. The computational techniques used are described and illustrated with typical examples.

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Electron optical image correction subsystem in electron beam projection lithographyLie algebraic aberration theory and calculation method for combined electron beam focusing-deflection systems Electron and ion optical design software for integrated circuit manufacturing equipment This article investigates, with computer simulations, whether electron optical aberration correctors could be used to improve the performance of electron beam equipment for the semiconductor manufacturing industry. The simulations are performed using the differential algebraic method. Three types of aberration corrector are investigated: ͑1͒ a quadrupole-octopole corrector for critical dimension scanning electron microscopy for metrology and inspection ͑it is shown that this type of corrector, which corrects spherical and chromatic aberrations, can provide a smaller probe diameter with a larger numerical aperture, thereby improving resolving power and throughput͒, ͑2͒ a hexapole planator for projection electron beam lithography ͑it is demonstrated that field curvature, astigmatism, and spherical aberration can be corrected, thereby permitting a larger field size͒, and ͑3͒ a mirror corrector for reflective electron beam lithography ͑it is shown how field curvature and chromatic aberration in such systems can be corrected by using an electron mirror͒.

Methods are described for computing the optical properties of any combination of magnetic lenses and deflection yokes, including the most general case in which the lens and deflector fields may be physically superimposed. These techniques can handle either toroidal or saddle deflection yokes, wound on either nonmangetic of ferromagnetic formers, and can handle cases where the magnetic materials of the lenses directly influence the deflection fields. The basic program for calculating the properties of any given lens and deflection system has been combined with an optimization program, which systematically searches (subject to given physical constraints) for the arrangement which minimizes the deflection aberrations for any specified field size and aperture angle. Illustrative computed results are presented. It appears that conventional postlens single-deflection systems can have better properties than conventional prelens double-deflection systems. However, the performance of double-deflection systems can be improved dramatically by placing the second yoke inside the lens and rotating it relative to the first yoke. An arrangement has been found, which, at the corners of a 5×5-mm deflection field with 0.005-rad aperture and 1 in 104 beam voltage ripple, produces a total aberration disk of 0.45 μm before dynamic corrections, or 0.15 μm after dynamic corrections. The properties of in-lens single-deflection systems have also been investigated. Such systems offer the possibility, for the same operating conditions as quoted above, of producing a total aberration disk of less than 0.2 μm after dynamic corrections. By introducing a ’’predeflection coil’’ before the main deflection coil, this value can be reduced to less than 0.1 μm.