Yao N. Focused Ion Beam Systems: Basics and Applications

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damage ranging from individual defects to continuous amorphous pockets

and layers. Calculated results are shown in Figure 2.6 for a critical transition

temperature where the rate of defect production and annihilation are com-

parable. Here, peak concentration of interstitial–vacancy (I–V) complex is

plotted as a function of implantation temperature and implantation dose. It

reproduces and explains features of the crystalline-to-amorphous transition.

When implantation cascades are annealed independently, many interstitials

escape recombination for a long enough period to contribute signiﬁcantly to

transient enhanced diffusion (TED). This situation happens at low doses,

high implant temperatures, and low dose rates. At high doses, low tem-

peratures, and high dose rates, the damage is accumulated during ion

implantation. During a high-temperature post-implant anneal, recombina-

tion of Frenkel pairs is efﬁcient and only the extra interstitial generated by

the implanted ion controls TED [33].

It is necessary to localize defects especially for a nanostructure fabrication

with a focused ion beam. Vieu et al. measured the diffusion length of defects

in GaAs/Ga

0.67

0.33

As multi quantum-well layers implanted with Ga

ions

to a dose of 1 · 10

ions/cm

by means of a photoluminescence (PL)

technique [34]. Obtained values are 65 and 270 nm for the depth and lateral

directions, respectively, at room-temperature implantation. That is, defect

diffusion in the III–V heterostructures occurs much more efﬁciently in the

lateral direction than in depth. Nonradiative recombination of electron–hole

pairs formed in the GaAlAs barrier layers by the irradiation possibly

enhances the defect diffusion. The fast diffusion of nonequilibrium defects is

drastically reduced, for a liquid nitrogen temperature (LNT) irradiation, to

1.0

0.8

0.4

0.2

0.0

0.6

1.0

0.8

0.4

0.2

0.0

0.6

200 300

400

500

600

Temperature (K)

Peak concentration

(5×10

–3

)

Peak concentration

(5×10

–3

)

50 ˚C 180 ˚C 250 ˚C

Ge Sn

0246810

Dose (10

–2

)

(b)

(a)

Figure 2.6 Peak concentration of the I–V complexes for 80 keV, 10

2

1

implants for Si, Ge, Sn ions. (a) Amorphization is not possible above the

transition temperature at a 10

2

dose. (b) A superlinear depend ence is

observed near the amorphizing dose. (Reprinted with permission from Comp

Focused ion beam systems48

values of 36 and 70 nm for the depth and lateral directions, respectively. The

low-temperature implantation is inevitable for localizing the implantation-

caused damages in the advanced nanostructure fabrication.

2.4 Sputtering

2.4.1 General remarks

In a low energy region where the nuclear collision process is dominant over

the electronic one, an incident ion makes a kinetic collision with an atom in a

solid and transfers a part of kinetic energy to the atom. The recoiled atom

successively collides with another atom and induces a cascade collision

process. During the process some of the recoiled atoms are ejected from the

solid surface as mostly neutral particles and partly positively or negatively

charged ions. Sigmund developed an analytical formula called the linear

collision cascade model which successfully describes the sputtering process

[9]. In a high-deposit energy condition, the recoiled atoms collide with not

only stationary atoms but moving atoms, and as a result the colliding local

region attains a thermal equilibrium. A thermal spike and a shock wave

model were proposed to describe the process in the condition that the atoms

behave collectively and the linear cascade collision process cannot be applied

anymore. Recently, several simulation codes have been developed using

Monte Carlo treatment, dynamic Monte Carlo treatment, molecular

dynamics, combined treatment of Monte Carlo and molecular dynamics, rate

equation, and so on. These models successfully reproduce the experimental

results on yields, emission energies, and angular distributions sputtered from

metal targets. Some of them cover mass spectra and yields of sputtered

neutral and ionized clusters.

On the other hand, in the cases of semiconductive and insulating materials,

even in the nuclear-collision-dominant low energy region, the electronic

collision process contributes to the sputtering process in a complex way and

the sputtering mechanism is material dependent and different from that

applied for the metals. In spite of the importance of such materials as

semiconductor, insulator, and organic- and bio-molecules, reliable models

are, therefore, very few.

Many excellent publications reviewed the experimental results and the

mechanisms of the sputtering process in the case of metal targets [35–38].

However, descriptions have been scarcely devoted space on dose and dose

rate dependences, an incident cluster effect, chemical and deposition effects,

and incident particle broadening (dispersion) that will become important for

Interaction of ions with matter 49

the focused ion beam process. This section is focusing on the experimental

and theoretical details of the above mentioned various effects on sputtering.

2.4.2 Sputtering yield

General scope

The sputtering yield, Y, is deﬁned as the average number of atoms removed

from a solid surface per incident particle, and is given by Y ¼

for multi-

elemental materials, where Y

is a partial sputtering yield for the element i.

Energy and angular distributions of sputtered particles are given by

Y=@K@˜

with an emission energy K and a solid angle ˜. The sputtering yield

depends on the following various parameters: incident ion (mass, energy, dose

rate, angle of incidence, and clustering), target materials (masses and fractions

of atoms, crystallinity, crystal orientation, surface binding energies, con-

ductivity, surface curvature), and so on. A threshold energy is about 20–40 eV

for normally incident ions and the yield generally increases with incident energy

having a broad maximum in the energy region of 5–50 keV. Sigmund developed

an analytical theory describing the linear collision cascade [9]. According to the

theory, the sputtering yield is given by the simple formula

YðE; ; dÞ¼

0:042F

ðE; ; dÞ

; ð2:27Þ

where F

is the deposited-energy depth distribution, d the depth of the sput-

tering surface from the entrance point of the projectile, E the projectile energy, 

the angle of incidence to the surface, N the density of the target material, and U

the average surface-binding energy. For backward sputtering at perpendicular

incidence, the formula is simpliﬁed into

Y ¼

0:042ﬁ M

ðÞS

ðE; Z

; Z

; ð2:28Þ

where S

is the nuclear stopping power and ﬁ is a function depending on the

mass ratio between the target (M

) and projectile (M

) atoms.

The linear collision cascade theory predicts the yields very well for light

targets, but for heavier targets, in particular in combination with heavier

projectiles, the yield increases substantially faster with Z

than that predicted

by the theory. The density and binding effects in sputtering by ions of Ne, Ar,

and Xe were studied by Shulga using the code OKSANA which is based on

the binary collision approximation and takes into account weak simulta-

neous collisions at larger distances [39]. The ion energy and target cover

ranges from 100 eV to 100 keV and from Mg to U, respectively. The linear

Focused ion beam systems50

cascade theory describes correctly the binding and mass effects at an incident

energy higher than 1 keV but fails to include the density effect. To study the

binding and density effects the following ﬁtting functions are applied:

Y ¼ A

ðS

Þ; ð2:29Þ

and

Y ¼ A

ðS

Þ; ð2:30Þ

where S

¼ð3=4

Þðﬁ M

ðÞK

Þ; (applied at the incident energy less

than 1 keV) and S

¼ 0:042ﬁ M

ðÞS

ðE; Z

; Z

Þ=NU

; A, p, and q are ﬁtting

parameters; and K

is the maximum transferred energy in the binary colli-

sion. The sputtering yield is shown in Figure 2.7 as a function of target

atomic number. The calculated data are obtained by applying the effects to

the Sigmund’s linear cascade theory.

For ion bombardment at an oblique angle of incidence the sputtering yield

increases monotonically with increasing angle of incidence up to a maximum

near 60–80



. A dependence on the angle of incidence is expected to be given

by Yð Þ=Yð0Þ¼1= cos

ﬂ

, where is measured from the surface normal. But

surface morphology inﬂuences the reproducibility of the experimental data

and the dependence is not clear. For single crystals the sputtering yields

depend also on the direction of particle incidence relative to the crystal

orientation.

Particles sputtered from a solid surface during particle bombardment are

mostly neutral atoms emitted with a cosine like angular distribution and with

a broad energy distribution that peaks at a few eV, about half the surface

binding energy. A small fraction of the sputtered particles are clusters con-

taining up to some 100 atoms. A very good review was presented by Betz

and Wien on the energy and angular distributions of atomic, molecular, and

cluster particles sputtered from solid surfaces under ion bombardment [38].

Experimental data are often compared with the Sigmund–Thompson

distribution as described by [9]

dKd

K þ U

ðÞ

32m

cos 2; ð2:31Þ

where 2 is the polar angle of the emitted particles with respect to the surface

normal and m is an adjustable parameter close to 0.

Interaction of ions with matter 51

In the case of single crystalline targets, the angular distribution is strongly

affected by the surface structure. Rosencrance et al. measured energy-

resolved angular distributions for Ni and Rh atoms desorbed from Ni and

Rh fcc{001} single crystals bombarded by keV Ar

ion and found that the

experimental spectra for the two elements are almost identical, implying that

the crystal and surface structures dominate the ejection process [40]. From

the comparison between the experimental results and the MD calculations

which are based on the molecular-dynamics/Monte Carlo corrected effective-

medium interaction potential, it was found that about 90% of the ejected

10 20 30 40 50 60 70 80 90

Target atomic number

10 20 30 40 50 60 70 80 90

Tar

et atomic number

10 keV Ar → different targets, normal incidence

polycrystalline & amorphous

S (atoms/ion)

1 keV Ar → different targets, normal incidence

polycrystalline & amorphous

experiment

Eq. (2.30)

Eq. (2.29)

Eq. (2.30)

(a)

(b)

Figure 2.7 The experimental yield data for (a) 1 keV and (b) 10 keV Ar and

their ﬁts by (2.29) and (2.30). (Reprinted with permission from Nucl. Instr.

Focused ion beam systems52

atoms originate from the ﬁrst top layer and at least three major ejection

mechanisms exist for the surface depending on the sequential collisions

between atoms on (i) the ﬁrst top layer, (ii) on the ﬁrst and second layers, and

(iii) on the ﬁrst and third layers. The dominant mechanism of ejection is the

above second case.

As described thus far, the main parts of the sputtering phenomena can be

physically understood by the analytical linear cascade models and by the

associated computer simulation schemes of binary-collision approximation

and Monte Carlo treatments. That is, these models can represent well the

experimental results as far as the energy deposit to the target is small enough

to be treated in the linear cascade regime and the contribution of the elec-

tronic excitation is small. In the case of high-energy deposition, various

phenomena have been observed as spikes, large cluster emission, chemical

effects, and so on, which cannot be explained in the linear cascade regime.

Therefore, the further understanding of these sputtering phenomena needs

the molecular dynamic treatment, because these phenomena contain many-

body interactions, electron–phonon coupling, and internal excitation of the

limited region. In addition, some of the MD calculations were applied to the

problems of bulk-binding energy and single-crystal sputtering, and further to

the understanding of preferential sputtering and electronic sputtering. These

will be discussed at each subsection described below.

Dose dependence of yield and preferential sputtering

Various BCA codes have been developed on the basis of the linear collision

cascade theory for crystalline targets (named MARLOWE [10], COSIPO

[41], ACOCT [42], crystal-TRIM [43], etc.) and for amorphous targets

(named TRIM [5], ACAT [44], SASAMAL [45,46], etc.). These codes do not

take into account compositional changes caused by the collision cascades and

are called ‘‘static’’ Monte Carlo (MC) code. The ‘‘dynamic’’ codes (named

TRIDYN [47], ACAT-DIFFUSE [44], dynamic-SASAMAL [45,46], etc.) are

improved to treat the compositional changes during the ion bombardment

and can reproduce the dose dependence of depth proﬁles of implanted ion

and preferential sputtering. An example of calculations by the dynamic-

SASAMAL code for Ar ion incidence, as shown in Figure 2.8, is the effect of

mass ratio of two components on the preferential sputtering [45,46]. The

TRIDYN code predicts that implantation of heavy ions into light materials

(low atomic number) leads to oscillations in partial sputtering yields as a

function of incident dose [47], as shown in Figure 2.9. In the BCA regime, the

kinetic energy is effectively transferred to atoms with similar mass as the incom-

ing particle. In addition, lower-mass atoms have larger ranges in the solid than

Interaction of ions with matter 53

heavier atoms, so that lighter atoms are depleted in the solid at the depth of

maximum energy deposition. As a result the lighter atoms are in general

preferentially sputtered at the surface.

Besides those reasons based on the BCA regime, factors inﬂuencing pre-

ferential sputtering are different binding energies of different atoms at the

surface, segregation of one element at the surface, and diffusion in the

implanted layers of the solid. These preferential sputtering have been studied

in more detail with various simulation codes such as molecular dynamic

treatment, thermal spike model, and ﬂuid dynamics calculation [48–52]. An

example of sputter preferentiality and partial sputter yields calculated by

molecular dynamics simulation [49] is presented in Table 2.2. The results

100

50 100

150

200 250

300

Sp. loss (Å)

. loss (Å)

Concentration (at.%)

01020304050

Dose (× 10

–2

) for 3 keV Ar

Dose (× 10

–2

) for 3 keV Ar

1 keV Ar

3 keV Ar

1 keV Ar

3 keV Ar

100

120

Concentration (at.%)

(a)

(b)

Figure 2.8 Change of surface atomic concentration in SiC (a) and WC (b)

during 1 and 3 keV Ar sputtering. (Reprinted with permission from Nucl.

Focused ion beam systems54

show that the sputter preferentiality in the Cu-Au alloy is mainly caused by a

mass difference rather than a binding energy and furthermore an enhanced

sputter preferentiality of Cu atoms for an ordered Cu

Au alloy compared to

a disordered alloy demonstrates a strong inﬂuence of local ordering on

sputtering emission.

Mass distribution

Mass distributions of emitted neutral large clusters have been systematically

measured by Wucher group using a post ionization method with a laser

induced single ionization technique [53,54]. Obtained cluster yields are very

large and have power law dependences n

–

on the cluster size n. The exponent

– depends on wavelength of ultraviolet, and the respective values for 193 nm

and 157 nm of ArF and F

lasers are Al (8.6, 7.7), Ag (6.0, 5.3), Nb

(—, 8.1), and Ta (—, 8.5). Further, the exponent depends on the total

sputtering, as shown in Figure 2.10. Start and Wucher carefully corrected the

apparent cluster yields on size dependent detection efﬁciency, and found that

a power-law yield distribution for In clusters by 15-keV Xe incidence has two

2.5

1.5

0.5

010203040

Dose (× 10

W cm

–2

)

, W partial sputtering yield

W → Be

W → C

W → Si

10 keV W → Be, C, Si

normal incidence

Figure 2.9 Dose dependence of partial sputtering yield of W. Be, C, and Si

are bombarded with 10 keV W at normal incide nce. (Reprinted with

Elsevier Science B.V.)

Interaction of ions with matter 55

Table 2.2 Sputter preferentiality – calculated by a molecular dynamics simulation.

(Reprinted with permission from Nucl. Instr. Meth. B, 1999, 152, 459–471. Copyright

1999 Elsevier Science B.V.)

Ordered- Disordered- Disordered- Disordered-

Cu Au Cu

Au Cu

CuAu

5.12 – 3.31 3.65 3.61 1.24

– 4.44 1.20 0.85 1.23 3.31

tot

5.12 4.44 4.51 4.50 4.84 4.55

– – 2.76 4.30 2.94 0.38

–(%)

– – 176.4 43.3 2.0 12.7

 ¼

 1;c

: atomic concentration at surface.

: an artiﬁcial light mass of Au.

024

14 16

Total sputter yield Y

tot

Our group

Rehn et al.

Exponent δ

Figure 2.10 Compilation of power-law exponents extracted from cluster

yield distributions versus total sputtering yield Y

tot

. The In data (solid

symbols) have been determined by correcting the cluster-size-dependent

detection probability: the remaining exponents (open symbols) are non-

corrected values for Ag, Cu, Al, Ge, Nb, and Ta. For comparison, the Au

data of Rehn et al.[55] have been included. (Reprinted with permission from

Society.)

Focused ion beam systems56

decay components of 3.9 for small (n 20) and 2.1 for large (20 n 

100) clusters (Figure 2.11)[54]. On the other hand, Rehn et al. measured size

distributions of very large clusters (n 500) by a transmission electron

microscope (TEM) and obtained a power law dependence of cluster yield

with a rather low value of exponent of 2, which is independent of total

sputtering yield as shown in Figures 2.10 and 2.12 [55]. These results are

explained in the following way: the inverse-square dependence reveals that

the very large clusters are produced when shock waves, generated by sub-

surface displacement cascades, impact and then they ablate the surfaces

[56,57]. Many smaller clusters detected with the post ionization method can

result from the break up of larger ones, which provides a plausible expla-

nation for the large negative exponents. This idea was simulated by Wucher

et al. with so-called ‘‘molecular dynamics and Monte Carlo-corrected effec-

tive medium potential (MD/MC-CEM).’’ That is, ﬁrst, the formation of

so-called very large highly excited nascent clusters, is calculated by the MD

100

Cluster size n

Relative yield

w/o detection prob. correction

with detection prob. correction

∝n

–3.9

∝n

–2.1

–1

–2

–3

–4

–5

–6

–7

–8

Figure 2.11 Relative yields of In

clusters sputtered from a pure,

polycrystalline indium surface under bombardment with 15 keV Xe

ions.

The data have been normalized to the partial yield of In atoms. (Reprinted

American Physical Society.)

Interaction of ions with matter 57