In this paper, some of the key techniques used in the computer modelling of charged particle optical systems are reviewed and illustrated. The topics covered include: Magnetic electron lens design using the finite element method; electrostatic lens design by finite element and finite difference methods; analysis of matrix lenses and multipole lenses, using a fully three- dimensional (3D) finite difference analysis; treatment of asymmetry errors in construction and alignment of electron lenses, using perturbation methods; analysis of electrostatic and magnetic deflection fields by finite difference, boundary integral and finite element methods; design of complete electron and ion beam columns containing arbitrary combinations of lenses and deflectors; simulation of discrete Coulomb interaction effects and diffraction effects; 3D simulation of fields and trajectories in secondary electron detectors for topographic and voltage contrast; design of electron sources, using second-order finite element method; design and aberration analysis of curved axis systems, such as imaging energy filters, using wavefront aberrations; and the dynamic correction of deflection aberrations in high- performance scanning systems. All the examples presented in the paper have been run and plotted on a personal computer system.

A new optical system has been developed which employs a snorkel type conical objective lens that allows high resolution imaging at high tilt angles, up to 45 degrees. An E cross B field for detecting secondary electrons is utilized in this optical system in order to avoid influence upon the primary beam from the extraction field generated by the usual scintillator secondary electron detector. Spatial resolution of better than 4 nm at an accelerating voltage of 1 kV has been obtained from a secondary electron image, with a working distance of 3 mm.

The increasing power of personal computers is offering accelerator designers new options for meeting their computational requirements. Standalone and highly portable machines provide accelerator scientists with different approaches to solving problems traditionally relegated to centralized mainframe, mini-computer or networked workstation environments. Advances in user interfaces, which have provided enhanced productivity for many business and technical applications, are now being implemented for accelerator design and analysis codes. We have developed new software packages for the Macintosh personal computer platform in this vein and discuss two of them here. For use with existing FORTRAN design and analysis codes, a unique graphical user interface (GUI) has been developed. The second package is the Numerical Electrodynamics Laboratory (NEDlab), a new two-dimensional (cylindrical or Cartesian) particle and field simulation program.

Numerical calculations were conducted on the electron optical characteristics of the accelerating tube (AT) for the high voltage electron microscope. The emitted electrons are firstly accelerated to V₀ by the TE gun or the FE gun and finally to V_a by the AT which consists of 34 electrodes with the inner diameter of 33 mm and has the overall length of 1423 mm. The AT is treated as a thick electrostatic accelerating lens. Several electron optical problems arising from a combination of the AT with a thermionic emission (TE) gun or a field emission (FE) gun are studied. For the TE gun the aberration effect of the AT lens is found to be safely neglected for any combination of Va and V₀. In the case of the FE gun, on the other hand, the aberration effect of the AT lens can not be neglected and deteriorates the brightness of the beam. This situation can be overcome by placing an electron lens between the FE gun and the AT.

Optimization programs are becoming available to support the designing of complicated lens systems in charged particle optics. By exploring the consequences of design decisions automatically, they can increase the effectiveness of the designer. This increases the quality of the resulting design, or makes it possible to design systems that are too complicated to develop by hand. A typical problem is that these optimization programs often only produce an optimized design for one mode of operation of the system, whereas the optical system has to function for a range of modes. For a designer these multi mode design constraints often are difficult to handle. In this paper we report how a single mode optimization program is used for designing an actual multi mode transport lens system. The final design, which is too difficult to develop in a conventional way, is presented. The optimization program used is based on the Second Order Electrode Method (SOEM). Because SOEM uses a very simple model to calculate the electrostatic field, the properties of the final design are checked with a more accurate simulation program. The optical properties calculated by SOEM are accurate enough to form a basis for design decisions.

The surface charge method (SCM) is an accurate electric field solver based on the numerical integration of the charge distribution on the electrode surface. The method is suitable for the field analysis of an electron gun and lens with complicated geometry, but it becomes the most time-consuming part when electron rays are traced for the analysis of the electron optical characteristics of these devices. We have studied the SCM and the electron ray-tracing on vector pipeline supercomputers, the CRAY X-MP and the Fujitsu VP2600. On these computers, a big reduction of the computing time is obtained by the optimization of the SCM- code. This enables us to trace many electron rays for the electron beam analysis. Some applications of the optimized SCM-code for the beam analysis are also presented.

Projection electron beam lithography employing the SCALPEL (scattering with angular limitation projection electron beam lithography) technique appears to be a potential successor to optical lithography for linewidths below 0.25 micrometers . An examination of previous projection electron-beam systems reveals that their lack of success was due to a combination of factors. The most significant of these were the lack of a suitable mask, and the use of an architecture mimicking optical tools. SCALPEL lifts the restrictions on operating voltage imposed by the absorbing stencil masks used previously. Consideration of the tool design from the system perspective suggests that a more fruitful approach to the problem is the use of a step-and-scan architecture. This employs dynamically corrected optics, and takes advantage of the ability of charged particles to be manipulated in an effectively inertialess manner. This obviates the need to produce a full-field projection optic, and also allows for correction of the printed image to compensate for chip-site distortions.

This paper discusses what appears to be a crisis in the field of electron microscope--a term which is broad enough to include ion microscopy, just as the term electron optics includes ion optics. The crisis is that we seem to have reached a performance limit in all instruments, and there are no known or proven ways to improve upon present levels.

The design of an achromatic mass separator which consists of two ExB filters, a stigmator, and the separation aperture is described. The optical properties of the ExB filters are derived. The influence of the designed mass separator on the spatial resolution of the column and the fringing field effects are discussed. First experimental results are shown.

Over the past several years we have studied in detail the H^- beam dynamics to design an efficient low energy beam transport (LEBT) system using simulation codes. One of the main objectives of this study is to design a LEBT system such that there is no significant emittance dilution of the beam.

A computer simulation program for calculating the energetic Boersch effect in the diode region of the field emission (FE) gun has been developed. The diode system consists of a hyperboloid of revolution as the cathode (FE tip) and a plane electrode as the first anode (extraction anode). The radius of curvature of the FE tip is R_o and the FE tip-to-1st anode distance is d. The simulation has been done for the various combinations of R_o (0.05 approximately 0.4 micrometers ) and d (0.5 approximately 10 mm). The work function of the cathode tip is assumed to be 4.5 eV. The electrons leave the cathode surface at time intervals selected to approximate a Poisson process and also realize a specific emission current using a random number. The positions and velocities of the electrons are successively calculated as a result of the force produced by both the Coulomb interaction and the electric field inside the gun. The resultant energy spread (Delta) E is found to be (Delta) E equals (root)(Delta) E²_o + (Delta) E²_B, where (Delta) E_o is the initial energy width of the emitted electrons and (Delta) E_B is the energy broadening of monochromatically emitted electrons. The simulation also shows that the dependence of (Delta) E_B on R_o, d, and the emission current I_E is given by (Delta) E_B (alpha) I^-0.75_E X R^-0.5_o X d⁰.

Scanning Electron Microscope (SEM) image simulation techniques have recently started to be used as a means of quantitative interpretation of SEM micrographs. A method of image simulation has been developed which takes into account image formation processes from the point of impact of the primary beam on the sample to the point of electron collection by the detector. Firstly the interaction between the specimen and the primary beam is modelled in order to determine the distribution of the electrons emitted from the specimen. The beam/specimen interaction model is based on original Monte Carlo programs by Joy and Luo. The paths of the electrons in the specimen chamber are then computed using software by Rouse. Images of a variety of samples with various surface topographies were simulated and the effect of varying the detector configuration was studied. All computations were performed using a 80486 Personal Computer. The results were then compared with micrographs taken using a Leica Cambridge S360 SEM.

Focused ion beam (FIB) machines are becoming an accepted part of the semiconductor industry. They are used in the repair of photomasks and X-ray masks, for direct modification of devices, for failure analysis, and for process verification. As the scale of the lithography shrinks, the demands on the FIB tool increase accordingly, both in terms of its accuracy (for repair and modification) and its resolution (for imaging). One key factor that affects these parameters in the FIB column itself, in terms of its spot size performance. Many of today's applications demand spot sizes as low as 15 nm, at beam currents of 10 - 20 pA. This paper proposes a figure of merit for FIB columns, based on the optimum magnification model, that provides the column designer with a consistent technique for assessing column performance. The figure of merit can be used either as a simple metric for the final column design, or more usefully as an aid to the designer to provide feedback on how to improve column performance.

In order to do ray tracing in a charge particle optics system it is necessary to be able to evaluate the field at an arbitrary point along the path. The finite element method (FEM) can yield the most accurate values for the potential at the mesh points when a variable quadrilateral mesh is used. The nonrectangular mesh, which is advantageous in simulating real geometries with a reasonable number of mesh points, is however, a disadvantage in field evaluation for direct ray tracing. A new method of interpolation is based on special polynomials of two variables which fulfill the Laplace equation. The polynomial representation of the potential is local to each quadrilateral in which field evaluation is done. Coefficients for these local polynomials are found by fitting to the quadrilateral corner points and their neighbors. The mesh geometry can be whichever is most suited to the FEM solution of the potential. The new method was tested on a two cylindrical electrode system used as an electron mirror, a system for which the analytical solution for the potential is known. The results indicate that for typical mesh geometries and with 20 X 20 mesh lines in the gap between the electrodes the error of the interpolation is about ten times smaller than the error of the linear finite element method.

The major design goals of photomultiplier tubes are: to maximize the collection between individual stages, thereby optimizing the tube sensitivity; and to minimize the transit time spread of electrons between individual emission and collection surfaces, thereby optimizing the time resolution. The numerical modelling involves computing the electrostatic fields and electron trajectories for various electrode structures. A fully three dimensional (3D) program is used to give a better representation of the tube's design, and also allows the freedom of using accelerating electrodes and focusing rings of different shapes and heights, which can be modelled accurately in 3D.

Focused ion beam (FIB) systems are now commonly used in the semiconductor industry for failure analysis and circuit modification of various integrated circuits. Secondary Ion Mass Spectroscopy (SIMS) is coming into use as a means to detect endpoint in sputtering holes in the integrated surface as well as to perform thin film analysis. A key requirement of the SIMS optics is very high sensitivity as the primary Ga ion beam is typically in the 10 - 11 to 10 - 9 A current range. The input lens must efficiently extract low energy ions from the surface and transport them into the quadrupole mass spectrometer and match its input spatial, solid angle and energy characteristics. In addition, the input lens must fit between the sample and primary ion column. In this paper the theoretical solution is compared to experimental results.

The effect of higher-order aberrations is shown for ion-optical systems that contain sector fields and quadrupole lenses. The importance of the more than approximate fulfillment of the Laplace equation throughout the ion-optical system is discussed.

A new evaluation method for the depth of field in a scanning electron microscope (SEM) images in terms of the quality of an optical image is introduced. The depth of field, in our method, is evaluated by calculating the image resolution along the optical axis defined in terms of the information passing capacity (IPC) of an optical system. The IPC corresponds to the mean information content included in an optical image, i.e., the quality of the image, evaluated based on the theory of Linfoot. The depth of field in a high resolution observation evaluated by our method depends on the accelerating voltage of the primary beam and signal- to-noise ratio of the image. The calculated results has agreed well with experiment.