Eric Munro

Computer programs for the design and optimization of electron and ion beam lithography systems

Abstract This paper describes computer programs, developed in the electron optics group at Imperial College during the last seven years, for the design and optimization of electron and ion beam lithography systems. These programs can also be used for designing other equipment, such as electron microscopes and electron beam inspection systems. The set of programs includes the following: (1) field computation for rotationally symmetric electrostatic and magnetic lenses; (2) field computation for electrostatic and magnetic deflectors; (3) programs for computing the aberrations of any combination of electron lenses and deflectors; (4) programs for plotting diagrams of the aberrated spot shape; (5) an optimization program that adjusts the positions, sizes and strengths of the lenses and deflectors to minimize the aberrations; (6) programs for designing electron guns, taking space charge and thermal velocities into account; (7) a program for computing discrete Coulomb interaction effects in electron and ion beams; (8) a direct ray tracing program for computing trajectories in combined electrostatic and magnetic fields; and (9) programs for computing the fields and aberrations of quadrupole and octopole focusing systems. The operation of these programs is described and illustrated with typical examples.

Three‐dimensional computer modeling of electrostatic and magnetic electron optical components

This paper describes and illustrates a suite of programs which have been written for the computer‐aided design of three‐dimensional electron optical systems. The programs can analyze electrostatic systems containing conductors and dielectrics with specified surface charge distributions and also magnetic systems with permeable polepieces and coil windings. The finite difference method is used to compute the potentials at points on a three‐dimensional (3D) rectangular grid but the difference equations at the material interfaces are modified to handle curved boundaries and permeable materials. The programs were written and run on a personal computer and have also been ported to several larger machines.

Miniature low voltage beam systems producable by combined lithographies

Abstract The project of a miniaturized vacuum microelectronic 100 GHz switch is described. It implies the development of a field emission electron gun as well as the investigation of miniaturized lenses and deflectors. Electrostatic elements are designed and developed for this application. Connector pads and wiring pattern are created by conventional electron beam lithography and a lift-off or etching process. Wire and other 3-dimensional structures are grown using electron beam induced deposition. This additive lithography allows to form electrodes and resistors of a preset conductivity. The scanning electron microscope features positioning the structures with nm precision. An unconventional lithography system is used that is capable of controlling the pixel dwell time within a shape with different time functions. With this special function 3-dimensional structures can be generated like free standing square shaped electrodes. The switch is built by computer controlled additive lithography avoiding assembly from parts. Lenses of micrometer dimensions were investigated with numerical electron optics programs computing the 3-dimensional potential and field distribution. From the extracted axial field distribution the electron optic characteristic parameters, like focal length, chromatic and spherical aberration, were calculated for various lens excitations. The analysis reveals that miniaturized optics for low energy electrons, as low as 30 eV, are diffraction limited. For a lens with 2 μm focal length, a chromatic aberration disc of 1 nm contributes to 12 nm diffraction disc. The spherical aberration blurs the probe by 0.02 nm, assuming an aperture of 0.01 rad. Employing hydrogen ions at 100 V, a probe diameter of 0.3 nm generated by chromatic aberration is possible. Miniaturized electron optical probe forming systems and imaging systems can be constructed with those lenses. Its application as lithography systems with massive parallel beams can be forseen.

Simulation methods for multipole imaging systems and aberration correctors

Two different methods have been derived and implemented for simulation of multipole imaging systems and aberration correctors. The first method uses an aberration theory for combinations of multipole lenses and deflectors, including primary and secondary aberrations up to the fifth order. A damped least-squares algorithm is used to minimise the dynamically correctable aberrations. This yields the appropriate signals for the dynamic correction elements, e.g. stigmators and dynamic focus lenses. The second method uses a direct ray-tracing approach. The numerically computed multipole lens and deflection fields are fitted with analytic functions through which trajectories are directly traced with a high degree of self-consistency. By computing the paths of many particles simultaneously, the combined effects of aberrations and discrete Coulomb interactions are accurately simulated. Furthermore, the effects of electrical and mechanical asymmetries on the multipole elements can readily be simulated with this approach.

Electron and ion optical design software for integrated circuit manufacturing equipment

This article describes methods for the computer aided design of electron and ion beam columns for the integrated circuit (IC) manufacturing industry. The techniques described include computation of field distributions in electron lenses and deflectors, electron trajectories and aberrations, dynamic corrections, effects of discrete Coulomb interactions, design of electron guns, treatment of diffraction effects, optimization, and tolerancing of complete columns. These techniques are illustrated with examples relevant to the IC manufacturing industry, including systems for high-throughput electron beam lithography, nanolithography systems, and electron beam systems for inspection, metrology, and voltage testing.

Analysis of off-axis-shaped beam systems for high-throughput electron-beam lithography

For high-throughput electron beam lithography, projection systems using symmetric magnetic doublet lenses can produce images with zero distortion. However, the projected pattern area is limited by beam blur at large off-axis distances. If an off-axis shaped beam pattern is imaged in a projection system, the aberrations can be greatly reduced by introducing deflectors, which steer the beam through the projection lenses in a modified path. In this paper, the principle of this type of projection with in-lens deflectors is first outlined. The method for computing the optical properties of such systems, based on an extension of our previously published unified aberration theory, is then described. To provide accurate simulation of systems with such large field sizes, our new software computes both the third and fifth-order aberrations. The computation of dynamic corrections, which can not only correct deflection field curvature and astigmatism but also reduce stitching errors, is also described. A design example of an off-axis shaped beam projection system with deflectors is presented, which has been optimized by the damped least squares method. The results show that such systems can have extremely small beam blur, distortion and stitching errors. The presented design images a 0.25 mm square shot over a 3 mm square region of the wafer, with 2 mrad beam half-angle, with a beam blur less than 26 nm, and distortions and stitching errors less than 19 nm.

Secondary electron detection in the scanning electron microscope

Abstract A method of image simulation in the Scanning Electron Microscope (SEM) 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. Since the interactions of electrons within the sample have previously been reported in detail (M. Balasubramanyam et al., SPIE Proc. 2014 (1993) 104), this paper concentrates on the 3D simulation of the paths of the secondary electrons once they leave the sample surface. The computer modelling allows the collection characteristics of secondary electron detectors to be investigated, and examples of simulated images are shown. The techniques described can be used to improve the design of detectors for the SEM.

Electron-optics method for high-throughput in a SCALPEL system: preliminary analysis

Abstract A likely technology to supplant optical tools for the manufacturing of sub-0.13 μm design rule ICs is one based upon SCALPEL ® (SCattering with Angular Limitation Projection Electron-beam Lithography). One serious barrier to the acceptance of any lithographic technique by the IC manufacturing community is an inability to provide economically viable wafer throughput levels. Using a simple, parametric, time-utilization model of a step-and-scan writing strategy, we have identified the areas of greatest influence on throughput in a SCALPEL system. Though issues such as stage speed, resist sensitivity, and space charge-limited beam current do constrain the problem, we have found that the effective size of the printing field is the most sensitive parameter for realizing high throughput levels in SCALPEL. In this paper we present an electron-optical method for attaining high-throughput in a SCALPEL-based exposure tool. Starting with a moderately large area beam (1 mm × 1 mm) at the mask plane and simple, telecentric reduction (4x) optics, we have investigated increasing the effective printed field size through a combination of beam deflections, image stitching, and dynamic corrections. A preliminary analysis of recent modeling results indicates that a 3 mm × 3 mm effective field size at the wafer can be achieved while maintaining beam blur within manageable limits. The extensibility of this electron-optical approach to a production-worthy level of wafer throughput is presented, including the potential impact on other system parameters.

Three-dimensional modelling of various aspects of the scanning electron microscope

Abstract Software tools for modelling three-dimensional (3D) electrostatic and magnetic electron-optical systems have been used to investigate various aspects of the inspection of insulating specimens in a scanning electron microscope (SEM). The theory and implementation of the software are summarised. Three design studies relevant to SEM imaging are presented, each requiring a full 3D field and trajectory computation: (1) 3D microfields and trajectories near the surface of charged insulating specimens, (2) design of a front end of an asymmetric photomultiplier tube, (3) an off-axis electrostatic secondary electron collector in the presence of a magnetic lens field.

Asymmetry aberrations and tolerancing of complete systems of electron lenses and deflectors

The computation of asymmetry aberrations in electron‐beam focusing and deflection system is discussed. The aberrations caused by the asymmetry errors (misalignment, tilt, and ellipticity) in magnetic and electrostatic defectors are especially emphasized. First, the method for evaluating the perturbations of electrostatic and magnetic fields due to the asymmetry errors are described; then the formulas for computing the asymmetry aberration coefficients are derived. A set of computer programs based on this paper and also our previous work [X. Zhu and H. Liu, in Proceedings of the International Symposium on Electron Optics, Beijing, 1986 (Institute of Electronics, Academia Sinica, Beijing, 1987), p. 309; E. Munro, J. Vac. Sci. Technol. B 6, 941 (1988); and H. Liu and X. Zhu, Optik 84, 123 (1990)] has been developed, which can handle the tolerancing of complete columns containing any combination of electrostatic and magnetic lenses and deflectors, such as are required for electron‐beam lithography and inspect...