The design of the optical elements for a focused ion beam (FIB) system having a 50 mm spot size over a 1 mm square field requires extensive computational analysis. We discuss the mathematical techniques applied to the components of interest in this submicron FIB system; the electrostatic lenses, the mass analyzer, and the electrostatic deflectors. The results of ion trajectory calculations predicted for the whole FIB column by the computer code snow are presented. The aberration coefficients to third order and a parametric study of a stigmatic Wien filter whose design includes entrance and exit fringe field effects will be considered. We also cover our optimization algorithms for selecting lens and deflector elements which demonstrate minimal chromatic and spherical aberrations and distortions. A spot symmetry and spot location map for the final 1 mm square field and its 50 nm image constraint is shown for mixed electronic configurations of dynamic focus, dynamic distortion, and dynamic stigmation correctors. A comparison of the computer predictions to measured values of lens parameters is given for a typical liquid metal source and its extractor lens. The equipotentials in the vicinity of a representative lens is plotted with emphasis on the dielectric‐conductor interface in order to demonstrate the significance of stressed electric fields to the hardware designer

Honjo, I.

Thompson, W.

Utlaut, Mark

English

University of Portland

University of PortlandPilot ScholarsPhysics Faculty Publications and Presentations Physics1-1984Computer simulations of submicron FIB systemopticsW. ThompsonI. HonjoMark UtlautUniversity of Portland, utlaut@up.eduFollow this and additional works at: http://pilotscholars.up.edu/phy_facpubsPart of the Plasma and Beam Physics CommonsThis Journal Article is brought to you for free and open access by the Physics at Pilot Scholars. It has been accepted for inclusion in Physics FacultyPublications and Presentations by an authorized administrator of Pilot Scholars. For more information, please contact library@up.edu.Citation: Pilot Scholars Version (Modified MLA Style)Thompson, W.; Honjo, I.; and Utlaut, Mark, "Computer simulations of submicron FIB system optics" (1984). Physics FacultyPublications and Presentations. 40.http://pilotscholars.up.edu/phy_facpubs/40mputer simulations of submicron FIB system optics W. Thompson, I. Honjo, and Mark Utlaut Varian Associates, Inc., Gloucester, Massachusetts 01930 H. Enge Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received 3 June 1983; accepted 13 September 1983) The design of the optical elements for a focused ion beam (FIB) system having a 50 nm spot size over a 1 mm square field requires extensive computational analysis. We discuss the mathematical techniques applied to the components of interest in this submicron FIB system; the electrostatic lenses, the mass analyzer, and the electrostatic deflectors. The results of ion trajectory calculations predicted for the whole FIB column by the computer code SNOW are presented. The aberration coefficients to third order and a parametric study of a stigmatic Wien filter whose design includes entrance and exit fringe field effects will be considered. We also cover our optimization algorithms for selecting lens and deflector elements which demonstrate minimal chromatic and spherical aberrations and distortions. A spot symmetry and spot location map for the final l mm square field and its 50 nm image constraint is shown for mixed electronic configurations of dynamic focus, dynamic distortion, and dynamic stigmation correctors. A comparison of the computer predictions to measured values of lens parameters is given for a typical liquid metal source and its extractor lens. The equipotentials in the vicinity of a representative lens is plotted with emphasis on the dielectric-conductor interface in order to demonstrate the significance of stressed electric fields to the hardware designer. PACS numbers: 41.80.Gg INTRODUCTION number of applications for focused ion beam systems are rging. Some microfabrication uses include etch rate en-cement, resist exposure, and direct microbeam doping. one ion optics design will meet all needs. The optics asso-with these ion beams systems are of necessity electro-·c and require design techniques that differ significantly those used in the design of SEM and e-beam litho-hy equipment. Since the majority of these systems may Ve the further constraints of compatability with existing dware and software, large deflection fields, circularly etric submicron images, mass analysis, accurate fea-placement, and variable beam energy, additional bur-dens are placed on the design tools. What follows is a pre-' ption for the design of customized ion beam systems ch can be tailored to meet the needs of a specific applica-~r which can be used to generate the evolutionary optics .nably required by the changing goals of the semiconduc-lndustry. Our first test of this design procedure was an column which would adapt to our model VLS-80 raster leane-beam lithography system as shown in Fig. 1. At each e of the design we require experimental confirmation of Iha Predictions of the computer code. This then guarantees 1 l~e system specifications can be met and that the hard-e IS not unreasonably complex. l DESIGN PROTOCOL ft.gure 2 shows a flowchart for a typical column design Identifies the major programs used for each engineering After the ion species of interest are selected the ion ce is mounted on an emittance measurement test stand 1 to establish the variation of beam phase space and brightness as a function of a number of source parameters. Once the range of operating conditions are determined, the emittance envelope is used as input to two first-order ray trace pro-grams called TRANS 1 and TRANSPORT.2 These programs have as additional input the matrix elements and approxi-mate locations of the optical components to be used in the system. The energy and magnification required of the system de-termine the lens dimensions and locations. The program ELFl 3 is then used to establish the aberration coefficients for each optical element. The program SNOW4 gives the equipo-tentials within the lenses and the trajectories of the ions throughout the system. Since several of the codes produce similar output, where possible we cross check one program's results against an-other. In addition, each lens is qualified on the emittance measurement stand to determine if it is actually meeting its design goals. The program EDF1 5 is used to design the system's multi-pole deflectors. The deflectors may be used for beam center-ing or high-speed scanning, but must be designed to have minimal deflection distortions and aberrations. The code RA v6 allows us to calculate the ion trajectories to fifth order in an arbitrary mix of static multipole elements which may range from dipoles to dodecapoles. It also will calculate the ion trajectories in an EXB velocity selector and its fringe fields. Since the majority of the FIB systems will use an EXB filter for mass analysis and these filters are typically not aberration free, we are designing a low aberra-tion stigmatic Wien filter as our mass analyzer with the pro-gram RAY. "· Vac. Sci. Technol. B 1 (4), Oct.- Dec. 1983 0734·211X/83/041125-04S01.00 © 1983 American Vacuum Society 1125 1126 Thompson et al. : Computer simulations FIG. I. Schematic of typical three Jens FIB column. Ill. DESCRIPTION OF THE COMPUTER CODES AND THEIR RESULTS The program EMITTN 1 used for gathering beam profile and phase space data steps a pair of slits across the beam envelope just downstream of the ion source or optical ele-ment being evaluated. The beam current for different X and X' or Y and Y' values is stored and presented as a current contoured emittance diagram. These measurements made by EMITTN define the angular distribution and current den-sity variation of the beam from the liquid metal sources used for most FIB systems. One can also determine the amount of spherical aberration introduced by a lens at different operat-ing potentials. The programs TRANS and TRANSPORT use as input the phase space information gathered by EMITTN. They assume a first-order matrix representation for each optical element in the system and translate the phase space through these elements and the drift space between them. From TRANS one can obtain a value for all X and X' and Y and Y' for selected trajectories within the beam phase space. From this informa-J. Vac. Sci. Technol. B, Vol. 1, No. 4, Oct.-Dec. 1983 FIG. 2. Flowchart for a system design. tion an estimate of the dimension of the full beam envel~ without apertures and the system magnification can be made. The results of both TRANS and SLAC's TRAJ"SPOIT agree with each other to within 2%. When more accurate representation of the trajectories and lens equipotentials is needed the programs SNOW and E~ calculate the interelectrode potentials to third order . solve the Lorentz force equation for the particle trajecton~ Figure 3 shows a complete representation of a FIB column• ,.;O FIG. 3. Electrodes, equipotentials, and trajectories as detennined bY Thompson et al.: Computer simulations Near axis trajectories as determined by SNOW for the central lens. ted by SNOW including the electrodes, equipotentials, ion trajectories. Figure 4 gives a closeup of the trajector-r the einzel lens. Both SNOW and ELFl have the ability urately represent the equipotentials in the vicinity of a electrode. Thus, the designer can know what field gths exist and how close to a breakdown condition it is. program SNOW also has the additional ability to pro-beam profile and emittance diagrams from the trajec-plot files. It is, therefore, possible to determine the cur-5· IJncorrected image for a spot deflected by a postlens octupole. Sci. Technol. B, Vol. 1, No. 4, Oct.-Dec. 1983 1127 FIG. 6. Corrected image for a spot deflected by a postlens octupole deflector. rent and power density anticipated at spray and blanking apertures. By varying the central electrode potential of the einzel lens, one can see the variation in image location produced by focusing with it. SNOW also will calculate the equipotentials at a vacuum, dielectric, electrode interface which makes it a powerful tool for locating regions of stressed electric fields. Although SNOW considers the particle charge distribution FIG. 7. Dispersion in a Wien filter as forecast by the program RAY. 1128 Thompson et al.: Computer simulations in its solving of Poisson's equation, we have not used SNOW for LMI source region analysis. In order to do a SNOW simu-lation of the source region, we would have to add variable mesh capability to the finite element algorithm and have a better model for the Taylor cone emitter geometry. Al-though SNOW has been used to successfully design the ex-tractor electrodes for both Freeman and duoplasmatron ion sources, we feel that it is unwise to model an LMI source with it. The programs of Eric Munro, ELFl and EDFl, are used after SNOW to determine the chromatic and spherical aberra-tion coefficients of each of the electrostatic lenses. They are also used to forcast the deflection distortion and aberrations associated with large fields and small spot sizes. It is, there-fore, possible to predict exactly what electronic corrections may be necessary to reduce the deflector distortions and ab-errations. Figure 5 shows a representative EDF! output giv-ing the spot size and position change for a 500 A spot de-flected over a 1 mm field by an electrostatic octopole deflector without any electronic corrections. Figure 6 shows the effects of making dynamic corrections to the focus, stig-mator, and distortion. With a color terminal, color coding can be added so that each trajectory is coded to represent the energy of the particle, with red being a low-energy particle and blue being a high-energy particle, for example. The sig-nificance of axial and deflection aberrations is evident. The last analytical tool needed to design a FIB system is one which models the trajectories of particles in the crossed fields of a Wien filter mass analyzer. The first-order treat-ment of our EXB filter has been done very thoroughly by Seliger et al.6 It was realized, however, that to produce a truly stigmatic element with equal focal lengths in the dis-persive and nondispersive planes that the effects of finite fill factor and fringe fields need to be considered. Stan Kowalski and Harald Enge7 at MIT have developed the code RAY which has the ability to calculate ion trajectories using po-tential distributions expanded to.fourth order of the distance from the median plane. This code models dipoles, quadru-poles, octupoles decapoles, and dodecapoles, but most im-portantly, it can simulate crossed electric and magnetic field velocity selectors. The velocity selector can have inclined pole pieces which are required to produce the nonzero field index necessary to accomplish stigmatic imaging.6 Theim-plications of realistic electric and magnetic fringe fields are also considered. Figure 7 shows the dispersive plane of the mass analyzing EX B filter with each ray corresponding to a single amu difference between it and its nearest neighbor. The equilibrium ray has a mass of 100 amu and rays of 1 amu difference are separated by 700 µm from their neighbor at J . Vac. Sci. Technol. B, Vol. 1, No. 4, Oct.- Dec. 1983 the resolving aperture. The convergent rays in the dispersi~ plane have exactly the same X; and Y; for equivalent .\" and Y ~ implying equal focal lengths in the dispersive ~ nondispersive planes. This system would thus be truly Sti. matic. The preservation of circular symmetry can only~ maintained, however, if there is complete balance between the magnetic and electric fringe fields. The implications of even the slightest imbalance are significant. The fringe field, assumed have a form defined by a Fermi function whose coefficients result from a least square fit to the results of dipole field simulation subroutine in the program Poisson. When a fringe field imbalance exists the wiggle imparted to all trajectories changes their energy and this changes their velocity such that they no longer satisfy the v0 = E/B crite. ria. It is clear that the pole pieces and electrodes in this type of mass analyzer must be designed very carefully. IV. CONCLUSION We have adopted the simulation tools of a broad range of charged particle designers and applied them to a focused ion beam system. From our own experience in the design of oth· er ion optical and electron lithography systems and from the success others have had with those computer models, we feel confident of their results. Wherever possible, experimental configurations are made of our theoretical predictions. ACKNOWLEDGMENTS The authors would like to thank Stan Kowalski of MIT and Dana Gould of Varian Associates, Inc., for their assi · tance with the computer simulations and the graphics. We would also like to acknowledge the effort of the original authors of the computer models we used. It is they who did the real work and deserve the credit. 'I. Honjo and W. Thompon, Proceedings of the International Symposium on Ion Sources and Ion Assisted Technology (1982), p. 99. 2K. L. Brown, F. Rothacker, D. Carey and C. Iselin, TRANSPORT-.4 Computer Program for Designing Charged Particle Beam Transporl S.vi· terns (Stanford University, Stanford, California, 1977). ' E. Munro, A Set of Computer Programs for Calculating the Properties 0 Electron Lenses (Cambridge University, Cambridge, England. 1975). 4J. E. Boers, SNOW-A Digital Computer ProgramfortheSi111ulatio11of/IJf> Beam Devices (Sandia, Albuquerque, New Mexico, 1980). · and 5H. C. Chu and E. Munro, A Set of Computer Programs/or the Design Optimization of Electron Beam Lithography Systems (Imperial Collegi London, England, 1981 ). 6 R. L. Seliger, J . Appl. Phys. 43, 2352 (1972). 7H. Enge and S. Kowalski (private communication). 8H. Enge and S. Kowalski (private communication). 

Computer simulations of submicron FIB system optics

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Computer simulations of submicron FIB system optics

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