Yao N. Focused Ion Beam Systems: Basics and Applications

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the interaction of ions with matter. On the basis of the binary-collision

approximation (BCA) Sigmund proposed a linear collision cascade model,

which has been successfully applied in a low-energy density collision [9].

Sigmund’s model is an analytical one. In order to include complex situations

depending on individual ion–solid combinations many researchers developed

simulation codes written by Monte Carlo method as listed in Table 2.1.

Those models were developed in the framework of BCA and resultantly it is

difﬁcult to reproduce experimental phenomena appeared in a high-energy

density collision. In this situation, various molecular dynamics simulation

codes using sophisticated potentials can work well and are listed, too, in

Table 2.1 Monte Carlo (MC) and molecular dynamics (MD) simulation codes discussed

in this chapter.

Section, subsection Name of code

2.2 Basic processes and outline of

theoretical models,

2.2.5 Energy loss SRIM

2.3 Ion implantation and

defect formation,

2.3.2 Ion range and defect distributions

2.3.3 Ion implantation

2.3.4 Defect formation

SRIM, MARLOWE

DYN-TRIM

MD, MARLOWE DADOS

2.4 Sputtering,

2.4.2 Sputtering yield

General scope

Dose dependence of yield and

preferential sputtering

OKSANA, MD, MD & MC

(1) ‘‘Static’’ Monte Carlo (MC)

(a) Crystalline targets

MARLOWE, crystal-TRIM,

COSIPO, ACOCT

(b) Amorphous targets TRIM,

ACAT, SASAMAL,

(2) ‘‘Dynamic’’ Monte Carlo (MC)

TRIDYN, dynamic-SASAMAL

ACAT-DIFFUSE,

(3) MD, thermal spike model,

ﬂuid dy namics

Mass distribution MD/MC-CEM

Incidental cluster-size dependence

of sputtering yield

Sputtering of nonmetals MD(AIREBO)

2.5 Surface morphology stochastic nonlinear continuum

equation based on Sigmund theory

Focused ion beam systems38

Table 2.1. Results predicted by these models and their comparisons with

experimental ﬁndings are presented in the respective related subsections.

2.3 Ion implantation and defect formation

2.3.1 General remarks

Ion implantation is a fundamental technique in the fabrication of semi-

conductive devices and has been used for materials modiﬁcation, too. Defect

formation following ion implantation plays, in general, unpleasant roles in

the above applications but sometimes can be used effectively. This section

presents recent experimental and theoretical ﬁndings on ion implantation and

defect formation.

For example, it was recently found that implanted atoms assemble by

themselves into nanoclusters and nanocrystals under thermal annealing and/

or radiation induced processes. The formation of these nanostructures is

closely related to the nanotechnology. In the high-density energy deposition

caused by very heavy ions and cluster ions, nonlinear effects on defect pro-

duction were found. To understand these experimental facts, a combined

code of Monte Carlo (MC), diffusion, and molecular dynamics (MD)

simulation codes were developed. In addition, it is necessary to localize

defects when one fabricates nanostructures with a focused ion beam. Diffu-

sion lengths were measured and an idea to localize the defects was presented.

This chapter includes the above experimental and theoretical results.

2.3.2 Ion range and defect distributions

An ion moving in matter loses its energy by the electronic and nuclear energy

losses and ﬁnally stops after the travel of a certain path. The total length of

the path is named as ‘‘range.’’ The atomic collision has a statistical nature

and, therefore, the range statistically distributes with a symmetric Gaussian

distribution around the mean value with a deviation called ‘‘range strag-

gling.’’ The range and the range straggling projected on the incident particle

direction are convenient for practical uses and the values are named ‘‘pro-

jected mean range’’ and ‘‘projected range straggling.’’ The moving ion recoils

one of the constituent atoms, which again strikes with and recoils another

constituent atom. Then, many atomic defects are generated along the passage

of the ion. This defect distribution is also important for the application of

energetic ions to material modiﬁcations.

For amorphous targets, the range and the range straggling can be calcu-

lated from the energy loss formulae given in Section 2.2.5. The more reliable

Interaction of ions with matter 39

values of the (projected) range, range and defect distributions can be

obtained by consulting the SRIM code developed by Ziegler et al.[5].

A Monte Carlo simulation code named MARLOWE, which was developed

by Robinson et al. on the basis of the binary collision approximation,

includes the time evolution of cascade collision and can treat the slowing

down both in crystalline and amorphous targets [10]. The code is opened for

researchers’ use and provides the calculation of sizes and shapes of dis-

placement cascades, sputtering, ion ranges, ion reﬂection, and so on.

In the case of crystalline targets, energy loss and range of an incoming ion

depend strongly on an incident angle against the crystal axis and plane. In a

channeling condition, that is, when the ion is incident along the crystal axis

or plane, the ion passes through the crystal with large impact parameters and

as a result the energy loss is very low compared with that for the amorphous

target of the same constituents. Then, the ion goes through deep inside the

crystal. Therefore, in order to avoid the trouble caused by the channeling

phenomena, ion implantation is usually carried out at an incident-angle

condition of off-axis or off-plane, or random incidence.

2.3.3 Ion implantation

The ion implantation technique has been a key element in the currently

established Si technologies and in the ﬁelds of materials modiﬁcation because

of its well-known advantages, such as low-temperature processing, control of

distribution and concentration of dopants, overcoming solubility limits

which cannot be realized via conventional techniques. Ion implantation

induces mixing of constituent elements, alloy formation, and clusterization

and crystallization in nanometer size in matrix. These processes are very

complex and depend not only on ion-related parameters of species, dose, and

energy but on a high-temperature chemical reactivity between the implanted

and matrix elements.

Related to the nanotechnology, formation processes of nanoclusters and

nanocrystals are one of the most exciting and promising topics. These

nanostructures are evidently produced by thermal annealing and/or radiation

irradiation after ion implantation as schematically shown in Figure 2.1.In

special conditions implanted atoms assemble at interfaces of different

materials and form nanostructures by themselves. A comprehensive review

was made by F. Gonella et al. on several evidences of clusterization of metal

atoms implanted in glass matrices [11,12]. Figure 2.2 shows that the chemical

bond of element implanted into silica glass changes depending on its con-

centration. The introducing criterion of cluster formation of implants in SiO

Focused ion beam systems40

Self-assembling and

nanocluster formation

induced by thermal- and

radiation-induced diffusion

Ion implantation

Figure 2.1 Schematic view graphs of nanocluster/nanocrystal formation.

5 10152025

Atomic fraction (%)

silicide

oxide

metal

Figure 2.2 Chemical bonds of the element implanted in silica glass as a

function of its concentration. (Reprinted with permi ssion from Nucl. Instr.

Interaction of ions with matter 41

glasses, presented by Hosono, is that the elements which do not react with the

matrix (for example, Ag, Cu, Au, ...) are considered to directly form metallic

precipitates and those which tend to form bonds with O from the silica

network are expected to form clusters when the Gibbs energy for metal oxide

formation is greater than that of SiO

at an extrapolated effective tempera-

ture of 3000 K [13]. A more general approach is due to Hosono et al., who

pointed out the importance of the chemical interaction strength among atoms

coming into play in the creation of defects [14].

The preparation of ‘‘mixed’’ nanostructures of different metals, or nan-

ometer-scale core-shell structures, has also generated a worldwide concern

for the possibility of further fabrication of functional nanostructures. Strobel

et al. developed a kinetic 3D lattice Monte Carlo model applicable for

simulating the diffusion, precipitation, and interaction kinetics of sequen-

tially implanted elements X and Y in a chemically inactive matrix [15]. By

applying annealing procedure pre-implanted atoms X form nanocrystals.

Then, implantation of a different type of element Y induces collisional

mixing of atoms. The model predicts that in the case of the following con-

ditions, the elements X and Y form a core/shell structure, shown in Figure 2.3

without making a random distribution of X and Y: if (i) the solubility of Y

exceeds the solubility of X in the matrix, if (ii) the atomic mass of Y is small,

i.e. low collisional mixing, and (iii) for a rather low ion dose rate of Y and/or

(a)

(b)

(b')

(c')

(d')

(c)

(d)

Figure 2.3 Sequence of snapshots from KLMC simulations. (a) The X-type

‘‘core’’ NC. The microstructure of the compound NC after the deposition

of N

¼2N

impurities is shown for (b) no mixing, (c) low intensity mixing,

and (d) high intensity mixing. The corresponding cuts through the NCs

(perpendicular to the plane of view) are shown in (b

), (c

), and (d

(Reprinted with permission from Nucl. Instr. Meth. B, 148 (1999), 104–9.

Focused ion beam systems42

a high second implantation temperature, which favors a compensation of

displacements by thermodynamically driven atomic movements.

Mattei et al. sequentially implanted Au and Cu ions into silica glass and

annealed the sample in either oxygen or hydrogen atmosphere [16]. They

found that the sequential alloying directly forms alloyed Au-Cu colloids

caused by an enhanced diffusion of copper in small gold clusters during

implantation. Subsequent annealing in hydrogen drives copper atoms dis-

persed in the matrix toward the clusters, increases the Au/Cu concentration

toward the normal 1:1 ratio, and consequently induces the structural

ordering of the alloy. Annealing of the formed Au-Cu alloy nanoclusters in

oxygen atmosphere leads to separation of gold and copper by the possible

reason that Cu is extracted from the nanoclusters by chemical interaction

with the incoming oxygen (Figure 2.4). Another dealloying is caused by

irradiation with light ions, which forms vacancies in the nanocrystal and

(a)

(b)

(c)

Figure 2.4 Bright-ﬁeld TEM cross-sectional micrograph of the sample

H (annealed in H

(4%)-N

atmosphere at 1173 K for 1 h) (a) before

and (b) after a thermal annealing in air at 1173 K for 15 min. The arrows

indicate some of the two-fold clusters made of a Au-enriched alloy and

O: (c) SAED (selected area electron diffraction) diffraction pattern from

the circular region of part (b). (Reprinted with permission from Phys. Rev.

Interaction of ions with matter 43

resultantly Au diffuses preferentially. A similar procedure of subsequent

implantation of two elements and post annealing was successfully applied by

White et al. for the formation of CdS and CdSe nanocrystals in SiO

and

[17].

Klimenkov et al. reported that Ge nanoparticles fabricated by the ion

implantation technique in a SiO

thin ﬁlm crystallize after irradiation with a

high-energy electron beam [18]. The crystallization process depends on

irradiation dose and dose rate. Irradiation with a dose above 3.7 · 10

/cm

results in cluster growth and above 2.5 · 10

/cm

in crystallization. An

irradiation with a dose rate below 150 A/cm

leads to the crystallization of

Ge nanoparticles in the form of single crystals. For an irradiation dose rate

above this value, the nanocrystals are fragmented into twinned and multiple

particles. Takeguchi et al. proposed a novel method of fabricating size-

and position-controlled Si nanocrystals by scanning an electron beam

intermittently, because the size of the Si nanocrystals depends on the beam

diameter [19].

Similar irradiation effects were found with ions and neutrons. Wang et al.

irradiated intermetallic and ceramic materials with 0.5 to 1.5 MeV Kr

ions [20]. As an example, when a U

Si target composed of large grains

tens of micrometers in size and large martensite plates is irradiated above a

critical temperature of 570 K for amorphization, martensite plates disappear

and small grains of < 20 nm in size appear below a dose of 2.7 · 10

/cm

and increase in number with increasing dose keeping their sizes. At a dose of

1 · 10

/cm

, the sample completely changes to polycrystalline materials

with grains of 20 nm in size. The mechanism of the radiation-induced

nanocrystallization is very complicated and needs a farseeing theoretical

understanding for its versatile application.

Formation of shallow bands of nanoclusters was observed for various

implanted species [e.g., Ge [21], Sn [22], Sb [23]] in the vicinity of a Si/SiO

interface. Heinig et al. explained the evolution of the near-interface

nanocluster band by a model taking into account collisional ion-beam mixing

and chemical reactions near the Si/SiO

interface [24]. That is, atomic dis-

placements during ion implantation and the action of the Si interface as a

sink for free oxygen result in a Si excess in the ﬁrst few nanometers of SiO

parallel to the interface. Then the excess Si acts as nucleation centers for

diffusing metal, which results in the formation of the near-interface

nanocluster band. The model predicts two prerequisites of a damage rate of

about one displacement per atom at the Si/SiO

interface and the diffusion

capability of the implanted impurities for the near-interface nanocluster band

formation. On the other hand, a study of Ge implanted into a SiO

ﬁlm

Focused ion beam systems44

revealed that annealing in hydrogen-containing atmosphere (7% H

þ93%

Ar) signiﬁcantly accelerates the Ge mobility at elevated annealing tempera-

tures (T > 1173 K, t ¼60 min). This results in the formation of very large Ge

clusters (typical size of 30–40 nm) together with a remarkable Ge loss in the

oxide. Klimenkov et al. concluded that by appropriate choice of the post-

implantation treatment conditions, especially the application of two-step

annealing procedure involving low-temperature hydrogen preannealing, the

nanoclusters in the bulk SiO

layer can be suppressed (Figure 2.5)[21].

Ignatova et al. studied the sputtering of SiO

/Si interfaces with Ga ions by

using secondary neutral spectrometry and found an oscillation of ion-

implanted Ga concentration at SiO

/Si interface, that is, the Ga concentration

1200

1300

1400

600

500

400

300

200

100

650

700

750

800

Channel

RBS yield

Energy (keV)

Si SiO

glue Si SiO

glue

(a) 400 ˚C

(b) 500 ˚C

After RTA treatment

with preannealing at

30 20 10 0

Depth

(nm)

(i) (ii) (iii)

10nm

(a)

(b)

Figure 2.5 (a) Ge depth distribution in SiO

ﬁlms with a thickness of 20 nm

after rapid thermal annealing (RTA) treatment and preannealing in 7%H

Ar atmosphere. (b) The Ge nanocluster formation after three different RTA

steps at 1223 K in N

atmosphere is shown: for 30 s with the formation of a

bulk cluster band (i), for 4 min with the additional occurrence of an

interface-near cluster band (ii), and for 12 min with the single –-like cluster

band near the interface (iii). (Reprinted with permission from J. Appl. Phys.,

Interaction of ions with matter 45

is depleted in a thin SiO

region close to the interface and is enhanced in a Si

thin region [25]. The phenomenon cannot be explained by a simple Monte

Carlo simulation based on a binary collision approximation but is explained

well by a dynamic DYN-TRIM simulation which includes additional defect

transport phenomena such as bombardment-induced segregation incorpo-

rated in an existing dynamic Monte Carlo computer code DYNTRIM.

Imanishi et al. studied hydrogen behavior in a Si-implanted SiO

sample at

several conditions of dose and annealing temperature for the Si implantation,

on which hydrogen trap sites depend [26]. At the condition of Si nanocrystal

formation, the implanted hydrogen moves to the interface of Si nanocrystal/

SiO

matrix through defects and is trapped at the interface passivating Si

dangling bonds.

2.3.4 Defect formation

The defect distribution in the linear cascade collision scheme is discussed in

Section 2.3.2 and can be accurately calculated with the SRIM code developed

by Ziegler et al. In the high-density energy deposition caused by very heavy

ions and cluster ions, the models based on the binary collision approximation

cannot reproduce experimental evidences of nonlinear effect on defect pro-

duction. The nonlinear effect is presently under exciting debate relating to the

nanotechnology, and, therefore, experimental evidences and theoretical

understanding of them are mainly treated in this subsection.

Canut et al. measured damage cross sections for silicon single crystals

irradiated with 200 keV/atom Au

clusters and found that the cross section

varies roughly as n

[27]. Shen et al. found a similar dependence in the case of

Si irradiated with a fullerene ion [28]. These experimental results provide

evidence for the existence of nonlinear spike effects in high-density collision

cascades. The spike effect cannot be treated by the models based on BCA but

can be done by MD simulation. Molecular-dynamics computer simulation

study was made by Koster et al. for processes occurring in amorphous Si

after irradiation with a projectile with energy E < 500 eV focusing on the

effects of high and low deposited energy density by Au and Si impact [29].

They found that damage production (creation of over- and under-coordi-

nated Si atoms) and recoil implantation are strongly enhanced under Au

impact. The Au impact deposits high-energy density at a local point and

creates a strong collision spike. That is, its center is strongly under-dense – a

‘‘hole’’ appears – and consequently suffers strong tensile pressure, which

induces a compressive shock wave radiating outwards. The process occurs on

a time scale of 0.4 ps and produces abundant defects and relocation of atoms.

Focused ion beam systems46

Relaxation processes follow it, reducing the number of defects formed (of

under-coodinated atoms, in particular) and transporting relocated atoms

back into the vicinity of their original sites. The Si impact does not create

such a collision spike and leads to a low damage production.

A series of MD simulation studies done by Nordlund et al. predicts the

following general trends [30]: Low-mass ions (like Ne in Pt) tend to mostly

produce linear cascades with no large heat spikes. Likewise, cascades in

materials with a low mass or open crystal structure like silicon also do not

exhibit a large surface enhancement of damage production. For heavy ions in

dense, close-packed materials like Ni, Cu, W, Pt, and Au, on the other hand,

a liquid-like state caused by a large heat spike is produced, and the ther-

modynamic and mechanical aspects of materials become important. In this

case, the presence of a surface can strongly affect the behavior of cascades by

hot liquid ﬂow to the surface, microexplosion of the hot liquid zone moved

out to the surface by the inside pressure wave, and coherent displacement. In

addition, a comparison of cascades in pairs of materials (Pt and Au, Ni and

Cu) expected to behave similarly in a ballistic collision revealed that melting

point and elastic hardness of a material are important parameters in deter-

mining the behavior of cascades. Because in all these materials the liquid has

a lower density than the solid, the heat spike formed by local high-energy

deposition leads to the subsequent liquid ﬂow and microexplosion processes.

Then, for similar irradiations, Pt and Ni with relatively high melting points

suffer smaller defects than Au and Cu with low melting points. On the other

hand, semiconductors have open crystal structures, which lead to medium-

energy recoils traveling further than in face centered cubic (fcc) lattices and

thus diminishing the energy density in the heat spike. In addition, since the

density of liquid phase is high compared with that of solid in these materials

and the heat spike tends to relax inwards rather than outwards, making the

‘‘thermodynamic’’ surface mechanisms unlikely to occur. Thus, heavy ions

produce a liquid-like state in dense, close-packed materials and its ﬂow onto

the surface results in a nonlinear sputtering regime and crater formation on

the surface.

Accumulation of defects in a crystal leads to the formation of a local

amorphous zone. Pelaz et al. studied the effects of dose, dose rate, and

implant and annealing temperatures on amorphization resulting from ion

implantation in Si by simulating with a combined code of MARLOWE and

DADOS [31]. They ﬁrst obtained coordinates of the displaced atoms in the

lattice with MARLOWE [10] which uses the binary collision approximation.

Then, the coordinates were continued in DADOS [32], which is the three-

dimensional kinetic Monte Carlo diffusion code and was improved to include

Interaction of ions with matter 47