This paper describes a 100-kV thermal-emission electron gun developed for the X-ray mask writer, EB-X2, which employs a variable-shaped electron beam with a beam edge resolution of 20 nm. The optimized design of the EB-X2 electron optical system requires that the electron gun have crossover diameters of 50 micrometers and an optical length of less than 100 mm. So the crossover diameters of the gun were accurately calculated with an electron ray tracing program, and a gun with the required crossover diameters and optical length was designed. The gun was constructed, and the crossover diameters were measured. The measured values agree well with the calculated ones, and this confirms that the gun is suitable for use in the EB-X2 electron optical system.

Mesh generation is an integral part of the finite element simulation of electron guns. This paper shows that conformal meshes are the ideal type of mesh to use, both in terms of accuracy and speed of computation, and presents a numerical method to generate quasi-conformal meshes for a wide variety of electron gun structures.

The first order finite element method allows an accurate computation of rotationally symmetric magnetic electron lenses with saturated materials. The paper gives an overview of six methods for the evaluation of the coefficients of FEM equations. Then we present a study of local and global errors in the axial flux density distribution. These effects are illustrated on computations of a simple magnetic lens, closed magnetic circuit, and an objective lens for 1 MeV microscope. Finally we give a recommendation on the use of meshes with sufficient number of mesh points and with graded mesh size, and provide information on the computation time and memory requirements on a personal computer.

Optical properties of two kinds of immersion lenses, i.e. the radial gap magnetic lens and the combined electric and magnetic field lens have been compared. When the specimen allows the application of a leakage electric field about 600 V and the accelerating voltage on the specimen is lower than 2 kV, the combined field lens is better than the radial gap lens, because the spherical and chromatic aberration coefficients are small and the collimation efficiency of secondary electrons is perfect. However, if the leakage electric field is not allowed, the radial gap lens is superior to the combined field lens. In the case of the radial gap lens, a weak electric field has to be applied to the specimen for collimating electrons emitted with large angle from the specimen. When the specimen is set lower than the magnetic field maximum position, a solenoid coil placed inside the yoke of the lens is useful to bring up the off axial electrons.

The first order finite element method allows an accurate computation of multipole components of electrostatic and magnetic fields. The paper presents an analytical expression of the first, the third and the fifth harmonic component of electrostatic deflectors defined on an electrostatic box and for magnetic deflectors made of straight or tapered saddle coils or straight toroidal coils in air. The axial field functions are compared with those computed with the first order finite element method for the same geometry, with a very good agreement of the results.

This paper describes numerical techniques for computing axial field functions in focusing and deflection systems for charged particle beams. For systems with a straight optical axis, the computation of axial field functions using first- order and second-order finite element methods are compared, for electron lenses, deflectors and stigmators. The results show that the second-order finite element method gives greater accuracy for the high-order derivatives of the axial functions, which are needed for computing the fifth-order aberrations. The extension of these methods to computing perturbation fields caused by mechanical defects in the optical elements is also described. Methods for computing multipole field functions using a fully 3D field analysis are then described. These 3D methods are of quite general applicability to systems with fully 3D electrode and polepiece structures, and either straight or curved axes. Illustrative examples are shown of a multipole aberration corrector with a straight axis and a bending magnet with a curved optical axis.

Deflection system containing two deflectors of opposite field directions has been studied. It is shown that achromatic deflection can be obtained in such a system by changing the beam energy between the deflectors. In the assumption that the deflection angles are small, the achromatic condition is derived analytically. The numerical computation has shown qualitative agreement with the analytical formulae. The scanning achromatic deflection system with intermediate retardation of charged particles between two deflectors is discussed in detail.

Designers of Charged Particle Optics instruments use different levels of complexity to model the components in the system. They may first describe a round magnetostatic lens just in terms of focal distance, later in the design add an estimated spherical and/or chromatic aberration coefficient, perhaps with a value depending on the focal distance. Only in the very last phase, they will use numerical simulation programs to find the magnetic fields and the associated optical properties of a detailed physical design. We are developing a design tool which enables interactive definition of a complete system and its components. An essential feature of this tool is the ability to describe the components at different levels of complexity and then to switch between those levels. For this it is convenient if the program can find some of the parameters necessary for the `new' level of complexity from the `old' level of complexity. For example, it should find typical pole piece dimensions given a focal distance plus spherical aberration coefficient, and vice-versa. The feasibility of these conversions is exemplified by numerical examples from our design tool POCAD.

In calculating potential field for a system consisting of several conductors by means of the boundary (or surface) charge method (BCM or SCM), every conductor surface is divided into n small surface elements, and the surface (or boundary) charge density on each surface element is obtained by solving a set of n-dimensional simultaneous linear equations, where the coefficient matrix element is expressed as a double integral. In the 3D BCM, the coefficient matrix element is usually obtained by direct double numerical integration, which is a serious obstacle to a practical use of the method because of extremely long computation time. We have been developing an improved 3D BCM, where any given conductor geometry can faithfully be modeled by a suitable combination of parts and/or all of several basic surfaces such as plane surface, cylindrical surface, conical surface, discoidal surface, spherical surface and torus surface. We have found that the first integration in the double integral of the coefficient matrix element can be done analytically for the above-mentioned basic surfaces, thereby greatly improving the computation time without any loss of accuracy.

This paper compares the accuracy of three high order interpolation methods to drive spatial derivative information from finite element meshes in the 2D rectilinear coordinate system. These methods involve using a C¹ triangle interpolant, spline/hermite cubic interpolation, and a local polynomial function fit. 2D electric potential distributions are analyzed for a test example on which the radial electric field is evaluated at scattered points in a domain composed of block regions. The results show that of the methods considered, a local polynomial expansion suing basis functions which satisfy Laplace's equation is the most accurate. The better accuracy of this method however, can only be obtained for potential distributions that have a low degree of discretization noise at their mesh nodes.

The paper discusses a possibility of application of perturbation methods to calculation of field distributions and optical properties of various electron and ion optical systems.

The electron-optical design of the Leica Vectorbeam Series lithography tool has been modified to reduce the writing spot-size to 2.5 nm; this has required two separate design approaches. Firstly, the current transmitted from the Schottky-emission source module into the column has been reduced from 500 to 25 nA. This makes stochastic beam broadening due to electron-electron interactions negligible. Secondly, a new final lens was designed with sufficiently small aberrations to achieve the desired spot-size. The design includes secondary electron detectors as well as the more usual back-scattered electron detectors. The conversion of the theoretical electron-optical design to reality has been greatly facilitated by the use of CAD solid modelling techniques.

A cumbersome necessity in lithography tools is the need to provide for a mechanical wafer rotation in order to achieve overlay. In contrast to photolithographic tools, charged particle lithography systems potentially offer a non- mechanical means of adjusting image orientation through the use of magnetic fields. I have identified a type of device, based upon simple, solenoid-like coils, which can simultaneously provide independent electronic adjustments to both image rotation and magnification. The implementation of such a device in a SCALPEL^TM-based proof-of-lithography tool is presented as a practical example.

In a series of recent studies, we evaluated the effects of statistical Coulomb interactions on the obtainable probe sizes and probe currents in Focussed Ion Beam (FIB) systems. In order to find the fundamental limits, we assumed that the final probe current was selected by an aperture very close to the source. However, in practical FIB's, the aperture is somewhere halfway the column, so the current is much higher in the first part of the column, with associated stronger Coulomb interactions. We have now analyzed the influence of the aperture position on the FIB performance and found that the position is very important, but only in the range of small probe sizes or low probe currents. Many FIB's have a fixed first aperture close to the source to limit the beam current early on and then a second aperture to select the final probe current. We have also analyzed the effect of the fixed aperture and found that it controls the statistical Coulomb interactions only if the current is limited very substantially, which then makes it impossible to operate in high current mode.

The trajectory and width of the pencils of rays in a point cathode thermionic emission gun have been analyzed with numerical methods. The numerical model of the gun consists of the point cathode with the tip radius of 0.4 micrometers , the wehnelt with the aperture diameter of 1 mm, and the anode. The electric field was computed with a surface charge method, which is one of the integral methods of the charge distribution on the electrode surface. A direct ray-tracing was done in 3D from the axial and off-axial positions on the spherical tip part of the cathode for different emitting conditions. The shape of each pencil of rays was estimated from these rays. Some 3D views of the pencils are given, together with the electrode geometry. The pencils have large widths when they pass through the wehnelt aperture, and then focus onto different positions with different cross- sections. The methods and results are presented.

A new theoretical line of attack to solve the self- coordinated problem in charge particle optics is developed basing on the aberration theory and (tau) -variation technique. The self-coordinated problem is treated as initial-value problem for the evolution integro-differential equation which directly follows from the Lorentz equation with taking into account the space charge effects. The Coulomb potential of a beam is presented in the form of integral taken over the initial parameters domain, and the induced potential (the `mirror image' potential) is presented in the convolution form with a Green function satisfying the adjacent Fredholm integral equation of the first kind. Some considerations to numerical solution of the evolution equation obtained are applied.