Xieqing Zhu

A computer program for electron gun design using second‐order finite elements

A computer program has been developed for the analysis and design of electron guns. The program uses second‐order, curved, isoparametric finite elements to obtain very accurate potential and field computation. Special features of the program include fast solution of the second‐order finite element equations with a specially written incomplete Choleski conjugate gradient (ICCG) algorithm, accurate field computation using biquartic interpolation, and direct ray tracing with a third‐order power series method. Space charge effects are taken into account, with an iterative solution of Poisson’s equation. The brightness is also computed. The second‐order finite elements permit accurate simulation of curved cathodes and very large changes in geometrical scale factor. This allows the program to handle all types of electron guns, ranging from field emission guns with submicron radius cathodes, to high current Pierce‐type guns. The computational techniques used are described and illustrated with typical examples.

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.

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.

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.

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...

Field computation techniques in electron optics

The authors describe the software for the computer-aided design of electron and ion optical systems, with special emphasis on field computation in devices with diverse physical structures. These include electron guns, magnetic and electrostatic lenses and deflectors for electron-beam lithography and inspection systems, wide-angle lenses and deflectors for cathode-ray tubes, components with constructional errors, multiple lenses, and structures with fully three-dimensional field distributions. The computed fields are accurate enough for reliable evaluation of the optical properties, including the aberrations. >

Solution of electron optics problems with space charge in 2D and 3D

Space charge effects are significant in many electron optical components, for example CRTs, LaB6 guns and magnetron injection guns. In such devices, the volume space charge influences the beam current and focusing properties. In systems with smaller beam currents, such as e-beam lithography columns, discrete Coulomb interactions cause defocusing, radial blurring and increased energy spread. Various techniques are described for simulation of systems with space charge, including software for modelling rotationally symmetric electron guns with magnetic fields, using second-order finite element method with iterative solution of Poissons equation. The software has a novel method for the allocation of space charge which simulates the effect of transverse thermal velocities and ensures an even distribution of the space charge. We present finite difference software for 3D systems with space charge, wherein a specified current is associated with each ray, space charge density is assigned to each grid node on the ray path, and then Poissons equation is iteratively solved for the self- consistent solution. Discrete Coulomb interactions in lithography columns have been modelled with a many-body Monte-Carlo simulation, and various new software features will be described, including the treatment of cell projection systems, and space charge interaction effects in multiple-beam lithography systems.

Aberration correction for charged particle lithography

At present, the throughput of projection-type charge particle lithography systems, such as PREVAIL and SCALPEL, is limited primarily by the combined effects of field curvature in the projection lenses and Coulomb interaction in the particle beam. These are fundamental physical limitations, inherent in charged particle optics, so there seems little scope for significantly improving the design of such systems, using conventional rotationally symmetric electron lenses. This paper explores the possibility of overcoming the field aberrations of round electron lense, by using a novel aberration corrector, proposed by Professor H. Rose of University of Darmstadt, called a hexapole planator. In this scheme, a set of round lenses is first used to simultaneously correct distortion and coma. The hexapole planator is then used to correct the field curvature and astigmatism, and to create a negative spherical aberration. The size of the transfer lenses around the planator can then be adjusted to zero the residual spherical aberration. In a way, an electron optical projection system is obtained that is free of all primary geometrical aberrations. In this paper, the feasibility of this concept has been studied with a computer simulation. The simulations verify that this scheme can indeed work, for both electrostatic and magnetic projection systems. Two design studies have been carried out. The first is for an electrostatic system that could be used for ion beam lithography, and the second is for a magnetic projection system for electron beam lithography. In both cases, designs have been achieved in which all primary third-order geometrical aberrations are totally eliminated.

Tolerancing of electron beam lithography columns

A new software package has been developed for the tolerancing of complete electron and ion beam columns. The software computes the asymmetry aberrations caused by small mechanical imperfections in the construction and alignment of the lenses and deflectors. The imperfections considered include misalignments, tilts and ellipticities of individual polepieces, electrodes, coil windings and deflection plates. The asymmetry fields due to these mechanical errors are computed by perturbation methods, and the resulting parasitic aberrations are evaluated with asymmetry aberration integrals. The effects of aberration correction elements, such as alignment coils and stigmators, are also handled by the software. The overall effects of the aberrations can be displayed graphically. Illustrative results are presented for nanolithography and high-throughput lithography systems.

Improved resolution in field-emission lithography machines

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.