A new software package has been developed for simulating electron mirrors, using Boundary Element Method. The program computes the surface charge density distribution on the electrode surfaces to very high accuracy at a set of sample points on the electrodes, based on the fact that the potential generated by rings of surface charge can be computed to the numerical rounding accuracy of the computer. A matrix equation is set up relating the surface charge densities at sample points on the electrodes to the known potentials at the same set of sample points. The matrix coefficients are computed extremely accurately, by evaluating a set of integrals, using a combination of 32-point Gaussian quadrature and 5-point Lagrange interpolation formulae for each set of 5 sample points. The matrix equation is then solved to compute the charge distribution on the electrodes in terms of the applied electrode voltages. From the charge distribution on the electrodes, the axial potential distribution is then computed with extreme accuracy using analytic functions. From this axial potential function the first-order properties and aberrations of the mirror are computed using a Differential Algebraic (“DA”) Method. This new BEM Software has great advantages over Finite Element Method (“FEM”) in this application. Firstly, the data specification is extremely simple, because it is only necessary to discretize the electrode surfaces, and not the space between the electrodes (as is required in FEM). Secondly, trajectories far from the axis can be computed with great accuracy, and this will simplify the computation of problems involving trajectories with large ray slopes or large off-axis distances. The program's accuracy has been demonstrated for a 4-electrode mirror. As a novel example, we have demonstrated how the new program can be used for simulating “Multi-Pass” Mirror Systems, including “Gated Electron Mirrors”, which can be used to inject and eject charged particles in “Multi-Pass” Mirror Systems. Such systems are used for Multi-Pass Time-of-Flight spectrometers, and Multi-Pass Mirror Systems for reducing specimen damage in Electron Microscopes.

It has been shown that N-fold symmetric line current (henceforth denoted as N-SYLC) produces 2N-pole magnetic fields. In this paper, a threefold symmetric line current (N3-SYLC in short) is proposed for correcting 3rd order spherical aberration of round lenses. N3-SYLC can be realized without using magnetic materials, which makes it free of the problems of hysteresis, inhomogeneity and saturation. We investigate theoretically the basic properties of an N3-SYLC configuration which can in principle be realized by simple wires. By optimizing the parameters of a system with beam energy of 5.5keV, the required excitation current for correcting 3rd order spherical aberration coefficient of 400mm is less than 1AT, and the residual higher order aberrations can be kept sufficiently small to obtain beam size of less than 1nm for initial slopes up to 5mrad.

Boersch, or stochastic space charge effect, is the effect of broadening of the e-beam axial energy spectrum. It limits resolution of fine electron optics by means of change in axial velocity of electrons. This is caused by a stochastic, discrete el ectron-electron interactions in an electron beam. We have computed beam energy spectrum widening in triode gun with magnetic lens.

Our SOURCE software handles 2D simulation and design of electron guns, including thermionic, thermal field and cold field emission guns, with electrostatic and magnetic focusing. The fields are computed by Second-Order Finite Element Method, which can handle large scale changes, curved cathodes and electrodes. Space charge effects are modeled by iterative solution of Poisson's equation. The program predicts source size and position, brightness, spherical and chromatic aberration. Recent enhancements include effects of secondary and back-scattered electrons, asymmetry aberrations due to tolerancing errors, N-body simulation of discrete Coulomb interactions, including energy and lateral broadening. The software runs in a Graphical User Interface, and post-processing features include through-focal plots of spot size, current density distributions, and emittance diagrams. The software handles a wide range of guns, from high-power klystrons to guns with Carbon Nanotube field emitters.

The differential algebra (DA) method has been employed to compute the optical properties and aberrations up to the fifth order of multipole systems containing electrostatic and magnetic round, quadrupole, hexapole and octopole lenses, and Wien filters. A new software package has been developed, which computes the geometrical and chromatic aberrations up to the fifth order by using a single DA ray trace. It also has an optimization module where a weighted set of aberrations can be minimized by the automatic adjustment of a set of user-defined system variables. In this paper, we present our new method for designing and optimizing multipole systems including Wien filters, and illustrate its application with three relevant examples.

Over many years, we have developed electron source simulation software that has been used widely in the electron optics community to aid the development of rotationally symmetric electron and ion guns. The simulation includes the modelling of cathode emission and the effects of volumetric space charge. In the present paper we describe the existing software and explain how we have extended this software to include the effects of discrete Coulomb interactions between the electrons as they travel from the cathode surface to the exit of the gun. In the paper, we will describe the numerical models we have employed, the techniques we have used to maximize the speed of the Coulomb force computation and present several illustrative examples of cases analyzed using the new software, including thermal field emitters, LaB6 guns and flat dispenser-type cathodes.

It is critically important to know backscattered electron (BSE) trajectories and current density in electron beam lithography tools, where a 50 keV electron beam is incident upon the target plane. The space near the target plane is occupied by closely-spaced optical components and sensors, all prone to surface charging. We have reported previously the results of testing SOURCEBS rev.1.0, a software for tracing BSE's of known energy value. Recently, we have developed SOURCEBS rev. 4.0. This software takes the full spectrum of BSE energies and initial coordinates from MONSEL, an electron-solid state modeling software program. SOURCEBS rev. 4.0 traces BSE's with their full energy spectrum in electrostatic and magnetic fields, and computes the BSE current density at user-chosen surfaces.

This paper summarizes currently used techniques for simulation and computer-aided design in electron and ion beam optics. Topics covered include: field computation, methods for computing optical properties (including Paraxial Rays and Aberration Integrals, Differential Algebra and Direct Ray Tracing), simulation of Coulomb interactions, space charge effects in electron and ion sources, tolerancing, wave optical simulations and optimization. Simulation examples are presented for multipole aberration correctors, Wien filter monochromators, imaging energy filters, magnetic prisms, general curved axis systems and electron mirrors.

In shaped-beam lithography tools, a 50 keV electron beam is incident upon structures consisting of thin layers of resist and metal on the top of a massive silicon or quartz substrate. The desired result, resist exposure, is achieved by primary and secondary electrons losing energy in inelastic collisions with resist molecules. The exposure resolution depends on the electron energy loss distribution in the resist. We have modeled electron scattering in the mask with MONSEL software and developed an algorithm for extracting the energy loss distribution. Results obtained are in agreement with known resist exposure data.

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: (1) 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 throughput), (2) 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 size), and (3) 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 mirror).

A set of formulae has been derived for computing paraxial rays, geometrical and chromatic aberrations of multipole systems containing electrostatic and magnetic round, quadrupole, hexapole and octopole lenses, and deflectors. Using these formulae, we have developed a software package for simulating and designing such systems. This new software, using the previously computed field functions as input, computes and plots paraxial rays, geometrical aberrations up to the third-order and the firstorder chromatic aberrations for the analyzed systems. It has an optimization module where a weighted set of aberrations can be minimized by the automatic adjustment of a set of user-defined system variables. We have also added a graphical user interface which affords a better overview of the design process and an interactive control of the system. An example of a hexapole spherical aberration corrector is presented to illustrate the functionality of this software package. © 2008 Elsevier B.V. All rights reserved.

A differential algebraic (DA) method has been developed for the aberration analysis of electron mirrors. Since large ray slopes occur near the turning points in mirrors, the axial position is no longer suitable as the independent variable and the electron trajectory equation used in conventional lens theory is no longer feasible. A DA solution of the electron motion equation, wherein a single DA ray trace is performed on a non-standard extension of real number space called nDv, enables the aberrations of a mirror system to be obtained, in principle up to arbitrary order n, and with very high accuracy, due to the remarkable algebraic properties of nDv. With the DA method, the enormous effort to derive explicit formulae for the aberration coefficients of electron mirrors is avoided. A software package MIRROR_DA has been developed for the aberration analysis of electron mirrors, based on the DA method. Two examples of electron mirrors are presented. For the first example, for which the electrostatic and magnetic fields are represented by analytical models, the results computed with MIRROR_DA were shown to be in good agreement with those extracted by direct ray tracing, with relative deviations of less than 0.065% for all the primary aberration coefficients. The second example consists of a real magnetic lens and electrostatic mirror, with numerically computed fields, and from the results of MIRROR_DA, the spherical aberration coefficient Cs3 is almost cancelled out because of the correction effect of the mirror. The MIRROR_DA software is a novel, effective and precise tool for the aberration analysis of electron mirrors, capable of handling realistic and complicated systems of electron lenses and electron mirrors.

Novel electron-optical components and concepts aiming at improving the throughput and extending the applications of a low energy electron microscope (LEEM) are elucidated: an immersion magnetic field in the objective lens and its implications for the illumination optics, a dual electron beam illumination approach, and imaging modes with tilted illumination. In an immersion magnetic objective lens, electrons do not form a sharp crossover in the back-focal plane, which substantially reduces e-e interactions and the associated blur. The resulting limited field of view of the immersion objective lens in mirror mode can be eliminated by immersing the cathode of the electron gun in a magnetic field. A dual beam approach, where two beams with different landing energies illuminate the field of view, is used to mitigate the charging effects when the LEEM is used to image insulating surfaces. We have experimentally demonstrated that the negative charging effect, created by a partially absorbed mirror beam, is compensated by the positive charging effect of the secondary beam with a net electron yield exceeding 1. On substrates illuminated with a tilted beam near glancing incidence, large shadows are formed on even the smallest topographic features, easing their detection. On magnetic substrates, the magnetic flux leaking above the surface can be detected with tilted illumination and used to image domain walls with high contrast. (C) 2008 Elsevier B. V. All rights reserved.

In this paper we describe the software tools that we have developed for the analysis of charged particle optical systems with curved optical axes. Examples of such elements are: omega filters, which are used for energy selection; magnetic prisms, used for bending and separating beams; Wien filters, which can be used for separating two beams of different mass or velocity; and wide angle scanning systems where aberrations referred to a straight optical axis can become meaningless. The analysis of curved axis systems can be sub-divided into three main tasks: the computation of the electric and magnetic fields that the beam passes through; the computation of the axis path and the extraction of the necessary field quantities; and the computation of the optical properties and aberrations. We discuss the methods we’ve employed to accomplish these tasks and demonstrate the use of the software with some illustrative examples. © 2008 Elsevier B.V. PACS: 41.85.-p; 41.85.Lc; 41.20.Gz; 02.70.Uu; 02.70.Bf; 02.70.Dh

In this paper we describe the software tools that we have developed for the analysis of charged particle optical systems with curved optical axes. Examples of such elements are: omega filters, which are used for energy selection; magnetic prisms, used for bending and separating beams; Wien filters, which can be used for separating two beams of different mass or velocity; and wide angle scanning systems where aberrations referred to a straight optical axis can become meaningless. The analysis of curved axis systems can be sub-divided into three main tasks: the computation of the electric and magnetic fields that the beam passes through; the computation of the axis path and the extraction of the necessary field quantities; and the computation of the optical properties and aberrations. We discuss the methods we've employed to accomplish these tasks and demonstrate the use of the software with some illustrative examples. (C) 2008 Elsevier B. V. All rights reserved.

A differential algebraic (DA) method has been developed for the aberration analysis of electron mirrors, and a software package MIRROR_DA has been developed. Time is used instead of axial position as our independent variable, and a reference ray is also employed. A single DA ray is traced in the fields of the mirror system, performed on a non-standard extension of real number space called D-n(v), and all aberrations coefficients can be obtained simultaneously, in principle up to arbitrary order and with extremely high accuracy. To demonstrate our software, an example of tetrode mirror is presented. From the results by MIRROR_DA, it is shown that when adjusting the voltages of two middle electrodes, C-s and C-c change signs from positive to negative, and their values vary in a wide range: therefore this tetrode mirror can be used to cancel C-s and C-c of round lenses. (C) 2008 Elsevier B. V. All rights reserved.

A novel approach for high-throughput maskless lithography is being developed by Arradiance Inc. The patented core technology is based on the combination of field emitters and microchannel electron amplifiers (MCAs) to produce a large array of individually controlled, high brightness electron beams. Brightness, stability, beam to beam uniformity, energy spread, achievable current, and many other parameters must be optimized simultaneously over a large field. Many of these parameters are determined by the characteristics of the amplification process in the MCA array that amplifies, stabilizes and shapes each electron beam. This paper describes a new three dimensional Monte Carlo model of the electron amplification process in a single microchannel. For a given input current and known MCA parameters, we calculate the (generally nonlinear) potential distribution along the channel utilizing a macroscopic saturation model. The static (3D with axial symmetry) electric field is calculated in and around the microchannel from the predicted potential distribution. That field is used to calculate individual electron trajectories along the pore length until their subsequent collision with the pore walls or arrival at the pore exit. The amplification process caused by secondary electron emission from those collisions is modelled for each electron. Evaluation of a large number of input electrons allows the MCA output to be predicted. The model is very useful for optimization of the MCA structure and operational parameters to meet the requirements of high-throughput lithography. (C) 2008 Elsevier B. V. All rights reserved.