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# Roadmap for focused ion beam technologies

Katja Höflich, Gerhard Hobler, Frances Allen, Tom Wirtz, Gemma Rius, Lisa Mcelwee-White, Arkady Krasheninnikov, Matthias Schmidt, Ivo Utke, Nico Klingner, et al.

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Katja Höflich, Gerhard Hobler, Frances Allen, Tom Wirtz, Gemma Rius, et al. Roadmap for focused ion beam technologies. Applied Physics Reviews, 2023, 10 (4), 10.1063/5.0162597. hal-04960530

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**Roadmap for focused ion beam technologies**

Katja Höflich ❉️ ⚙️ ; Gerhard Hobler ❉️ ⚙️ ; Frances I. Allen ❉️ ⚙️ ; Tom Wirtz ❉️ ⚙️ ; Gemma Rius ❉️ ⚙️ ;

Lisa McElwee-White ⚙️ ; Arkady V. Krasheninnikov ⚙️ ; Matthias Schmidt ⚙️ ; Ivo Utke ⚙️ ; Nico Klingner ⚙️ ;

Markus Osenberg ⚙️ ; Rosa Córdoba ⚙️ ; Flyura Djurabekova ⚙️ ; Ingo Manke ⚙️ ; Philip Moll ⚙️ ;

Mariachiara Manoccio ⚙️ ; José María De Teresa ⚙️ ; Lothar Bischoff ⚙️ ; Johann Michler ⚙️ ;

Olivier De Castro ⚙️ ; Anne Delobbe ⚙️ ; Peter Dunne ⚙️ ; Oleksandr V. Dobrovolskiy ⚙️ ; Natalie Frese;

Armin Gölzhäuser ⚙️ ; Paul Mazarov ⚙️ ; Dieter Koelle ⚙️ ; Wolfhard Möller; Francesc Pérez-Murano ⚙️ ;

Patrick Philipp ⚙️ ; Florian Vollnhals ⚙️ ; Gregor Hlawacek ❉️ ⚙️

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Appl. Phys. Rev. 10, 041311 (2023)

https://doi.org/10.1063/5.0162597

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# Roadmap for focused ion beam technologies F

Cite as: Appl. Phys. Rev. **10**, 041311 (2023); doi: **10.1063/5.0162597**

Submitted: 15 June 2023 · Accepted: 13 October 2023 ·

Published Online: 26 December 2023 · Corrected: 26 January 2024

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Katja Höflich,<fnref n="1" />,ª ID Gerhard Hobler,<fnref n="2" />,ª ID Frances I. Allen,<fnref n="3" />,ª ID Tom Wirtz,<fnref n="4" />,ª ID Gemma Rius,<fnref n="5" />,ª ID

Lisa McElwee-White,<fnref n="6" /> ID Arkady V. Krasheninnikov,<fnref n="7" /> ID Matthias Schmidt,<fnref n="8" /> ID Ivo Utke,<fnref n="9" /> ID Nico Klingner,<fnref n="7" /> ID

Markus Osenberg,<fnref n="10" /> ID Rosa Córdoba,<fnref n="11" /> ID Flyura Djurabekova,<fnref n="12" /> ID Ingo Manke,<fnref n="10" /> ID Philip Moll,<fnref n="13" /> ID

Mariachiara Manoccio,<fnref n="14" /> ID José María De Teresa,<fnref n="15" /> ID Lothar Bischoff,<fnref n="7" /> ID Johann Michler,<fnref n="9" /> ID Olivier De Castro,<fnref n="4" /> ID

Anne Delobbe,<fnref n="16" /> ID Peter Dunne,<fnref n="17" /> ID Oleksandr V. Dobrovolskiy,<fnref n="18" /> ID Natalie Frese,<fnref n="19" /> Armin Gölzhäuser,<fnref n="19" /> ID

Paul Mazarov,<fnref n="20" /> ID Dieter Koelle,<fnref n="21" /> ID Wolfhard Möller,<fnref n="7" /> Francesc Pérez-Murano,<fnref n="5" /> ID Patrick Philipp,<fnref n="4" /> ID

Florian Vollnhals,<fnref n="22" /> ID and Gregor Hlawacek<fnref n="7" />,ª ID

## AFFILIATIONS

## ABSTRACT

The focused ion beam (FIB) is a powerful tool for fabrication, modification, and characterization of materials down to the nanoscale. Starting with the gallium FIB, which was originally intended for photomask repair in the semiconductor industry, there are now many different types

<footnote n="1">¹Ferdinand-Braun-Institut gGmbH, Leibniz-Institut für Höchstfrequenztechnik, 12489 Berlin, Germany</footnote>

<footnote n="2">²Institute of Solid-State Electronics, TU Wien, 1040 Vienna, Austria</footnote>

<footnote n="3">³Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA</footnote>

<footnote n="4">⁴Advanced Instrumentation for Nano-Analytics (AINA), MRT Department, Luxembourg Institute of Science and Technology (LIST), 4422 Belvaux, Luxembourg</footnote>

<footnote n="5">⁵Institute of Microelectronics of Barcelona, IMB-CNM-CSIC, 08193 Cerdanyola del Vallès, Spain</footnote>

<footnote n="6">⁶Department of Chemistry, University of Florida, Gainesville, Florida 32611-7200, USA</footnote>

<footnote n="7">⁷Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany</footnote>

<footnote n="8">⁸Department of Isotope Biogeochemistry, Helmholtz-Centre for Environmental Research GmbH-UFZ, 04318 Leipzig, Germany</footnote>

<footnote n="9">⁹Laboratory for Mechanics of Materials and Nanostructures, EMPA Swiss Federal Laboratories for Material Science and Technology, CH 3602 Thun, Switzerland</footnote>

<footnote n="10">¹⁰Institute of Applied Materials, Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany</footnote>

<footnote n="11">¹¹Institute of Molecular Science, University of Valencia, 46980 Paterna, Spain</footnote>

<footnote n="12">¹²Department of Physics, Helsinki Institute of Physics, University of Helsinki, 00014 Helsinki, Finland</footnote>

<footnote n="13">¹³Max Planck Institute for the Structure and Dynamics of Matter, 22607 Hamburg, Germany</footnote>

<footnote n="14">¹⁴CNR-NANOTEC Institute of Nanotechnology, 73100 Lecce, Italy</footnote>

<footnote n="15">¹⁵Instituto de Nanociencia y Materiales de Aragon (INMA), Universidad de Zaragoza-CSIC, 50009 Zaragoza, Spain</footnote>

<footnote n="16">¹⁶Orsay Physics S. A., 13710 Fuveau, France</footnote>

<footnote n="17">¹⁷Université de Strasbourg, CNRS, IPCMS UMR 7504, 67034 Strasbourg, France</footnote>

<footnote n="18">¹⁸Faculty of Physics, University of Vienna, 1090 Vienna, Austria</footnote>

<footnote n="19">¹⁹Faculty of Physics, Physics of Supramolecular Systems, University of Bielefeld, 33615 Bielefeld, Germany</footnote>

<footnote n="20">²⁰Raith GmbH, 44263 Dortmund, Germany</footnote>

<footnote n="21">²¹Physikalisches Institut, Center for Quantum Science (CQ) and LISA⁺, Universität Tübingen, 72076 Tübingen, Germany</footnote>

<footnote n="22">²²Institute for Nanotechnology and Correlative Microscopy gGmbH, 91301 Forchheim, Germany</footnote>

<footnote>ª) Authors to whom correspondence should be addressed: katja.hoeflich@fbh-berlin.de; gerhard.hobler@tuwien.ac.at; francesallen@berkeley.edu; tom.wirtz@list.lu; gemma.rius@csic.es; and g.hlawacek@hzdr.de</footnote>
of FIB that are commercially available. These instruments use a range of ion species and are applied broadly in materials science, physics, chemistry, biology, medicine, and even archaeology. The goal of this roadmap is to provide an overview of FIB instrumentation, theory, techniques, and applications. By viewing FIB developments through the lens of various research communities, we aim to identify future pathways for ion source and instrumentation development, as well as emerging applications and opportunities for improved understanding of the complex interplay of ion-solid interactions. We intend to provide a guide for all scientists in the field that identifies common research interest and will support future fruitful interactions connecting tool development, experiment, and theory. While a comprehensive overview of the field is sought, it is not possible to cover all research related to FIB technologies in detail. We give examples of specific projects within the broader context, referencing original works and previous review articles throughout.

© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0162597

TABLE OF CONTENTS

I. INTRODUCTION.................................................. 4

II. INSTRUMENTATION.................................................. 4

A. Ion sources.................................................. 4

B. Beam transport.................................................. 6

C. Analytical tools and detectors.............................. 8

D. Other FIB accessories........................................ 10

E. FIB processing of radioactive samples.................. 10

F. Software and correlative approaches.................... 11

III. SIMULATION APPROACHES FOR FIB

PROCESSING.......................................................... 12

A. Simulation techniques based on the binary collision approximation (BCA).............................. 13

1. Principles and limitations .................................... 13

2. Specific BCA codes................................................ 14

3. BCA-based simulations of FIB processing .................... 14

B. Molecular dynamics and molecular statics .................... 15

1. Principles and simulation codes.............................. 15

2. Models for the potential energy function .................... 16

3. Applications of molecular dynamics to FIB irradiation.................................................. 18

4. Limitations and extensions .................................... 19

C. Kinetic Monte Carlo (kMC)...................................... 20

D. Continuum modeling................................................ 20

1. Ion implantation and milling .................................... 20

2. Gas-assisted deposition and etching ............................ 21

3. Applications to FIB processing................................. 23

IV. APPLICATIONS OF FOCUSED ION BEAMS.................... 24

A. Applications of subtractive FIB processing.................. 25

1. FIB for materials science...................................... 25

2. FIB for mechanical testing .................................... 25

3. FIB in the semiconductor industry .............................. 27

4. FIB for quantum materials .................................... 28

5. FIB for photonics and plasmonics............................ 28

6. FIB fabrication of custom probes................................. 29

7. Outlook.............................................................. 30

B. Engineering materials properties through defects ................ 30

1. Basics of irradiation induced defect creation.............................. 30

2. Engineering electronic properties.............................. 31

3. Engineering magnetic properties .............................. 31

4. Engineering optical/quantum properties.................... 31

5. Engineering of low-dimensional materials .................... 34

6. Study of irradiation damage mechanisms.................. 34

7. Outlook.............................................................. 35

C. FIB-based imaging and tomography .......................... 35

1. A brief history of FIB-based imaging and analysis.................................................. 35

2. HIM—A tool for imaging of the tiniest living objects.................................................. 37

3. FIB tomography in the life sciences............................ 38

4. FIB tomography of energy materials............................ 40

5. Data processing of FIB tomographies............................ 40

6. Outlook.............................................................. 41

D. Elemental analysis using FIB-SIMS ............................ 41

1. Overview............................................................ 41

2. FIB-SIMS in materials science .................................... 41

3. FIB-SIMS in the life sciences .................................... 42

4. Outlook.............................................................. 42

E. Applications of gas-assisted FIB processing .................... 43

1. Basics of ion induced chemistry................................. 43

2. FIBID nanostructures for electronics............................ 45

3. FIBID nanostructures for mechanics............................ 46

4. FIBID nanostructures for photonics and plasmonics.................................................. 47

5. Outlook.............................................................. 47

F. Novel and unconventional approaches in FIB processing.................................................. 48

1. Resist patterning by FIB ...................................... 48

2. Cryo-FIBID ........................................................ 49

3. FIB irradiation of metalorganic spin-coated layers.................................................. 49

4. FIB induced mass transport ...................................... 50

5. Hybrid fabrication and heterogeneous integration .................................................. 50

6. Outlook.............................................................. 51

V. ROADMAP.............................................................. 51

A. Drivers for future applications .................................... 51

B. The generic needs of the community.............................. 53

C. Important future developments .................................... 55

1. Ion beam generation and transport.............................. 55

2. Accessories and complementary instrumentation.................................................. 56

3. Automation and data management .................................... 59

4. Process modeling ........................................................ 61

VI. EXECUTIVE SUMMARY AND PERSPECTIVE .................... 62
## IMPORTANT OVERVIEW TABLES

<table><tr><td>Table I Common FIB sources.</td><td>5</td></tr><tr><td>Table II FIB based analytic methods.</td><td>9</td></tr><tr><td>Table III BCA simulation codes.</td><td>14</td></tr><tr><td>Table IV Useful interatomic potentials.</td><td>17</td></tr><tr><td>Table V Subtractive FIB processing.</td><td>26</td></tr><tr><td>Table VI FIB based materials property engineering.</td><td>32</td></tr><tr><td>Table VII FIB based imaging of biological structures.</td><td>36</td></tr><tr><td>Table VIII Applications of FIBID.</td><td>44</td></tr><tr><td>Table IX Common FIBID precursors.</td><td>46</td></tr></table>

## NOMENCLATURE

<table><tr><td>AES</td><td>Auger electron spectroscopy</td></tr><tr><td>AFM</td><td>Atomic force microscopy</td></tr><tr><td>API</td><td>Application programming interface</td></tr><tr><td>APT</td><td>Atom probe tomography</td></tr><tr><td>ASIS</td><td>Atomic-size ion source</td></tr><tr><td>BCA</td><td>Binary collision approximation</td></tr><tr><td>BI</td><td>Backscattered ion</td></tr><tr><td>CAD</td><td>Computer-aided design</td></tr><tr><td>CMNT</td><td>Colloidal micro Newton thrusters</td></tr><tr><td>CMOS</td><td>Complementary metal-oxide-semiconductor</td></tr><tr><td>CNT</td><td>Carbon nanotube</td></tr><tr><td>COMB</td><td>Charge optimized many body</td></tr><tr><td>DAC</td><td>Digital-to-analog converter</td></tr><tr><td>DC</td><td>Direct current</td></tr><tr><td>DFT</td><td>Density functional theory</td></tr><tr><td>EAM</td><td>Embedded atom method</td></tr><tr><td>EBIT</td><td>Electron beam ion trap</td></tr><tr><td>EBL</td><td>Electron beam lithography</td></tr><tr><td>EBSD</td><td>Electron backscatter diffraction</td></tr><tr><td>ECR</td><td>Electron cyclotron resonance</td></tr><tr><td>EDS</td><td>Energy-dispersive X-ray spectroscopy</td></tr><tr><td>ESI</td><td>Electrospray ionization source</td></tr><tr><td>EELS</td><td>Electron energy loss spectroscopy</td></tr><tr><td>ESEM</td><td>Environmental scanning electron microscopy</td></tr><tr><td>ETD</td><td>Everhardt-Thornley detector</td></tr><tr><td>EUV</td><td>Extreme ultraviolet</td></tr><tr><td>ESA</td><td>Excited surface atom</td></tr><tr><td>FEB</td><td>Focused electron beam</td></tr><tr><td>FEBID</td><td>Focused electron beam induced deposition</td></tr><tr><td>FEBIE</td><td>Focused electron beam induced etching</td></tr><tr><td>FEEP</td><td>Field emission electric propulsion</td></tr><tr><td>FIB</td><td>Focused ion beam</td></tr><tr><td>FIBID</td><td>Focused ion beam induced deposition</td></tr><tr><td>FIBIE</td><td>Focused ion beam induced etching</td></tr><tr><td>FIM</td><td>Field ion microscopy</td></tr><tr><td>FinFET</td><td>Fin field-effect transistor</td></tr><tr><td>FMR</td><td>Ferromagnetic resonance</td></tr><tr><td>FOV</td><td>Field of view</td></tr><tr><td>GAP</td><td>Gaussian approximation potential</td></tr><tr><td>GUI</td><td>Graphical user interface</td></tr><tr><td>FWHM</td><td>Full width at half maximum</td></tr><tr><td>GFIS</td><td>Gas field-ionization source</td></tr><tr><td>GIS</td><td>Gas injection system</td></tr><tr><td>hBN</td><td>Hexagonal boron nitride</td></tr><tr><td>HIBL</td><td>Helium ion beam lithography</td></tr></table>

<table><tr><td>HIM</td><td>Helium ion microscope</td></tr><tr><td>HRTEM</td><td>High resolution transmission electron microscopy</td></tr><tr><td>HSQ</td><td>Hydrogen silsesquioxane</td></tr><tr><td>IBIC</td><td>Ion beam induced charge</td></tr><tr><td>IC</td><td>Integrated circuit</td></tr><tr><td>ICD</td><td>Image charge detector</td></tr><tr><td>ICP</td><td>Inductively coupled plasma</td></tr><tr><td>IIAES</td><td>Ion induced Auger electron spectroscopy</td></tr><tr><td>IL</td><td>Ionoluminescence</td></tr><tr><td>ILIS</td><td>Ionic liquid ion source</td></tr><tr><td>kMC</td><td>Kinetic Monte Carlo</td></tr><tr><td>LE-FIB</td><td>Low energy focused ion beam</td></tr><tr><td>LJ</td><td>Lennard-Jones-type</td></tr><tr><td>LMAIS</td><td>Liquid metal alloy ion source</td></tr><tr><td>LMIS</td><td>Liquid metal ion source</td></tr><tr><td>LoTIS</td><td>Low temperature ion source</td></tr><tr><td>MC</td><td>Monte Carlo</td></tr><tr><td>MCP</td><td>Micro channel plate</td></tr><tr><td>MD</td><td>Molecular dynamics</td></tr><tr><td>MFM</td><td>Magnetic force microscopy</td></tr><tr><td>ML</td><td>Machine learning</td></tr><tr><td>MS</td><td>Molecular statics</td></tr><tr><td>MEMS</td><td>Micro-electro-mechanical systems</td></tr><tr><td>MOTIS</td><td>Magneto-optical trap ion source</td></tr><tr><td>MRAM</td><td>Magnetic random access memory</td></tr><tr><td>NAIS</td><td>Nano-aperture ion source</td></tr><tr><td>NEMS</td><td>Nano-electro-mechanical systems</td></tr><tr><td>NIL</td><td>Nanoimprint lithography</td></tr><tr><td>NSOM</td><td>Near-field optical microscopy</td></tr><tr><td>NV</td><td>Nitrogen vacancy</td></tr><tr><td>PEMFC</td><td>Proton exchange membrane fuel cell</td></tr><tr><td>PFIB</td><td>Plasma focused ion beam</td></tr><tr><td>PI</td><td>Primary ion</td></tr><tr><td>PIXE</td><td>Particle induced X-ray emission</td></tr><tr><td>PMMA</td><td>Poly(methyl methacrylate)</td></tr><tr><td>QMS</td><td>Quadrupole mass spectrometer</td></tr><tr><td>RBS</td><td>Rutherford backscattering spectrometry</td></tr><tr><td>SDD</td><td>Silicon drift detector</td></tr><tr><td>SE</td><td>Secondary electron</td></tr><tr><td>SEM</td><td>Scanning electron microscopy</td></tr><tr><td>SFIM</td><td>Scanning field ion microscope</td></tr><tr><td>SI</td><td>Secondary ion</td></tr><tr><td>SII</td><td>Single ion implantation</td></tr><tr><td>SIMS</td><td>Secondary ion mass spectrometry</td></tr><tr><td>SNMS</td><td>Secondary neutral mass spectrometry</td></tr><tr><td>SNR</td><td>Signal to noise ratio</td></tr><tr><td>SPE</td><td>Single photon emitter</td></tr><tr><td>SPM</td><td>Scanning probe microscopy</td></tr><tr><td>SSPD</td><td>Superconducting single-photon detector</td></tr><tr><td>STEM</td><td>Scanning transmission electron microscopy</td></tr><tr><td>STIM</td><td>Scanning transmission ion microscopy</td></tr><tr><td>SQUID</td><td>Superconducting quantum interference device</td></tr><tr><td>TDDFT</td><td>Time-dependent density functional theory</td></tr><tr><td>TEM</td><td>Transmission electron microscopy</td></tr><tr><td>TIC</td><td>Total ion counter</td></tr><tr><td>TOF</td><td>Time-of-flight</td></tr><tr><td>UHV</td><td>Ultra-high vacuum</td></tr></table>
YBCO Yttrium barium copper oxide

YIG Yttrium iron garnet

YVO Yttrium orthovanadate

YSZ Yttrium stabilized zirconia

ZBL Ziegler-Biersack-Littmark

ZPL Zero-phonon line

## I. INTRODUCTION

The technological origin of the focused ion beam (FIB) instruments we use today lies in outer space, or more precisely, in the application of ion beams for spacecraft propulsion. In space, thrust can only be generated by ejecting matter, the so-called reaction mass, which must be carried along with the spacecraft. In addition to chemical thrusters based on combustion, ion thrusters have emerged as an important tool for high-precision movement. The positively charged ions that are generated by field ionization or by electrospraying are accelerated by electric or magnetic fields and then neutralized before being ejected in the opposite direction to that of the intended motion. (Neutralization is important here because otherwise the spacecraft would accumulate negative charge and thus attract the ejected positive ions.) Different types of thrusters based on liquid metal ion sources are currently being tested in space for ultra-precise position control of satellites, e.g., for the LISA gravitational wave interferometer.¹ One of these thruster technologies, the electric field emission propulsion system (part of the LISA Pathfinder mission² and more recent CubeSat launches³) is in fact very similar to the heart of many of our ground-based FIB instruments.

Whereas ion thrusters enable the exertion of forces in the micro-mass range for the navigation of space objects, our ground-based FIB instruments enable fabrication, modification, and characterization of micrometer- to nanometer-sized objects.

The leading example of FIB processing is still the site-selective preparation of samples for high-resolution imaging techniques, in particular, for transmission electron microscopy (TEM) and atom probe tomography (APT) and for 3D volume imaging using scanning electron microscopy (SEM). Several reviews have already been devoted to these important, well-established applications.⁴⁻⁶

However, since focused ion beams can be used to modify any material down to the nanoscale in a variety of ways, from targeted doping to structural modification and geometric shaping, the FIB is a powerful tool in all areas from basic research to technology. Our focus is, therefore, on these novel and advanced applications of the FIB.

This document presents the state of the art of FIB research and development today and discusses future perspectives. It is organized as follows: Sec. II gives an overview of FIB instrumentation, starting with the generation and control of the focused ion beam, followed by detectors and other complementary tools and accessories. Section III summarizes the theoretical approaches that can be used to describe various aspects of ion-matter interactions, including the binary collision approximation (BCA), molecular dynamics (MD), kinetic Monte Carlo (kMC) techniques, density functional theory (DFT), and continuum modeling. The last of these enables modeling over the longest length- and timescales, including treatment of ion- and electron-induced surface chemistry. The wide range of applications of the FIB is discussed in Sec. IV, which is organized according to the various experimental techniques (subtractive processing, defect engineering, imaging and tomography, elemental analysis, gas-assisted processing, and several other emerging directions). For each application field, a selection of examples is

discussed. As a service to the community, summary tables with references have been compiled in order to provide a more comprehensive (albeit non-exhaustive) literature review of each of these application fields. These tables can be used as a starting point to help the reader identify new FIB opportunities for their own research.

Central to this document is the roadmap in Sec. V, which highlights future perspectives for FIB research and development based on the state of the art in instrumentation, theory, and applications previously described. Here, key drivers for the FIB in different areas of science and technology have been identified and linked to FIB-specific challenges and the steps needed for future developments. We hope that this roadmap can serve as an incubator for future developments and will provide inspiration for scientific and technological breakthroughs, as well as serve as a unique resource for funding agencies and industry.

## II. INSTRUMENTATION

The creation of a finely focused beam of ions presents several engineering challenges. Moreover, the beam requirements can vary widely depending on the application, sometimes with conflicting specifications. For example, for many applications, a high-current beam is desired to enable efficient milling (i.e., material removal by sputtering). However, high-current sources tend to deliver ions with a large energy spread, resulting in strong chromatic aberrations. Because of this (and other reasons, such as spherical aberrations from the lenses, as discussed later), it is challenging to build a high-current high-resolution source. Similar conflicting scenarios present themselves in many other areas of focused ion beam (FIB) instrumentation.

In the following, the various components of the FIB instrument are discussed. We start by describing the different ion sources that are used (Sec. II A). The source defines many properties of the final instrument, including the achievable spot size. Then we address beam transport via the ion optical column (Sec. II B), and subsequently detectors and analytics (Sec. II C); these elements, which are used to steer, shape, and detect the ions, must be designed in such a way as to ensure the best possible end performance of the particular source being used. In the sample chamber, there are several other components that can be incorporated, including specialized sample stages for *in situ* or *in operando* experiments, micro-/nan/manipulators, and gas injectors. These are discussed in Sec. II D. Next, we address considerations concerning experiments with radia/oactive samples (Sec. II E). Finally, we outline software needs and correlative approaches for beam control, automation, and multi-modal analysis (Sec. II F). An overview of these topics can also be found in the book chapter by Note.⁷

### A. Ion sources

In order to achieve high spatial resolution in a FIB instrument, an ion source with high brightness is required.⁸ Analogous to the definition in electron microscopy, the brightness *B* of an ion source is a measure of the compactness and directionality of the ion beam, according to

$$B = \frac{I}{A\Omega}, \qquad (1)$$

where the emission current *I* from a source area *A* is emitted into a solid angle $\Omega$.⁹,¹⁰ In practice, this means that ions are suitable for microscopy and nanofabrication if they are emitted from a highly localized area into a well-defined direction. The reduced brightness is derived from the above definition by taking into account the acceleration voltages of the
<table><caption>**TABLE I.** FIB sources compared according to key parameters. Only common ion species are listed. All published or commercially available ion species can be found in Fig. 1. Superscript *q* marks different charge states (from 1 to 3) obtained from LMIS/LMAIS; for plasma sources even higher charge states are obtained. Subscript *n* for LMIS/LMAIS indicates the possible emission of polyatomic clusters comprising up to ten ions (or even more). Parameters for ionic liquid ion source (ILIS) indicated by * are estimated values from Ref. 11. For better comparison, the lateral spatial resolutions have been converted to FWHM values assuming a Gaussian beam profile resulting in an error-function-like edge profile.</caption><thead><tr><th>Source</th><th>Common ion species</th><th>Reduced brightness (A m<sup>-2</sup> sr<sup>-1</sup> V<sup>-1</sup>)</th><th>Min. energy spread (eV)</th><th>Max. current (nA)</th><th>Lateral resolution FWHM (nm)</th><th>Key applications</th></tr></thead><tbody><tr><td>LMIS/LMAIS</td><td>(Li, Si, Ga, Ge, In, Sn, Sb, Au, Pb, Bi, ...)<sup>q+</sup><sub>1..n</sub></td><td>1 &times; 10<sup>6</sup> (Ref. 12)</td><td>2-40 (Refs. 12 and 13)</td><td>100</td><td>2-2.8 (Refs. 14 and 15)</td><td>Surface patterning and cross-sectioning, volume imaging, local doping and implantation, SIMS, mask edit, ion thruster</td></tr><tr><td>ILIS</td><td>EMI<sup>+</sup>, BMI<sup>+</sup>, BF<sub>4</sub><sup>-</sup>, I<sup>-</sup>, ..., cluster ions</td><td>5 &times; 10<sup>6*</sup> (Ref. 11)</td><td>7-10 (Refs. 16 and 17)</td><td>0.75* (Ref. 11)</td><td>50*-30 000 (Ref. 11)</td><td>Ion thruster, reactive ion etching, SIMS</td></tr><tr><td>PFIB</td><td>(Xe, Ar, Kr, N, O ...)<sup>q+</sup></td><td>1 - 10 &times; 10<sup>3</sup> (Ref. 18)</td><td>7-10 (Ref. 18)</td><td>2500 (Ref. 19)</td><td>20-100 (Refs. 18-20)</td><td>High rate sputtering, volume imaging, implantation of gaseous elements</td></tr><tr><td>GFIS</td><td>(He, Ne)<sup>+</sup></td><td>1 - 4 &times; 10<sup>9</sup> (Refs. 21-23)</td><td>0.25-1 (Refs. 21 and 24)</td><td>0.15 (Ref. 23)</td><td>0.5/4.0 (Refs. 25-27)</td><td>High resolution imaging and nanostructuring, mask repair, implantation of gaseous elements</td></tr><tr><td>LoTIS/MOTIS</td><td>(Li, Cs, Cr, Rb)<sup>+</sup></td><td>1 - 240 &times; 10<sup>5</sup> (Ref. 28)</td><td>0.2-2 (Refs. 29 and 30)</td><td>25 (Ref. 31)</td><td>4.9 (Ref. 28)</td><td>SIMS, implantation</td></tr><tr><td>NAIS</td><td>H<sup>q+</sup>, Ar<sup>q+</sup></td><td>4 &times; 10<sup>5</sup> (Ref. 32)</td><td>0.9-2.3 (Ref. 33)</td><td>0.2-20 (Ref. 32)</td><td>&asymp;2000 (Ref. 32)</td><td>SEM as an ion source, proton beam writing</td></tr></tbody></table>

FIB instrument; representative values for the different ion sources are given in Table I. In general, a smaller (virtual) source size means a higher brightness and, consequently, a higher achievable lateral resolution. However, for the final resolution of the instrument, additional parameters such as the extractable ion current, energy spread, and of course the performance of the ion optics are also of importance.

In the field of ion sources, the first breakthroughs came in the 1970s with the development of the liquid metal ion source (LMIS) and the gas field-ionization source (GFIS). While the latter evolved from field ion microscopy (FIM) dating back to the 1950s³⁴ and was first employed for scanning transmission ion microscopy (STIM) of biological specimens,³⁵,³⁶ the LMIS was originally developed for space thruster applications.³⁷⁻³⁹

The LMIS consists of a capillary or a sharp needle tip, wetted with a molten metal. Through a combination of surface tension and applied electric field, the so-called Taylor cone⁴⁰ is formed, resulting in the extraction of ions from the source apex by field evaporation. The most common form of LMIS is based on gallium due to its low melting temperature and low vapor pressure. In fact, the Ga-LMIS is still the most used source for FIB instruments, not only because of its high brightness, but also because of its high source stability.

Directly related to the LMIS is the liquid metal alloy ion source (LMAIS), which through the use of a variety of alloys enables access to

a much wider range of ion species,¹²,¹⁵,⁴¹⁻⁴⁹ but with strongly varying source lifetimes from minutes to months. Based on the same source principle, the ionic liquid ion source (ILIS) is wetted with a compound that dissociates into molecular anions and cations such as the ionic liquids C₆N₂H₁₁-BF₄ (EMI-BF₄), C₆N₂H₁₁-GaCl₄ (EMI-GaCl₄), or C₈N₂H₁₅-I (BMI-I).¹⁶,⁵⁰⁻⁵⁵ The ILIS is, thus, capable of producing beams of molecular ions, both positively and negatively charged, but has not yet been implemented commercially.

The GFIS operates at low temperature, producing ions from the field ionization of adsorbed gas atoms, and is characterized by the highest brightness and hence the highest deliverable spatial resolution of all sources developed to date.²¹,²⁵,⁵⁶ This is a consequence of the atomically sharp emitter, which consists of only three atoms at its tip, the so-called trimer, whereby each atom emits a beamlet and thus forms a virtual source with a size in the Angstrom range. The trimer must be formed by the user and has a typical lifetime between a few days and a few weeks. The source gases that are widely used for high-resolution imaging and high-resolution (metal-free) milling are He and Ne. Operation of the GFIS with H₂,⁵⁷ N₂,⁵⁸,⁵⁹ Xe,⁶⁰ and Kr⁶¹ has also been demonstrated. A closely related source technology is the atomic-size ion source (ASIS) source,⁶²,⁶³ which uses field emission of adatoms (Au and Ag have been demonstrated) deposited onto a tip
made from refractory metal or another inert material with a high field ionization strength. High resolution is to be expected due to the single atomic ionization site employed in this technology. However, among other issues, it is the limited lifetime of the ASIS which has hindered its application in actual FIB instruments so far.

Another source option offering nonmetallic ions is the plasma ion source of the so-called plasma focused ion beam (PFIB) instrument. Plasma ion sources achieve high currents of up to 2 µA and have a long lifetime, but lower brightness than LMIS sources. The plasma can be generated by electron impacts, as in a duoplasmatron,<sup>18,64</sup> by inductive coupling of alternating currents in a radio frequency antenna [an inductively coupled plasma (ICP)],<sup>65</sup> or by microwaves in an electron cyclotron resonance (ECR) ion source.<sup>66</sup>

In addition to the systems mentioned above, most of which are commercially available, there are other less common types of ion source. One example is the so-called cold atom ion source, of which there are two varieties: the magneto-optical trap ion source (MOTIS) and the low temperature ion source (LoTIS). These use magneto-optical trapping (in combination with laser-cooling in the case of the LoTIS) to generate a trapped cloud of atoms or an intense atomic beam with a (transverse) temperature in the microkelvin regime.<sup>31,67–72</sup> The atoms in the trap or beam are then field- or photoionized to produce an isotopically pure, singly charged ion beam of high brightness and low energy spread.<sup>29,30,73–75</sup> MOTIS/LoTIS achieve good resolution at low energies and are suitable for a wide variety of ions<sup>75</sup> but require a high degree of sophistication in their design and handling. Consequently, these sources have so far only been demonstrated for a few ion species (see Table I and Fig. 1).

Another example is the nano-aperture ion source (NAIS) that uses an electron-impact gas ion source<sup>76,77</sup> and can be installed on standard scanning electron microscopy (SEM) instruments to deliver ions from all noble gases or protons. Further less common source types are Paul traps,<sup>78</sup> the electron beam ion trap (EBIT),<sup>79,80</sup> the multicusp plasma ion sources,<sup>81</sup> the solid electrolyte ion source (SEIS),<sup>82</sup> and the electrospray ionization source (ESI).<sup>83</sup>

A systematic overview of all ion species currently available for FIB instruments is displayed in the form of the periodic table of elements in Fig. 1. The most common types of ion sources that are used for FIBs, and their key parameters are compared in Table I.

Crucial factors to be optimized for the routine use of new ion sources are source lifetime and stability. Lifetime issues are usually related to contamination and can often be handled by working in cleaner conditions. However, in other cases, lifetime and stability issues can be traced to the source itself. For example, the formation of stable beams from certain elements, such as Al and P extracted from a LMAIS, remains challenging. The exact reasons for these complications are not yet fully understood. Source stability is also of particular importance for large volume sputtering applications, as well as for focused ion beam induced deposition (FIBID) and resist-based FIB lithography. For maximum patterning fidelity, these applications require FIBs with highly stable emission currents and beam positioning. Examples of poor stability are the short term current fluctuations and long term current drift of the Ne-GFIS<sup>27</sup> and effects such as pulsation, droplet, and globule emission from the source tip in LMIS and LMAIS.<sup>84</sup>

## B. Beam transport

The main components responsible for transporting the beam in a FIB column from the source to the sample are shown in Fig. 2. The labels on the left correspond to components found in more standard instruments and the labels on the right correspond to additional components found in more specialized instruments. To summarize: after extraction from the source, the ions are formed into a beam by the condenser lens (often after passing through an entrance aperture) and then guided toward the probe current selecting aperture (often via a quadrupole lens). The current selecting aperture defines the probe current by selecting a small portion of the beam and thereby also reducing its angular dispersion. To monitor the beam current, the beam is

<figure><img src="image_11.png" /><figcaption>FIG. 1. Periodic table of elements of available ion species for FIBs. The color of each element shows the corresponding ion source type. Ions of elements that are not available, toxic or only available as radioactive isotopes are also indicated by color. If ions from a particular element are available using multiple types of ion source, this is shown as labeled. Diagonal stripes indicate that the ions of those elements are not widely used and/or are produced with a low yield.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**FIG. 2.** Principal components for beam transport in a FIB column (not to scale). Components labeled on the left are found in standard Ga-FIB columns, whereas labels on the right indicate components usually only found in special-purpose columns.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**FIG. 3.** Example of an electrostatic (Einzel) lens, showing three cylindrical electrodes (in orange) where the central one is biased to focus the ions onto a given position. Equipotential lines are drawn in red, ion trajectories in blue, and the black arrows indicate the direction and magnitude of the electrostatic force.</figcaption></figure>

deflected into a Faraday cup. The lower part of the column often houses a stigmator for final beam shaping, plus an octupole for beam scanning and a second electrostatic lens (objective) for beam focusing. In more specialized instruments, a Wien filter is used to select isotopes, i.e., ions of a specific mass-to-charge ratio.

The condenser and objective lenses are convergent electrostatic lenses with a cylindrical geometry and are used to steer and focus the ion beam. They are composed of several electrodes (typically three, i.e., an Einzel lens), which are electrically biased to generate electric fields that change the trajectories of the transiting ions through the electric force $\vec{F} = q\vec{E}$ (see Fig. 3). Electrostatic lenses can be operated in retarding mode where the ion energy is reduced inside the lens, or in accelerating mode where the ion energy is increased inside the lens. Figure 3 shows an example of a lens operated in retarding mode. Given the curved shape of the field lines inside the lens, the electric forces imposed on the ions have a radial component in addition to the deceleration and acceleration axial components of these forces. The radial force components result in the overall focusing effect of the lens.⁸⁴ The focal length of an electrostatic lens depends on the ion energy, the charge state of the ions, the voltage applied to the lens, and the lens geometry (and not on the ion mass, as would be the case for a magnetic lens). For a lens operated at a given voltage, the focal length

will be smaller if the retarding mode is implemented compared to the accelerating mode.

The beam blanker comprises an electrostatic deflector that diverts the ion beam into a Faraday cup. This allows the user to both blank the beam to prevent ion impingement on the specimen as needed, and also to measure the probe current. Beam blanking is an important feature, not only for standard applications such as nanostructuring by FIB milling or FIBID but also for ion implantation tasks. In the most extreme case, beam blanking must be fast enough so as to allow implantation down to the single ion level from a non-deterministic ion source. In this context, fast means that for an assumed primary ion current of 1 pA, it is necessary to deliver a 10 ns ion pulse in order to achieve the correct probability, following Poisson statistics, of no more than one ion per pulse. Fast blanking is achieved using dedicated electronics and electrodes located at a specific position in the column such that the beam is blanked in a really short time without creating any beam tail artifacts. Detection on the sample must also be able to count the arrival of each ion, one by one (see Sec. II C on detectors).

Other optical elements present in nearly all FIB columns are quadrupoles and octupoles, which are used to steer the beam and are key for proper alignment of the beam with respect to the major optical elements in the column (such as the lenses and apertures). These elements are comprised of two sets of either four or eight electrostatic deflectors, which allow the user to tilt and shift the beam (by applying two counteracting deflections) onto the vertical axis of the subsequent optical element. In the lower part of the column, close to the final lens, a stigmator is often implemented, which allows the user to correct the shape of the beam by applying electric fields that compress (or expand) the beam along directions perpendicular to the optical axis. All three of these elements (the quadru-/octupoles and stigmator) enable some compensation for the aberrations introduced by the imperfections of the lenses as well as correction for the mechanical alignment of the column. In the FIB instruments commercially available today, chromatic or spherical aberrations are not routinely corrected. This is mostly because the magnitude of both is strongly defined by the source. However, theoretical papers have shown the possible benefits of such corrections⁸⁵,⁸⁶ and prototypes have been built using an electrostatic corrector.⁸⁷,⁸⁸
More specialized columns are equipped with a Wien filter,⁸⁹,⁹⁰ by which perpendicular electric and magnetic fields separate the ions in the primary beam according to their mass-to-charge ratio (see Fig. 4). This is necessary when the ion source produces ions from several elements and/or ions of different charge states. The electromagnetic selection of ion species has of course no effect on any neutral atoms that may be present in the beam. To prevent neutral atoms reaching the specimen, the beam can be sent through an electrostatic chicane blanker,⁹¹ whereby all non-deflected particles (neutrals) are blocked such that only the charged particles (ions) reach the sample.

As mentioned previously, the performance of a given FIB instrument ultimately depends on the specifications of the ion source. Most of the optical elements typically used in today's FIB columns do not correct for any beam aberrations, although they might create some due to inherent/manufacturing imperfections. If the source has a poor performance, this will inevitably be propagated to the sample. Consequently, adjusting the design of the beam transport elements on a state-of-the-art FIB instrument will typically only result in small improvements in the overall FIB performance.⁸⁴,⁹²,⁹³

The main gap between the desired performance of a FIB instrument and its actual performance is currently in the area of low energy beams (<2 keV). With the ongoing trend to reduce the dimensions and increase the complexity of (3D) device and sample architectures, the interactions between the ion beam and the sample become ever more critical. Thus, the penetration depth and straggle of the ions inside the material must be minimized. The key way to reduce these effects is to decrease the energy of the beam, but the consequence is an increase in beam spot size. This increase in beam spot size is due to chromatic aberrations from the energy spread of the ions in the beam, whereby the relative energy spread and hence aberrations become more pronounced when the beam is retarded.

Finally, the performance of current FIB systems is also limited in terms of the attainable processing speeds. Using a single focused beam requires scanning with varying exposure and move/blank sequences, and is inherently serial. In contrast, template masking of a broad ion beam on the sample can provide much higher throughput, but at the expense of flexibility and spatial resolution. Therefore, it has been theoretically proposed to combine masking of a broad beam with full control of single beams in a multibeam approach that significantly improves throughput for nano-applications.⁹⁴ A working proof-of-concept demonstration of such a multibeam FIB column has been built around a controllable array of ion beamlets.⁹⁵ In brief, an aperture plate splits a broad parallel ion beam into a large number of 2.5 µm-wide beamlets. Each of these 43 000 beamlets can be individually deflected by an array of apertures with adjacent electrostatic electrodes,

fabricated using complementary metal-oxide-semiconductor (CMOS) technology. All the beamlets are then passed through 200× reduction optics, which blocks any deflected beamlets. The remaining beamlets irradiate a user-defined pattern of pixels with a resolution of less than 20 nm. This multibeam technique has been optimized for electron irradiation⁹⁶ and is commercially available as a mask writer,⁹⁷ but further development of the concept for different ion species is highly desirable.

### C. Analytical tools and detectors

Irradiating a sample with an ion beam to trigger and measure a response is a very common analytical technique, and FIB instruments that perform imaging, local irradiation, milling, etc., are typically equipped with various accessories to confer a range of analytical capabilities. For imaging purpose, the secondary electrons (SEs) emitted from the sample surface are routinely detected using an Everhardt-Thornley detector (ETD).⁹⁸ The ETD is scintillator-based, converting SE strikes to photons inside the sample chamber that then travel via a light guide to a photomultiplier outside the chamber. As a complementary imaging channel, secondary ions (SIs) can be detected using a total ion counter (TIC) (typically in positive SI detection mode using a Faraday cup or a channeltron). In addition to these imaging modes, various other analytical techniques are implemented on FIB platforms; a general overview is given in Table II.

Secondary ion mass spectrometry (SIMS) enables the mapping of elemental/chemical compositions in the form of 2D/3D images or depth profiles with high sensitivity (down to the ppm level) in combination with a high dynamic range (i.e., a given element can be measured over a concentration range of several orders of magnitude). In principle, all elements including their isotopes can be measured. However, for a truly quantitative analysis, reference samples are required since the ionization yields strongly depend on the local environment in the sample (known as the matrix effect).¹⁷⁸ Several implementations of FIB-secondary ion mass spectrometry (SIMS) systems have been explored with three main system types described in the literature for units installed on both FIB and FIB-SEM instruments:

(1) Historically, quadrupole mass spectrometer (QMS) systems have been used on FIB platforms due to their simple design, low weight, and reduced costs.¹⁰¹,¹⁰⁴ In a QMS, only ions with a specific mass-to-charge ratio are able to travel through the applied quadrupole field. Ions with different mass-to-charge ratios travel on unstable trajectories, thus leaving the mass spectrometer before the final exit aperture and so are not counted. QMSs, therefore, have the disadvantage of not allowing parallel detection (i.e., only one mass can be detected, the detection of several masses requiring sequential analyses and hence a duty cycle) and also have a lower performance in terms of sensitivity.

(2) More recently, various orthogonal and linear time-of-flight (TOF)-based mass spectrometers have been introduced.¹²¹,¹²² Here, mass separation is achieved because ions with different mass-to-charge ratios will reach different velocities; measuring their time-of-flight allows the mass of the ions to be inferred. The TOF systems offer the advantage of parallel detection, but since pulsing of the primary or secondary ion beam (or both) is required, a duty cycle results.

(3) Magnetic sector SIMS systems can offer parallel detection if using so-called continuous focal plane detectors¹⁰⁷,¹⁷⁹ and the

<figure><img src="image_14.png" /><figcaption>FIG. 4. Principle of a Wien filter, with orthogonal electric and magnetic fields and an aperture to select the desired ion velocity.</figcaption></figure>
<table><caption>TABLE II. Overview of FIB based analytical methods.</caption><thead><tr><th rowspan="2">Technique</th><th rowspan="2">Primary ion</th><th rowspan="2">Detected signal</th><th colspan="2">Spatial resolution</th><th rowspan="2">References</th></tr><tr><th>Lateral</th><th>Depth</th></tr></thead><tbody><tr><td>QMS-SIMS</td><td>He<sup>+</sup>, Ne<sup>+</sup>, Ga<sup>+</sup>, Cs<sup>+</sup>, Xe<sup>+</sup>, O<sup>+</sup>, Bi<sup>+</sup>, Bi<sup>n+</sup>, Au<sup>+</sup>, Au<sup>n+</sup>, O<sup>-</sup></td><td>Secondary ions</td><td>100 nm</td><td>&lt;20 nm</td><td>99–106</td></tr><tr><td>Magnetic sector SIMS</td><td></td><td></td><td>&lt;15 nm</td><td>&lt;2 nm</td><td>107–115</td></tr><tr><td>TOF-SIMS/orthogonal TOF</td><td></td><td></td><td>&lt;50 nm (&lt;30 nm)</td><td>&lt;10 nm</td><td>101,116–127</td></tr><tr><td>SNMS</td><td>Ga<sup>+</sup></td><td>Post-ionized neutrals</td><td>20 nm</td><td></td><td>87,128–131</td></tr><tr><td>STIM</td><td>He<sup>+</sup></td><td>Transmitted ions/neutrals, backside SEs</td><td>&lt;5 nm</td><td></td><td>132–140</td></tr><tr><td>Backscattering spectroscopy</td><td>He<sup>+</sup></td><td>Backscattered ions/neutrals</td><td>≈50 nm</td><td></td><td>120,141–150</td></tr><tr><td>Backscattering yield</td><td>He<sup>+</sup></td><td>Backscattered ions/neutrals</td><td>5 nm</td><td></td><td>151,152</td></tr><tr><td>Ion induced SE spectroscopy</td><td>He<sup>+</sup>, Ar<sup>+</sup></td><td>Secondary electrons</td><td>Several nm</td><td></td><td>153–161</td></tr><tr><td>IIAES</td><td>Si<sup>+</sup>, Ne<sup>+</sup>, Ar<sup>+</sup>, Au<sup>+</sup>, Kr<sup>+</sup>, Ga<sup>+</sup></td><td>Auger electrons</td><td>10 nm</td><td></td><td>162–167</td></tr><tr><td>PIXE</td><td>He<sup>+</sup>, Ne<sup>+</sup>, Ga<sup>+</sup></td><td>X-rays</td><td>100 nm</td><td></td><td>168,169</td></tr><tr><td>IL</td><td>He<sup>+</sup></td><td>Photons</td><td>20 nm</td><td></td><td>170–177</td></tr></tbody></table>

highest sensitivity enabling high-resolution imaging applications.¹⁴⁰ In a magnetic sector mass separator, ions are forced onto circular trajectories by a perpendicular magnetic field. The radius of curvature of this trajectory depends again on the mass-to-charge ratio of the ion. Parallel detection of all masses can be achieved using focal plane detectors and the appropriate spectrometer geometry. Magnetic sector systems are operated in direct current (DC) mode, i.e., they feature a 100% duty cycle. In terms of disadvantages, these systems typically have a larger footprint and are heavier because of the integrated electromagnet.

By combining a gas injection system (GIS) with FIB-SIMS, further improvements in analytical output have been demonstrated. For example, in work combining FIB-TOF-SIMS with a GIS, ionization probabilities and hence SI signals were found to significantly increase by 2–3 orders of magnitude, thereby improving the quality of 2D and 3D chemical maps.¹²³ Furthermore, it was observed that co-injection of XeF₂ during the ion bombardment can reduce mass interference¹²⁵,¹²⁶ and invert the polarity of the negatively charged SIs to positive,¹²⁷ thus allowing the collection of more complete chemical information. Enhancements in SI yields have also been obtained with magnetic sector SIMS instruments using Cs deposition and O₂ flooding to boost the yield of negative and positive secondary ions, respectively.¹⁸⁰,¹⁸¹

Related to SIMS, secondary neutral mass spectrometry (SNMS)¹³⁰,¹³¹ can obtain similar information, analyzing sputtered neutrals through laser-based post-ionization, and has the advantage of matrix-independent ion yields. However, while resonant post-ionization is an efficient process, non-resonant ionization yields are low. SNMS requires significant experimental effort and is, therefore, associated with high costs.

Scanning transmission ion microscopy (STIM) is performed using the ions of light elements. It can provide mass-thickness contrast and also crystal structure information due to ion channeling.¹³⁸ Several different STIM implementations have been investigated, most

based on the collection of secondary electrons generated from impact of the transmitted ions on a conversion plate,¹³²,¹³³,¹³⁹ but also some using direct detection of the transmitted ions.¹³⁴,¹³⁵,¹³⁸ STIM is a quasi-nondestructive imaging technique and for biological specimens has been shown to deliver structural contrast comparable to scanning transmission electron microscopy (STEM).¹⁴⁰ Similar to STEM, STIM demands thin samples (<100 nm). STIM can also be used to obtain high-resolution images that can be correlated with elemental/chemical maps determined by SIMS.¹¹⁰

Backscattering spectroscopy in a FIB instrument is similar to Rutherford backscattering spectrometry (RBS) but is performed at much lower energies of around several tens of keV. This results in multiple scattering events due to the relatively large nuclear scattering cross sections. Even when performing time-consuming simulations of the ion spectra, quantitative results from the raw energy spectra are difficult to obtain. However, it has been shown that when coupled with a TOF setup, backscattering spectroscopy can deliver damage-free depth-resolved elemental compositions.¹²⁰ Signal levels are good, since in addition to the SIs, the backscattering method is also sensitive to the large number of neutrals generated during the primary ion impact.

One can also analyze the yield of the backscattered primary particles, for which larger solid angles and higher signals can be achieved. This is accomplished using an annular micro channel plate (MCP) located beneath the objective lens of the microscope. While the backscatter yield approach is feasible regardless of FIB instrument type, it is most useful in a helium ion microscope (HIM). In this case, the backscatter yield of the primary He ions is high enough (in particular upon interaction with heavier elements) that damage from the primary beam can be neglected.¹²⁰ Backscatter yields depend strongly on the atomic number of the target.¹⁴¹ To a certain extent, elemental analysis is also possible but requires prior knowledge of the elements in question.¹⁴⁷ The backscatter approach has been shown to reveal elemental contrast from buried layers¹⁵¹ and has also been applied to biological specimens.¹⁸²,¹⁸³ Since backscatter yields depend strongly on ion channeling effects, this approach can be used to map crystal orientations.¹⁴⁹,¹⁵²,¹⁸⁴–¹⁸⁶ SE yields are in fact also influenced by ion
channeling and provide stronger signals, hence crystal orientation mapping based on the detection of SEs offers a simple alternative¹⁴⁹ and has been shown to enable the visualization of interfacial nanoscale dislocation networks in thin-film alloys.¹⁸⁷ The ability to infer crystallographic information from the SE yield has been extended to other ions and automated.¹⁸⁸

Ion induced SE spectroscopy (using He ions) draws on variations in SE energy to map chemical variations on a sample surface.¹⁵⁵,¹⁸⁹⁻¹⁹¹ The approach allows the user to maximize imaging contrast, thus permitting short beam exposure times, which is beneficial for beam-sensitive samples. However, a quantitative application of the SE spectroscopy method is currently limited by the complicated nature of the data obtained and the lack of a suitable reference database.

Ion induced Auger electron spectroscopy (IIAES) allows the chemical identification of surface layers, including bond structure, via the energy-resolved detection of Auger electrons emitted following an ion induced inner-shell electronic transition.¹⁶⁶,¹⁹² For elements in the third row of the periodic table, ion induced Auger electron spectroscopy (IIAES) has a superior signal-to-noise ratio compared to electron beam based Auger electron spectroscopy (AES).

Ion/particle induced X-ray emission (PIXE) in a FIB instrument is essentially the equivalent of energy-dispersive X-ray spectroscopy (EDS) in the SEM, whereby characteristic X-rays (used for elemental mapping) are generated as a result of particle bombardment. However, in the FIB case, PIXE suffers from extremely low X-ray yields and, hence, has not proved practical thus far.

The final entry in Table II, ionoluminescence (IL), has been tested on various materials.¹⁷² However, the authors of these works concluded that the merits of this technique only really emerge in the case of *in situ* characterization of beam induced defects¹⁷³ and for the localization of rare earth elements.¹⁷⁵

Specialized ion detection methods for single ion implantation (SII) also deserve mention (see Sec. IV B for more detail). These methods can be categorized into pre- and post-detection techniques. In the pre-detection category, one example is the use of an image charge detector (ICD) incorporated into the FIB column that registers the passage of a single ion (or ion bunch) and is coupled with fast blanking electronics.¹⁹³,¹⁹⁴ Post-detection can involve standard SE detection¹⁹⁵ or more complex sample-integrated detection schemes such as ion beam induced charge (IBIC) or source-drain current measurements.¹⁹⁶⁻¹⁹⁹

## D. Other FIB accessories

In addition to the above-described key components, a number of other accessories have been developed that extend the capabilities of FIB instruments even further. A summary of these is given below.

The most common addition to a FIB instrument is an electron column (SEM). Vice-versa, FIB columns are often added to SEMs. The electron column enables correlative imaging, *in situ* monitoring of milling processes, FIB-SEM volumetric reconstructions, and SEM-based analytics such as EDS. The SEM addition facilitates sample navigation, since by imaging with electrons rather than ions, beam damage to the sample can be rendered negligible. Certain FIB-SEM implementations also allow automated metrology and analysis.²⁰⁰,²⁰¹

For high-resolution, large-area direct patterning applications, laser interferometer stages become critical, since the positioning accuracy and stability of standard mechanical stages are not sufficient for

these high-end applications. In conjunction with specialized sample holders, laser interferometer stages enable a sample positioning accuracy in the nanometer range over a lateral distance of several 100 mm.²⁰²

A further rather common addition is a gas injection system (GIS), which enables focused ion beam induced deposition (FIBID) and, in combination with an electron column, also focused electron beam induced deposition (FEBID).²⁰³

FIB columns are also sometimes operated in conjunction with an electron flood gun, whereby *in situ* charge neutralization is achieved by illuminating an insulating specimen with low energy electrons. In particular for HIM, this enables imaging of insulating samples at high spatial resolution without the need for conductive coatings²⁰⁴ (see Sec. IV C 2), and more generally, FIB milling of insulating samples.²⁰⁵ A low resolution approach to allow charge-free macroscopic sample navigation is to use an optical camera. The latter has been extended to enable *in situ* fluorescence²⁰⁶ and Raman spectroscopy.²⁰⁷

Various types of micro/nanomanipulators have been developed for intuitive control and mechanical manipulation of micro- to nanoscale objects, including *in situ* lift-out of lamella specimens for transmission electron microscopy (TEM),²⁰⁸ and to allow local electrical connections for various *in situ* experiments as demonstrated for SEM.²⁰⁹⁻²¹¹

Through the addition of a femtosecond laser ablation system, large amounts of material can be removed very efficiently from around the final target area for subsequent finer milling with the FIB. This enables higher throughput for applications such as advanced package failure analysis and process optimization in the semiconductor industry.²¹²

Numerous add-ons for a wide range of *in situ* characterization experiments have also been developed, both by manufacturers and by researchers. These solutions include electrical probing stations, systems using Peltier elements for sample heating or cooling (not to be confused with more complex cryo-FIB add-ons), *in situ* mechanical testing, plasma-based sample cleaners, and automatic laser-based height sensing. Other often sought-after add-ons are inert gas transfer boxes to allow oxygen-free loading (and unloading) of air-sensitive samples.²¹³ Various solutions for incorporating atomic force microscopy (AFM) into FIB and FIB-SEM instruments have also been developed, e.g., Ref. 214, which can be implemented in combination with FIB-SIMS to allow an assessment of surface roughness and thus improve the accuracy of the 3D reconstructions.¹⁷¹ A recent review article summarizing state-of-the-art solutions for *in situ* characterization and micro-/nanomanipulation has been published by Shi *et al*.²¹⁰

## E. FIB processing of radioactive samples

The investigation of radioactive samples using a FIB system raises a number of critical issues (legal and technical) that need to be addressed. The reason the FIB is such a useful instrument in the analysis of these samples is that it allows the preparation of small-scale specimens (by FIB milling), which by default have significantly reduced radioactivity levels. These small-scale samples can then be handled much more easily for a wide range of characterization experiments, both *in situ* and *ex situ*, including specimens for small-scale mechanical testing,²¹⁵ 3D volume imaging,²¹⁶,²¹⁷ lamellae for TEM or synchrotron investigations,²¹⁶,²¹⁸,²¹⁹ and needle-shaped specimens for atom probe tomography (APT).²²⁰
The exact protocols to follow may vary widely depending on the national guidelines, individual facility, and the local safety regulations. For example, individual sub-samples prepared from a larger radioactive sample may still be subject to radiation protection guidelines even in cases where radioactivities are below a clearance limit for which the sample can be considered quasi non-radioactive. The type of material, form of radioactivity, and isotopes involved are all key factors to take into account.

FIB instruments that are used for radioactive samples can be categorized as follows, depending on the laboratories where they are installed and on the shielding implemented:

1. Instruments classed for “low-medium” radioactivity samples. These instruments are typically also used for experiments with non-radioactive samples, and are installed in labs with radiation protection guidelines and moderate shielding.

2. “Hot cell” instruments that are highly shielded (lead wall around the whole instrument) and may even allow spent fuel samples.

Irrespective of the particular regulations, the main concerns when working with radioactive samples in FIB instruments are:

* Dose limits for the operator when loading and unloading the sample;

* Contamination of the instrument to the extent that system maintenance becomes difficult;

* Cross contamination between samples in the case of work with radioactive and non-radioactive samples;

* Lifetime of detectors and other add-ons installed on the instrument (EDS, EBSD, etc.).

Regarding contamination of the instrument itself, it has been determined that most of the milled material that does not redeposit on the sample is deposited on the pole piece and surrounding areas.<sup>221,222</sup> In the case of materials that generate dust, the sample stage can also easily become contaminated. One approach to address contamination of the pole piece is to use a dedicated pole piece insert for experiments with radioactive samples. FIB-SEM instruments with environmental scanning electron microscopy (ESEM) capabilities can also be helpful here, as these provide another aperture for low-pressure mode, and the water vapor that is typically injected helps to volatilize the radioactive sputtered material. Frequent cleaning of areas prone to contamination is another effective strategy to increase the lifetime of the instrument. The inside of the chamber can also be covered to protect from contamination. Some approaches use sample shields to reduce the spread of the sputtered material by capturing most of it inside the shield. However, sooner or later, the entire FIB chamber will need to be treated as radioactively contaminated equipment and handled appropriately.

## F. Software and correlative approaches

The software infrastructure of a FIB instrument needs to control various elementary subsystems, e.g., the vacuum system and sample stage, as well as the ion source and column functions (beam extraction parameters, aperture selection, column alignments, etc.). This is implemented by the manufacturer using a graphical user interface (GUI) that allows control of all FIB system components and integrated add-ons. Customized FIB setups employing, e.g., specialized, noncommercial FIB columns, or nonstandard add-ons, usually use separate control

software developed for these specific use cases, which are often difficult to set up and maintain due to closed hardware interfaces and patent issues. Regardless of the particular configuration, software control for the following applications is required:

* Imaging (including 3D volume imaging) and elemental analysis using various detectors, see Secs. II C, IV C, and IV D;

* Milling, ion irradiation, and implantation, see Secs. IV A and IV B;

* Gas-assisted processing and resist-based lithography, see Secs. IV E and IV F.

All of the above demand a scan generator that controls the path of the ion beam on the sample with high precision and repeatability.

Beam scanning is realized using a digital-to-analog converter (DAC) patterning board that determines the number of addressable pixels in each direction (e.g., 65 536 for 16 bits) and sets the voltages of the beam deflection system accordingly. The beam path is then a sequence of pixels with a certain dwell time and spacing depending on the field of view. Simple line-by-line scanning routines are used for imaging and elemental analysis, and the respective detector output is synchronized to assign a signal (e.g., a gray value or a mass spectrum) to each pixel position.

For subtractive processing, deposition, resist lithography, etc., special beam paths are needed. Here, manufacturers typically offer software tools that enable the creation of geometric shapes that are rastered according to a chosen set of parameters. Grayscale patterning offers an even easier way to realize complex shapes and the milling of 3D profiles, by loading an image in which the grayscale values of the individual pixels correspond to the local relative ion doses to be applied. The latter is an appealing plug-and-play solution for markers, text, and other non-quantitative designs, yet it is difficult to optimize systematically and is, therefore, not commonly used for actual structures. In the case of more advanced patterning needs, design files can be imported from lithographic software, assigned with parameters, and rasterized, thus enabling complex and large-scale structuring tasks.<sup>223</sup> Standalone lithography systems from third-party manufacturers can also be directly integrated as accessories via the use of an external scan control unit for the FIB column. Such systems typically also have access to stage control, allowing multi-step processing with marker-based registration or stitching, the latter requiring a laser interferometer stage for the highest level of positioning accuracy.

The capabilities of these various patterning systems are sufficient for many applications, but reach their limits when more complex geometric shapes and the highest spatial resolution are required, and/or when the position of the beam must be known with certainty at all times. This is because with these systems, the user has limited control over the actual raster process and possible auxiliary routines can be hidden in the proprietary software (e.g., for stabilization of the beam position). The most robust solution is to address pixels directly on the patterning board using a point cloud, which can be encoded in so-called stream files or deflection lists. This allows arbitrary rasterized beam paths to be executed by the integrated patterning software. Various groups have developed codes to generate such beam paths and the corresponding point clouds for specific tasks.<sup>224,225</sup> For arbitrary geometric shapes, an open-source Python-based solution is available, which allows the generation of patterns and geometry-adapted beam paths that can be both variably rasterized and optimized.<sup>226</sup> For
the creation of 3D profiles, approaches based on computer-aided design (CAD) have also been developed.²²⁷⁻²³¹ These solutions implement material removal via thin slices plane-parallel to the sample surface, which allows systematic optimization since the amount of material removed per slice remains constant (a significant advantage over the grayscale patterning mentioned above). Modeling of the milling process can also be used to take into account angle-dependent sputtering²²⁸ and redeposition,²³² or more generally, non-isotropic surface erosion.²²⁹ For more details, see Secs. III A and III D.

In addition to beam control, another software need focuses on enhancing the analytical capabilities of the instrument. Commercial FIBs are often coupled to a SEM column and/or equipped with analytical instrumentation such as SIMS. Most FIB instruments are thus furnished with electron detectors for the collection of SEs to allow for SEM-like imaging (albeit the physics of the signal formation is different).²³³ Additional detectors offer a variety of other imaging possibilities via the detection of transmitted ions,¹³⁸ backscattered ions,¹²⁰ secondary ions,¹⁴⁰ photons,¹⁷⁰,¹⁷¹ Auger electrons,¹⁶⁶,¹⁶⁷ etc., see Table II. These FIB instruments, thus, need to be equipped with the necessary interfaces to allow for either direct control of the beam position, or synchronization between the detector signal and internal scan generator. Such interfaces are standard for the commercial FIB platforms offering these analytical modalities.

For common repetitive FIB tasks, instrument users can employ various forms of software automation. Examples of automated tasks include column alignments and focusing, trench milling (including for TEM lamella preparation), large-scale sequential lithography projects, serial sectioning, and complex analytical tasks such as 3D tomography using multiple detectors. In the past, the technical challenges of many of these processes were handled largely without automation by expert FIB operators following intensive training. However, over the last decade, this situation has been significantly relieved by the introduction of various semi and fully automated processes by the major FIB manufacturers. It must be stressed that there is still room for improvement and further automation is highly desired. Here, automation routines that are more customizable or user-programmable with well documented application programming interfaces (APIs) or scripting environments within the FIB software stack would be of great benefit. This would allow standard automation routines to be set up and executed by lab technicians after just a short training period.

Finally, the correlative microscopy and spectroscopy functionalities of modern FIB instruments (both for 2D¹¹⁰ and 3D²⁵⁴⁻²³⁶ analysis, see Secs. IV C and IV D) require a combination of the aforementioned software controls as well as advanced software tools for correlation, analysis, and visualization.²³⁷,²³⁸ In the simplest case, a correlative dataset is acquired using multiple detectors and a single scan of a surface (or in the case of 3D analysis, a stack thereof) such that multichannel data are available for every beam location (pixel). If this is not possible, datasets from separate experiments have to be combined post-acquisition under the condition that some form of alignment is possible, e.g., via fiducial markers. For the correlation of 2D images, open-source software is available, e.g., in the form of the Fiji/ImageJ image processing package²³⁹ and its plug-ins such as Correlia.²⁴⁰,²⁴¹ Additional resources can be found on the webpages of the COMULIS project²⁴² and the BioImage Informatics Index.²⁴³ For the most complex cases (e.g., the correlation of X-ray and FIB tomography data),

dedicated analytical software²⁴⁴ and novel approaches for data storage and management are required, see Sec. V C 3.

### III. SIMULATION APPROACHES FOR FIB PROCESSING

Simulations carried out at various levels of sophistication have the potential to provide insights into the interaction of the FIB with the target. These calculations can help rationalize the experimental results, optimize the beam parameters (ion energy, incidence angle, etc.), and guide the experimental work. Various theoretical methods have been developed to describe the interaction of the impinging ions with the target and to assess the amount and type of sample modification produced by a given ion irradiation.²⁴⁵⁻²⁴⁷ Among them, atomistic computer simulations, which describe the system as a collection of interacting atoms, have provided much insight into the behavior of materials under the impact of energetic ions. These approaches can give precise information on ion ranges and energy losses and on the types of irradiation induced defects. Defect stability and long-term evolution under ambient conditions or at elevated temperatures during annealing can also be simulated. Continuum models, on the other hand, can be computationally more efficient and eliminate the statistical noise inherent to many atomistic methods. They describe the system under investigation by continuum quantities, such as concentrations or surface contours, which conceptually require averaging over finite volumes. In practice, these quantities are often discretized on a mesh of elements with sizes larger than atomic dimensions. Continuum models also require parameters to be provided by experiments.

The choice of simulation method is dictated not only by the main goal of the simulation (e.g., to assess the electronic stopping power or to calculate ion ranges, amount and type of damage, atomic mixing, surface evolution, etc.), but also by the system size, the required level of sophistication, and the computational costs. A typical approach is to find a suitable compromise between the necessary computational resources and accuracy. Multiscale simulations are frequently used, in which more accurate but computationally demanding approaches are employed as tests, or to provide parameters for lower spatial or temporal resolution techniques.

An overview of the time and length scales accessible via the various simulation methods is given in Fig. 5. The binary collision approximation (BCA) method, discussed in Sec. III A, describes the ballistic phase of the slowing down of the ions and of the development of collision cascades. Since the ballistic phase is over in less than a picosecond, application of the BCA method makes sense only on a sub-picosecond timescale. Ab initio methods, in practice mostly density functional theory (DFT), are the most accurate techniques, but are restricted to picosecond and nanometer ranges because of their computational cost. Classical molecular dynamics (MD) may be used for system dimensions of roughly up to 100 ns and 100 nm. These methods are described in Sec. III B. Longer time scales are accessible by the kinetic Monte Carlo (kMC) method (Sec. III C), which describes the evolution of a system given the probabilities of events. The actual limits of kMC are determined by the event frequencies and the density of objects in the system to be studied. Finally, continuum models (Sec. III D) usually study systems beyond the single digit nanometer range, as they do not resolve materials on the atomic level.

In the following subsections, a concise review of the available computational techniques, with examples of their use, is presented. It
<figure><img src="image_15.png" /><figcaption>FIG. 5. Time and length scales accessible via simulation methods. The smallest time scales are accessible only using certain types of continuum models. kMC can cover the entire length-time space displayed depending on the details of the system studied and on the sub-method used, and is therefore not included in the graph. For more information, see Ref. 248.</figcaption></figure>

is hoped that this overview provides a clear picture of the opportunities simulation provides for FIB processing.

## A. Simulation techniques based on the binary collision approximation (BCA)

The BCA approach is the most widely used method to assess the scattering and slowing of energetic ions in matter and the effects of the associated collision cascades, i.e., sputtering, atomic mixing, and the formation of point defect damage. The motion of each energetic atom is described as a sequence of asymptotic trajectories between binary collisions with target atoms that are at rest before the collision. Detailed information on the associated algorithms is provided in the book by Eckstein.²⁴⁹

### 1. Principles and limitations

The binary collisions are normally treated as elastic with repulsive-only screened Coulomb interaction potentials, as, e.g., in the “universal”²⁵⁰ or “Kr–C”²⁵¹ parameterization. Energy transfer to the target electrons is included either nonlocally along the free paths between the collisions (e.g., using a universal analytical description²⁵² or specific semiempirical data²⁵³) or locally dependent on the collisional impact parameter²⁵⁴ or as a combination of both.

Simulations based on the BCA method are often denoted as Monte Carlo (MC) simulations due to the random choice of collisional parameters, such as the impact parameter and the azimuthal position of the target atoms relative to the trajectory of the moving atom. In random and amorphous media, this applies to all binary collisions during the simulation. In contrast, in crystalline media only the initial position of the incident projectile relative to the lattice atoms is treated randomly, while the subsequent slowing down, including the generation and termination of a collision cascade, is largely deterministic due to the positions of the lattice atoms being fixed except for thermal vibrations.

A prominent advantage of BCA simulations is their low computational cost and very fast performance, which allows modeling even of

large systems up to the macroscale and the treatment of incident ion energies up to the MeV regime. However, in contrast to MD simulations (see Sec. III B), the BCA model fails if a significant fraction of the collisions occurs between moving atoms. Such so-called “collisional spikes” or “elastic thermal spikes”²⁵⁵ form in dense cascades generated under heavy-ion bombardment in the energy regime centered around the maximum of the nuclear stopping force²⁵⁶ (typically around 100 keV). However, any collision cascade also dissipates into a collisional spike before its final thermalization, which sets a low-energy limit on the validity of the BCA. Depending on the material, estimates²⁴⁹ and comparisons with molecular dynamics simulations²⁵⁷,²⁵⁸ indicate a failure at energies below several tens of eV. However, experience shows that sputtering, which is dominated by cascade atom energies slightly above the surface binding energies of 2–8 eV,²⁵⁶ is rather well described.²⁵⁹,²⁶⁰ This suggests a practical lower energy limit of validity. Undoubtedly, BCA breaks down below the bulk binding energy of typically a few eV, where the purely repulsive interaction potential is no longer appropriate and many-body interaction has to be taken into account. This excludes, e.g., the derivation of local atomic configurations after thermalization.

It must also be noted that BCA simulations require predefinition of a number of options and parameters, such as the choice of interaction potential, the addition of “soft” collisions with more distant target atoms, the type of electronic interaction, and the surface binding and atomic relocation threshold energies, which are often difficult to identify and unavailable in the literature, particularly for compounds. (Note that except for the electronic interaction, these predefinitions are unnecessary in MD simulations because proper choice of the interaction potential ideally covers all bulk and surface interactions down to thermal energies.) Whereas ion ranges derived from BCA simulations are mostly reliable within 5%–10%, sputtering and defect results are significantly influenced by these preselections. As a result of parameter variations within physically sound limits, calculated sputtering yields may easily change by more than 50%.²⁶¹ For the different BCA codes, parameters are often not chosen from theoretical or experimental information, but justified based on prior experience comparing the simulation results to experimental data.

Originally, BCA codes were designed for “static” simulations during which the system is assumed not to be altered by the irradiation. This allows the prediction of range and damage distributions as well as sputtering yields with high statistical precision when a sufficiently large number of incident projectiles is employed. In the simulation of ion implantation into single-crystalline targets, “dynamic” consideration of damage buildup is required if the fluence exceeds a certain threshold,²⁶²,²⁶³ as crystal damage reduces or suppresses channeling. This is achieved by choosing collision partners randomly instead of from the crystal lattice, with a probability proportional to the damage. More often, the term “dynamic BCA simulation” refers to the modification of the chemical composition and geometry of the target, which occurs experimentally for a sufficiently large number of incident ions. Specific BCA codes track implanted ions as well as relocated and sputtered recoil atoms in order to continuously update the local composition in multicomponent systems and the surface position or the surface contour in 1D or 2D/3D systems, respectively. Simultaneously, the composition-dependent local atomic density must be updated by volume relaxation and/or material transport. (Again, this dynamic modification is straightforward in MD simulations, but in systems exceeding
the nanoscale and for higher ion energies it is often impeded by excessive computational cost.)

## 2. Specific BCA codes

Among the large variety of BCA-based simulation codes that have been described in the literature, we will in the following only address a few selected ones, in particular those that are presently in broader use and/or offer new features with respect to nanosystems, specifically for FIB applications. For a rough classification, see Table III, access information for most of the codes can be found in Ref. 264.

TRIM<sup>265,266</sup> has been the most widely used BCA code for several decades. It offers a very convenient graphical user interface<sup>253</sup> for fast generation of range and damage statistics, and rough estimates of sputtering yields in amorphous semi-infinite or thin-film systems with a flat surface. The restriction to amorphous media is often not a severe limitation, since many materials become highly damaged or even amorphized under irradiation and, depending on the conditions, most ion or recoil atom trajectories are random in nature, even in crystalline materials. TRIM partly fails in detail, such as for sputtered atom angular/energy distributions.<sup>292</sup>

Sometimes the crystal structure of the irradiated material does matter. Typical cases include low-fluence or single-ion implantation aligned with a low-index crystallographic direction<sup>293</sup> and the sputtering of elemental metals.<sup>260</sup> Codes that consider the crystal structure are Crystal-TRIM,<sup>262,271</sup> which is restricted to certain materials, and IMSIL,<sup>263,272-274</sup> which allows more general crystal systems and sputtering simulations.

Based on the early TRIM sputtering version TRIM.SP,<sup>261</sup> 1D dynamic relaxation has been implemented in TRIDYN<sup>267,268</sup> and in SDTrimSP.<sup>269</sup> In connection with the recent broad interest in nanostructures, BCA codes have been extended to treat 2D and 3D systems using pixel and voxel grids, respectively. For static operation only, the surface for simple bodies may be defined analytically, such as in TRI3DST<sup>278</sup> and IM3D,<sup>280</sup> or triangularized as in a second option of

IM3D. With a pure voxel approach, the stepped surface contour resulting from pixel or voxel grids may cause artifacts by, e.g., capturing atoms at glancing incidence (which could in fact occur experimentally). This may be overcome by a local adjustment of the near-surface nodes<sup>274</sup> (IMSIL) or by local planarization of the surface<sup>284</sup> (TRI3DYN). In IMSIL for 2D dynamic simulation,<sup>273</sup> pixels that are affected by collisional transport become distorted based on an algorithm which optimizes their volumes and are subsequently projected onto the original pixel grid. In contrast, SDTrimSP-2D<sup>275</sup> relaxes the pixel volumes along one dimension only toward a specified surface. 3D dynamic simulations have been demonstrated using TRI3DYN<sup>282-284</sup> and EnvizION.<sup>285-291</sup> For overall volume and surface relaxation, TRI3DYN makes use of material exchange with nearby voxels or the surface, whereas in EnvizION the relaxation is limited to near-surface regimes. TRI3DYN even works for macroscopic systems, while EnvizION is limited to the nanoscale, since each voxel contains only one atom. A characteristic result of a TRI3DYN simulation is presented in Fig. 6, demonstrating surface erosion and contamination during irradiation of a Au nanosphere on a Si surface.

## 3. BCA-based simulations of FIB processing

1D static BCA simulations have often been employed for understanding experimental findings in FIB processing such as in recent studies of FIBID.<sup>294-297</sup> These have also been used to generate, e.g., angle-dependent sputtering yields and angle-energy distributions of sputtered atoms to describe erosion and re-deposition, respectively, in 2D and 3D “level set”<sup>298</sup> or “segment based”<sup>299-301</sup> simulation models of the surface contour development during FIB induced erosion, see Sec. III D.

A direct 2D dynamic BCA simulation of FIB induced erosion is described in Ref. 273, where the milling of trenches is exemplified. The results shown in Fig. 7 demonstrate the slowing of the milling process by atoms sputtered from the bottom and redeposited to the sidewalls. In addition, a high concentration of implanted atoms at the bottom of

<table><caption>TABLE III. Classification of selected BCA simulation codes. Note that the individual codes contain specific algorithms, use different parameters, and/or are designed for specific application areas, which are not detailed here.</caption><thead><tr><th>Code</th><th>Geometry</th><th>Atomic structure</th><th>Surface</th><th>Dynamic relaxation</th></tr></thead><tbody><tr><td>TRIM<sup>253,265,266</sup></td><td>1D</td><td>Amorphous</td><td>Planar</td><td>...</td></tr><tr><td>TRIDYN<sup>267,268</sup></td><td>1D</td><td>Amorphous</td><td>Planar</td><td>1D</td></tr><tr><td>SDTrimSP<sup>269</sup></td><td>1D</td><td>Amorphous</td><td>Planar</td><td>1D</td></tr><tr><td>IMINTDYN<sup>270</sup></td><td>1D</td><td>Amorphous</td><td>Planar</td><td>1D</td></tr><tr><td>Crystal-TRIM<sup>262,271</sup></td><td>1D</td><td>Crystalline</td><td>Planar</td><td>...</td></tr><tr><td>IMSIL<sup>263,272-274</sup></td><td>1D/2D</td><td>Amorph./cryst.</td><td>Polygons/pixeled (adjusted)</td><td>-/1D/2D</td></tr><tr><td>SDTrimSP-2D<sup>275</sup></td><td>2D</td><td>Amorphous</td><td>Pixeled</td><td>2D</td></tr><tr><td>CORTEO<sup>276,277</sup></td><td>3D</td><td>Amorphous</td><td>Voxeled</td><td>...</td></tr><tr><td>TRI3DST<sup>278</sup></td><td>3D</td><td>Amorphous</td><td>Analytical</td><td>...</td></tr><tr><td>IRADINA<sup>279</sup></td><td>3D</td><td>Amorphous</td><td>Voxeled</td><td>...</td></tr><tr><td>IM3D<sup>280</sup></td><td>3D</td><td>Amorphous</td><td>Analytical/triangularized</td><td>...</td></tr><tr><td>SDTrimSP-3D<sup>281</sup></td><td>3D</td><td>Amorphous</td><td>Voxeled</td><td>2D</td></tr><tr><td>TRI3DYN<sup>282-284</sup></td><td>3D</td><td>Amorphous</td><td>Voxeled (planarized)</td><td>3D</td></tr><tr><td>EnvizION<sup>285-291</sup></td><td>3D</td><td>Amorphous</td><td>Voxeled</td><td>3D, near-surface</td></tr></tbody></table>
<figure><img src="image_16.png" /><figcaption>FIG. 6. Sputter shaping of Au nanosphere of diameter 50 nm on Si, (a) initially and (b) after irradiation with 30 keV Ga ions under normal incidence for fluences of 4 × 10¹⁵ and (c) 1 × 10¹⁶ cm⁻². The TRI3DYN simulation (with periodic lateral boundary conditions) demonstrates size reduction and shaping by sputtering, substrate surface erosion, and contamination of the original sphere with sputtered substrate material and vice versa. The incorporation of Ga is small and not shown. For more information, see Ref. 283.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>FIG. 7. Bombardment of Si target with a sharp 50 nm-wide, 50 keV Ga beam with a fluence of 5 × 10¹⁸ cm⁻². Final target composition displaying concentrations (cm⁻³) of (a) Ga atoms, and (b) Si atoms that originate from a depth greater than 30 nm in the virgin sample. Surface contours track fluence increments of 5 × 10¹⁷ cm⁻². The scan area of the beam is in the center of the top boundary. The simulations have been performed with IMSIL. For more information, see Ref. 273.</figcaption></figure>

the trench emerges, which pushes material upward along the trench sidewalls via volume relaxation. The simulation of the milling of a slit in a membrane is described in Ref. 274.

With particular focus on FIB processing, Rack and co-workers have published a series of 3D dynamic results obtained with EnvizION.²⁸⁵⁻²⁹¹ In addition to the collisional BCA simulation and relaxation algorithms used, simplified models have been implemented for reactive-gas assisted erosion and deposition, including secondary-electron mechanisms.¹⁶⁰ Selected results have recently been reviewed in Ref. 302. For an introduction to gas-assisted processes, see also Sec. III D 2.

Dynamic BCA simulations may also be employed to characterize specific FIB based nanoanalytical methods. An example is a 1D TRIDYN simulation of damage buildup during FIB milling of nano-membranes for TEM analysis.³⁰³ Another example is the 3D TRI3DYN simulation of STIM in a HIM device, as shown in Fig. 8. Simulations such as those presented in Fig. 8(a) help us to identify the detector geometry for optimum image contrast and resolution. Furthermore, Fig. 8(b) indicates that there is only minor degradation

of the sample by surface sputtering and recoil atom transport between the core and the shell and between the sphere and the substrate.

## B. Molecular dynamics and molecular statics

Although BCA methods are able to provide insight into processes developing during the ballistic (sub-picosecond) phase of ion irradiation, they cannot predict details of the permanent modification of the target's atomic structure, such as defect clusters or dislocations including their strain fields. Particularly with heavy ions, heat spikes may develop even in keV energy cascades, and the local melting of the target affects the amount of damage formation and atomic mixing.³⁰⁴ The accuracy of the BCA approach diminishes²⁵⁷,²⁵⁸ at energies roughly below 100 eV, and it completely fails in the low single-digit eV energy range. Hence, MD is often the method of choice for the simulation of phenomena associated with atomic motion at eV and sub-eV kinetic energies.

### 1. Principles and simulation codes

Most approaches in practical use are based on the Born-Oppenheimer approximation, which assumes that the electronic subsystem relaxes instantaneously to its ground state at any time as the atomic nuclei change their positions. Consequently, the effect of the electrons can be embodied in a potential energy function that depends only on the nuclear positions.³⁰⁵ Analysis of this energy function allows determination of many material properties as well as the time evolution of the system, e.g., in an irradiation experiment. This is even true when deposition of energy into electronic degrees of freedom dominates, such as for 30 keV He ions impinging on Au clusters³⁰⁶ where defect production is still governed by ballistic energy transfer as excitations are quickly delocalized.
<figure><img src="image_18.png" /><figcaption>FIG. 8. TRI3DYN simulation of scanning transmission ion microscopy (STIM) in a helium ion microscope (HIM). (a) Ion transmission relative intensity image for Au (20 nm diam.)/SiO₂ (50 nm diam.) core/shell nanosphere on Si₃N₄ membrane of thickness 20 nm. A 20 keV He⁺ beam with a Gaussian beam profile of 0.5 nm full width at half maximum (FWHM) is scanned across an area of 90 mm × 90 nm up to a fluence of 2 × 10¹⁶ cm⁻², with the transmitted ions being registered in an annular dark-field detector of 0.6 and 5 cm inner and outer radius, respectively, mounted 2.5 cm behind the sample. Custom evaluation software correlates the detection of the transmitted ions with the actual y-z scan position of the beam. (b) Cross-sectional image of the total atomic density after the irradiation, averaged over a central slice of thickness 2 nm.</figcaption></figure>

In the MD method, Newton's equations of motion are solved for all atoms in the system, using forces calculated from the potential energy function.305,307,308 This is done iteratively with time steps on the order of 1 fs with the time step being dependent on the ion/atom velocities and their masses. At the end of the simulation, when the energy is equilibrated everywhere in the system, the final structure can be analyzed. Due to the short time step required, total simulation times are limited to the nanosecond or at most microsecond range for classical MD and to picosecond for ab initio MD. Effects corresponding to longer timescales are sometimes mimicked by increasing the temperature in the system, which then allows observation of annealing (recombination) of defects and the relaxation of strain.309 Detailed descriptions of the principles of these MD methods can be found in Refs. 247 and 310.

Molecular statics (MS) methods are concerned with finding minima and saddle points in the potential energy function. The former identify (meta-) stable atomic configurations, while the latter allow the determination of energy barriers for diffusion and chemical reactions. Finding global minima, corresponding to stable as opposed to metastable configurations, can be tricky. Various methods have been developed, see Ref. 305 for details.

Simulation codes can be classified into classical and ab initio codes. In the first group, the potential energy and forces are calculated by evaluating mathematical expressions with empirical parameters, while in the second group, they are determined by solving approximations to the Schrödinger equation. The most widely used classical MD code is LAMMPS.311,312 Another general purpose MD code is DL_POLY.313 Codes specifically designed for the simulation of radiation effects include PARCAS,314 DYMOCA,315 and MOLDYCASC.316 GROMACS317 and NAMD318 mainly target biomolecular systems. Popular ab initio codes capable of performing MD simulations are VASP319 and QUANTUM ESPRESSO.320

## 2. Models for the potential energy function

Among the ab initio methods, DFT321 with local and semilocal exchange-correlation (XC) functionals provides a good compromise between accuracy and computational expense for the calculation of the potential energy function. Some phenomena, such as van der Waals interactions, magnetism (especially when spin-orbit coupling is taken into account) or accurate evaluation of the bandgap in semiconductors, require one to go beyond “vanilla” DFT by either using more sophisticated XC functionals222 or post-DFT methods, such as GW/RPA (many body perturbation theory/random phase approximation).323 Yet otherwise, DFT simulations normally provide reliable results with respect to the atomic coordinates and energetics on the scales relevant for the modeling of ion irradiation effects. DFT is capable of predicting charge states of defects and static charge transfer,324 while time-dependent density functional theory (TDDFT) can describe charge transfer dynamics in ion collisions. The advantage of ab initio simulations is that they do not require any material-dependent parameters from the user. The disadvantage is their high computational cost, which scales as $n^2...^3$, where n denotes the number of valence electrons or atoms in the simulation. This imposes a practical limit on the system size that can be handled by DFT, which using supercomputers is currently on the order of 1000 atoms.

If larger systems need to be handled, empirical interatomic potentials (sometimes called force fields) must be used to describe the potential energy function. The computational expense of these simulations scales nearly linearly with the number of atoms. On the downside, the mathematical expressions describing the interatomic potentials are only approximations of the true potential energy function, and the parameters in these models must be fitted for each combination of chemical elements in order to reproduce the physical properties of the material (e.g., lattice parameters, elastic properties, bond energies, energetics of defects, stability of sputtered fragments, etc.). Care is needed if the simulation results in atomic arrangements that are outside the range of atomic arrangements used for the fit. Moreover, the availability of force field parameters can be a limiting factor when looking for new applications, since the development of new parameter sets is a tedious task.325 To overcome this bottleneck, various methods have been developed in recent years.326–333
Collections of 1000+ interatomic potentials together with their parameters for individual systems are available in the NIST Interatomic Potentials Repository³³⁴ and the Knowledgebase of Interatomic Models (OpenKIM).³³⁵ Educated choice of an appropriate interatomic potential is essential for the success of a simulation. In Table IV, the most popular options are listed together with the types of atomic interactions they can describe and their computational expense. All but the CHARMM force field, which is mainly used to describe biochemical molecules such as proteins, lipids and nucleic acids, allow for bond breaking, a prerequisite for the simulation of almost all irradiation effects. For an introductory text on interatomic potentials, see Ref. 305.

Overall fitting of a single functional form with a limited number of parameters to reproduce a vast range of material properties has frequently proven to be an unmanageable task. To overcome this limitation, machine learning (ML) potentials have recently been developed.³⁴⁸,³⁴⁹ Common to all flavors of ML potential is their description of the potential energy using multiparameter functions of the local environment around each atom. To determine the parameters, a large dataset of potential energies and corresponding interatomic forces for a specific set of chemical elements in different configurations is generated by DFT calculations. Hence, the flexibility of these potentials is much greater than that obtained using empirical interatomic potentials, and if carefully developed, they are able to provide results with an accuracy comparable to DFT. There have also been attempts to train ML potentials on-the-fly to handle situations that had not originally been anticipated, such as large surface reconstructions or rare chemical events.³⁵⁰,³⁵¹

As an example, Fig. 9(a) demonstrates the ability of the Gaussian approximation potential (GAP)³⁵² to reproduce the DFT results for the cohesive energy of pure W as a function of atomic volume in

<table><caption>TABLE IV. Some popular interatomic potentials listed with the type of interaction they are able to describe and the execution times per atom relative to the Lennard-Jones potential taken from Refs. 336 and 337 using LAMMPS. Mean values are given in cases where both of these references list values. Execution times for ML potentials vary widely, depending on which formalism they are implemented in (see main text), but still scale linearly with the number of atoms *n*. DFT times are usually orders of magnitude larger than those for empirical interatomic potentials. Ratios strongly depend on the system size, since DFT times scale as *n*²⁻³, hence it is not reasonable to give a scaling factor for DFT.</caption><thead><tr><th>Interatomic potential</th><th>Type of interaction</th><th>Execution time</th></tr></thead><tbody><tr><td>Lennard-Jones<sup>338</sup></td><td>van der Waals</td><td>1</td></tr><tr><td>EAM<sup>339</sup></td><td>Metallic</td><td>1.8</td></tr><tr><td>Stillinger-Weber<sup>340</sup></td><td>Covalent</td><td>3.4</td></tr><tr><td>Tersoff<sup>341</sup></td><td>Covalent</td><td>4.4</td></tr><tr><td>Coulomb-Buckingham<sup>342</sup></td><td>Ionic</td><td>4.7</td></tr><tr><td>CHARMM<sup>343</sup></td><td>Biomolecules</td><td>14.1</td></tr><tr><td>MEAM<sup>344</sup></td><td>Metallic/covalent</td><td>16.5</td></tr><tr><td>COMB<sup>345</sup></td><td>Chem. reactions</td><td>188</td></tr><tr><td>ReaxFF<sup>346</sup></td><td>Chem. reactions</td><td>197</td></tr><tr><td>Kieffer<sup>347</sup></td><td>Chem. reactions</td><td>...</td></tr><tr><td>Machine learning (ML)</td><td>All</td><td>≈10–10 000</td></tr><tr><td>DFT</td><td>All</td><td>≫</td></tr></tbody></table>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /><figcaption>FIG. 9. Example of the agreement between DFT training data sets and machine-learned interatomic potentials using (a) GAP³⁵³ and (b) tabGAP³⁵⁴ for computing the cohesive energy of pure W in different phases, and the mixing energies and bulk moduli of various alloy combinations, respectively. The symbols are the DFT data points and the lines show the GAP and tabGAP results. (a) Reproduced with permission from Byggmästar et al., Phys. Rev. B 100, 144105 (2019). Copyright 2019 American Physical Society. (b) Reproduced with permission from Byggmästar et al., Phys. Rev. B 104, 104101 (2021). Copyright 2021 American Physical Society.</figcaption></figure>

different phases.³⁵³ Similar agreement between predictions of the tabGAP potential (a more efficient version of GAP³⁵⁴) and the DFT calculations of mixing energies and bulk moduli is shown in Fig. 9(b) for multiple combinations of binary, ternary, and quaternary alloys.

The interatomic potentials discussed so far describe the potential energy function near equilibrium or a few eV above equilibrium. During irradiation simulations, much higher potential energies occur in close collisions. In this regime, purely repulsive potentials such as also used in BCA simulations, e.g., the universal Ziegler-Biersack-Littmark (ZBL) potential³⁵⁵ or the potential obtained with the all-electron DFT code DMol,³⁵⁶ provide accurate results. These potentials need to be smoothly joined with the material-specific empirical potential
at small distances.³⁵⁷ For ML potentials, it is advantageous to already include the repulsive potential in the training phase.³⁵³

### 3. Applications of molecular dynamics to FIB irradiation

Large-scale MD simulations have been employed to gain insight into nanostructure formation and the modification of nanostructures. Das, Freund, and Johnson³⁵⁸ investigated the Ga FIB-induced formation of nanopores in Si membranes, which are of interest for biological applications. They identified a local boiling mechanism that could be explosive at high enough ion fluxes.³⁵⁸ Moreover, they found recirculating material flow, which they explained as being driven by temperature-gradient induced surface tension gradients.³⁵⁹ Another interesting phenomenon occurs during ion irradiation of Si nanopillars. At room temperature, the pillars shorten [Fig. 10(a)], while at elevated temperature, they become thinner [Fig. 10(c)]. In the MD simulation performed at room temperature [Fig. 10(b)], Si amorphizes, which initiates viscous flow due to the ion hammering effect³⁶¹ resulting in a shortening of the nanopillar as seen in the experiment. In contrast, in the BCA simulations shown in Fig. 10(d), the nanopillar mainly shrinks in diameter, in agreement with the experimental results at elevated temperature. This is explained by the neglect of viscous flow in the BCA simulations, which in fact does not occur when the

target remains crystalline at the higher temperature. As a third example, MD simulations have examined how a balance among beam spreading, erosion, and defect-induced strain limits the thinning of FIB lamellae.³⁶²

Chemical effects in sputtering cannot be described by BCA simulations but can be using MD simulations employing reactive force fields. For instance, the sputtering of Si by low-energy O and Si ions using the Kieffer force field³⁴⁷ showed that two mechanisms are mainly responsible for sputtering: (i) emission of atoms forming clusters a few Angstroms above the surface, and (ii) ejection of clusters that are loosely bound to the surface.³⁶³ As another example, the impact of residual water molecules on sputter yields of Si bombarded with Ar has been studied (cf. Fig. 11). Here, MD simulations using the ReaxFF potential optimized for the Si–C–O–H system³⁶⁴ are compared to SDTrimSP BCA simulations. For the MD simulations, a much weaker dependence of the O and H partial sputter yields on the incidence angle is found. The difference might be explained by the random positions of the H and O atoms in the SDTrimSP simulations, presenting more efficient scattering centers than the more regular atomic configurations in the MD simulations at incidence angles between about 50° and 80°. At angles closer to perpendicular and grazing incidence, the MD results show higher sputter yields than BCA. This may be explained by the desorption of water molecules, which is not included

<figure><img src="image_21.png" /></figure>

**FIG. 10.** Comparison of the deformation of Si nanopillars under high fluence 25 keV Ne or Si ion irradiation. (a) scanning electron microscopy (SEM) images before (left) and after (right) Ne ion fluence of $2 \times 10^{16} \text{ cm}^{-2}$ at room temperature.³⁶⁰ Note the short, but still wide shape of the pillars after irradiation. (b) Results of MD simulations for the Si/SiO$_2$/Si pillar ($r = 5$, $h = 50 \text{ nm}$) before and after Si fluence of $7.6 \times 10^{15} \text{ cm}^{-2}$. In the top-down views, the dashed squares outline the bottom pedestal and the purple circles show the size of the ion beam irradiation pattern used throughout the simulation.³⁶¹ (c) Experimental images of the evolution of Si nanopillar under prolonged Ne ion irradiation at 400 °C.³⁶⁰ Since the Si does not amorphize, the shape is modified only due to erosion from the top and the sides of the pillar, which is well captured by BCA simulations. (d) Corresponding nanopillar images from BCA simulation.³⁶⁰ (a), (c), and (d) Reproduced with permission from Xu *et al.*, Semicond. Sci. Technol. 35, 015021 (2019). Copyright 2019 Authors, licensed under a Creative Commons Attribution (CC BY) license and (b) reproduced with permission from Fridlund *et al.*, Phys. Rev. Mater. 4, 013601 (2020). Copyright 2020 Authors, licensed under a Creative Commons Attribution (CC BY) license.

<figure><img src="image_22.png" /></figure>

**FIG. 11.** Results obtained by MD and BCA (SDTrimSP) simulations after 100 eV Ar irradiation of Si covered with a monolayer of water molecules to a fluence of $5 \times 10^{15} \text{ ions/cm}^2$. For the MD Si(100) was used. The SDTrimSP sample was amorphous. The evolution of (a) the sputtering yields and (b) the fraction of sputtered H and O atoms, are shown as a function of incidence angle.
in the BCA model. Note that the maximum Si sputtering yield is found at around 65°, whereas the maxima for H and O are found between 70° and 80°. As a practical conclusion, when the mixing of contaminants into the sample should be minimized, angles closer to grazing incidence should be favored.

Defect formation in all kinds of materials has been a traditional application field for MD simulations.²⁴⁷ Although much insight has been gained, quantitative and sometimes also qualitative results are in doubt due to the inaccuracies of empirical interatomic potentials. For instance, the threshold displacement energy, the essential parameter for damage calculations in the BCA method, turned out to be substantially different for Si when calculated by DFT-MD compared to using the Tersoff or Stillinger-Weber interatomic potentials.³⁶³ On the other hand, when using a ML potential, essentially the same values were obtained as with DFT.³⁶⁶ Likewise, sputter yields for low-energy Ar irradiation of Si obtained with the ML potential were found to be close to experimental values, while the empirical interatomic potentials largely underestimate the yields.³⁶⁶ Moreover, it was shown that damage buildup in keV energy cascades is strongly overestimated by the empirical potentials (see Fig. 12).

MD simulations have also provided good understanding of ion induced defect formation in free-standing³⁶⁷⁻³⁶⁹ and supported³⁷⁰⁻³⁷² 2D materials, which is of interest for developing ultrathin membranes to encapsulate gases and other volatile systems for ion beam analysis³⁷³ and also for the development of nanoporous membranes for advanced nanofiltration applications. As with bulk materials, new insight is gained for 2D materials using DFT-MD.³⁷⁴⁻³⁷⁶ As an example, in the study by Kretschmer et al.³⁷⁶ the importance of accounting for chemical interactions when evaluating the threshold displacement energy in graphene and hexagonal boron nitride (hBN) has been demonstrated.

<figure><img src="image_23.png" /><figcaption>FIG. 12. Typical snapshots of 2 keV collision cascades at the heat spike phase and the resultant defects in Si. Heat spike snapshots (left panel) present the atoms with kinetic energy above 1 eV. Atoms have been color-coded based on the time of generation after firing the primary knock-on atom. Surviving defects (right panel) are acquired from Wigner-Seitz analysis of the cell after cooling to 300 K ambient temperature. The comparison visualizes the overestimated defect formation in Si predicted by the classical potential Tersoff (T3)³⁴¹ compared to Gaussian approximation potential (GAP).³⁶⁸ For more information, see Ref. 366.</figcaption></figure>

### 4. Limitations and extensions

While in the BCA method, trajectories are only followed for atoms with energies exceeding a few eV, MD simulates all atoms in a region encompassing the collision cascade. Therefore, MD simulations are much more computationally demanding than BCA simulations. Taking into account that actual FIB processes often use rather high fluences, it is clear that the computational cost of this may be a challenge. Moreover, due to the limitation of the MD time step to values that resolve lattice vibrations, the time between collision cascades cannot be fully simulated. Thermally activated events occurring during these time spans may be covered by kMC simulations as needed (see Sec. III C). Often, however, such thermally activated events are neglected, and in addition, the system is artificially quenched to ambient temperature at the end of each cascade in order to shorten the time required to dissipate the energy deposited by the collision cascade.³⁶³ This comes at the risk of possibly missing some relevant defect annealing.

The limitations of empirical interatomic potentials have already been discussed above. Another drawback of Born-Oppenheimer MD is the absence of an inherent description of electrons in the system. Electronic stopping can be included in MD as a frictional force,³⁷⁰ and the same stopping powers may be used as in BCA simulations. Modeling of electronic stopping of channeled ions, however, cannot be directly transferred from BCA to MD. Here, attempts have been carried out on a more sophisticated level.³⁷⁷,³⁷⁸ In addition, there is uncertainty about the low-energy limit to electronic stopping, which has been shown to be relevant for predicting sputter yields³⁷⁹ and damage formation.³⁸⁰ A related problem is electron-phonon coupling, which describes the exchange of energy between the electronic and ionic subsystems. Electron-phonon coupling may be included in MD simulations by the so-called two-temperature model.³⁸¹ However, so far no general consensus on the model for electron-phonon coupling nor its significance at FIB-relevant energies has been reached.³⁸² Recent insights from TDDFT³⁸³ show promise for enabling a physically motivated parameterization of how electronic stopping and electron-phonon coupling relate to one another.³⁸⁴⁻³⁸⁶ Other possible effects to consider include the modification of atomic interactions due to electron excitations in the system.³⁸⁷

Born-Oppenheimer MD also fails to describe, e.g., the transitions between electronic states or the neutralization of ions in the vicinity of a 2D target. These situations may be treated by TDDFT-MD (Ehrenfest dynamics). In irradiation simulations using Ehrenfest dynamics, the nuclei are usually approximated as classical particles moving in the time-dependent average potential of the electrons, while the electron subsystem evolves according to TDDFT. Due to their complexity and high computational cost, Ehrenfest dynamics simulations using massively parallel computers are currently only feasible for systems comprising tens of atoms and for times up to picoseconds. The method has been successfully applied to electronic stopping power calculation in various targets,³⁸⁸⁻³⁹¹ excitation mediated diffusion modeling,³⁹² and simulations of the behavior of inorganic 2D materials under electron beam irradiation,³⁹³ but its applicability is limited by the mean-field approximation and the resulting propagation of mixed states. For example, the sputtered atoms may have fractional charges that are unphysical. It is also worth noting that this approach has been demonstrated to work for describing the formation of HIM images by assessing the spatial distribution of excited electrons immediately after the ion impact.³⁹⁴
### C. Kinetic Monte Carlo (kMC)

The timescale accessible by MD simulations is in the nanosecond range, which is sufficient for the system to reach thermal equilibrium after an ion impact. After this time, diffusion and interaction of defects take place by thermally activated events. Examples of such events are diffusion hops, attachment of an atom to a cluster, or recombination of two defects. The rate constant of each event may be determined by the transition state theory using the potential energy function of the system, e.g., using DFT and the nudged elastic band (NEB) method.395 Sometimes, this parameterization can be achieved directly from experimental data, e.g., by fitting to a known temperature-dependent diffusion coefficient. kMC is a method that evolves systems described by such events stochastically. For a basic introduction to the method, see Ref. 396. Another review is found in Ref. 397, and more recent ones with special emphasis on radiation effects and semiconductor processing can be found in Refs. 398 and 399, respectively. Other approaches for extending the timescale of MD are discussed in Ref. 400.

Several variants of the kMC method have been developed. On-the-fly kMC determines energy barriers of possible events during the course of a simulation. This technique has been used to simulate defect diffusion in Fe,401 defect evolution in graphite402 as well as deposition and sputtering.403 On-the-fly kMC can easily be combined with MD, since both methods can use the same potential energy function, and neither needs prior knowledge of possible events. However, the search for possible events makes the on-the-fly variant of kMC the most computationally expensive.

Setting up a catalog of events a priori can be approached in two ways. In lattice (or atomistic) kMC, a lattice is defined where each site can be empty or occupied by an atom. Events are hops from one lattice site to another with rates modeled based on the local environment of each site. Use cases include vacancy diffusion,404 solid-phase epitaxial regrowth,405,406 sponge structure formation in Ge,407 self-organized surface pattern formation,408 knock-on damage in hBN,409 and phase decomposition of substoichiometric SiO₂ into Si nanoclusters in an amorphous SiO₂ matrix.410

In object kMC, in addition to vacancies and impurity atoms, other defects including clusters are treated as individual objects that are tracked as they move and/or react with each other. The atoms of the “background” material are not explicitly represented. Therefore, the system size accessible by object kMC is determined by the number of objects in the simulation, rather than by some fixed volume. The object kMC approach has mainly been used in simulations of radiation effects in nuclear materials411 and semiconductor processing.399,412

Lattice and object kMC can be combined not only with MD402,403,408,411 but also with BCA.404,410–412 In addition, kMC schemes are occasionally also used to describe system evolution due to non-thermally activated events. For instance, in Ref. 373, the accumulation of defects in a graphene sheet is modeled based on defect production probabilities obtained by MD simulations of ion impacts.

### D. Continuum modeling

Unlike the methods described in Subsections III A–III C, continuum models do not use individual atoms as the objects of simulation, but instead use quantities that are continuous functions of space and time. For example, in a continuum approach, the ion beam is described by its spatially dependent flux (number of ions per area and time increment), the adsorbed precursor molecules are described by their

concentration (number of molecules per surface area), and the boundaries of solids are described by mathematical surfaces.

#### 1. Ion implantation and milling

In the absence of ion beam mixing and other secondary effects, the distribution of implanted ions may be obtained by the convolution of the beam flux $F_{\text{beam}}(x, y)$ and a “point response” $f(x, y, z)$. The point response is the probability density function for the stop position of an ion entering a planar target at the origin of the coordinate system. For the purpose of this discussion, we assume the ions to be incident along the negative z axis; x and y denote the other two Cartesian coordinates. If the surface is described by a height function $z = h(x, y)$, the increase in the concentration of implanted atoms $C(x, y, z)$ with time t is given by413

$$ \frac{\partial C}{\partial t} = \iint F_{\text{beam}}(\xi, \eta, t) f(x - \xi, y - \eta, z - h(\xi, \eta)) d\xi d\eta. \quad (2) $$

For practical reasons, $f(x, y, z)$ is often approximated by a Gaussian function whose parameters can be determined by a BCA simulation. For an unscanned beam, the beam flux $F_{\text{beam}}(x, y, t)$ is constant in time, for a digitally scanned beam it is piecewise constant, and for an analog scanned beam it is a continuous function of time.

Displaced atom and deposited energy distributions can be calculated in a similar way. They may be of interest for estimating the damage to the target, and as input for solving the heat transport equation, respectively.

Sputtering causes the surface to recede. The resulting surface velocity in the direction of the surface normal is given by

$$ v_{\perp} = \Omega F, \quad (3) $$

where $\Omega$ denotes the atomic volume of the target atoms and $F$ is the flux of atoms through the surface element around the point under consideration. In the absence of secondary effects, $F$ is given by the flux of sputtered atoms, $F = F_{\text{beam}}Y(\theta) \cos \theta$, with $\theta$ being the local incidence angle of the ions and $Y(\theta)$ being the sputter yield. The sputter yield may be determined by BCA simulations or experiment.

As long as an initially flat surface, $h(x, y, t = 0) = 0$, develops only small slopes, the surface contour reflects the beam profile

$$ h(x, y, t) = - \int_{0}^{t} v_{\perp} dt = - \Omega Y(0) \int_{0}^{t} F_{\text{beam}}(x, y, t) dt. \quad (4) $$

Once larger slopes occur, further prediction of the target topography usually requires iteration414 or more refined numerical techniques. One option is to move surface marker points along the surface normal.415 The drawback of this method is that as the nodes move, they tend to form loops which have to be removed. A simple technique to avoid loops, which works for surfaces that remain as height functions $h(x, y)$ throughout the simulation (i.e., the surface has no overhanging structures), is to interpolate the surface back to an $(x, y)$ grid after each time step.416 More general solutions are cell-based and level-set methods. The former represent the target by filled or partially filled voxels, while the latter describe the surface as the zero level-set of a distance function and solve a differential equation for this quantity.415 Implementations of the marker and level-set methods for FIB milling have been presented in Refs. 417–422 and Refs. 298 and 423–426, respectively.
When the surface develops larger slopes, two additional effects come into play (see Fig. 13). First, sputtered atoms may be redeposited on other regions of the surface (dark blue arrow). Second, ions may be backscattered from their primary incidence point and impact the target somewhere else (red arrow), where they cause sputtering. The secondary sputtered atoms may then be redeposited (light blue arrow). These processes add significantly to the complexity of the simulation: the angular (and possibly energy) distributions of the sputtered and backscattered atoms (blue and red elliptical lines, respectively) have to be described in some way, and the computation of the fluxes at each marker point (D₁ and D₂) requires the summation over the contributions of all other marker points (S₁ and S₂).²³²,⁴²¹,⁴²² This summation may be substituted by randomly starting individual rays at the source points, which adds a MC aspect to the simulation.⁴²³,⁴²⁷ In contrast to a BCA simulation, however, the atom trajectories are not followed within the target, but their exit characteristics are chosen according to precalculated angular (and energy) distributions. Either way, redeposition and backscattering add contributions to the flux F of Eq. (3). The same applies to contributions from etching and deposition in the case of gas-assisted processes (see Sec. III D 2).

In principle, many physical and chemical effects may be considered in a continuum approach. However, when a new ion-material combination is considered, each model requires input from more fundamental simulations or experiments. This may be straightforward for the parameters of the most basic models, such as the mean values and standard deviations of implanted ions or the sputter yields. However, as the model complexity increases, parameter determination becomes more cumbersome.

Our discussion so far has neglected dynamic changes to the target composition. As the irradiation proceeds and ions are implanted, however, the stopping power for the ions changes, and so does the point response f(x, y, z) in Eq. (2). The same applies to sputter yields and angular distributions. Consideration of dynamic effects would also require modeling of atomic mixing. This has not been attempted so far in a multidimensional continuum approach. Moreover, sputtering is a nonlocal effect, i.e., the sputtered atoms are not emitted exactly at the

impact point of the ion, which may be important in nanofabrication. In addition, ion implantation and atom relocation may cause topography changes through volume relaxation (cf. Sec. III A). These effects are building blocks of the theory of spontaneous pattern formation⁴²⁸ but have not been considered in continuum simulations of FIB processes so far.

Another effect that can be treated within a continuum approach is beam induced heating. Temperature distributions can be calculated by solving the heat transport equation with heat sources given by the energy deposition of the collision cascades, using finite element or finite difference methods.⁴²⁹,⁴³⁰ The estimates are important because elevated temperatures may reduce deposition rates in FIBID (see Sec. III D 2) and may lead to heat damage in biological samples (see Sec. III D 3).

## 2. Gas-assisted deposition and etching

Gas assistance enables selective 3D nanoprinting and enhanced etch rates in FIB processing. Continuum models attempt to quantify the local deposition or etch rate caused by the chemical surface reaction between the volatile adsorbates and the primary ions (PIs), their locally generated SEs, and excited surface atoms (ESAs), as follows.

Deposition reaction:

$$ \text{adsorbate} + (\text{PI, SE, ESA}) \xrightarrow{\text{FIBID}} \text{deposit fragments} + \text{volatile fragments.} \quad (5) $$

Etch reactions:

$$ \text{adsorbate} + (\text{PI, SE, ESA}) \xrightarrow{\text{FIBIE}} \text{reactive fragments} + \text{volatile fragments,} \quad (6a) $$

$$ \text{reactive fragments} + \text{substrate atoms} \rightarrow \text{volatile compound.} \quad (6b) $$

FIBID typically employs volatile metalorganic compounds to deposit metal-containing nanostructures.⁴³¹ For focused ion beam induced etching (FIBIE), the adsorbed precursor needs to dissociate upon irradiation into a reactive species that removes atoms from the underlying substrate by forming a volatile compound but does not leave traces of other dissociated precursor elements.

Present FIBID and FIBIE models treat the desorption of volatile fragments in reactions (5) and (6) as instantaneous and assume that the etch reaction (6b) is fast compared to reaction (6a), see Ref. 432 for a review. Both processes share the same formalism to calculate the surface coverage Θ (normalized concentration) of adsorbates, which is defined by the rate equation (in units of inverse time)

$$ \frac{\partial \Theta}{\partial t} = \nu_{\text{gas}}(1 - \Theta) - \nu_{\text{des}}\Theta - \nu_{\text{dis}}\Theta + D\nabla^2\Theta. \quad (7) $$

The terms $\nu_{\text{gas}}(1 - \Theta)$ and $\nu_{\text{dif}} = D\nabla^2\Theta$ are adsorbate source terms describing gas and surface-diffusion transport, respectively, while the other two terms are adsorbate sink terms related to the rates of desorption and dissociation, $\nu_{\text{des}}$ and $\nu_{\text{dis}}$, respectively, as schematically depicted in Fig. 14. This approach could be extended to multiple chemical pathways, as in models developed for FEBID and focused electron beam induced etching (FEBIE).⁴³³

<figure><img src="image_24.png" /><figcaption>FIG. 13. Illustration of ion backscattering (red lines) and redeposition of sputtered atoms (dark and light blue lines) during FIB milling of a trench.²³² The ellipse-like curves represent angular distributions. In this case, the surface may be described by a height function $z = h(x)$. For clarity, no variation in y direction is assumed. Reproduced with permission from Lindsey et al., Nucl. Instrum. Methods Phys. Res., Sect. B 341, 77–83 (2014). Copyright 2014 Elsevier.</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>FIG. 14. Concept of selective (local) gas assisted FIBID. Volatile physisorbed molecules are dissociated by irradiation into volatile and nonvolatile fragments, the latter forming the deposit (green spheres). Primary ions typically arrive at keV energy while ESAs and SEs have an eV energy spectrum. ESAs are generated by the collision cascade (recoil atoms) and have energies below the surface binding energy (not sputtered). Rates (ν) are explained in the text. Note that ion sputtering, ligand codeposition, and incomplete adsorbate dissociation have been omitted for clarity. For more information, see Ref. 434.</figcaption></figure>

PIs, SEs, and ESAs are the co-reactants. The concentration of impinging PIs is given by the ion beam spatial profile $F_{\text{beam}}(x, y)$ and the FIB exposure time. Energy and spatial distributions $f(E, \vec{x})$ of SEs and ESAs result from the interaction of the PIs and the recoils with the etched substrate or growing deposit. $f(E, \vec{x})$ must be determined from more fundamental simulations. For SEs, BCA simulations of PIs and recoils combined with MC simulations of electron transport$^{435}$ have been performed using a simple model for SE generation. More refined theories of SE generation also exist.$^{436–438}$ For ESAs, BCA simulations reach their low-energy limit of applicability, since atom energies of around 1 eV can already dissociate the precursors. An alternative for simulations of ESAs would be MD. Recently, first attempts of MD were undertaken for FEBID where atomistic detail on metal grain size, distribution, and composition in the deposited metal-carbon material could be obtained.$^{439,440}$ The treatment of adsorbate dissociation by electrons relied on experimentally measured fragmentation mass spectra and fragment ion yields for structurally similar molecules, which needed smart appropriate scaling. Desorption of the adsorbate fragments was approached using an external force field. Both approaches limit the predictive power of the simulations at present but show promise if appropriately refined in the future. Modeling of FIBID would require inclusion of the ESA and milling mechanisms into the simulation.

Finally, the chemical fluxes of deposition $F_{\text{dep}}$ or etching $F_{\text{etch}}$ (in units of atoms per area per time) are proportional to the dissociation rate $\nu_{\text{dis}}$ and the coverage of adsorbates $\Theta$ as shown

$$F_{\text{dep,etch}} = m\nu_{\text{dis}}\Theta n_s, \qquad (8)$$

where m denotes the number of atoms deposited or etched per dissociated precursor molecule and $n_s$ is the number of adsorbate sites per unit surface area. Note that the product $\nu_{\text{dis}}\Theta$ defines the rate of deposition or etching for a single site in units of inverse time. The flux according to Eq. (8) must be added to the flux of sputtered and redeposited atoms discussed in Sec. III D 1.

Modeling of the four terms on the right-hand side of Eq. (7) is key to the successful simulation of FIBID and FIBIE. The first term $\nu_{\text{gas}}(1 - \Theta)$ represents a widely used pragmatic simulation approach. It assumes non-dissociative Langmuir adsorption, which treats adsorption as physisorption with a maximum coverage of one monolayer of adsorbates. Other adsorption schemes include dissociative adsorption,$^{441}$ multilayer adsorption,$^{442}$ and chemisorption.$^{443}$ Open source MC codes are available for the calculation of the gas impingement rate $\nu_{\text{gas}}$ on the irradiated area for a given geometrical arrangement of nozzle and substrate.$^{433,444,445}$ Typical values are in the range $0.1 \le \nu_{\text{gas}} \le 10^3 \text{ s}^{-1}$.

The desorption rate $\nu_{\text{des}}$, contained in the second term on the right-hand side of Eq. (7), is the inverse of the surface residence time. It depends exponentially on the temperature as well as on the type of adsorption occuring on the growing/etched surface being irradiated. The desorption rate can cover several orders of magnitude depending on the molecule-surface interaction.

The third term, the adsorbate dissociation by irradiation, is key for selective FIBID and FIBIE as it captures the crucial non-thermal irradiation-driven chemistry of the process. Different contributions involving PIs, SEs, and ESAs are involved in adsorbate dissociation, see Fig. 14. In principle, the dissociation rate can be calculated from the energy dependent dissociation cross section $\sigma(E)$ and the energy distribution $f(E, \vec{x})$ of the SEs or ESAs via

$$\nu_{\text{dis}}(\vec{x}) = \int_{0}^{\infty} \sigma(E)f(E, \vec{x}) \, dE. \qquad (9)$$

$\sigma(E)$ describes the efficiency of reactions (5) and (6) as functions of the energy of the PIs, SEs, and ESAs. Such energy dependent calculation is hampered by the fact that so far reliable $\sigma(E)$ only exist for electron induced dissociation reactions of molecules in the gas phase, see, for example, Ref. 446. A pragmatic approach assumes that such gas phase $\sigma(E)$ can be linearly scaled to the net deposition (etch) cross section (see below). This approach omits the quenching of certain dissociation channels (fragment production) due to the adsorbate state situation.$^{432,447–449}$ Simulations will thus not be accurate with respect to deposit composition, but the deposit (etch hole) shape can probably be adequately modeled. The only established energy dependent cross section for deposition conditions exists for the molecule $(CH_3)_3Pt-CpMe$ under electron irradiation,$^{450}$ describing the observed dissociation of one volatile $CH_3$ ligand from the adsorbed molecule leading to a deposit of atomic composition Pt:C = 1:8.

So far, the ESA induced adsorbate dissociation reactions have not been studied, probably due to experimental issues in deconvolution of the naturally involved (secondary) electron contributions. Recent condensed phase studies using Ar-ion irradiation$^{451}$ point to the importance of the additional mechanical sputtering effect of the PIs, which can help remove more ligand fragments than SEs alone and thus achieve a higher metal content material. The elemental species, charge,
and energy of the ions open up a wide field of fragmentation chemistry with metalorganic or “etch” adsorbates, which is still unexplored, particularly with respect to missing $\sigma(E)$. Moreover, the energy distributions $f(E, \vec{x})$ in Eq. (9) are not easily obtained in a continuum approach. Therefore, while using Eq. (9) with a MC approach for SE generation and transport is a promising approach, for the ESA mechanism, one has to resort to simpler approaches, as is also often undertaken to describe the SE mechanism.

In a simpler approach, dissociation is generically modeled via the dissociation rate $\nu_{dis}(\vec{x}) = \sigma f(\vec{x})$, where $f(\vec{x})$ is the local flux of the PIs and $\sigma$ is the so-called net deposition or etching cross section, which is deduced from fitting the shape of the deposit or etch hole. Such cross sections do not distinguish between the different contributions of PIs, SEs, and ESAs, nor do they distinguish between the fragmentation reactions. The modeled shape or rate can sometimes retroactively be attributed to a certain mechanism, when the yield and/or spatial distribution of either PIs, SEs, or ESAs matches the deposit or etch hole dimensions. In this way, the ESA dissociation mechanism was identified to be dominant for FIBID using noble gas ions heavier than He$^{434,452}$ and the SE dissociation mechanism was identified as important for He-FIBID nanopillar growth.$^{453}$ In those cases, $f(\vec{x})$ may be interpreted as the flux of ESAs or SEs. Experimental net cross sections (yields) obtained from ion and electron induced deposition are available for a few precursor molecules,$^{431}$ and deposit compositions upon electron irradiation were recently reviewed in Refs. 454 and 441.

The fourth term in Eq. (7), the surface diffusion rate, is proportional to the surface diffusion coefficient $D$ and the second spatial derivative $\nabla^2\Theta$ of the adsorbate coverage $\Theta$. Thus, it becomes largest for intense and finely focused ion beams and can result in the delivery of considerable amounts of adsorbates to non-irradiated surface areas. Increasing temperature increases the surface mobility of the adsorbates exponentially.

The generation of local heat during ion irradiation can be an important factor influencing the outcome of a deposition process. Thermal contributions can alter the nonthermal irradiative dissociation pathways and exponentially change the diffusion constant (mobility) and residence times of the adsorbates on the surface. As an example, thermal effects are thought to be responsible for the bending of lateral nanowires as they grow.$^{455}$ As mentioned in Sec. III D 1, the temperature distribution needed as input for temperature dependent models of mobility and residence time can be obtained by numerically solving the heat transport equation.$^{429,430}$

### 3. Applications to FIB processing

Simulations of FIB milling may be used to investigate the influence of beam shape and scan strategy on the final topography of the target$^{417}$ and to better understand the milling process. For instance, Lindsey et al.$^{301}$ investigated microtrench formation in trench milling and clarified the roles of redeposition and backscattering. In practice, often the inverse problem of determining beam and scan parameters for a desired geometry must be solved. In the simplest case, for low aspect ratio structures, this can be achieved approximately by choosing the pixel dwell times proportional to the desired depth at the respective pixel positions.$^{228}$ For higher accuracy, a system of linear equations for the pixel dwell times must be solved in order to consider the effect of beam overlap.$^{414,456}$ For higher aspect ratio structures, when redeposition and/or backscattering need to be considered, repeated numerical

simulations of the milling process must be performed until convergence to the desired structure is achieved. In practice, such structures are fabricated by applying variable dwell times across the scan area in multiple passes. Here, one can either choose to apply the same pattern in each pass$^{232}$ or define layers to be milled in each pass and determine individual dwell time profiles.$^{229}$

Finite element and finite difference simulations of heat transport have been performed by Wolff et al.,$^{430}$ who used them to verify a simple model for the estimation of target heating. Schmied et al.$^{457}$ employed a similar numerical approach to find beam scanning strategies that minimize local thermal stress in soft matter.

Gas-assisted FIB processes have been treated in a continuum approach mostly to help identify in which regime the surface reactions (5) and (6a) take place, i.e., whether they are mass-transport-limited (adsorbate-limited), or reaction-rate limited (PI, ESA, and/or SE limited), or driven by desorption or surface diffusion. These regimes strongly influence shape fidelity, homogeneity, and resolution, all of which are of utmost importance for 3D nanoprinting/nanoetching approaches. A review of both time dependent and steady-state analytical solutions of Eqs. (7) and (8), using simplifying assumptions, is found in Ref. 432. This theoretical framework closely resembles the one used for gas-assisted focused electron beam processing (FEBID/FEBIE) with the exception of physical sputtering and redeposition. Hence, analytical solutions established for the analog electron-based FIBID/FIBIE variants straightforwardly apply. These include expressions obtained for steady-state surface diffusion and flat-top focused beam profiles,$^{458,459}$ long freestanding rods,$^{460}$ 1D time dependent solutions,$^{461}$ and expressions for lateral resolution$^{462}$ and etch/deposition gas mixtures.$^{463,464}$ Analytical solutions without surface diffusion can be used in the PI, ESA, SE limited processing regimes (no concentration gradient of adsorbates due to high supply from the gas phase) or approximately when adsorbates cannot diffuse into the center of the FIB spot profile due their deposition at the perimeter. These conditions translate into very small FIB current and exposure (dwell) time.$^{465}$ Without the surface diffusion term, analytical solutions are more easily

<figure><img src="image_26.png" /><figcaption>**FIG. 15.** Flying roof structure fabricated by FIBID.$^{300}$ (a) Schematic illustration of the structure. (b) Side view SEM image and simulation (green line) of the structure obtained using a 30 keV Ga ion beam with a FWHM of 60 nm and pentamethylcyclopentasiloxane as the precursor. After wall formation, the ion beam was moved to the left in 16 steps of spacing 60 nm. Reproduced with permission from Ebm et al., J. Vac. Sci. Technol., B 29, 011031 (2011). Copyright 2011 American Vacuum Society (AVS).</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>FIG. 16. Schematic overview of the different FIB techniques.</figcaption></figure>

derived and thus cover a broader range of adsorbate-related dissociation mechanisms. These include the resulting deposit composition upon injection of two precursor species,<sup>466</sup> multistep reactions involved in gas enhanced etching,<sup>433,467</sup> and experimental parameter maps.<sup>442</sup>

Full numerical continuum simulations of a FIBID process using Eqs. (7) and (8) have been performed by Ebm *et al.*,<sup>300</sup> see Fig. 15. In these simulations, an ESA-based model was used, assuming the concentration of ESAs to be proportional to the flux of sputtered atoms. The authors considered the nonlocal nature of sputtering, a prerequisite for obtaining parallel sidewalls in the lower part of the structure and the flying roof in the upper part. Simulations of pillar growth using voxel grids have been reported in Ref. 468.

Presently, simulations of FIBID/FIBIE are more advanced in the BCA-based approaches (cf. Sec. III A 3). One reason for this might be that pure continuum approaches require the modeling of the SE/ESA intensities $f(\vec{x})$ as an additional step. Also, BCA-based approaches include several collision cascade related effects, which cannot easily be modeled in a continuum approach (see Sec. IIID 1). On the other hand, uncertainties in some of the assumptions of both the BCA and the continuum approaches might be more significant in practice. These include the manner in which the energy and spatial distributions of the ESAs and SEs are determined and assumptions about the fragmentation paths. Further development of either approach holds promise for model-assisted 3D nanoprinting, which has already been demonstrated for FEBID<sup>469,470</sup> and has been started for FIBID.<sup>287,291,455</sup>

## IV. APPLICATIONS OF FOCUSED ION BEAMS

The various processes that are triggered when a beam of ions interacts with a sample form the basis of the multitude of FIB applications that are routinely used today. Accordingly, this section is intended to provide a comprehensive overview of this wide variety of experimental applications and is structured according to the different FIB processing techniques involved (see Fig. 16 for an overview).

In the following paragraphs, the breadth of FIB techniques is briefly outlined, to be highlighted in more detail in subsections IV A-F. Further reviews of these topics can be found in a number of recent articles.<sup>7,43,302,471,472</sup>

**Subtractive FIB processing:** local material removal by a focused ion beam is based on physical sputtering. The incident projectiles not only knock out substrate atoms by momentum transfer but also penetrate the material in a collision cascade. While the ejection of atoms is desired here, all other interactions with the substrate can cause unwanted side effects such as amorphization, mixing, doping, dealloying, and others. Conventional Ga-FIB tools provide spatial resolution and sputtering yields high enough for multiple prototyping purpose, but other ion species may offer advantages in terms of increased spatial resolution or sputter yield, and reduced damage or chemical reactivity. Section IV A provides an overview of the rich variety of subtractive FIB milling applications.

**Defect engineering:** FIB irradiation of materials at doses significantly lower than those used for milling has been implemented in a range of applications to locally tune material properties through the introduction of defects (vacancies and implanted ions). For example,
by varying the dose, different concentrations of vacancy defects can be introduced into a crystalline material, thus modulating properties such as electrical, magnetic, and thermal behavior in the patterned regions. In the case of ion implantation, this can be directed at single ion implantation or can be used to modify the chemical and structural properties of surfaces for resistless patterning. An overview of defect engineering applications is given in Sec. IV B.

**Imaging and tomography:** just as is the case with the SEM, scanning the ion beam over a surface generates secondary electrons that can be detected to form an image. In this respect, imaging using a focused ion or a focused electron beam is equivalent. Even the same secondary electron detectors can be used. However, what strongly differs, is the mass of the probe. The mass of the ions is more than three orders of magnitude larger than that of the electrons, which significantly influences the contrast mechanisms and interaction volumes, and can also inflict significant damage on the sample. In this respect, the light ions of the He-FIB bring great benefit. Section IV C is dedicated to the application of the He-FIB specifically for the imaging of biological specimens. The FIB can further be used in a subtractive manner as described above to slice the sample and image the resulting cross sections by SEM. The images are then used for reconstruction of the full 3D information via so-called FIB-SEM tomography (see Subsections IV C 3 and IV C 4).

**Elemental analysis:** during ion beam induced physical sputtering, atoms and ions originating from the sample are ejected and can be used to study its chemical composition. In SIMS, the generated secondary ions are collected and separated by their mass in a spectrometer as detailed in Sec. IV D. Other analytical techniques, such as EDS or electron backscatter diffraction (EBSD), are of minor importance in conventional FIB systems because the generation rate of X-ray quanta is negligible, and the typical penetration depth of the conventional Ga ions is too low to generate sufficient information on lattice orientation.

**Gas-assisted FIB processing:** gases can also be locally introduced into the FIB chamber to take advantage of other processing opportunities. For example, a reactive gas can be introduced to enhance sputtering yields in subtractive processing by milling (see, for example, Sec. IV A 3). Alternatively, precursor gases can be selected to enable the highly localized deposition of material, which is referred to as focused ion beam induced deposition (FIBID). The flexibility of FIBID in terms of shape and spatial resolution (20–30 nm for Ga-FIBID, and 10 nm for He-FIBID) make it highly desirable for applications that require unique and precise planar or 3D designs. Top-down FIBID applications are discussed further in Sec. IV E.

**Unconventional FIB processing:** similar to gas-assisted processing, FIBs can also be used for the local chemical modification of lithographic resists and condensed or spin-coated metalorganic precursors. Such “unconventional” FIB processing can increase processing speeds and provide new chemical reaction pathways for ion induced deposition of high-purity metals. Focused ions can also be used to form self-assembled structures or combined with other micro-/nanofabrication techniques for advanced multiscale processing. Recent advances in the area of FIB based resist lithography and other nonstandard FIB approaches are described in Sec. IV F.

## A. Applications of subtractive FIB processing

As material removal using a focused ion beam is local and direct, it offers extraordinary flexibility in terms of the target geometry to be

realized, as well as the substrate materials and their geometries. Often FIB processing can be monitored *in operando* using SEM for direct alignment and quality control. Table V provides an overview of the variety of applications based on subtractive FIB processing.

### 1. FIB for materials science

Arguably the most widespread application of the FIB has been the site-selective fabrication of cross section samples for high-resolution imaging using TEM.<sup>4,6,618–620</sup> Due to the prevalence of Ga-FIB instruments, Ga ions are most typically employed and various strategies have been developed to mill and extract cross sections from bulk materials and to thin samples to electron transparency. This includes low-energy FIB milling under glancing incidence to minimize surface amorphization and the use of material specific capping layers and rocking stages to avoid “curtaining” artifacts. More recently, the use of other FIB species for TEM lamella preparation has been demonstrated such as the Ne-FIB<sup>473</sup> and the Xe-FIB.<sup>474</sup> The advantage of a noble gas ion species is that it does not chemically react with the sample or accumulate along grain boundaries, as can be the case with Ga.<sup>621</sup>

In the same manner, FIB milling has emerged as an important tool for the creation of needle-shaped specimens for APT.<sup>5,477,622</sup> The required needle geometry is achieved via annular milling with different currents and successively smaller milling areas. Similar considerations regarding beam damage apply as for TEM sample preparation. For example, minimizing the damage layer is important and possible indif-usion of, e.g., Ga atoms<sup>623</sup> has to be taken into account. In this respect, a final polish with Ne-FIB has recently been shown to remove all resid-ual Ga contamination from Ga-FIB-milled APT needle specimens.<sup>624</sup> Performing the Ga-FIB milling at cryogenic temperatures has also been shown to limit Ga diffusion into the specimen.<sup>625</sup>

Another important application is the site-specific preparation of cross section cuts that enable *in situ* and *ex situ* imaging<sup>626</sup> and/or other analysis such as EDS or EBSD (e.g., Ref. 497). By automating this process, full (destructive) tomographies can be performed by slicing the sample, extracting the desired information from each slice, and reconstructing the data in three dimensions (see, for example, Refs. 103 and 627). Tomography and its applications for the study of energy materials and, in particular, complex organic systems in the life sciences, are discussed in more detail in Sec. IV C 3.

All of these techniques are part of the standard materials science repertoire used to study the microstructure, composition, and properties of materials and devices at specific target locations. In depth overviews on these topics can be found, for example, in Ref. 628. One specific area in materials science that particularly benefits from the 3D sculpting capabilities of FIB concerns small-scale mechanical testing and is discussed in more detail in Sec. IV A 2.

### 2. FIB for mechanical testing

As technology miniaturizes, the external dimensions of device components approach critical internal length scales such as dislocation interspacings. The mechanical properties of such small material volumes are still not fully understood. In 2004, Uchic *et al.*<sup>480</sup> suggested the use of FIB milling to machine micropillars to study size dependent mechanical properties of metals, exploiting conventional nanoindentation equipment for microcompression experiments. In contrast to
<table><caption>TABLE V. Overview of applications of subtractive FIB processing, in which material is locally removed by FIB based physical sputtering. Applications of FIB-SEM tomography are discussed in Sec. IVC3.</caption><thead><tr><th>Research area</th><th>Application</th><th>Ion</th><th>Material/geometry/device</th></tr></thead><tbody><tr><td rowspan="10">Materials science</td><td rowspan="3">TEM sample preparation</td><td>Ne</td><td>Al alloy and Si<sup>473</sup></td></tr><tr><td>Ga</td><td>Wide range of materials<sup>4</sup></td></tr><tr><td>Xe</td><td>Al and Si,<sup>474</sup> Al alloy<sup>475</sup></td></tr><tr><td rowspan="3">APT sample preparation</td><td>Ne</td><td>Al alloy and AlO<sub>x</sub> thin-film structure<sup>476</sup></td></tr><tr><td>Ga</td><td>Wide range of materials<sup>477</sup></td></tr><tr><td>Xe</td><td>Al alloy,<sup>478</sup> Ti alloy<sup>479</sup></td></tr><tr><td rowspan="2">Mechanical testing</td><td>Ga</td><td>Micro/nanopillars,<sup>480-489</sup> notches and micro-cantilevers,<sup>489-497</sup> “dogbone” tensile bars,<sup>491,498,499</sup> suspended membrane beams,<sup>500</sup> other geometries<sup>501-503</sup></td></tr><tr><td>Xe, Ne</td><td>Micro/nanopillars,<sup>488</sup> trenches<sup>503</sup></td></tr><tr><td rowspan="6">Semiconductor technology</td><td rowspan="3">Mask repair</td><td>He, H, N</td><td>Molybdenum silicide photomasks<sup>57,504-507</sup></td></tr><tr><td>Ga</td><td>Cr-on-glass photomask<sup>508,509</sup> including deposition for repair of clear defects<sup>510</sup> and gas-assisted etching for opaque defects in TiN EUV masks<sup>511</sup></td></tr><tr><td>Au</td><td>Cr-on-glass photomask,<sup>508</sup> Au-on-Si X-ray mask including deposition and gas-assisted etching<sup>512</sup></td></tr><tr><td rowspan="2">Circuit edit</td><td>He, H, N</td><td>Complementary metal-oxide-semiconductor (CMOS) circuits<sup>507,513</sup></td></tr><tr><td>Ga</td><td>Decomposition of Pd acetate for conductive lines<sup>514</sup></td></tr><tr><td rowspan="10">Quantum and magnetic materials</td><td>Superconductivity</td><td>Ga</td><td>Unconventional superconductivity in Sr<sub>2</sub>RuO<sub>4</sub>,<sup>515,516</sup> Josephson-vortices in strongly layered high-T<sub>c</sub> superconductors,<sup>517,518</sup> vortex pinning,<sup>519</sup> directional vortex motion,<sup>520-522</sup> high-T<sub>c</sub> superconductivity<sup>523-525</sup></td></tr><tr><td rowspan="3">Superconductive circuitry</td><td>Ne</td><td>Nanoconstrictions and nanoSQUIDs in Nb<sup>526-528</sup></td></tr><tr><td>Ga</td><td>Nanoconstrictions and nanoSQUIDs in Nb,<sup>529-536</sup> NbN,<sup>537</sup> and YBCO<sup>538-541</sup></td></tr><tr><td>Xe</td><td>nanoSQUIDs in Nb<sup>542</sup></td></tr><tr><td rowspan="2">Spintronics and magnonics</td><td>Ne</td><td>Permalloy microstrip trimming,<sup>543</sup> environment dependent FMR<sup>544</sup></td></tr><tr><td>Ga</td><td>Magnetic reversal,<sup>545</sup> spin wave phase inverter<sup>546</sup></td></tr><tr><td>Magnetism</td><td>Ga</td><td>Surface time-reversal symmetry breaking in delafossites<sup>547</sup></td></tr><tr><td>Topology</td><td>Ga</td><td>Topological semi-metals,<sup>548-550</sup> Fermi-arc surface states,<sup>551</sup> Kagome conductors<sup>552</sup></td></tr><tr><td>Strain engineering</td><td>Ga</td><td>Sr<sub>2</sub>RuO<sub>4</sub>,<sup>553</sup> CeIrIn<sub>5</sub>(Refs. 554 and 555)</td></tr><tr><td rowspan="10">Optics</td><td rowspan="2">Photonic components</td><td>O</td><td>Optical bridge in diamond<sup>556</sup></td></tr><tr><td>Ga</td><td>Aspherical microlens in Si,<sup>557</sup> solid immersion lenses in Si<sup>558</sup> and around pre-localized quantum emitters in diamond,<sup>224,559,560</sup> photonic crystal cavity around quantum emitters in diamond,<sup>561</sup> triangular nanobeam cavities in diamond<sup>562</sup> and in YVO<sub>4</sub>,<sup>563-565</sup> Fresnel zone plates for X-ray microscopy,<sup>566</sup> Fresnel lenses milled through hard mask,<sup>567</sup> metasurfaces for polarization and phase engineering,<sup>568</sup> tapered nanoantenna for single photon emission of CdSe quantum dots<sup>569</sup></td></tr><tr><td>Fiber-based optical components</td><td>Ga</td><td>Lab-on-a-fiber,<sup>570</sup> Bragg gratings and microlenses in silica nanofibers,<sup>571</sup> superconducting single-photon detector (SSPD) on optical fiber<sup>572,573</sup></td></tr><tr><td rowspan="2">Plasmonic components</td><td>He</td><td>Al bowtie antennae,<sup>574</sup> Au dimer antennae of different shapes,<sup>575-581</sup> Au coaxial<sup>582</sup> and split-ball<sup>583</sup> and nanoslit<sup>584</sup> resonators, pores in Au pyramidal<sup>585</sup> and microsphere<sup>586</sup> cavities, Au oligomers<sup>587</sup>, inverse Au trimers<sup>587</sup> and oligomers<sup>588,589</sup></td></tr><tr><td>Ga</td><td>Au groove waveguides<sup>590</sup> forming logic gates,<sup>591</sup> Au bowtie antennae for EUV light generation,<sup>592</sup> inverse Ag bowties,<sup>593</sup> ring-shaped beam patterning of Au antenna arrays,<sup>594</sup> Yagi-Uda-type antennae,<sup>590,595</sup> λ/2 antennae,<sup>596</sup> asymmetric Ag oligomers,<sup>597</sup> two-wire waveguides in Au<sup>598,599</sup> forming spin-optical nanodevice<sup>600</sup></td></tr><tr><td rowspan="3">Custom probes and sensors</td><td rowspan="3">Near-field microscopy</td><td>He</td><td>Square nanopores in pyramidal Au nanocavities,<sup>585</sup> Au nanopyramid antenna<sup>601</sup></td></tr><tr><td>Ga</td><td>Circular<sup>602</sup> and bowtie<sup>603</sup> nanoaperture, tip-on-aperture geometry,<sup>604,605</sup> Au bowtie<sup>606</sup> and nanocone antenna,<sup>607</sup> nanoslit grating in Au conical taper<sup>608</sup></td></tr><tr><td>Xe</td><td>Probe shaping for near-field scanning microwave microscope<sup>609</sup></td></tr></tbody></table>
<table><caption>TABLE V. (Continued.)</caption><thead><tr><th>Research area</th><th>Application</th><th>Ion</th><th>Material/geometry/device</th></tr></thead><tbody><tr><td></td><td>Atomic force microscopy</td><td>Ga</td><td>Nanoscale apertures for liquid and ion transport,<sup>610-612</sup> tip sharpening,<sup>613</sup> modified mechanical response<sup>614</sup></td></tr><tr><td></td><td>Magnetic force microscopy</td><td>Ga</td><td>V-shaped magnetic nanostructure at probe tip<sup>615</sup></td></tr><tr><td></td><td>SQUID microscopy</td><td>Ga</td><td>SQUIDs on AFM cantilever<sup>532</sup></td></tr><tr><td></td><td>Mechanical high-Q resonators</td><td>He</td><td>Phononic crystal<sup>616</sup></td></tr><tr><td></td><td></td><td>Ga</td><td>Graphene trampoline<sup>617</sup></td></tr></tbody></table>

conventional cleanroom-based lithography and etching, FIB machining allows for virtually any material to be shaped into a micropillar at a specific target location. To achieve uniform pillar circumferences with minimal taper, lathe milling in combination with annular milling is often applied.⁴⁸¹ Here, lathe milling refers to a particular FIB approach in which the sample is rotated stepwise, and the ion beam performs a line scan along the rim of the pillar. While lathe milling can introduce severe levels of stress requiring careful interpretation of the micromechanical testing results,⁴⁸⁶ it is well suited for insulating or very inhomogeneous samples comprising layers with very different sputter yields.

Today, most small-scale mechanical testing experiments are performed by SEM or TEM to capture changes from the atomic to micrometer scale (e.g., formation of dislocations, stacking faults, twins, grain orientations, contraction and expansion of volume). Complex workflows include some or all of the following steps: (a) machining of micro-/nanopillars and other geometries, (b) *in situ* mechanical testing under SEM observation, (c) deposition of a regular pattern of points by FIBID (or FEBID) to follow deformations via digital image correlation algorithms, and (d) postmortem FIB slicing for 3D tomographic or 3D EBSD analysis of the deformed microstructure or the fracture pattern inside the sample.⁴⁹⁷ Popular types of geometry used for mechanical testing are shown in Fig. 17. For example, FIB machining of sharp notches with a specific orientation to the loading axis has enabled a number of fracture mechanics studies,⁶²⁹ and for *in situ* TEM tensile testing, various milling protocols have been developed to produce electron transparent specimens.⁴⁹³

To reduce ion beam induced surface damage defects, a multistep milling strategy is typically employed. In this approach, the beam voltage and current are sequentially stepped down to the last polishing step.⁴ Among the still open questions are how much damage (amorphization, implantation) is induced by FIB milling into the structures and how the damaged zones affect the mechanical behavior of the milled structure.⁴⁸⁴ Key factors are the penetration (implantation) depth of ions and the collision cascade (amorphization) they trigger (see Secs. III A 3, III B 3, and III D 1).

Once other ion sources, in particular, He, Ne, and Xe ion sources, became available, the hope was to be able to circumvent some of the Ga damage issues. Best *at al.*⁴⁹⁶ found, however, that using either He, Xe or Ga for the machining of notches affected the measured fracture pattern.⁴⁹⁷ In all cases, while He ions were shown to yield suitable sharp notches with radii below 10 nm, Xe ion beams were

resolution limited. It was unclear how the penetration depth of the different ions affects the fracture toughness. Currently, combinations of FIB milling with other technologies are becoming more and more popular. For example, the option of laser machining of large volumes followed by FIB fine sculpting has recently become available from several manufacturers in a single setup.

### 3. FIB in the semiconductor industry

In the field of semiconductor processing, FIBs are most relevant during the debugging of new products and for identifying production errors in the context of circuit edit and fault isolation, as well as for the repair of photomasks. Among other applications, FIBs have been used for failure analysis, fault isolation, TEM sample preparation, mask repair, and backside circuit edit.⁶²⁸,⁶³⁰,⁶³¹ The ongoing scaling of the transistor fin, gate, and interconnect via linear and volumetric shrinking, as well as the introduction of new transistor technologies, has led to a reduction of the critical length scale from 22 nm in 2012 to the current 3 nm technology node to be introduced by all major manufacturers between 2022 and 2024.⁶³²⁻⁶³⁴

FIBs have been used since the 1980s for mask repair, initially using Ga and Au ions from LMIS and LMAIS.⁵⁰⁸ However, staining from implanted ions was quickly identified as a problem limiting the application.⁵⁰⁹ Later, the application of GFIS based $H^+$, $H_2^+$, $N_2^+$, and $He^+$ for phase-shift mask and extreme ultraviolet (EUV) mask repair was investigated.⁵⁷,⁵⁰⁵,⁵⁰⁶ For $H_2^+$, the minimal repairable dimension is reported to be 11 nm, which is half of what could be achieved using electron beams.⁵⁰⁴ The application of FIBID was investigated early on for adding missing material to masks and for repairing pin holes using Ga-FIB induced carbon deposition.⁵¹⁰ This has been extended using other deposition precursors. The addition of reactive gases such as $Cl_2$,⁵¹¹,⁶³⁵ $Br_2$,⁵¹¹ $XeF_2$,⁶³⁶,⁶³⁷ and $O_2$,⁶³⁷ has also been investigated for mask repair. These gases can significantly increase etch rates, remove carbon contamination, and trigger resist development. In particular, $XeF_2$ is now readily available in commercial FIB systems.

For circuit edit and fault isolation applications, Ga-FIB was used initially,⁵¹⁴ but later Ne ions from GFIS instruments were employed. The latter yielded minimal trench widths of 14 nm for high aspect ratio vias,⁵⁰⁷ and comparable/less collateral damage compared to Ga-FIB as measured from changes to ring oscillator timing.⁵¹³ Recently, GFIS-based H ions have been demonstrated for successful delayering.⁶³⁸ Other source technologies, e.g., Cr ions from MOTIS,⁶³⁹ also show potential for circuit edit applications.⁶⁴⁰ In general, it is found that
lower beam energies are be required while still maintaining a suitably high spatial resolution.

To better understand the effects of the beam profile on the achievable mill resolution, approaches have been developed to elucidate the probe current distribution.⁶⁴¹,⁶⁴² This is of particular importance for via fabrication and also for the fabrication of high aspect ratio holes/pores created by milling with a stationary beam. For these applications, a good signal to noise ratio is needed for reliable end point detection, and a new figure of merit—SE yield per sputtered atom—can be defined. GFIS-based He and Ne milling of these structures promises superior spatial and temporal precision compared to Ga-based FIB processing.⁶⁴³ However, GFIS-based milling suffers from the formation of gas bubbles and the creation of defects far below the milled surface of bulk samples.⁶⁴⁴

### 4. FIB for quantum materials

“Quantum materials” are materials in which quantum phenomena manifest in non-trivial ways, leading to response functions that are qualitatively distinct from those of standard electronic materials such as Si or Cu. These functions generally arise from the non-locality of quantum systems, with topology, frustration, and correlation all playing a central role.⁶⁴⁵,⁶⁴⁶ The key goal is to refine our microscopic or phenomenological understanding of these exotic quantum states and develop predictors to find promising materials candidates within the vast space of possible compounds. A second main driver of quantum materials research is novel electronic applications that harness this exotic behavior for solving technological challenges. Most famous is quantum information technology, including quantum computation, which directly utilizes the entanglement and vast configurational space of quantum coherent systems. The search for the most effective materials platform to realize systems like qubits remains an open and very active field, i.e., the search for the “silicon” of quantum technology. Beyond coherent information processing, a large materials space has developed in sensing and data communication that utilizes quantum coherence indirectly, such as in strongly correlated oxides. The ubiquity of quantum mechanics is the greatest challenge, in that interdisciplinary efforts in materials science, chemistry, physics, engineering, and informatics are required to realize these concepts in a useful way. In this search for new physics and new quantum platforms, the FIB excels as a versatile patterning tool that is ideal for rapid processing of nonstandard materials,⁶⁴⁷ as it (a) avoids exposure to wet chemistry as compared to resist-based lithography, (b) can operate with crystallites and microparticles, i.e., nonstandard samples that do not resemble polished wafers, and (c) enables 3D structure control that is critical to many electronic 3D quantum materials. The operational goal of this research is to fabricate hybrid structures that join micro-/nanostructures of a quantum material to a Si chip of conventional architecture, both to demonstrate advanced functionalities and to probe the underlying novel physics.

Quantum systems generically respond strongly to changes in their boundary conditions, in this case, their physical shape. FIBs enable the sculpting of non-trivial boundary conditions in crystals, which has been used to study and functionalize superconductivity, e.g., investigating the unconventional superconductivity of $Sr_2RuO_4$,⁵¹⁵,⁵¹⁶ and studying Josephson vortices in strongly layered high-$T_c$ superconductors and their excitations.⁵¹⁷,⁵¹⁸ Controlled patterns guide the motion of Abrikosov lattices by surface structuring⁵²⁰ toward non-

trivial electronic responses such as vortex diodes.⁵²¹,⁵²² Further toward superconducting applications on small dimensions, FIB milling also enables direct nanopatterning of Josephson junctions, nanowires, and nanoSQUIDs.⁶⁴⁸,⁶⁴⁹ The nanoSQUIDs are used for magnetization reversal detection of individual magnetic nanoparticles⁵²⁹,⁵⁴⁰ and for magnetic and thermal sensing in scanning SQUID microscopy.⁵³² In microwave circuits, nanoSQUIDS can be used as tunable inductors, e.g., to enable tuning of the resonance frequency of microwave resonators.⁵²⁶

Beyond superconductors, other exotic materials and properties can be probed, such as quasiparticle transport in ultra-clean metals,⁵⁴⁷ and the magnetic exchange bias in time-reversal symmetry breaking topological semi-metals.⁶⁵⁰ Reducing the sample size to the micrometer scale further enhances the contribution of surface properties to the overall physics. This is particularly important in the quest to probe the contribution of topologically protected surface states, which have been proposed to enable novel electronic and spintronic applications in topological semi-metals.⁵⁴⁸⁻⁵⁵¹ Precise FIB machining also enables optimization of the edge quality of structures, which is a prerequisite for the fabrication of efficient superconducting single-photon detectors (SSPDs).⁵⁷² In addition, the flexibility of FIB processing on highly 3D substrates has enabled FIB milling on top of an optical fiber.⁵⁷³

Subtractive FIB processing has also been applied in the fields of spintronics and magnonics. Examples include guiding and control of propagating spin waves, which has been enabled using the Ga-FIB.⁵⁴⁶ High resolution metal free FIB processing using GFIS ion species has also enabled fine tuning of the interaction of spin waves across gaps.⁵⁴³

Not all applications of FIB aim to alter the material. In addition, there is a wide class of FIB milling experiments aimed at probing the bulk properties of novel materials that can be difficult to access when the material is in its native form, e.g., microcrystals that are too small for conventional measurements. This has allowed insights into microscopic effects on critical charge transport in Fe-based superconductors,⁵²³,⁵²⁴ the determination of topological bandstructures in microcrystals,⁵²⁵ and probing of the switchability of antiferromagnetic states under the high current densities achievable in FIB-machined crystals.⁶⁵¹,⁶⁵² The rich physical responses of quantum materials tend to be rooted in the competition between multiple electronic ground states, which leads to a strong (and potentially discontinuous) change in their properties under weak applied stimuli.⁶⁵³ One can hardly overstate the importance of residual stress in the samples, with a famous example being the enigma of the “3K phase” of superconductivity in $Sr_2RuO_4$, which originated from strain mismatch.⁵⁵³ Here, a crucial advantage of FIB milling over mechanical sample preparation techniques, such as polishing or wire sawing, is its kinetic nature, which results in samples of low residual stress. Precision control over the physical shape of a sample has also enabled microscopic control over desired strain fields and their gradients, which imprint correlation landscapes into quantum materials.⁵⁵⁴,⁵⁵⁵

### 5. FIB for photonics and plasmonics

Miniaturized on-chip photonic components are designed to guide or focus light while having a footprint as small as possible. The fabrication of these relies mostly on conventional large-scale lithographic techniques, but there are applications where a maskless direct-write strategy has significant advantages. Prime examples are localized light
sources, with the extreme case of single photon sources, where the optical component often has to be built around a pre-localized (quantum) emitter. Such quantum emitters may be defects in wide-bandgap materials (see Sec. IV B 4), where outcoupling of the generated quantum light is typically hindered by the large refractive index of the host material, e.g., diamond. Here, FIB milling either using Ga ions²²⁴,⁵⁵⁹,⁵⁶⁰ or, to reduce Ga-induced damage, O ions,⁵⁶² has been successfully used to engrave solid immersion lenses that enhance photon collection efficiencies. In the same manner, photonic crystal cavities with small mode volumes have been milled into a suspended diamond layer around pre-localized quantum emitters and proven to enhance spontaneous emission.⁵⁶¹ An even further reduction of optical mode volume can be achieved using metallic nanostructures, since these have the ability to concentrate light below the diffraction limit by collective excitations of the free electron gas.⁶⁵⁴ Since such plasmon-polariton modes are strongly dependent on geometry, FIB processing is a powerful tool for rapid prototyping of nanoscale resonators, sub-wavelength apertures,⁶⁵⁵ and optical antennae.⁶⁵⁶

Furthermore, extreme plasmonic field confinement allows the detection of molecular species down to the single molecule level by surface enhanced Raman scattering⁶⁵⁷ (the prime example), enhanced fluorescence,⁶⁵⁸ or enhanced Förster resonant energy transfer.⁶⁵⁹ The latter two examples employ Ga-FIB milling to fabricate an antenna-in-a-box geometry, where the gap region of a dimer antenna provides the local electric field enhancement and correspondingly an enhanced local density of optical states. The remaining metallic film around the antenna blocks fluorescence from contributing to the background. In general, Ga-FIB top down patterning, especially of single-crystalline Au or Ag nanoflakes, is often employed for high-fidelity rapid prototyping of plasmonic components.⁵⁹⁹,⁶⁶⁰⁻⁶⁶³ When comparing the performance and material properties of plasmonic antennae, electron beam lithography (EBL) may lead to better results than FIB milling, depending on the actual geometry and processing conditions, especially in the case of Ga-FIB.⁶⁶⁴ However, electron beam lithography (EBL) fails in fabricating truly 3D profiles. In contrast, FIB milling has been used to, e.g., mill out 3D Janus plasmonic helical nanoapertures for polarization-encrypted data storage.⁶⁶⁵

A particularly beautiful example of 3D FIB-milling capabilities combines local material removal by Ga-FIB milling of a suspended gold film with low dose Ga ion irradiation at selected edges. The latter induces a stress distribution that leads to up- or downward bending of the predefined structures.⁶⁶⁶ This nano-kirigami approach has been demonstrated for various designs realizing optical chirality, polarization and phase engineering, and showing potential for optomechanical applications.⁶⁶⁸

The resolution and shape fidelity of FIB milling especially with light ions stands out compared to any other lithographic techniques²²⁶,⁴⁷¹ but comes at the cost of the slow speed of the inherently serial process. To resolve this issue, lithographic large area processing by EBL can be combined with, e.g., He-FIB for the ultimate in resolution. Extremely narrow gaps between large areas of lithographically defined plasmonic Au⁵⁷⁷ and Al⁵⁷⁴ antennae have been realized using this approach. By combining Ga-FIB patterning with He-FIB patterning, the achievable spatial resolution can be significantly improved while keeping a reasonable processing speed.⁵⁷⁵ Another approach to increase the speed of top-down FIB processing relies on milling only the outlines of desired plasmonic features, which are then subsequently

obtained by peeling off the surrounding material.⁵⁷⁹,⁶⁶⁷,⁶⁶⁸ This “sketch and peel technique,” combining Ga-FIB patterning for the outlines with He-FIB for the definition of ultra-narrow gaps, was used to reproducibly demonstrate strong coupling in plasmonic dimer antennae.⁵⁸⁰

## 6. FIB fabrication of custom probes

Since FIB milling is not restricted to planar sample geometries, a vast body of research exists on the modification of optical fibers,⁵⁷⁰ nanofibers,⁵⁷¹ and nano-probes. The comprehensive review by Sloyan et al.⁵⁷⁰ presents examples for optical near-field imaging, plasmonics, beam shaping, fiber-based photonic cavities, fiber-chip coupling, and many more. He-FIB manufacturing was reviewed in detail by Allen.⁴⁷¹ Direct control over precise nanostructure geometries by FIB milling is especially interesting for near-field optical microscopy (NSOM), where a metal coated glass fiber tip localizes the excitation and/or collection of light by making use of a nanoaperture or antenna for plasmonic field concentration. In applications concerned with NSOM, FIB milling has been employed to fabricate high-definition plasmonic circular nanoapertures at the apex of a metal coated glass fiber tip.⁶⁰² Further signal enhancement and fluorescent background reduction can be achieved by adding a tip at the aperture rim, combining the concepts of scattering and aperture NSOM.⁶⁶⁹,⁶⁷⁰ While the tip was grown by FEBID in these works and metalized afterward, later work engraved the tip-on-aperture geometry into the metallic (Al) fiber coating by Ga-FIB milling and tuned the tip resonance to behave as a monopole antenna, thus achieving single molecule imaging⁶⁰⁴ and imaging of proteins on cell membranes.⁶⁰⁵ Additional geometries realized in this

<figure><img src="image_28.png" /><figcaption>**FIG. 17.** Popular FIB-machined sample geometries for micromechanical testing: (a) micropillar⁴⁶⁰ reproduced with permission from Uchic et al., Science 305, 986-989 (2004). Copyright 2004 The American Association for the Advancement of Science. (b) Notched micro cantilever.⁶²⁹ Reproduced with permission from Ast et al., Mater. Des. 173, 107762 (2019). Copyright 2019 Authors, licensed under a Creative Commons Attribution (CC BY) license. (c) Micro-tensile bar⁴⁹⁹ Reproduced with permission from Casari et al., J. Mater. Res. 34, 2517-2534 (2019). Copyright 2021 Authors, licensed under a Creative Commons Attribution (CC BY) license and (d) micro-shear test structure⁵⁰² reproduced with permission from Heyer et al., Acta Mater. 62, 225-238 (2014). Copyright 2014 Elsevier.</figcaption></figure>
way are bowtie nanoapertures on the end of metal-coated fiber tips<sup>603</sup>
and square plasmonic nanoapertures in pyramidal cavity structures,<sup>585</sup>
with the latter example employing He-FIB milling.

Further specific geometries of metallic tips and metal-coated fiber
tips have been fabricated to control the plasmonic response for other
purpose. These include nanocones for resonance and radiation pattern
tuning by Ga-FIB milling,<sup>607</sup> nanopyramids for optimizing local electric
near-fields by He-FIB milling,<sup>601</sup> and nanoslit gratings into the conical
taper of metallic tips for nanofocusing upon far-field illumination,
again by Ga-FIB milling.<sup>608</sup> FIB milling has also been employed to
modify AFM probes for specialized applications. In one example, FIB-
milling was used to partially remove the magnetic layer from a com-
mercial magnetic force microscopy (MFM)-probe. The V-shaped
nanostructure remaining on one side of the triangular pyramid results
in enhanced magnetic phase contrast without compromising spatial
resolution.<sup>615</sup> Another example employs nanoscale apertures milled
into hollow pyramidal AFM tips that can be loaded with liquid to dis-
pense attoliter volumes and create droplet arrays.<sup>610</sup> Such tips can also
be used for the manipulation and analysis of single cells via so-called
fluidic AFM.<sup>611</sup> Tips can be sharpened using FIB milling and can also
be detached from their initial substrate and mounted onto a cantilever
of choice with the help of a micro-manipulator. This technique has, for
example, been used to produce customized tips with high aspect
ratios.<sup>613</sup> In other works, the AFM cantilevers themselves have been
fashioned with FIB-milled apertures to enable ion implantation
through those apertures aided by scanning probe alignment.<sup>612</sup> FIB
milling of larger patterns into piezoresitive cantilevers has been used to
increase deflection sensitivity to optimize cantilever performance.<sup>614</sup>
Recently, Ga-FIB milling has also been used for shaping AFM tips to
produce mesa structures on the cantilever onto which Nb
nanoSQUIDs have been fabricated. Such structures simultaneously
enable topographic, magnetic, and thermal imaging.<sup>532</sup>

7. Outlook

As an all-in-one processing tool, the FIB provides a versatile plat-
form for flexible and fast top-down fabrication and prototyping of
nanostructures and devices.

To further advance these developments, FIB technology needs
improvement not only in spatial resolution but also in the *in situ* con-
trol of the material removal process. Critical issues include material
sputtering selectivity and increasing the signal to noise ratio of SE
monitoring during the milling of high aspect ratio structures.
However, FIB top-down nanofabrication is intrinsically limited by the
fact that the energetic particles and the chemical species involved cause
structural and chemical damage or changes, such as amorphization or
poisoning. While traditional Ga-FIB still represents the FIB standard,
some of the aforementioned fundamental limitations may be resolved
by using other ion species, such as those offered by GFIS, MOTIS,
LoTIS, PFIB, or LMAIS (see, e.g., Sec. II A).

Additionally, scale-up of FIB based top-down nanofabrication
will only be achieved when increased throughput and reproducibility
are realized. Here, advances in software and hardware tools for, e.g.,
modeling-informed automated operation will be beneficial, also allow-
ing in-line integration of FIB processing into larger (nano)-fabrication
pipelines. Theoretical knowledge, modeling, and simulation tools that
provide precise descriptions of FIB modifications to materials, from
the atomic to the microscopic scale, are a prerequisite for predictive

design and for the realization of tailored properties and functionalities
of nanostructured surfaces and operating devices.

There are also opportunities for coordinated FIB system develop-
ment based on specific experimental needs. For example, strong inter-
est in emerging fields such as quantum technology, as well as novel
miniaturized platforms in the fields of microfluidics for lab-on-a-chip
or organ-on-a-chip developments, would benefit from synergies with
theory groups and tool makers in the FIB application community.

B. Engineering materials properties through defects

In addition to the subtractive nanofabrication applications
described above, site-specific and dose-controlled irradiation of sam-
ples with the FIB is used to tune material properties in spatially defined
regions down to the nanoscale and even down to the single-atom level,
without surface erosion or deposition. These applications are based on
the local introduction of varying concentrations of defects (vacancies,
dopants, and dopant-vacancy complexes), controlled by the dose.

1. Basics of irradiation induced defect creation

A common technique used to create defects in crystals relies on bombardment with high energy ions or electrons,<sup>246,671,672</sup> and in some cases photons, protons, or neutrons.<sup>673</sup> For example, tuning the fluorescence properties or the refractive index of a material for optical applications by bombardment with ions is a well-established technique.<sup>674,675</sup> Ion implanters are often employed for such applications. Since these deliver broad beams with spot sizes in the millimeter regime, a lithographically defined mask is needed when higher spatial resolution is required. However, the large collision cascades that are inherent to both high energy ion beams and light ion bombardment make mask design rather challenging. This is where FIB processing comes into play.

As described in Sec. III, the incident ion induces a collision cascade in the solid with a size that is determined by the target material and the ion's kinetic energy, as defined by the primary beam voltage. In a simplified picture, when a recoil is generated, it leaves behind a vacancy and forms an interstitial when it comes to rest.<sup>676</sup> In reality, defect clusters and amorphous pockets may form depending on the target material<sup>677</sup> and on the ion mass and energy.<sup>678</sup> Larger defect structures such as these are usually undesirable for defect engineering, as their properties are less well defined than those of simple defects. They are best avoided by using light ions, which cause more dilute collision cascades than heavier ions due to the lower nuclear stopping power. The recoils in these cases are also less energetic because of the unequal masses of the ion and target atoms. In addition, light ions cause less sputtering, which is generally an unwanted effect in defect engineering. Regardless, the applied ion doses and beam parameters still have to be carefully adjusted. Considering the example of He ion irradiation of Si and Cu substrates, Livengood et al.<sup>644</sup> differentiated the various defect regimes according to dose, ranging from individual point defects at low fluence, to extended subsurface microbubbles at very high fluence. While the picture will vary somewhat for other ion-substrate combinations, the same overall trends apply.

Table VI gives the reader a flavor of the breadth of FIB based
defect engineering applications, categorized according to the specific
materials property engineered (electrical/electronic, magnetic, optical,
quantum, chemical, thermal, and mechanical). Further examples can be
found in the review articles by Gierak,<sup>679</sup> Orús et al.,<sup>680</sup> and Allen.<sup>471</sup>
In the remainder of this section, we focus on those applications in Table VI that are concerned with engineering the electronic, magnetic, and optical/quantum properties of materials, with additional detail on property engineering of low-dimensional materials (in particular, thin films and 2D materials). The study of irradiation damage mechanisms (e.g., the formation of gas nanobubbles) is also discussed.

## 2. Engineering electronic properties

From the outset, FIBs have been used to fabricate electronic devices at the nanoscale. Early examples, using Ga-FIB milling, are the fabrication of GaAs quantum wires⁶⁹³ and a quantum wire transistor.⁶⁹⁵ More recently, however, Ga-FIB irradiation at lower dose was employed for the fabrication of a lateral diode based on a 2D heterostructure of MoSe₂ and graphene.⁶⁹⁹ Here, the preferential sputtering of Se locally transformed the top MoSe₂ layer into a quasimetallic state, generating a pn junction with rectification performance comparable to that of a vertical diode. These examples illustrate a development from the prevalence of subtractive materials modification by FIB milling to increased interest in engineering the electrical and electronic properties of materials at lower dose through defects.

Here, light (and often preferably inert) ion beams are of relevance due to their high resolution defect engineering capabilities. Ion beams of electronically active elements (e.g., P, Sb, As) also have the potential for interesting applications such as local doping with high spatial resolution or the generation of qubits by SII. For applications in superconductivity, Josephson junctions, i.e., weak links between two superconducting electrodes, are key elements for superconducting electronic devices. For Josephson junctions based on conventional metallic superconductors, such as Nb or Al, thin-film devices with grown insulating (I) or normal conducting (N) barriers, sandwiched between superconducting (S) electrodes, are well established. However, in the case of the high-$T_C$ cuprate superconductors this as-grown approach does not produce well-defined SIS or SNS junctions, due to the complex nature of these materials and their strong sensitivity to defects on the atomic scale. As an alternative approach, the local FIB-enabled modification of superconducting thin films in order to “write” thin N or I layers as Josephson barriers in prepatterned thin film structures has been successfully demonstrated. Here, the high spatial resolution offered by He-FIB has been shown to be of great importance. Prime examples are the fabrication of insulating or normal-conducting barriers in yttrium barium copper oxide (YBCO) or MgB₂ thin films by He-FIB irradiation that locally suppress superconductivity on the nanometer scale,⁷⁰⁵,⁷⁰⁷,⁷¹² and the creation of He-FIB-induced nanoconstrictions in $Bi_2Sr_2CaCu_2O_8$ (BSCCO) single crystal flakes. The latter form the basis of two-dimensional cuprate nanodetectors with single telecom photon sensitivity.⁷¹³,⁷¹⁴ Moreover, He-FIB irradiation of YBCO films has produced artificial pinning arrays with unprecedented lattice constants down to 30 nm,⁷¹⁷,⁷¹⁸ which opens a new regime for motion control of Abrikosov vortices in superconducting fluxonic devices.

Due to the nanoscale beam size that is achievable with FIBs, in particular with GFIS-based FIBs, these are ideal tools for the fabrication of single quantum dots, tunneling devices and single electron transistors. Examples include the fabrication of single electron transistors in $Si/SiO_2$ stacks⁴¹⁰ and the fabrication of single quantum dots in carbon nanotubes (CNTs).⁷¹⁵

## 3. Engineering magnetic properties

Ion irradiation, in general, has been used for many decades for the modification of magnetic materials.⁸⁰¹ To achieve this sort of modification, complex and expensive masking processes have to be used unless one employs FIBs, which can modify the magnetic properties locally with nanometer precision. In 1989, Ishii et al.⁷³³ used Si and Ge ions from a LMAIS-FIB to create nucleation sites for controlled switching of the magnetization in Bi- and Ga-substituted yttrium iron garnet (YIG) films. Ga-FIB processing has also been used for creating read/write heads⁸⁰² for magnetic hard disks, and for modern approaches such as magnetic random access memories (MRAMs) composed of magnetic multilayer structures.⁸⁰³ FIB-induced local changes in magnetic anisotropy have been used to create isolated tracks of single domain islands in recording media⁸⁰⁴ and to control the injection location and field dependency of magnetic domain walls in multilayers with perpendicular magnetic anisotropy (using Ga- and He-FIB).⁷²⁶ In the case of Co nanowires fabricated by FEBID, irradiation with Ga-FIB has allowed modification of the propagation speed of the magnetic domain wall.⁸⁰⁵ In some materials, FIBs can be used to generate ferromagnetism in selected regions such as in paramagnetic FeAl alloys. For example, the spatially resolved creation of disorder-induced ferromagnetism using Ga-FIB modification has been demonstrated by Menéndez et al.,⁷⁴³ achieving a spatial resolution of below 100 nm with the possibility of erasing the pattern by annealing. Later, $Fe_{60}Al_{40}$ was studied in depth for order-disorder phase transitions and ferromagnetic resonance (FMR) in magnetically written single structures induced by Ne-FIB irradiation.⁵⁴⁴,⁷⁴² Paramagnetic regions in non-magnetic materials can also be created by FIB irradiation, as has been done for InGaAs using Ga-FIB to create a spin filter device.⁸⁰⁶

The continued quest for an increase in storage density in combination with novel data processing approaches (i.e., neuromorphic computing) has triggered the development of advanced patterning of complex magnetic alloys and multilayer systems.⁸⁰⁷⁻⁸⁰⁹ In these systems, various interactions due to the intrinsic anisotropy, or lattice and system geometry, may lead to topologically protected spin configurations such as skyrmions or the controlled formation and transport of spin waves. Here, the FIB stands out, as it enables tuning of magnetic anisotropy landscapes without any topographical changes to the devices. This was demonstrated for the nucleation control of skyrmions in Co/Pt multilayers using Ga-FIB⁷³⁹ and He-FIB,⁷³⁸ and through the patterning of skyrmion racetracks in a Pt/Co/MgO thin film using the He-FIB.⁷³¹ The patterning of dots as nucleation sites within a low-dose racetrack using He-FIB realized both the deterministic generation and movement of skyrmions with nanometric precision.⁷³² Finally, spin-wave optical components such as graded-index lenses for applications in magnonics can be created by ion induced modification of the local magnetization in YIG, which corresponds to an effective refractive index for spin wave propagation. Here, 50 keV Ga-FIB was employed and the penetration depth of about 100 nm allowed for an effective refractive index of up to 1.8, comparable to light-based optics. Since this depth was only one third of the actual device thickness, the much lighter He ions are expected to significantly improve the optical device performance.⁷⁴⁵

## 4. Engineering optical/quantum properties

Typical applications of ion irradiation in optics include the local change of refractive index and the creation of fluorescence.⁸¹⁰ Since