Design Software for Electron Beam Systems

Design Software for Electron Beam Systems

Microscopy Analysis & Inspection Lithography

Software Catalogue

May 2012

Introduction

Software Catalogue P a g e 2 © MEBS Ltd., May 2012

Preface to Software Catalogue This brochure is divided into several sections. So you can “cut to the chase” and find the most relevant part for your immediate needs, the main sections are as follows:

Page 3: Introduction to MEBS – Who we are, what we do and how we do it.

Page 6: Recent & On-going Developments – Our plans for the future, things we are working on now, or packages we have recently released.

Page 11: Overview of MEBS Software – A summary of the packages we offer, the tasks they do and how they relate to each other.

Page 13: Detailed Descriptions of Off-the-Shelf Packages – For selected packages, we give a multi-page description of the software and its capabilities.

For more details on any of the software or for any other questions or comments, please see our web-site at: www.mebs.co.uk

or send an e-mail to:

[email protected]

http://www.mebs.co.uk/

mailto:[email protected]

Introduction


Introduction to MEBS

Munro's Electron Beam Software Ltd. ("MEBS") is a company based in London, England. Our company's aims are to provide:

• Specialised software for the computer aided design of electron and ion optical systems. • Expert consultancy services in the design of electron and ion beam devices and systems. • Training courses in theory and design methods in charged particle optics.

MEBS is run jointly by Eric Munro, John Rouse and Haoning Liu, who jointly have over 80 person-years of expertise in the field.

Eric Munro pioneered the use of finite element methods in electron optics and his electron lens design software has been used by most electron microscope manufacturers worldwide. John Rouse has wide experience in three-dimensional field modelling and ray tracing in electron optics. Haoning Liu is skilled in tolerancing theory of complete optical columns and is currently writing related software tools at MEBS.

On a scientific level, we’ve contributed to many aspects of the development of the subject, including the aberration theory of general combinations of electron lenses and deflectors, multipole systems, electron guns, discrete Coulomb interaction effects, asymmetry aberrations and tolerancing, and the analysis of fully three-dimensional fields and trajectories. We have applied these techniques to the design of a diverse range of instruments and components, including electron microscopes, lithography machines, e-beam testing systems, CRTs, photomultiplier tubes, e-beam welding guns, focused ion beam systems (including multipole aberration correctors) and microwave tubes. We have acted as scientific consultants to many electron optical equipment manufacturers in USA, Europe and the Far East.

Much of our time is spent writing software, under contract in response to requests from clients and also in building a range of software tools for general applications in electron optical design.

Our software is developed on Windows-based PCs and is compatible with Windows 2000, XP, Vista and Windows7 systems. We aim to provide state-of-the-art electron optical design tools design tools, so as to maximise the designer's productivity and creativity.

Because of the specialised nature of electron optical design, our philosophy is to provide a customised service to meet the needs of individual clients. We are happy to discuss specific requirements and to provide expert guidance, specialised software and support.

Dr. Eric Munro Tel: (+ 44) - 20 - 7581 – 4479 Munro’s Electron Beam Software Ltd. 14 Cornwall Gardens London SW7 4AN e-mail: [email protected] England URL: http://www.mebs.co.uk

mailto:[email protected]

http://www.mebs.co.uk/

Contents


Table of Contents Preface to Software Catalogue ............................................................................................................... 2

Introduction to MEBS ............................................................................................................................ 3

Recent & Ongoing Developments .......................................................................................................... 6

OVERVIEW .......................................................................................................................................... 6

SOURCE-CI: FOR COULOMB INTERACTIONS IN ELECTRON GUNS ........................................................ 6

IMAGE SOFTWARE ................................................................................................................................ 7

MIRROR-IMAGE AND MIRROR-DA SOFTWARE ............................................................................... 8

SECTION SOFTWARE .......................................................................................................................... 10

OTHER SOFTWARE IN DEVELOPMENT ................................................................................................... 10

PRISMS ............................................................................................................................................ 10

CURVED AXIS SYSTEMS ................................................................................................................ 10

Overview of MEBS Software ............................................................................................................... 11

SOFTWARE GROUPED ACCORDING TO FUNCTIONALITY ....................................................................... 11

Field Computation and Direct Ray-tracing ..................................................................................... 11

Electron Optical Column Design ..................................................................................................... 11

Electron Gun Simulation .................................................................................................................. 11

Multipole System Design .................................................................................................................. 11

Wien filter and Multipole System Design ......................................................................................... 12

Discrete Coulomb Interactions ........................................................................................................ 12

Software for Diffraction Effects ....................................................................................................... 12

Curved-Axis Systems ........................................................................................................................ 12

TABLE OF PACKAGES ACCORDING TO FUNCTIONALITY ........................................................................ 13

Detailed Descriptions of Off-the-Shelf Packages ............................................................................... 13

OPTICS .............................................................................................................................................. 14

OPTICS FAMILY OVERVIEW ......................................................................................................... 15

FIELD COMPUTATIONS .......................................................................................................................... 15

COLUMN SIMULATIONS ........................................................................................................................ 16

POST-PROCESSING TOOLS .................................................................................................................... 16

DYNAMIC MODULE (OPTIONAL) ....................................................................................................... 19

REFINE MODULE (OPTIONAL) ............................................................................................................ 19

TOLERANCE MODULE (OPTIONAL)................................................................................................... 20

ABER-5 .............................................................................................................................................. 22

SOURCE .............................................................................................................................................. 24

SOURCE FAMILY OVERVIEW ....................................................................................................... 25

Contents


COMPUTING ELECTROSTATIC POTENTIAL ............................................................................................. 25

COMPUTING ELECTRON TRAJECTORIES ................................................................................................ 26

COMPUTING ABERRATION COEFFICIENTS ............................................................................................. 26

COMPUTING SOURCE BRIGHTNESS ....................................................................................................... 26

PLOTTING EQUIPOTENTIALS AND TRAJECTORIES .................................................................................. 27

POST-PROCESSING FUNCTIONS ............................................................................................................. 28

MAGNETIC-LENS MODULE (OPTIONAL) .......................................................................................... 29

TOLERANCE MODULE (OPTIONAL)................................................................................................... 30

MULTIPOLE ........................................................................................................................................ 33

MULTIPOLE ....................................................................................................................................... 33

MULTIPOLE_REFINE ....................................................................................................................... 34

MULTIPOLE_TOLERANCE ............................................................................................................. 36

WIEN .............................................................................................................................................. 37

WIEN FAMILY OVERVIEW ............................................................................................................. 38

WIEN (BASE PACKAGE)........................................................................................................................ 38

WIEN-5 MODULE (OPTIONAL) ............................................................................................................ 40

WIEN-REFINE AND WIEN-REFINE-5 MODULES (OPTIONAL) ......................................................... 40

Aberration Correction using WIEN-5 and WIEN-REFINE-5 .......................................................... 42

IMAGE .............................................................................................................................................. 43

IMAGE-TOLERANCE ....................................................................................................................... 45

WAVE .............................................................................................................................................. 46

SOFEM .............................................................................................................................................. 47

3D .............................................................................................................................................. 49

SPACE CHARGE UPGRADE FOR 3D SOFTWARE ..................................................................................... 52

PROJECTION ...................................................................................................................................... 54

MECH .............................................................................................................................................. 56

EMECH ............................................................................................................................................... 56

MMECH .............................................................................................................................................. 58

CMECH ............................................................................................................................................... 60

Recent and Ongoing Developments


Recent & On-going Developments OVERVIEW We have a comprehensive set of programs for analysing and designing optical systems containing round and multipole lenses and Wien filters. We are developing software for more complex multipole systems, mirrors, prisms, and curved axis systems, including high-order aberrations and Coulomb interactions. We are bringing graphical user interfaces (GUI) to our existing packages. The GUI packages run on the latest Windows systems and have many advantages over our command-line versions. In this section of the brochure we bring you a flavour of what we have been working on recently. The software described in this section is either already in release form or is due for release in the coming year.

SOURCE-CI: For Coulomb Interactions in Electron Guns Our SOURCE software computes the Poisson potential distribution in electron sources. The post-processing tools contained in SOURCE (formerly in the SOURCE_PP package), reads in the computed Poisson potential distribution computed and computes large number of trajectories (typically 50,000) with appropriate distributions of initial conditions, set by Monte Carlo simulation, to model the initial energy spread, initial angular spread and initial spatial distribution of the emitted electrons. This computation, however, ignores discrete Coulomb interactions (CI) effects between the electrons in the gun region.

The optional upgrade module, SOURCE-CI, extends SOURCE to include the effects of inter-particle CI effects. It does this by computing the trajectories of emitted electron in bunches (e.g. 1,000 particles or 5,000 particles per bunch) simultaneously, with the inter-particle Coulomb interactions within the bunch being modelled with our fast tree-code Coulomb algorithm, that we have used previously in our IMAGE software. The electrons are still traced through the Poisson potential distribution already computed by SOURCE. The enhancements of SOURCE-CI in the post-processing tools enable the computation of the position and size of the virtual source and its emittance, including the energy broadening due to the Börsch effect and radial broadening due to the Löffler effect.

To compute the gun properties, including CI effects, we employ a two-stage process. Firstly we compute the Poisson potential distribution, assuming no inter-particle interactions. Secondly, we directly trace many thousands of electrons through this pre-computed Poisson field from cathode to gun exit, taking CI effects into account. By recording the electrons’ data at the exit of the gun we can subsequently post-process the information to determine the properties of the gun, including the virtual source properties, energy spread and emittance.

For the CI ray trace, we consider the continuous beam of particles to be composed of one or more discrete bunches of particles. Each bunch of particles is traced from cathode to gun exit plane and the CI effects from each particle in the present bunch are computed. More bunches of particles can be used to improve statistics. To achieve good modelling of the CI effects, we typically need to use bunches of electrons containing >5000 particles per bunch.

To illustrate the capabilities of SOURCE-CI, we consider the LaB6 gun of Fig. 1, which shows the electrode structure, equipotentials and electron trajectories used in the Poisson solution. We directly traced two bunches each of 5,000 electrons from cathode to gun exit and considered two cases: (1) CI effects ignored and (2) CI effects computed. Using the positions and slopes of the electrons at the gun exit, we then computed the position and size of the virtual source, as viewed from the exit plane of the gun, looking back towards the cathode.



Fig. 2 shows the position and size of the virtual source (defined here as the diameter containing 60% of the beam current, D60) for the two cases. As can be seen, the CI effects do not change the position or size of the virtual source significantly.

Fig. 3 shows histograms of the energy of the particles at the gun exit for the two cases considered. As can be seen, the CI forces cause a significant increase in energy spread (Börsch effect).

Fig. 3: Final energy histograms for CI ignored (left) and CI computed (right).

So, for this example, we see that by ignoring the CI effects in the model we obtain a good estimate of the position and size of the virtual source, but an underestimate of energy spread in the beam. The bigger energy spread in the gun computed by the SOURCE-CI software will impact the final spot size when the beam is subsequently focused using lenses with chromatic aberrations and so provides useful new information for the column designer.

IMAGE Software We are working on two developments for the IMAGE software: IMAGE GUI and PARALLEL-IMAGE. The IMAGE GUI package combines the IMAGE capabilities within an easy-to-use graphical interface. The data can be entered or viewed in a tabbed set of forms that separate the specification of the source, column, optical elements, particles and ray trace data on separate pages. The data is specified on the forms with drop down options wherever possible, thereby eliminating the need for the user to remember the correct keywords and permitted options. The graphical output is also displayed on a tabbed form so that the user can quickly switch between the various graphical displays provided by the IMAGE package (ray plots, spot diagrams, etc.). The text file output is also available in a tabbed form, so that all the output is collected together in one place so the user can quickly view the results from any program module.

CI

Anode @ 20

Cathode @ 0 V

CI ignored

Fig. 1. LaB6 gun, showing electrode structure, equipotentials and electron rays.

Fig. 2. Curves of D60 vs. defocus for CI ignored and CI computed.

5 eV 5 eV

FWHM = 0.83 eV FWHM = 0.46 eV



IMAGE GUI β-version Main Screen

In PARALLEL_IMAGE we have introduced new algorithms that take advantage of the new multi-core CPUs available in most modern PCs. The time-intensive parts of the programs involve the computation of the discrete Coulomb forces between particles in the system. This force computation has been significantly speeded up by using a hierarchical tree algorithm that operates in parallel so that the Coulomb forces on each time-step of the ray-trace can be computed on all the available processors in the PC.

MIRROR-IMAGE and MIRROR-DA Software

We are developing software to analyse electron mirrors, which are becoming increasingly important in electron optics. Mirrors generate aberrations of negative sign which compensate round-lens aberrations, as well as being useful in systems such as cathode lens columns. We have two packages for mirror systems: MIRROR-IMAGE and MIRROR-DA.

The MIRROR-IMAGE software package is a set of programs for simulating the optical properties of electron mirrors by direct ray-tracing. The software handles electron mirrors containing any combination of rotationally symmetric electrostatic and magnetic fields. The software can handle combinations of electron mirrors and electron lenses.

MIRROR-IMAGE is based on the MEBS software package IMAGE. It uses the same fundamental methods as IMAGE, including representation of the fields by Hermite series, direct ray-tracing using a fifth-order Runge-Kutta method with adaptive step size, and calculation of the discrete Coulomb interaction effects by Monte Carlo simulation with many discrete bunches of charged particles.

The MIRROR-IMAGE package includes a main program for computing the paths of charged particles through the mirror by direct ray-tracing and post-processing programs for plotting spot diagrams of the aberrations at the image plane and for plotting the trajectories. The main program allows initial conditions to be specified, to enable spot diagrams of the overall beam shape at the image plane to be computed and plotted. It also allows random initial conditions to be assigned to bunches of particles, to enable the discrete Coulomb interaction effects in the beam to be computed. It should be noted that the Coulomb interaction calculation does not take into account the interaction between the forward and reflected beams.



MIRROR_IMAGE Plot showing incident and reflected electrons in a mirror system

The MIRROR-DA software package is a set of programs for simulating the optical properties of electron mirrors, including the aberration coefficients, by the differential algebra method. The software handles electron mirrors containing any combination of rotationally symmetric electrostatic and magnetic fields. The software can handle combinations of electron mirrors and electron lenses.

MIRROR-DA is based on the MEBS software package MIRROR-IMAGE. It uses a lot of the fundamental ideas as MIRROR-IMAGE, including representation of the fields by Hermite series and direct ray-tracing using a fifth-order Runge-Kutta method with adaptive step size, but also introduces some new principles to compute the aberration coefficients. The data format for MIRROR-DA is very similar to that used in MIRROR-IMAGE, so the same data can be used to compute the aberration coefficients (using MIRROR-DA) and the overall spot size, including aberrations and coulomb interactions (using MIRROR-IMAGE).

The MIRROR-DA package includes a main program for computing optical properties in the mirror by differential algebra method, and a post-processing program for plotting spot diagrams of the aberrations at the mirror screen plane.

MIRROR-DA Plots showing fields and paraxial rays in a mirror system



SECTION Software The SECTION software package is a set of programs for simulating a column which consists of different sections, each of which can be either:

- Straight axis region - Mirror region - Bending region The software will compute the paraxial map, and then the optical properties and aberration coefficients by the differential algebra method, region by region. It uses representation of the fields by Hermite series and direct ray-tracing using a fifth-order Runge-Kutta method with adaptive step size. The regional data format for SECTION is very similar to that used in packages CURVED-IMAGE, MIRROR-DA etc.

The SECTION package includes a main program for computing optical properties from object plane to final image plane region by region, and a post-processing program for plotting spot diagrams of the aberrations at final image plane or any regional image plane.

lens

quadrupole

lensQuadru-pole

Bending fields

mirror

Object plane

Image plane

Bendingregion

Mirrorregion

Schematic of kind of system handled by SECTION

Other Software in Development

PRISMS We are working to produce software for the analysis of magnetic prisms. These are bending magnets that are often used to separate an incoming and outgoing beam, for example in a LEEM. Our software can focus the beam and compute the primary aberrations of the system for a 90 degree bending of the axis.

CURVED AXIS SYSTEMS We are working on software that will compute the aberration coefficients of systems with curved optical axes. The software will handle any combination of electrostatic and magnetic round lens, and multipole lenses, as well as Wien filters and prisms.

Overview of MEBS Software


Overview of MEBS Software Software Grouped According to Functionality In this section, we show how our off-the-shelf packages and our packages that are under development (shaded items) can be grouped according to complementary functionality.

Field Computation and Direct Ray-tracing SOFEM

3D

Overview: These packages can be used as stand-alone modules for field computation and ray tracing. They are also used to provide the axial field functions and potential distributions for our other optical computation packages.

Electron Optical Column Design OPTICS

REFINE

DYNAMIC

TOLERANCE

ABER-5

Overview: This is the core package family for electron optical computations in systems of lenses, deflectors and dynamic correction elements arranged along a straight optical axis.

Electron Gun Simulation SOURCE

SOURCE-MAGNETIC

SOURCE-TOLERANCE

SOURCE-BS

SOURCE-CI

Overview: These programs form the core of our electron gun computation software. The software allows the computation of a wide variety of rotationally symmetric guns and the post-processing of the numerical data in graphical form. For certain types of guns, we can also compute the effects of mechanical asymmetries in the gun construction. We are working on packages to model backscattered electrons in guns, which can cause electrical breakdowns. We are also working on a package to simulate the effects of Coulomb interactions in electron guns.

Multipole System Design MULTIPOLE

MULTIPOLE-REFINE

MULTIPOLE-TOLERANCE

Overview: These packages enable the optics of systems with round and multipole lenses to be computed and optimized, including the primary aberrations up to 3rd order. The effects of mechanical asymmetries can also be evaluated.



Wien filter and Multipole System Design WIEN

WIEN-5

WIEN-REFINE-5

Overview: The WIEN and WIEN-5 handle combinations of round lenses, multipole lenses and Wien filters. The packages compute the primary aberrations (WIEN) and secondary aberrations (WIEN-5). The systems can also be optimized up to 5th-order aberration terms (WIEN-REFINE-5).

Discrete Coulomb Interactions IMAGE-LENS

IMAGE

Overview: These packages enable the optical effects of discrete interparticle Coulomb repulsion forces to be computed. This can be done in systems composed of just round lenses (IMAGE-LENS) and in systems containing round lenses, multipole lenses and Wien filters (IMAGE).

Software for Diffraction Effects WAVE

Overview: This is our software for computing diffraction effects in on-axis beams.

Curved-Axis Systems PRISM

FILTER

CURVED-IMAGE

Overview: These are our development packages for curved axis systems

The shaded packages contain software that is still under development.



Table of Packages According to Functionality The following table summarizes the core packages in terms of their functionality and the optical elements they can handle.

Optical Elements Mag & Elec. round lens

Multipole lens Wien filter Deflectors

Primary Aberrations

OPTICS

MECH

MULTIPOLE

IMAGE

WIEN

OPTICS

IMAGE

Secondary Aberrations

ABER-5

PROJECTION WIEN-5 WIEN-5

ABER-5

PROJECTION

Optimisation REFINE MULTIPOLE-REFINE

WIEN-REFINE-5 WIEN-REFINE-5

REFINE

PROJECTION

Tolerancing TOLERANCE

MECH IMAGE-TOLERANCE IMAGE-TOLERANCE

TOLERANCE

IMAGE-TOLERANCE

Coulomb Interactions IMAGE-LENS IMAGE IMAGE IMAGE

Potential computation and

ray tracing SOFEM 3D 3D

SOFEM

3D

Diffraction Effects WAVE Please contact us Please contact us Please contact us

Table of packages suitable for analyzing systems containing various optical elements

In the following sections, we give more details of our individual off-the-shelf packages.

Detailed Descriptions of Off-the-Shelf Packages

In this section, we give detailed descriptions of our software packages that are available now as off-the-shelf products.

OPTICS Family


OPTICS

Software for Electron and Ion Beam Column Design

• An integrated workplace for simulating and optimizing electron and ion beam columns • Base Package (OPTICS)

• Field computation • Imaging and paraxial focusing properties • Primary geometrical and chromatic aberrations • Graphical output of fields, trajectories and aberration spot diagrams, etc.

• Optional Upgrade Modules: • DYNAMIC – For designing dynamic deflection aberration correctors • REFINE – Column optimization to minimize aberrations • TOLERANCE – To simulate aberrations due to mechanical asymmetries

• Graphical User Interface Features: • GUI provides high interactivity during the design process • Multiple Document Interface (MDI) for simulating several electron optical elements

and columns in a unified environment • Input data and graphical output can be viewed simultaneously • Batch processing capability

• System Requirements: • Runs under Microsoft Operating System (Windows 7, Vista or XP)

OPTICS Family


OPTICS FAMILY OVERVIEW

The OPTICS software is a package for the simulation and computer aided design of electron optical columns consisting of any combination of electron lenses and deflectors. Its purpose is to assist the electron optical designers with three main tasks:

1. Computing field distributions in individual electron lenses and deflectors.

2. Computing the optical properties and aberrations of any combination of such elements.

3. Graphical display of the effects of the aberrations.

A few screen shots of the new program are shown on the next pages. The operation of the program is controlled through the menus and speed buttons at the top of the screen.

Field Computations Figure 1 shows a simulation of the field distribution in a magnetic lens. The screen is divided into four panels. The upper half of the screen shows, on the left, the data that defines the finite element layout, and, on the right, the actual layout of the mesh. In the lower half of the screen, the results of the magnetic field computation are shown, consisting of the computed data for the axial flux density distribution B(z) (lower left) and the corresponding graph of B(z) (lower right). In this environment, it is easy to modify the input data and observe the effects immediately. The mesh data can be edited directly, in the top left hand panel, and the effect on the mesh layout immediately displayed in the top right hand panel. The corresponding change in the field distribution can then be observed, both numerically and graphically, in the bottom panels, just by clicking a button.

Figure 1: Screen shot showing field computation in a magnetic lens

OPTICS Family


Column Simulations Figure 2 illustrates the simulation of a complete electron optical column. The screen is again divided into four panels. The top panels show the data and layout for the column, while the bottom panels show the numerical values of the aberration coefficients and a spot diagram of the aberration effects. The imaging conditions, such as numerical aperture and field size can be altered by the user and the corresponding effects on the aberrations can be observed interactively.

Figure 2: Screen shot showing simulation of the aberrations of a complete electron optical column

Post-Processing Tools The new program has a set of comprehensive post-processing tools, which the user can access by clicking AB. Effect button. Figure 3 shows the post-processing control screen.

Figure 3: Post-processing control screen

OPTICS Family


As examples, Figure 4 and Figure 5 show the aberration spot diagrams without and with the asymmetry aberrations included, which correspond to unchecking and checking the Asymmetry Aberration checkbox on the control screen shown in Figure 3.

Figure 4: Aberration spot diagram without the asymmetry aberrations included

Figure 5: Aberration spot diagram with the asymmetry aberrations included

The post-processing tools also include the ability to generate plots computed using a Point Spread Function (PSF). This method provides the current density distribution of the PSF and a quantitative assessment of the aberrations, defined in terms of the rise distance of the PSF, in a through-focal series of planes. The rise distance of a PSF has been proven to be equivalent to the pattern edge sharpness, which can be measured experimentally. For these types of diagram, extra plotting data is required and the right-hand side of the Plotting Conditions Data form will become active if these diagram types are selected (see Figure 6).

Figure 7 shows an example of spots and contours for a through-focal set of planes for the PSF located at the top right corner of a shaped beam on axis. Figure 8 shows an example of spots and contours at selected axial plane for a shaped beam on the axis.

OPTICS Family


Figure 6: Post-processing control screen for PSF-type plot

Figure 7: Spots and contours at different planes for PSF located at the top right corner

Figure 8: Spots and contours at selected plane for shaped beam on axis

OPTICS Family


DYNAMIC Module (Optional) The DYNAMIC module can analyse electrostatic and magnetic stigmators and dynamic focus lenses in the same environment. The field functions of the stigmators and dynamic focus lenses are used to compute the required strengths to correct the deflection astigmatism and field curvature, respectively. DYNAMIC module computes and outputs the dynamic correction coefficients for the stigmators and dynamic focus lenses in the systems, as shown in Figure 9.

THIRD-ORDER DYNAMIC CORRECTION COEFFICIENTS STIGMATOR COEFFICIENTS (for 1 mm x-deflection): 0 deg elements 45 deg elements MAIN-FIELD STIGMATOR 1 ..... NORMAL 6.978223e-03 3.610953e-02 Amps 4-FOLD 3.268213e-19 -3.175038e-18 Amps DYNAMIC FOCUS LENS COEFFICIENTS (for 1 mm x-deflection): MAIN-FIELD DYN LENS 1 ............. -5.919559e-01 Ampere-turns

Figure 9: Third-order dynamic correction coefficients

REFINE Module (Optional) The REFINE module can be activated by clicking Optimization button. Figure 10 shows the window to set up the variable for the optimization process

Figure 10: Optimization control screen

OPTICS Family


Figure 11 shows the aberration spot diagrams before and after four optimization cycles.

Figure 11: Optimization Process Window for after four optimization cycles for the sample data.

TOLERANCE Module (Optional) The new program has TOLERANCE module integrated. The user can compute the perturbation fields of the lenses and deflectors due to the asymmetry errors by clicking Pert Field button. Figure 12 shows a simulation of the perturbation field due to misalignment of an electrode in an electrostatic lens.

Figure 12: Electrostatic lens simulation, with the computed axial perturbation field functions

For a complete column, the user can assign the asymmetry errors to each optical element by clicking Asy Errors button which starts Asymmetry Errors window, as shown in Figure 13.

OPTICS Family


Figure 13: Asymmetry errors window

After assigning the asymmetry errors, the user can compute the asymmetry aberrations by clicking Aberration button. Figure 14 & Figure 15 show the aberration spot diagrams without and with the asymmetry aberrations included, respectively.

Figure 14: Aberration spot diagram without the asymmetry aberrations included

Figure 15: Aberration spot diagram with the asymmetry aberrations included

ABER-5


ABER-5

For Computing Fifth-order Aberrations

This software package is supplied as an upgrade to the OPTICS package. It extends the capabilities of the OPTICS package to compute the higher-order aberrations of complete electron and ion beam columns, as well as the primary aberrations.

ABER-5 computes all the same aberrations as OPTICS - i.e. the third-order geometrical and first-order chromatic aberrations, and in addition it computes the fifth-order geometrical and third-order chromatic aberrations. The accurate prediction of these higher-order aberrations is important in designing electron and ion beam systems which use large-area projection or large-field scanning. Such systems are required for high-throughput lithography applications.

The software handles the same types of systems as the OPTICS package. This includes columns with any combination of electrostatic and magnetic lenses and deflectors. Gaussian round beams or extended shaped beams can be handled. The deflection can be dual-channel (main and sub field), using multipole and planar deflectors, and the x and y deflectors can be located either at the same axial location or at sequential positions along the z-axis. All the rotationally symmetric and multipole aberrations are computed, including the fourfold aberrations of fifth-order, created by both the third and fifth harmonics of the deflection fields.

The software computes the higher-order aberrations using specially derived aberration integrals. The axial field functions of the lenses and deflectors are first obtained with the SOFEM package. The radial expansions of these field functions, up to fifth-order terms in the off-axis distance, are then obtained by taking several axial derivatives of each axial field function. The high accuracy inherent in the fields computed with the SOFEM software is essential for obtaining accurate values of the high-order derivatives of the axial field functions.

The ABER-5 software operates in the following way. First, the principal paraxial rays are computed, by retaining only the first-order terms in the field expansions. Then, in the next approximation, the third-order terms in the field expansions are retained in order to compute the third-order geometrical aberrations, using aberration integrals in the standard way. These primary aberration integrals are evaluated using the principal paraxial rays. After that, in the final approximation, the fifth-order terms in the field expansions are retained in order to compute the fifth-order geometrical aberrations, using specially derived aberration integrals.

The fifth-order aberration integrals are very complicated, since some of the terms in them must be evaluated using the third-order trajectories. Integration by parts is used to minimize the required order of the derivatives of the axial field functions. A great simplification in the complexity of the formulae has been obtained, by expressing the aberration integrals in terms of general aberration functions with dummy arguments. These functions are then evaluated with different combinations of the paraxial and third-order rays as their specific arguments, in order to extract all the individual aberration coefficients.

For a dual-channel deflection system (with main-field and sub-field deflection), there are 124 complex fifth-order geometrical aberration coefficients in the case of a point source, and 380 for a shaped beam system. All chromatic coefficients up to third order are also computed.

The results are output in tabular form, and also graphically in the form of distortion diagrams and aberration spot diagrams. Typical examples of output from the software are shown on the following page. They illustrate the large effects that the fifth-order aberrations can have.

ABER-5


Pure magnetic focusing and deflection system Mixed focusing and deflection system

zo = 0 mm, zi = 263 mm, αi = 2 mrad, zo = 0 mm, zi = 450 mm, αi = 5 mrad, field size = 6×6 mm, Vi = 1 kV, ∆V = 1 eV field = 12 mm, Vi = 25kV, ∆V = 2.5 eV

Third order distortions only Third and fifth order distortions

Distortion diagrams for the pure magnetic focusing and deflection system

Third order aberrations only Third and fifth order aberrations Aberration spot diagrams for the mixed (electrostatic and magnetic) focusing and deflection system

zo zi

Magnetic Lens

Magnetic Deflectors

Electrostatic Lens

Magnetic Lens

Magnetic Deflectors

6 mm6 mm

6 mm 1 umGrid Scale Spot

6 mm 1 umGrid Scale Spot

SOURCE Family


SOURCE

Software for Modelling Electron and Ion Sources

• An integrated workplace for analysing electron sources

• Base Package (SOURCE) • Computing electrostatic potentials including space charge effects • Computing electron trajectories • Computing source aberrations • Computing source brightness • Graphical output of fields, trajectories, beam diameter curves, spot diagrams,

current distributions and source emittance, etc.

• Optional Upgrade Modules: • MAGNETIC-LENS – For handling magnetic lenses in source regions • TOLERANCE – To compute asymmetry aberrations of source

due to mechanical asymmetries

• Graphical User Interface Features: • GUI provides high interactivity during the design process • Multiple Document Interface (MDI) for simulating several electron sources in a

unified environment • Input data and graphical output can be viewed simultaneously

• Compatibility: • Fully compatible with MEBS’ SOURCE V3.0 and SOURCE_PP V3.2


SOURCE Family


SOURCE FAMILY OVERVIEW The SOURCE software is a package for the simulation and computer aided design of electron sources including magnetic lenses. Its purpose is to assist the electron source designers with four main tasks:

1. Electron Source Analysis 2. Post-processing for Electron Source Analysis 3. Magnetic Lens Simulation 4. Source Tolerance Simulation

A few screen shots of the new program are shown on the next pages. The operation of the program is controlled through the menus at the top of the screen.

Computing Electrostatic Potential Figure 16 shows a simulation of the electrostatic potential distribution in an electron source. The computed electrostatic potential and space charge (if required) distribution are displayed numerically and graphically in the lower right hand panel of the screen (see Figure 17 & Figure 18).

Figure 16: Screen shot showing potential computation in a LaB6 gun

Figure 17: Computed electrostatic potential

Figure 18: Graph of electrostatic potential

SOURCE Family


Computing Electron Trajectories Figure 19 shows the computed results for electron trajectories which are displayed in the lower right hand panel of the screen.

Figure 19: The computed results for electron trajectories in a LaB6 gun

Computing Aberration Coefficients Figure 20 shows the computed source aberration coefficients which are displayed in the lower right hand panel of the screen.

Figure 20: The computed aberration coefficients of a LaB6 gun

Computing Source Brightness Figure 21 and Figure 22 show the computed source brightness versus the beam half angle and the corresponding graph, which are displayed in the lower right hand panel of the screen.

SOURCE Family


Figure 21: The computed brightness versus the beam half angle

Figure 22: Graph of the computed brightness versus the beam half angle

Plotting Equipotentials and Trajectories Figure 23 shows the plot of the equipotentials and electron trajectories in an electron source.

Figure 23: Plot of the equipotentials and trajectories in a LaB6 gun

SOURCE Family


Post-Processing Functions The new SOURCE software also provides the following post processing functions for analysing electron sources:

• Computing many rays in the source region with randomly generated initial ray conditions on the cathode surface and storing the positions and slopes of rays at the source exit plane in an output file.

• Plotting spot diagrams, current density and current histograms, current distributions through the knife-edge and emittances of the source, from the computed positions and slopes of rays at the source exit plane.

• Transferring the positions and slopes of the rays from the source exit plane to any planes in the subsequent lens, and then plotting spot diagrams, current density and current histograms, current distributions through knife-edge, and emittances in the lens region.

• Transferring the positions and slopes of the rays from the source exit plane to some specified plane in the subsequent lens.

The following screenshots show some of the post-processing tools for analysing electron sources.

Figure 24: Curve of beam diameters containing 60% of the beam current

Figure 25: Spot diagrams, current density and current histograms at the five planes around the virtual

crossover (z = 1.5, 2.0, 2.5, 3.0 and 3.5 mm)

SOURCE Family


Figure 26: Current distribution through knife-edge and 12-88% rise distance

Figure 27: Source emittance at z = 2.5 mm for the beam radius of 68 μm

MAGNETIC-LENS Module (Optional) Figure 28 and Figure 29 show the simulations of the magnetic lenses with the defined polepiece region and magnetic circuit region, respectively.

Figure 28: Magnetic lens data and results (polepiece region)

SOURCE Family


Figure 29: Magnetic lens data and results (magnetic circuit region)

Figure 30 shows the simulation of a field emission gun with a magnetic lens included.

Figure 30: Simulation of a field emission gun with a magnetic lens

TOLERANCE Module (Optional) The new SOURCE program has TOLERANCE module integrated. The user can compute the perturbation fields due to the asymmetry errors of cathode and electrodes. Figure 31 shows a simulation of the perturbation field in an electron source. The computed electrostatic perturbation field functions are displayed numerically and graphically in the lower right hand panel of the screen (see Figure 32 & Figure 33).

SOURCE Family


Figure 31: Simulation of a field emission gun with a magnetic lens

Figure 32: Computed perturbation fields

Figure 33: Graph of perturbation field

The TOLERANCE module also computes the corresponding asymmetry aberrations at the virtual source plane. The computed results are stored in *.abn file as shown in Figure 34.

Lab6 gun Diameter of virtual crossover (um) = 18.202668 Position of virtual crossover (mm) = 8.849574 Individual Asymmetry Aberrations at Virtual Crossover : (Coma and astigmatism are computed for beam aperture angle = 1 mrad) ------------------------------------------------------------------------------- Defect Electrode X-shift Y-shift X-slope Y-slope Coma Astigmatism Type Number (microns) (microns) (mrads) (mrads) (microns) (microns) ------------------------------------------------------------------------------- Misalignment Cat 3.7012 - 0.422584 - 0.0028762 - (1 micron) 1 -3.6976 - -0.424657 - 0.0028760 - 2 -0.003595 - 0.002073 - 0.0000001 -

SOURCE Family


Tilt Cat 6.8409 - 0.920644 - 0.0034236 - (1 mradian) 1 -5.2586 - -0.672219 - 0.0025456 - 2 -0.520124 - -0.146271 - 0.0000079 - Ellipticity 1 - - - - - 0.28556 (1 micron) 2 - - - - - 0.0000864 ------------------------------------------------------------------------------- Overall Asymmetry Aberrations at Virtual Crossover : (Coma and astigmatism are computed for beam aperture angle = 5.000 mrad) --------------------------------------------- Asymmetry Errors Amplitude Direction (um or mrad) (degrees) --------------------------------------------- Cathode : Misalignment 3.000 0.000 Tilt 2.000 90.000 Electrode 1 : Misalignment 3.000 90.000 Tilt 2.000 60.000 Ellipticity 1.000 30.000 Electrode 2 : Misalignment 2.000 30.000 Tilt 3.000 45.000 Ellipticity 1.000 90.000 --------------------------------------------- ------------------------------------------------------------------------------- X-shift Y-shift X-slope Y-slope Coma Astigmatism (microns) (microns) (mrads) (mrads) (microns) (microns) ------------------------------------------------------------------------------- Overall Effect 4.7356 -7.6299 0.288836 -0.905637 0.29410 1.428 -------------------------------------------------------------------------------

Figure 34: Asymmetry aberration values of a LaB6 gun

MULTIPOLE Family

MULTIPOLE

For Simulation and Design of Multipole Lens Systems

MULTIPOLE MULTIPOLE computes the optical properties and aberrations of charged particle optical systems comprised of electrostatic and magnetic lenses and deflectors (Figure 35). The lenses can be round lenses, quadrupoles, hexapoles and octopoles.

MULTIPOLE has a graphics user interface (GUI), which affords a better understanding and control of the system and its parameters during the design and optimisation procedures (Figure 36).

The program uses as input a set of imaging conditions specified by the user, together with the field functions of the round and multipole lenses. These fields are computed with our SOFEM and CO-3D software packages.

Figure 36: Screen shot showing the graphical user interface of the MULTIPOLE software.

IMAGE PLANE

MAGNETIC ROUND LENS

OBJECT PLANE

ELECTROSTATIC ROUND LENS

ELECTROSTATIC & MAGNETIC MULTIPOLE ELEMENTS

ELECTROSTATIC & MAGNETIC MULTIPOLE ELEMENTS

APERTURE

Figure 35: Column containing multipole lenses

MULTIPOLE Family


The first-order optical properties are computed by numerical solution of the paraxial ray equation The computed paraxial rays are displayed on the screen. The primary aberrations are computed by evaluating appropriate aberration integrals involving the paraxial rays. The computed geometric aberrations are second and third-order aberrations, if hexapole lenses are present, and third-order aberrations, otherwise.

The program can handle both Gaussian round-beam and shaped-beam systems. The output is the computed optical properties, including a table of the first-order optical properties and a table of the aberration coefficients.

MULTIPOLE also has an integrated aberration spot generator to visually show the aberration effects (Figure 37) using the computed aberration coefficients and given initial image conditions, such as beam half angle, beam size, deflection parameter at either object or image plane.

Figure 37: The aberration spot diagram for a multipole column containing 2 electrostatic round lenses, 4

electrostatic quadrupole lenses and 4 electrostatic octopole lenses to cancel Cs.

MULTIPOLE_REFINE An extension to the MULTIPOLE software is MULTIPOLE_REFINE. This is analogous to the OPTICS and REFINE packages, in that MULTUPOLE_REFINE allows selected parameters of the multipole column to automatically adjusted to minimise a chosen combination of aberrations.

MULTIPOLE_REFINE computes and optimises the third-order geometrical aberrations and first-order chromatic aberrations for systems that do not include hexapole lenses; for systems with hexapoles lenses, the program additionally computes the second-order geometrical aberrations. Intermediate images do not need to be stigmatic, however the computed aberration coefficients are meaningful only if the beam is stigmatically focused at the final image plane.

Because of the complicated nature of multipole columns, the optimisation of the system is often crucial to the successful design of the system. It also requires the visualisation and control of many parameters and for this reason, MULTIPOLE_REFINE uses a graphical user interface (GUI) to enter and control the system parameters (Figure 38) and the optimisation procedure (Figure 39).

MULTIPOLE Family


Figure 38: Screen shot of the MULTIPOLE_REFINE GUI showing the forms for controlling the system data

and optimisation weighting factors

Figure 39: Screen shot showing the form for controlling the optimisation process

MULTIPOLE Family


MULTIPOLE_TOLERANCE An important consideration in multipole systems is the optical effect of mechanical asymmetries in the lenses. An extension to the MULTIPOLE software to compute these effects is MULTIPOLE_TOLERANCE. MULTIPOLE_TOLERANCE computes the additional third-order geometrical aberrations and first-order chromatic aberrations due to lens tolerancing errors in systems that do not include hexapole lenses; for systems with hexapoles lenses, the program also computes the additional second-order geometrical aberrations due to the tolerancing errors. It should be noted that MULTIPOLE_TOLERANCE cannot handle deflectors.

The normal lens fields are computed with our SOFEM and 3D software. The asymmetry fields for round lenses are computed by the field programs from our TOLERANCE package and, for multipole lenses, the asymmetry fields are computed with a modification of our 3D software that computes the difference between the ideal and perturbed lens.

The software is driven from a graphical user interface that allows clear control of the system and the tolerancing errors (Figure 40) and the plotting of spot diagrams.

Figure 40: Screen shot showing the form for specifying the asymmetry errors.

WIEN Family


WIEN

Software for Design of Columns Containing Wien Filters and Multipole Lenses

• An integrated workplace for analysing and optimising the column optics

• Base Package (WIEN) • Handles round lenses, quadrupoles, hexapoles, octapoles, Wien filters • Imaging and paraxial focusing properties • Primary geometrical and chromatic aberrations • Graphical output of fields, trajectories and aberration spot diagrams, etc.

• Optional Upgrade Modules: • WIEN-5 – To simulate aberrations up to fifth order • WIEN-REFINE – Column optimization to minimize aberrations • WIEN-REFINE-5 – Optimization to minimize aberrations up to 5th order

• Graphical User Interface Features:

• GUI provides high interactivity during the design process • Intuitive control of system variables • Seamless integration of package features


WIEN Family


WIEN FAMILY OVERVIEW The Wien filter family handles the analysis and optimization of the optics of straight-axis systems that contain a Wien filter plus any combinations of electrostatic and magnetic round lenses, quadrupole lenses, hexapole lenses and octopole lenses. If a Wien filter is not present, then a deflection system consisting of a magnetic or electrostatic dipole element can also be included. The program can handle both Gaussian round-beam and shaped-beam systems. The magnetic field of the Wien filter is automatically adjusted to give the Wien condition.

The output includes: the optical element settings after focusing and filter adjustment (e.g. the lens excitations, the filter deflector strengths); the first-order optical properties (e.g. column magnifications and dispersions); and the coefficients. These coefficients are used to display the aberration spot diagrams and to compute the aberration values for the given initial conditions.

WIEN (base package) The Wien filter program, WIEN, will handle the primary beam optics of straight-axis systems, as shown schematically in Figure 41.

Figure 41: Schematic of system handled by WIEN

Wien Filter

Magnetic Round Lens

Electrostatic Quadrupole

Magnetic Quadrupole

Electrostatic

Round Lens

Return Beam Primary Beam

Object

Image

WIEN Family


The system can contain a Wien filter plus any combinations of the following optical elements:

(1) Electrostatic and Magnetic Round Lenses, (2) Electrostatic & Magnetic Quadrupole lenses, (3) Electrostatic & Magnetic Hexapole lenses, and (4) Electrostatic & Magnetic Octopole lenses.

If a Wien filter is not present, then a deflection system consisting of a magnetic or electrostatic dipole element can also be included.

WIEN has a Graphic User Interface (GUI), which affords a better understanding and control of the system and its parameters during the analytical and design procedures. A typical screen-shot of the WIEN GUI is shown in Figure 42.

Figure 42: WIEN Control Panel

The input data of WIEN includes the imaging condition data (e.g. the positions of object and image planes) and the optical element parameters (e.g. the positions and strengths of the elements). The field functions of the round lenses, quadrupole lenses and Wien filters are computed with our software packages SOFEM and 3D (available separately). The axial field functions are fitted with Hermite series to enable their high-order derivatives to be computed accurately. The program can handle both Gaussian round-beam and shaped-beam systems.

The program will compute the first-order optical properties for any setting of the electric and magnetic deflection parts of the Wien filter. This enables the required strength of the deflectors to be chosen to give the desired deflection of the return beam. For the primary beam, the user can set the strength of the electrostatic dipole field and the program will adjust the strength of magnetic dipole field in the filter in order to satisfy the Wien condition to allow the beam to pass through the filter with zero net deflection. The first-order optical properties are computed by numerical solution of the paraxial ray equation. The aberrations are computed by evaluating a differential algebra ray-trace.

The computed optical properties include: the optical element settings after focusing and filter adjustment (e.g. the lens excitations, the filter deflector strengths); the first-order optical properties (e.g. column magnifications and dispersions) and tables of the second and third-order geometric and 1st order chromatic aberration coefficients. This numerical output can subsequently be displayed graphically as aberration spot diagrams and is used to compute the aberration values for the given initial conditions.

WIEN Family


If the Wien filter is replaced by a single-channel deflection system, the program can operate the deflectors in two modes: scanning or rocking. In scanning mode, the deflectors move the beam linearly over the target. In rocking mode, the beam does not move linearly over the image plane but is fixed on the optical axis: instead, the deflector can be used to tilt the beam.

WIEN-5 Module (Optional) WIEN-5 is an extension of WIEN which computes the second, third, fourth and fifth-order geometrical aberrations and chromatic aberrations up to fourth-rank. Intermediate images do not need to be stigmatic, however the computed aberration coefficients are meaningful only if the beam is stigmatically focused in both x and y directions at the final image plane.

WIEN-5 also has an integrated aberration spot generator to visually show the aberration effects using the computed aberration coefficients and given initial image conditions, such as beam half angle, beam size, deflection parameter at either object or image plane. The spot plots can include only the primary aberrations or a combination of all aberrations up to 5th-order.

Layout of Hexapole Cs Corrector Paraxial Rays in quadrupole/octopole Cs corrector

Spot for Cs Corrector – 3rd-order aberrations Spot for Cs Corrector – 3rd& 5th-order aberrations

Figure 43: WIEN-5 Example Plots

WIEN-REFINE and WIEN-REFINE-5 Modules (Optional) WIEN-REFINE and WIEN-REFINE-5 are extensions to WIEN and WIEN-5, respectively. They compute and optimise the optical properties and aberrations of the system.

WIEN Family


WIEN-REFINE computes and optimises the third -order geometrical aberrations and chromatic aberrations up to second-rank.WIEN-REFINE-5 computes and optimises the third and fifth-order geometrical aberrations and chromatic aberrations up to fourth-rank.

After defining the imaging conditions data, optical element settings and parameter values and the focus constraints for the autofocus scheme, as in WIEN or WIEN-5, you can specify and the weighting factors for the optimization scheme via the Weighting Factors Window control screen.

Figure 44: WIEN-REFINE-5 Weighting Factors Control Screen

The weighting factors assigned on this form are used in the refining process to target certain aberrations for special consideration when minimizing the overall spot size. In general terms, each aberration will contribute a certain fraction to the overall size of the final spot. During the refine cycle, the chosen positions, sizes, strengths and rotations of the elements are adjusted so as to minimise a weighted sum of squares of the individual contributions to the overall spot size from each aberration. The user can choose the weighting factor to assign to each contributing aberration.

When the appropriate weighting factors have been selected, the optimization control screen allows the user to interactively refine the system to minimize the selected aberrations, subject to the constraints and weighting factors chosen.

After the system has been optimized to the user’s satisfaction, the column data can then be updated and the final aberration values computed. After this, a diagram of the final, optimized spot shape can be plotted, for any desired initial imaging data.

WIEN Family


Figure 45: WIEN-REFINE-5 Optimisation Control Screen

Aberration Correction using WIEN-5 and WIEN-REFINE-5 Use of additional optical elements can reduce the aberrations introduced in the original system. Examples of using hexapoles or a combination of quadrupoles and octopoles to reduce primary spherical aberration have been shown above.

In addition, if we have a deflection system to scan or rock the beam, the deflection aberrations will, in general, scale with deflection field strength: we call these aberrations the dynamic deflection aberrations. We can use additional optical elements whose strength varies with deflection field strength to correct some aberrations introduced by the deflection system: we call these additional optical elements the dynamic correction elements.

Common dynamic correction elements include a round lens to correct for normal deflection field curvature, a quadrupole element to correct for normal deflection astigmatism.

Both WIEN-5 and WIEN-REFINE-5 can handle round lenses and multipole lenses that can be used to compensate the dynamic deflection aberrations. In addition, the optimization function in WIEN-REFINE-5 can be used to compute the required settings (strength and/or rotation angle) for the dynamic correction elements to compensate the deflection aberrations.

In the software, the dynamic correction elements are not energized during the autofocus procedure, but they are switched on when the beam is in focus and the deflection system is energized. The settings of the dynamic correction elements are then optimized to reduce or eliminate the chosen set of deflection aberrations.

IMAGE Family


IMAGE

For Aberrations and Coulomb Interactions This software package computes effects of aberrations and discrete Coulomb interactions in electron and ion beams, in a unified way, by direct ray-tracing. The software is applicable to a very wide range of systems, including combinations of round lenses, deflectors and stigmators, multipole systems, cathode imaging systems and electron mirrors. Accurate direct ray tracing eliminates the need to use conventional aberration theory, and the method is therefore applicable to systems with aberrations of any order. The software handles fields with an arbitrary combination of multipole components, and can compute the effects of asymmetry errors, for use in tolerancing calculations. Post-processing facilities are included, for plotting point spread functions (with systematic or random initial conditions) and through-focal series of edge blur diagrams. To analyze a system containing any combination of optical elements (e.g. lenses, deflectors, stigmators, dynamic focus coils, etc.), the axial field functions of each element are first computed using any suitable field analysis software (e.g. SOFEM for lenses, deflectors and stigmators, or EO-3D and MO-3D for multipole elements). The axial field function of each optical element is then fitted with a set of orthogonal analytic functions. Two sets of fitting functions are provided: Fourier series and Hermite series. Fourier series are suitable for electrostatic potential distributions, while Hermite series are convenient for magnetic lenses and deflection fields, since these are generally of finite axial extent, and can usually be fitted well with a few terms of a Hermite series. After fitting the axial fields by exact analytic functions, the off-axis fields at any point are obtained very accurately by radial power series expansions. The software can compute these expansions to the 11th power of the off-axis distance (r11), for all multipole field components up to dodecapole (12-pole) fields. Thus the software can handle the aberrations of all types of optical element likely to be encountered in practice. The analytic representation of the fields for each optical element means they are all exact solutions of Laplace’s equation, suitable for use in direct ray-tracing. The paths of electrons or ions are traced through these analytic fields by direct ray-tracing, using a fifth-order Runge-Kutta formula, with adaptive step size for automatic error control. This ray-trace algorithm typically gives an accuracy of better than 1 picometre over a column length of 1 metre. In the ray tracing, a whole ensemble of particles can be traced down the column simultaneously. This makes it possible to include the Coulomb fields between the N particles in the ensemble, on each time step. The N-body Coulomb fields can be computed in two ways: either directly, in a pair-wise fashion, for the N(N-1)/2 discrete interactions, or using a fast hierarchical tree-code algorithm, that enables the inter-particle fields to be computed in O(Nlog2N) operations. This enables the discrete Coulomb interaction effects (both stochastic and global) to be included, and for their effects to be combined with the geometrical and chromatic aberrations of the imaging elements in a unified and rigorous way. The fact that the electrons and ion paths are calculated directly, as functions of time, means that there are no restrictions on the imaging conditions. In particular, there are no limitations on the magnitudes of the ray slopes relative to the axis, and there are no restrictions on the particles reversing their axial direction. These freedoms allow the software to handle systems such as cathode imaging systems and electron mirrors in a unified way, which is not normally possible with software that uses conventional paraxial ray equations and aberration theory. A subset of the software, called IMAGE-LENS, can be supplied which allows the analysis of the combined effects of aberrations and Coulomb interactions, in systems containing round lenses only. The diagrams on the following page show some illustrative results with the IMAGE software.

IMAGE Family


Fourier series fits to the axial field function of a magnetic lens with asymmetric pole-pieces. Fits are shown with 2, 8 and 32 terms of the Fourier series. 32 terms gives an excellent fit.

Computed point spread functions for a projection system. (a) Spot diagrams of geometrical aberrations, for a

system with a deflected sub-field, with systematic initial conditions. (b) Spot diagrams for an on-axis sub-field, showing combined effect of aberrations and discrete Coulomb interactions.

OBJECTIVE LENS

TRANSFER DOUBLET 1

TRANSFER DOUBLET 2

IMAGING LENS

OBJECT PLANE

IMAGE PLANE HEXAPOLE 1 HEXAPOLE 2

Schematic diagram of a hexapole corrector for spherical aberration.

Hermite series fit to field function of the hexapole lenses, with 20, 40 and 100 terms of the Hermite series.

Spot diagrams for hexapole corrector. (a) Under-corrected, (b) Best correction, (c) Over-corrected,

(d) Enlarged view of spot at best correction.

M = 2 M = 8 M = 32

(a) (b)

IMAGE Family


IMAGE-TOLERANCE We have an extension to the IMAGE software that allows the combination of aberrations and coulomb interactions to be computed for a system with asymmetry errors. This package, called IMAGE-TOLERANCE, uses our 3D software to compute two sets of potential distributions for each perturbed optical element – an ideal distribution for the perfectly constructed lens, and a perturbed potential distribution for the lens with asymmetry errors. From these distributions, IMAGE-TOLERANCE extracts the asymmetry fields along the optical axis for any size of asymmetry error (assuming the effects are linear).

The resulting axial asymmetry harmonics are then fitted with Hermite series and are used in the IMAGE-TOLERANCE program, along with the ideal fields of the non-perturbed elements, to compute the optical properties of the system, in an analogous way to that used in IMAGE. The graphical post-processing features of IMAGE-TOLERANCE are similar to those in IMAGE, where the spot shape at the object or image plane can be displayed.

As an example of the use of IMAGE-TOLERANCE, suppose one of the hexapoles in the above example of a spherical aberration corrector was constructed with a misalignment of one of the poles. The diagrams below show the use of IMAGE-TOLERANCE in this case, and it can be seen that the level of correction obtained in the perturbed system is not as good as that obtained in the ideal system.

Cross-section through Perturbation potentials Dipole and quadrupole

Ideal hexapole lens for misaligned pole asymmetry fields

Figure 46: Asymmetries and perturbation fields in IMAGE-TOLERANCE

Figure 47: Spot diagrams for various correction settings in perturbed hexapole corrector system

Under corrected Over corrected Best correction

Quadrupole Field

Dipole Field

WAVE


WAVE

Wave Optical Simulation of Current Density Distributions

Software WAVE is for computing current density distributions in electron beams using a wave optical treatment, with Kirchhoff's diffraction integral. In this software package, the following four effects are taken into account: (1) the diffraction effect; (2) the spherical aberration; (3) the chromatic aberration; and (4) the demagnified Gaussian image of the source. Five programs are included in this software package. They are:

WAVE1 for computing the beam current density distribution with the combined effects of diffraction and spherical aberration. (This current density distribution is called the monochromatic point spread function.)

WAVE2 for computing the beam current density distribution with the combined effects of diffraction, spherical aberration and chromatic aberration. (This is called the polychromatic point spread function.)

WAVE3 for computing the beam current density distribution with the combined effects of diffraction, spherical aberration, chromatic aberration and demagnified Gaussian image of the source. (This is called the overall current density distribution with an extended source.)

WAVEP1 for plotting the beam current density distribution from the results computed by Programs WAVE1, WAVE2 and WAVE3.

WAVEP2 for plotting the normalised beam current density distribution from the results computed by Programs WAVE1, WAVE2 and WAVE3.

Typical graphical output from the software is shown below.

Figure 48: Typical Plot of Normalised Overall Current Density Distribution with Extended Source

Radius R (nm) 0 80.00

Normalised

beam

current

Density

0

1Half-angle (mrad) = 2.000Beam current (pA) = 1.000Beam voltage (kV) = 1.000Wavelength (nm) = 0.039

Defocus distance (um) = 10.000Spherical ab. (mm) = 100.000Chromatic ab. (mm) = 50.000Energy spread (eV) = 1.000(Gaussian, 1/e full width)

Source diameter (nm) = 10.000

Diameter (50%) (nm) = 35.649Diameter (75%) (nm) = 67.195Diameter (90%) (nm) = 143.955

Rise distance(20%-80%) (nm) = 49.379

Jmax (A/cm**2) = 0.170

3D Family


SOFEM

Potentials, Fields and Raytracing in Lenses and Deflectors

This software computes potential and field distributions in electrostatic and magnetic lenses and deflectors, using the second-order finite element method (SOFEM). The program provides at least an order of magnitude greater accuracy than the first-order FEM for a given number of mesh-points. As successively more mesh-points are used, the relative accuracy with respect to the first-order method becomes progressively greater. The second-order method is also less sensitive to the distribution of mesh-points than the first-order method.

After the field distributions have been computed, facilities are provided for direct ray-tracing through the electron lens fields. Since the field components are obtained to a high accuracy (typically better than 1 part in 104), the trajectories obtained with this software are very accurate, and can be used to estimate the lens aberrations directly from the raytrace. (This is difficult to do very accurately with the first-order FEM.)

This software can also be used in conjunction with the ABER-5 software package, to compute the fifth-order geometrical and third-order chromatic aberrations of complete columns of electron lenses and deflectors.

The numerical technique used in the software is the second-order finite element method (SOFEM). The space between the electrodes or polepieces is divided into a mesh of second-order finite elements, using linear Coons patches to perform the sub-division. Each finite element is a curvilinear quadrilateral with 9 nodes. The potential in each element is modelled as a bi-quadratic function on to a unit square in the isoparametric mapping plane. The potential distributions are computed by minimizing an appropriate variational functional.

Facilities are provided for plotting the mesh layout, to check graphically that it has been specified correctly in the data.

For electrostatic lenses, curved electrodes and dielectric materials can be handled easily. A set of basis solutions are computed, corresponding to 1 volt applied to each electrode in turn.

For magnetic lens field analysis, there are three programs. The first computes the magnetic scalar potential distribution in the polepiece region assuming constant permeability polepieces. The second computes the vector potential distribution in the magnetic circuit and coil windings, again assuming constant permeability. The third program computes the vector potential in the magnetic circuit and coil windings, taking magnetic saturation into account, with numerically specified B-H curves, defined by the user.

Magnetic deflectors with toroidal or saddle coils can be handled, located inside rotationally symmetric magnetic circuits or wound on rotationally symmetric magnetic formers. The program computes the first, third and fifth harmonic components of the deflection field.

Electrostatic multipole deflectors can be handled. To enable the field to be computed as a set of multipole harmonic components, the electrostatic potential is assumed to vary linearly in the azimuthal direction in the azimuthal gaps between adjacent electrodes. Again, the first, third and fifth harmonics of the deflection field are computed.

After computing the lens fields, direct ray-tracing in the rotationally symmetric fields is performed using a Runge-Kutta formula. The field components at each point on the trajectory are obtained by interpolation between 5 second-order finite elements.

3D Family


Facilities are provided for plotting equipotentials, magnetic flux lines, axial focusing and deflection functions, and plots of the electron or ion trajectories from the direct ray-tracing.

Typical examples of output from the software are shown below.

Electrostatic lens with Highly saturated Axial flux density in gap region, curved ceramic insulators magnetic lens computed and experimental values

Electrostatic deflector Toroidal deflector Computed deflection field harmonics with curved electrodes inside a magnetic lens for toroidal deflector

Ray-trace in combined magnetic-electrostatic lens Direct ray-trace in an electrostatic mirror

Figure 49: Graphical output from SOFEM

4 0 m m

CoilCoil

Coil Coil

Z coordinate (mm)-30 30

Axial FluxDensity(Teslas)

0

2.5

32000 AT

28000 AT

24000 AT

EXCITATION(Experimental)

(SOFEM)

First Harmonic(x10 AT/m)-5

Third Harmonic(x10 AT/m )-1 3

Fifth Harmonic(x10 AT/m )+4 5

0

2

4

6

-2

-4

-6Axial Ordinate (mm)-80 30

Electrodes

500 Ampturns 20kV 20kV-3.5kV

Polepieces

5 mm

10000 V –3193.6 V

3D Family


3D

3D Field Computation and Ray-tracing

3D computes the properties of electrostatic and magnetic electron optical systems, using a fully 3D potential computation and direct electron ray-tracing around 3D electrode and polepiece structures. Equipotentials in 2D sections of the structure in any (x,y), (y,z) or (z,x) plane can also be plotted. In cases where the structure has a straight optical axis but a departure from rotational symmetry (e.g. an off-axis electrostatic secondary electron collector in a SEM column or a magnetic matrix lens), the axial field functions can be extracted and plotted. These axial field functions can then be used to compute the optical properties of the system, taking the 3D deflection and quadrupole fields into account. The spot shape at the image plane can then be plotted, including the beam shift, coma and astigmatism caused by the 3D fields.

The finite difference method (FDM) is used to compute the potential distribution, wherein the potentials are obtained at points on a 3D rectangular grid. However, the surfaces of the electrodes do not have to conform to the grid lines and thus, 3D objects of varied shape can be analysed without the need for the user to define a complicated mesh to fit around the objects. The regular mesh topology afforded by the FDM and use of a point relaxation method to solve the equations enormously reduces the storage requirements compared with other methods (eg. finite element).

The programs require one main data file to run, in which the FD mesh, the object structures and potentials (or permittivities), the boundary conditions and any required symmetry planes in x, y or z, are defined. The data file is in free format, uses key-words to define the data and allows the use of comment lines, thereby making the file easily readable and compact.

The specification of the FD mesh is achieved by defining independently the x, y and z mesh line numbers and their positions; the use of the 3D Cartesian grid makes the mesh definition compact. The form of each electrode or dielectric structure involves three levels of hierarchy, namely: surfaces, objects and groups. Each object consists of a number of intersecting surfaces, and several objects at the same potential can be collected together in a group. The user can define each surface of the object separately, or can use key-words to define all the surfaces for the commonly encountered shapes listed below. Each object is usually composed of one solid object from Figure 50, plus one or more cutting planes or holes.

Key-Word Arguments Purpose CYLINDER x1, y1, z1, x2, y2, z2, r1, r2 Defines a cylinder ELLIPCYL x1, y1, z1, x2, y2, z2, x3, y3, z3, r1, r2 Defines an elliptical cylinder SPHERE xc, yc, zc, r1, r2 Defines a sphere BOX xc, yc, zc, xp, yp, zp, xq, yq, zq, su, sv, sw Defines a box CONE x1, y1, z1, x2, y2, z2, α Defines a cone FRUSTUM x1, y1, z1, x2, y2, z2, r1, r2, r3, r4 Defines a frustum CYLHOLE x1, y1, z1, x2, y2, z2, r Defines a cylindrical hole ECYLHOLE x1, y1, z1, x2, y2, z2, x3, y3, z3, r Defines an elliptical cylindrical hole SPHHOLE xc, yc, zc, r Defines a spherical hole CONHOLE x1, y1, z1, x2, y2, z2, α Defines a conical hole PLANE xp, yp, zp, xn, yn, zn Defines a plane cut GENERAL c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 Defines a general quadric surface

Figure 50: Command list for 3D object definition

3D Family


For the calculation of trajectories the initial positions, energies and emission angles of each charged particle are specified. The path of the particle (whose mass and charge can be specified) through the 3D fields is computed using a Runge-Kutta algorithm, and the data at the initial and final point on the ray are output, as is the position and velocity at each step of the ray-trace, if required.

To compute the optical properties, the program reads the object and image planes, and the beam half-angle. The beam can be interactively focused at the selected image plane by adjusting any of the electrode potentials or the magnetic field either manually or automatically in an autofocus mode. The first-order optical properties and the normal and 3D aberration coefficients are printed out.

The field computation parts of 3D are available separately, if required. These modules are used to compute the fields for 3D optical elements, such as multipole lenses and Wien filters, and the axial fields can be interfaced with many of our optical design packages, such as WIEN, MULTIPOLE and IMAGE. Also, the electrostatic and magnetic parts of the 3D package (EO-3D and MO-3D, respectively) are also available separately, if required.

Sample input and output from the 3D package is shown below.

TITLE Example Secondary Electron collector UNITS Millimetres MESH X-lines 1 0.00000 11 70.00000 Y-lines 1 -70.00000 11 70.00000 Z-lines 1 -30.00000 11 100.00000 OBJECTS ELECTRODE lens FRUSTUM 0 0 20, 0 0 100, 5 10, 50 65 ELECTRODE lens FRUSTUM 0 0 35, 0 0 100, 5 7, 10 35 GRID sample BOX 0 3.536 -3.536, 1 3.536 -3.536, 0 0 0, 30 10 30 ELECTRODE collector CYLINDER 0 -65 5, 0 -50 5, 0 10 DIELECTRIC light_pipe CYLINDER 0 -50 5, 0 -30 5, 0 10 BOUNDARIES N lens, N lens, chamber_base lens POTENTIALS GROUP lens -1.0 GROUP sample 0.0 GROUP collector 10.0 GROUP chamber_base -2.0 PERMITTIVITIES GROUP light_pipe 5.0 SYMMETRY S N N

Example electrostatic data file

Ray and equipotential output

Finite difference mesh layout

Tilted Sample

Lens polepiece

Secondaries

Equipotentials

Collector

3D Family


Axial deflection function

Spot for optic axis through side bore of matrix lens

Rays and equipotentials in combined field system

Rays and equipotentials in magnetic matrix lens

Screen-shot of 3D software in action

1.109e-09

5.700e-05

T

-250.000 250.000 MILLIMETRES

---------------------------

Semi angle (mr) = 10.000

Beam energy (eV) = 5000.000 Beam ripple (eV) = 1.000

Spherical Cs(mm) = 1267.700 Chromatic Cc(mm) = 115.511

---------------------------

X-shift Dx(um) = 1516.222 Y-shift Dy(um) = -276.427

Coma Cx(um) =-14677.340 coeffs Cy(um) = -8325.750

Astig. Ax(um) = 466.293 coeffs Ay(um) = -390.523

---------------------------

Defocus Dzi(um) = 0.000

---------------------------

Dx

25.000 um

Dy

2 5 . 0 0 0

u m

Example Secondary Electron collector

Conical Magnetic Lens with Side Hole z-y plane, x = 0 mm

z-y plane, x = 0 mm

lower z = -130 mm, upper z = 30 mm lower y = -70 mm, upper y = 70 mm lower z = -130 mm, upper z = 30 mm lower y = -70 mm, upper y = 70 mm

electron beam

lens bores

magnetic scalarequipotentials

3D Family


Space Charge Upgrade for 3D Software GO-3D is an upgrade to the 3D package that computes the properties of electrostatic electron optical systems, using a fully three-dimensional (3D) potential computation and direct electron ray-tracing around 3D electrode and dielectric structures, taking space-charge effects into account. The software also handles emission from flat cathodes. GO-3D takes magnetic fields into account in computing the electrostatic potentials and rays, if the corresponding 3D magnetic field has already been computed. The data format and running of the programs is similar to the 3D package.

To compute the effects of volume space charge, the potential distribution, φ, should be a solution of Poisson’s equation ∇ = −2

0φ ρε

At the outset of the solution, neither φ nor the space charge distribution, ρ, are known.

Poisson’s equation is solved by an iterative scheme, which involves successively computing the 3D electrostatic potentials, cathode emission current (if a flat cathode is present) and space charge density distribution, until a self-consistent solution is obtained. A flowchart showing how the program works when a cathode region is analysed is shown in Figure 51.

If the cathode region is not analysed, the user can assign a specified current to each of the electron rays defined in the ray-trace initial conditions. Alternatively, GO-3D will interface with the SOURCE software and reads the output data from a 2D cathode region analysed using SOURCE and computes the space charge effects in the subsequent 3D electric and magnetic field regions.

The space charge distribution is computed by tracing the current-carrying rays through the system. As a ray carrying current ∆I passes through each cell of the mesh (Figure 52), it deposits a charge

tIQ ∆∆=∆ . , where ∆t is the transit time of the ray through the cell. The space charge density in the cell is increased by vol

Q∆=∆ρ where vol is the cell volume. An incremental charge density, δρ = ∆ρ/8, is then assigned to each node bounding the cell.

Figure 51: GO-3D Flowchart

Flat cathode regions are defined using a relatively small number of key-words, specifying the cathode shape, temperature, work function, Richardson constant, etc.

Some examples of the graphical output from the package are shown below.

Compute emission current from cathode cells

Assign currents to rays

Perform direct ray trace & assign space charge

Compute Poisson potential distribution

Start with initial potential distribution

Converged?

Write out results and quit

NO YES

FD mesh cell(Volume = vol)

∆I

Currentcarrying ray

+δρ

+δρ +δρ

+δρ

+δρ+δρ

+δρ +δρ

Transit time ∆t

Figure 52: Assignment of space charge

3D Family

(a)

(b)

(c)

Figure 53: Equipotentials and rays in triple in-line CRT gun. (a) Cross-section through the gun, along the optical axis. (b) Section normal to the optic axis through the grid, showing the circular apertures. (c) Section

normal to the optic axis through the anode,

(a) (b)

Figure 54: Equipotentials and rays for Poisson solution of SCALPEL-type gun. (a) cross-section through the gun, along the optical axis. (b) cross-section through the grid, normal to the optical axis

cathode grid anode

grid cathode

PROJECTION


PROJECTION

For the Design and Optimisation of Projection Systems

PROJECTION helps design and optimization electron and ion beam projection systems for high-throughput lithography. The type of column that can be designed with the software is shown below.

Figure 55: Schematic structure of an electron or ion beam projection system, with an off-axis shaped beam.

The two groups of deflectors (Group-A and Group-B) act as aberration-reduction elements.

An electron or ion beam passes through a rectangular region of a mask (located at the “object plane”), forming a rectangular shaped beam. This shaped beam may be centered either on or off the optical axis. The general off-axis case is illustrated above. A system of magnetic or electrostatic projection lenses (Lenses A and Lenses B) is then used to form a demagnified image of this rectangular shaped beam at a target plane (located at the “image plane”). The lenses can be magnetic, electrostatic or both. An aperture is generally placed between the two sets of lenses.

Two groups of deflectors, which can be either magnetic or electrostatic, can also be located on each side of the aperture. The deflectors on the object side are called “Group-A Deflectors”, and those on the image side are called “Group-B Deflectors”. If the shaped beam is centered off-axis, the deflectors can steer the beam though the lenses along a modified path to reduce the aberrations, and thereby act mainly as aberration-reduction elements, rather than as conventional deflectors.

A conventional projection system, in which the projected area of the mask is centered on the optical axis, is simply a special case of the system shown above, with the shaped beam centered on the axis, and the deflectors either switched off or omitted. For the case where the shaped beam is located off-axis and there are two sets of deflectors, PROJECTION can handle the so-called “balanced case”, in which the Group-A and Group-B deflections exactly cancel each other out. PROJECTION can also handle the general “unbalanced case”, in which the two deflections do not cancel, but some residual net deflection remains. The unbalanced case is often required when the mask contains “grillage bars” between adjacent shot areas in the mask plane, since in this case the beam must be shifted so as not to leave gaps between adjacent projected shots on the wafer.

PROJECTION computes the optical properties of such systems, including the geometrical aberrations of 3rd-order and 5th-order and chromatic aberrations of up to 4th rank. The software can also refine the design to optimise the optical performance. The properties of dynamic correction elements (i.e. stigmators and dynamic focus lenses) can be computed. Several graphical post-processing facilities are included in PROJECTION for plotting the principal paraxial rays, the lens

Lenses A

Lenses BGroup-A Deflectors

ApertureMask

(Object Plane)

Off-AxisShaped Beam

Off-AxisShaped Beam

Target(Image Plane)

Group-B Deflectors

Dynamic Stigmators

Dynamic Focus Lenses

PROJECTION


and deflector axial field functions, aberration spot diagrams in the image plane and curent density contours in the final spot. Some of these graphical output capabilities are highlighted below.

The three principal paraxial rays. Lens and deflection axial field distributions

used to compute the optical properties.

Aberration spot diagram

Beam current density contours

MECH Family


MECH

For Design and Tolerancing of Electron Lenses

The MECH software package computes the properties of electron lenses, including the effects of mechanical defects in lens construction and alignment, such as misalignments, tilts and ellipticities of the individual electrodes or polepieces. There are three components to the package: EMECH, for electrostatic lenses; MMECH, for magnetic lenses; and CMECH for combined field lenses.

EMECH The EMECH software package computes the properties of electrostatic lenses, including the effects of mechanical defects in lens construction and alignment, such as misalignments, tilts and ellipticities of the individual electrodes.

The electrostatic potential distribution is computed by the finite difference method. Electron or ion trajectories are computed through the computed electrostatic field by direct ray-tracing. Optical properties are computed by solving the paraxial ray equation and evaluating aberration integrals.

Perturbation field distributions due to small mechanical defects in electrode construction are computed by a perturbation method, based on Sturrock's principle. The program computes the deflection fields due to small misalignments and tilts of each individual electrode, and the quadrupole fields due to small ellipticities of each electrode. The effects of these asymmetry fields on the optical properties are then computed. The program computes the beam displacement and coma due to small misalignments and tilts, and the astigmatism caused by electrode ellipticities.

Data input is very simple. In the data, there is an option to specify either rotational symmetry (z,r) or planar symmetry (x,y). The finite difference mesh is rectangular in the (z,r) or (x,y) plane. The grid spacing can be varied in different parts of the finite difference mesh. The electrode geometry is defined by any combination of straight-line segments, circular arcs and cubic spline curves. The electrode cross-sections are defined independently of the finite difference mesh layout, and the electrode profiles are not constrained to pass exactly through the grid-points. Specially modified finite difference equations are used at grid points adjacent to the electrode surfaces, to maintain high accuracy in the potential solution. Up to 10 independent electrodes can be specified in the data. After setting up the data, it can be checked with a pre-processor program that displays the mesh layout and electrode structure.

The finite difference equations are solved by Gaussian elimination. A set of basis solutions is computed, corresponding to one volt applied to each electrode in turn, with all the other electrodes grounded. This enables the potential distribution corresponding to any specific set of electrode voltages to be generated very rapidly, by linear superposition of the basis set of solutions.

In the direct ray-trace program, the field components are computed by bi-cubic interpolation on the finite difference mesh, and the equations of motion are solved by a power series method. The direct ray-trace program runs extremely fast, and the electrode structure, equipotentials and trajectories can be displayed graphically, almost instantly.

The program for computing the perturbation fields due to small mechanical asymmetries uses Sturrock's principle, in which small geometrical perturbations δr of the electrode positions are replaced by equivalent perturbations δΦ of the potential at the electrode surface, according to the formula δΦ = – δr · ∇Φ , where ∇Φ is the potential gradient at the electrode surface.

MECH Family


The program that computes the optical properties uses an iterative focusing algorithm, with graphical display, that allows the lens to be manually focused at a specified image plane. There is an algorithm for autofocusing the beam by automatically adjusting a chosen electrode voltage.

The optical properties are output in tabular form, including the asymmetry aberrations. These is an additional program for plotting the perturbation field functions caused by mechanical defects. The values of the asymmetry aberrations caused by the mechanical defects can be used to specify suitable tolerances for the construction and alignment of electrostatic lenses.

Typical output from the software is shown below.

Mesh layout and electrode structure Computed equipotentials and electron trajectories

ILLUSTRATIVE BIPOTENTIAL LENS Focusing conditions: Object plane ................. zo(mm) = -30.000 Image plane ................. zi(mm) = 14.000 Semi angle at zi ......... alphai(mr) = 10.000 Electrode voltage ......... V1(Volts) = 2000.000 Electrode voltage ......... V2(Volts) = 20704.029 Beam voltage ripple ...... DVi(Volts) = 1.000 Round lens properties: Magnification ..................... M = -0.329727 Spherical ab coeff ........... Cs(mm) = 835.756 Chromatic ab coeff ........... Cc(mm) = 208.996 Spherical ab disk ....... ds(microns) = 0.418 Chromatic ab disk ....... dc(microns) = 0.101 Asymmetry aberrations: ----------------------------------------------------------------------------- Electrode X-shift Y-shift Coma Astigmatism Type of defect Number (microns) (microns) (microns) (microns) ----------------------------------------------------------------------------- 1 micron Misalignment 1 1.64352 - 0.00629 - 2 -0.33228 - 0.00017 - 1 milliradian of Tilt 1 9.57508 - 0.00722 - 2 4.99075 - -0.00339 - 1 micron Ellipticity 1 - - - -0.90058 2 - - - 0.08942

Computed optical properties, including asymmetry aberrations

ILLUSTRATIVE BIPOTENTIAL LENS

ROTATIONAL SYMMETRY

MECH Family


MMECH The MMECH software package computes the properties of magnetic lenses, including the effects of mechanical defects in lens construction and alignment, such as misalignments, tilts and ellipticities of the individual polepieces.

The magnetic scalar potential distribution between the lens polepieces is computed by the finite difference method. Trajectories are computed through the magnetic field by direct ray-tracing. Optical properties are obtained by computing the paraxial rays and evaluating aberration integrals.

Perturbation field distributions due to small mechanical defects in polepiece construction are computed by a perturbation method, based on Sturrock's principle. The program computes the deflection fields due to small misalignments and tilts of each individual polepiece, and the quadrupole fields due to small ellipticities of each polepiece. The effects of these asymmetry fields on the optical properties are then computed. The program computes the beam displacement and coma due to small misalignments and tilts, and the astigmatism caused by polepiece ellipticities.

Data input is very simple. The finite difference mesh is rectangular in the (z,r) plane. The grid spacing can be varied in different parts of the finite difference mesh. The polepiece geometry is defined by any combination of straight-line segments, circular arcs and cubic spline curves. The polepiece cross-sections are defined independently of the finite difference mesh layout, and the polepiece profiles are not constrained to pass exactly through the grid-points. Specially modified finite difference equations are used at grid points adjacent to the polepiece surfaces, to maintain high accuracy in the potential solution. Up to 4 independent polepieces can be specified in the data. After setting up the data, it can be checked with a pre-processor program that displays the mesh layout and polepiece structure.

The finite difference equations are solved by Gaussian elimination. A set of basis solutions is computed, corresponding to one Ampère-Turn applied to each polepiece in turn, with all the other polepieces grounded. This enables the magnetic scalar potential distribution corresponding to any specific set of polepiece excitations to be generated very rapidly, by linear superposition of the basis set of solutions.

In the direct ray-trace program, the magnetic flux density components are computed by bi-cubic interpolation on the finite difference mesh, and the equations of motion are solved, in Cartesian coordinates, by a power series method. The direct ray-trace program runs extremely fast, and the electrode structure, equipotentials and trajectories can be displayed graphically, almost instantly. (z,r), (z,x), or (z,y) views of the trajectories can be plotted.

The program for computing the perturbation fields due to small mechanical asymmetries uses Sturrock's principle, in which small geometrical perturbations δr of the polepiece positions are replaced by equivalent perturbations δΦ of the potential at the polepiece surface, according to the formula δΦ = – δr · ∇Φ , where –∇Φ is the magnetic field at the polepiece surface.

The program for computing the optical properties uses an autofocus algorithm for automatically adjusting the lens excitation to provide exact focusing.

The optical properties are output in tabular form, including the asymmetry aberrations. These is an additional program for plotting the perturbation field functions caused by mechanical defects. The values of the asymmetry aberrations caused by the mechanical defects can be used to specify suitable tolerances for the construction and alignment of magnetic lenses.

Typical output from the software is shown below.

MECH Family


Mesh layout and polepiece structure Computed equipotentials and electron trajectories

ILLUSTRATIVE MAGNETIC LENS, WITH D1 = 10MM, D2 = 10MM, S = 10MM Focusing conditions: Object plane ................. zo(mm) = -100.000 Image plane ................. zi(mm) = 10.000 Semi angle at zi ......... alphai(mr) = 10.000 Beam voltage .............. Vi(Volts) = 20000.000 Beam voltage ripple ...... DVi(Volts) = 1.000 Excitation ............. NI(Ampturns) = 1104.920 Round lens properties: Magnification ..................... M = -0.107395 Rotation angle ........... Theta(deg) = 82.107 Spherical ab coeff ........... Cs(mm) = 21.771 Chromatic ab coeff ........... Cc(mm) = 9.741 Spherical ab disk ....... ds(microns) = 0.011 Chromatic ab disk ....... dc(microns) = 0.005 Asymmetry aberrations: ----------------------------------------------------------------------------- Polepiece X-shift Y-shift Coma Astigmatism Type of defect Number (microns) (microns) (microns) (microns) ----------------------------------------------------------------------------- 1 micron Misalignment 1 1.20676 -0.51102 0.00010 - 2 -0.26276 0.61687 0.00009 - 1 milliradian of Tilt 1 17.00047 -10.73073 0.00099 - 2 6.53502 -9.92950 0.00142 - 1 micron Ellipticity 1 - - - 0.09210 2 - - - 0.02547

Computed optical properties, including asymmetry aberrations

ILLUSTRATIVE MAGNETIC LENS, WITH D1 = 10MM, D2 = 10MM, S = 10MM

ROTATIONAL SYMMETRY

MECH Family


CMECH This software package is supplied as an upgrade to the EMECH and MMECH software. It is used for computing the properties of combined electrostatic and magnetic lenses with superimposed fields. It computes the primary optics and the spherical and chromatic aberration. It also computes the asymmetry aberrations caused by mechanical defects in lens construction and alignment, such as misalignments, tilts and ellipticities of the individual electrodes and polepieces.

The electrostatic and magnetic potential distributions are first computed by the finite difference method, using EMECH and MMECH. Electron or ion trajectories through the combined electrostatic and magnetic fields can then be computed with CMECH by direct ray-tracing. Optical properties and aberrations are computed by solving the paraxial ray equation and evaluating aberration integrals using CMECH.

Perturbation field distributions due to small mechanical defects in the electrodes and polepieces are computed by a perturbation method, based on Sturrock's principle, using EMECH and MMECH.

In the direct ray-trace program, the electrostatic and magnetic field components are computed by bi-cubic interpolation on the finite difference mesh, and the equations of motion are solved by a power series method. The direct ray-trace program runs extremely fast. The electrode and polepiece structures, the electrostatic and magnetic scalar equipotentials, and the electron or ion trajectories can be displayed graphically, almost instantly.

The program for computing the optical properties uses an iterative focusing algorithm, with graphical display. This allows the electrostatic or magnetic lens to be manually focused at a specified image plane, and there is an autofocus algorithm for automatically adjusting a chosen electrode voltage or the magnetic lens excitation to provide exact focusing.

The optical properties are output in tabular form, including the asymmetry aberrations. The values of the asymmetry aberrations caused by the mechanical defects can be used to specify suitable tolerances for the construction and alignment of combined electrostatic and magnetic lenses. Typical output from the software is shown below and on the following page.

Mesh layouts, showing electrodes and polepieces Computed equipotentials and trajectories

ILLUSTRATIVE BIPOTENTIAL LENSILLUSTRATIVE MAGNETIC LENS, WITH D1 = 10MM, D2 = 10MM, S = 10MM

MECH Family


ILLUSTRATIVE BIPOTENTIAL LENS ILLUSTRATIVE MAGNETIC LENS, WITH D1 = 10MM, D2 = 10MM, S = 10MM Focusing conditions: Object plane ................. zo(mm) = -30.000 Image plane ................. zi(mm) = 14.000 Semi angle at zi ......... alphai(mr) = 10.000 Electrode voltage ......... V1(Volts) = 2000.000 Electrode voltage ......... V2(Volts) = 10000.000 Magnetic excitation .... NI(Ampturns) = 380.063 Beam voltage ripple ...... DVi(Volts) = 1.000 Round lens properties: Magnification ..................... M = -0.373007 Rotation angle ........... Theta(deg) = 59.094 Spherical ab coeff ........... Cs(mm) = 278.262 Chromatic ab coeff ........... Cc(mm) = 82.892 Spherical ab disk ....... ds(microns) = 0.139 Chromatic ab disk ....... dc(microns) = 0.083 Asymmetry aberrations: ----------------------------------------------------------------------------- Polepiece X-shift Y-shift Coma Astigmatism Type of defect Number (microns) (microns) (microns) (microns) ----------------------------------------------------------------------------- 1 micron Misalignment Elec 1 0.71027 0.61655 0.00169 - Elec 2 -0.28530 -0.04305 0.00008 - Pole 1 0.84085 -0.85790 0.00086 - Pole 2 -0.13227 0.62119 0.00014 - 1 milliradian of Tilt Elec 1 5.36801 3.40208 0.00583 - Elec 2 3.69889 1.28791 0.00052 - Pole 1 11.14763 -14.75039 0.00507 - Pole 2 3.49742 -9.99674 0.00237 - 1 micron Ellipticity Elec 1 - - - 0.38446 Elec 2 - - - 0.07759 Pole 1 - - - 0.16379 Pole 2 - - - 0.04314

Computed optical properties, including the asymmetry aberrations due to misalignment, tilt and ellipticity of each electrode and polepiece

Design Software for Electron Beam Systems

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