Yao N. Focused Ion Beam Systems: Basics and Applications

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Micro-machining and mask repair

mark utlaut

University of Portland

10.1 Introduction

Transistors are, by far, the largest number of artiﬁcial objects made by human

technology. This device has caused and fueled the ‘‘Third Wave’’ of history.

As integration and miniaturization of devices continue to progress, auxiliary

techniques have been invented to aid in their development and failure analysis.

Focused ion beams (FIB) is one of those techniques without which such

progress would have been very slow or even impossible. The primary use of FIB

is in micro-machining, which is the programmed, controllable removal or

addition of material for fabrication, analysis, or repair on a sample at the sub-

micrometer scale. As modern small-scale fabrication and repair of structures

progresses, FIB has become an essential tool for work at the micro- and

nano-scales. An FIB system is capable of being used as a combined milling/

deposition machine and as a scanning ion microscope (with different modes of

contrast generation), so that as the milling/deposition work proceeds, it can be

inspected. In addition, the marriage of an FIB with an SEM (scanning electron

microscope) or an AFM (atomic force microscope), allows a natural integra-

tion of techniques so that metrology can be performed and the work can be

viewed using different imaging modes. The term ‘‘milling,’’ which is the sput-

tering of material, is borrowed in analogy with larger conventional machine

tools such as lathes which remove material by cutting. FIBs are the micro- and

nano-level lathes and milling machines used in modern small-scale technology

[1,2,3]. As the feature sizes of structures become smaller, FIB technology is

being pushed to the physical limits of operation. Some of these limits have been

addressed in other chapters in this book, and we reiterate some of them as

applied to micro-machining.

Focused Ion Beam Systems: Basics and Applications, ed. N. Yao.

Published by Cambridge University Press. ª Cambridge University Press 2007.

268

10.2 Scanning strategy

The basic structure and operation of an FIB system has been covered in

Chapter 2. In a typical FIB system, the beam is sequentially placed at adjacent

positions to form an area of quadrilateral or more general shape. The ‘‘beam

size,’’ typically determined by the beam current and system optical properties,

and the ‘‘beam overlap,’’ typically an adjustable parameter, both inﬂuence the

quality of the shape and quality of the milled region (Figure 10.1).

Most FIB systems employ digital scanning where the beam is stepped along

pixels to ﬁll out a programmed shape. When imaging, the beam is rastered

across the sample and information generated in the sample in the form of

secondary electrons or ions are synchronously collected to form an image.

When milling or depositing material, the beam is rastered through the pattern

shape for a predetermined time. In order to mill a smooth pattern, the ion

dose delivered to the sample must be uniform. Since the ion beam has a

quasi-Gaussian proﬁle, in order to achieve uniform dose there must be suf-

ﬁcient overlap of the pixel spacing. The effect of beam overlap can be seen in

Figure 10.2, where the ion dose uniformity is shown as a function of spatial

distance for different amounts of beam overlap. Assuming the beam shape to

be a Gaussian distribution, with standard deviation , one performs a con-

volution of the beam shape with the pixel spacing, p

to calculate the ion dose

spatial variation. As can be seen in the ﬁgure, a uniform dose is achieved

when p

/ 1.5, although for some applications a p

/ 2 might be accep-

table. In most FIB machines the beam overlap is an adjustable parameter

Beam diameter

Pixel spacing

Direction of bea

advance

FIB beam

Substrate

Figure 10.1 The ion beam is moved sequentially from one site to another, with

the possibility of overlapping positions. (Courtesy of Ampere Tseng [4].)

Micro-machining and mask repair 269

that can be chosen as a ‘‘percentage of beam size’’ overlap. For a Gaussian,

the ‘‘beam diameter’’ d

¼2.35. For p

/ ¼1.5 this is equivalent to

¼0.64, or 64% overlap. If the pixel spacing does not have sufﬁcient

overlap, the resulting milled volume will have a bottom with divots, which for

most applications is unacceptable [2,3,4].

10.3 Sputtering

The sputtering process occurs when incident ions onto the sample transfer

sufﬁcient momentum to surface and near-surface atoms to allow them to

escape through collisional cascades [3,5]. The number of sputtered atoms per

incident ion is called the sputter yield, Y . For ions incident perpendicular to

the surface, and without the introduction of reactive gases, such as Cl, I, or

XeF

, typically 0 < Y < 5 for energies of ions normally used (35 keV), but

for some materials it can be several times higher. If gases are introduced Y

can increase by as much as 20·.

Often it is useful to express the sputter yield in terms of the volume of

material removed per quantity of incident charge (cubic micrometers, mm

per nanocoulomb, nC). Typical values of sputter yields for 25 keV Ga

incident ions lie in the range 0.05–0.7 mm

/ nC. The advantage of using these

units is the ease afforded in calculating the removal rate (volume removed

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

012345678910

Normalized coordinate (x/si

ma)

/sigma = 1.5

/sigma = 2.0

/sigma = 4.0

/sigma = 8.0

Normalized ion intensity

Figure 10.2 Convolution of the beam shape (assumed to be Gaussian) with

different pixel spacings (beam overlap). For a ﬁxed dwell time per pixel, the

curves represent the spatial variation of the ion dose. For the case p

/ ¼1.5,

corresponding to a beam overlap of 64%. (Courtesy of Ampere Tseng [4].)

Focused ion beam systems270

per time) by forming the product of incident beam current and the sputter

yield. For example, the sputter yield of Si is 0.27 mm

/ nC so that if one were

using a beam current of 100 pA, the sputter rate would be 0.027 mm

/s. If a

10 mm square hole 3 mm deep were to be milled, then it would take roughly 3

hours to remove the 300 mm

. If, in this example, one were to use a beam

current of 10 nA, the milling time would be a much more reasonable 1.85

min. Table 10.1 gives some measured sputter rates and yields for common

materials of interest [6 ]. The sputter yield Y is calculated from the sputter rate

by the relationship

Y ¼ 96:4



;

where m is the mass (in amu) and  is the density of the sample.

Numerous attempts have been made to calculate sputter yields from basic

theory. One model frequently used is that of Sigmund [7]. According to this

model, for ion energies E

, the total sputtering yield (integrated over a solid

angle) is given by:

tot

ðE

Þ¼

4:2 · 10

ﬁS

½target atoms=primary ion;

where

ﬁ ¼ 0:15 þ 0:13

target

ion

;

Table 10.1 Sputter yields for selected elements.

Element

Density

(g/cm

)

Sputter yield

(mm

/nC)

Sputter yield

(atoms/ion)

C (diamond) 3.57 0.18 2.73

Al 2.7 0.30 2.89

Si 2.33 0.27 2.08

Ti 4.5 0.37 3.35

Cr 7.19 0.09 1.20

Zn 7.13 0.34 3.57

Ge 5.32 0.22 1.55

Se 4.81 0.43 2.52

Mo 10.2 0.12 1.32

Ag 10.5 0.42 0.92

Sn 5.76 0.25 1.17

W 19.25 0.12 1.22

Pt 21.47 0.23 2.44

Micro-machining and mask repair 271

and

¼ 8:462s

ð"Þ

ion

þ M

target

ion

target

ðZ

2=3

ion

þ Z

2=3

target

1=2

;

and U

is the surface potential. The ‘‘reduced energy’’ " and the ‘‘reduced

nuclear cross section’’ s

are given by

" ¼

sample

ion

sample

ðM

ion

þ M

sample

½E in ergs;

and

ð"Þ¼

0:5lnð1 þ "Þ

" þ 0:14"

0:42

;

where a is the Thomas–Fermi radius (in angstroms), and a ¼ 0:468

ðZ

2=3

ion

þ Z

2=3

sample

1=2

. Extensive tables [2] can be found for these quantities, and

an illustration of the dependence of sputtering on the incident energy and

sample composition is shown in Figure 10.3.

The dependence of sputter yield on incident energy is shown in one

example in Figure 10.4, where it can be seen that there is an increase in yield

with increasing energy that levels out somewhere near 40 keV [3,4]. This is

due to the deeper penetration depth of the ions, where the collisional cascades

are generated too deep to transfer sufﬁcient energy to atoms to escape from

the surface.

60.0

50.0

40.0

30.0

20.0

10.0

0.0

0 1020304050607080

Atomic number of substrate

Sputter yields

Ga 30 kV

Ga 50 kV

In 30 kV

In 50 kV

Sputter yield

Figure 10.3 From the Sigmund model, calculated sputter yields for 30 keV

and 50 keV Ga and In impinging on solid mono-elemental substrates [2].

Focused ion beam systems272

The sputtering yield is also dependent upon the incident angle of the ion

beam to the surface. In the Sigmund model the angular sputter yield

dependence is

Yð2Þ¼Yð0Þcos

f

ð2Þ;

where f is a constant depending on the mass ratio M

sample

ion

. Simulations

of this effect and experimental data are shown in Figure 10.5. This depen-

dency can be used to advantage when milling shapes near edges [2].

10.4 Redeposition

One deleterious complication to milling is the redeposition of sputtered

material into the volume that is being milled [3,4]. In conventional large-scale

machining, the swarf is carried away by liquid or air streams. In FIB milling,

the redeposition is very dependent on the milling strategy used. It has been

shown that for the same total dose incident onto a sample, that repeated

scans to mill a rectangular area cause less redeposition than a single slow

pass. In the case of a single slow scan, redeposited material is not removed,

while for many repeated scans some fraction of the redeposition is milled

away by the primary beam. Figure 10.6 shows this effect.

These results can be understood partially by a simple geometrical analysis.

Consider milling a groove in one dimension of width d and height h,as

Sputtering yield (atoms/ion)

0 20 40 60 80 100

Ion ener

(keV)

Ion/target TRIM Experiment

As/Au

a: [12]; b: [13]

c: [14]

d: [18]; e: [15]; f: [16]

g: [17]

Ga/Au

Ar/Au

As/Si

Ga/Si

Figure 10.4 Theoretical curves and experimental data points of sputtering

yield dependence on the energy of the incident ion for several ion/target

combinations. (Courtesy of Ampere Tseng [4].)

Micro-machining and mask repair 273

shown in cross section in Figure 10.7. Assuming that the sputtered efﬂux has

a cosine distribution, and falls off as 1/r, and that the sticking coefﬁcient is

unity for the F

atoms/length emitted, then it can be shown that the ﬂux

density of sputtered material from the bottom redeposited onto a sidewall at

a height h is

FhðÞ¼

cos ’ cos 

dx ¼

xdx

;

(a) (b)

Figure 10.6 SEM photos of 5 mm · 5 mm milled boxes in Si by 30 keV Ga

for the same total dose in each case. Box (a) was mil led with a single pass of

the ion beam, box (b) was milled with 50 passes. Both milled boxes are

viewed at 45



Sputtering yield (atoms/ion)

03015 45 60 75 90

Incident an

le (de

rees)

correlation: cos

–2

30 keV

Ion/target TRIM Experiment

As/Au

[17]

[19]

Ga/Au

As/Si

Ga/Si

Figure 10.5 Angular dependence of sputtering yield of As and Ga ions onto

Si and Au. (Courtesy of Ampere Tseng [4].)

Focused ion beam systems274

and the ﬂux density of atoms that escape is

ðÞ¼

cos



dx ¼

;

where x

is the distance from the sidewall. The total ﬂux onto a sidewall and

the escaping ﬂux are given by

wall

FðhÞdh;

x = 0

x

x =

x = 0

x = d

(a) Wall flux

(b) Escaping flux

Au Substrate

Resist mask sidewall

Figure 10.7 Geometry used for calculation of redeposition effects.

Micro-machining and mask repair 275

and

lost

FðxÞdx:

The redeposition for the case of two sidewalls forming a groove of aspect

ratio h/d is shown in Figure 10.8. Clearly the aspect ratio is an important

parameter to consider when milling a volume.

10.5 Channeling

Another effect that can cause complications when micro-machining is due to

channeling [3,5]. As discussed in Chapter 3, channeling occurs in crystalline

materials where ions can penetrate deep into low index directions, interacting

so deep that sputtering cannot happen. In polycrystalline materials, this

means that low index crystals will not sputter as rapidly as others, resulting in

differential milling rates in mono-elemental samples. Figure 10.9 shows the

result of milling into polycrystalline Cu with 30 keV Ga

The uneven bottom in the milled volume is due to differential sputtering

rates of the microcrystals, and not redeposition.

2.5

2.0

1.5

1.0

0.5

0.1 0.2 0.3 0.4 0.5

Normalized deposition rate, F/F

Normalized height, h/d

Figure 10.8 Normalized redeposition effect. Here F is the ﬂux of sputtered

atoms that escape without striking the walls.

Focused ion beam systems276

There are remedies for reducing or nearly completely eliminating chan-

neling. One method is to introduce a gas near the sample surface. The

channeling axes are very sensitive to incident ion direction, and the intro-

duction of sufﬁcient scattering centers on the surface can deﬂect incident ions

enough to eliminate channeling, thus reducing differential milling. This may

happen at the expense of reduced effective milling rate, but can yield good

results (Figure 10.10).

Figure 10.9 A 10 mm square milled in Cu. The uneven bottom is due to the

differential milling rate of the different microcrystals.

Figure 10.10 The same region of Cu milled in Figure 10.9, but with the

introduction of a gas, which uniformly clears the milled area by completely

disturbing the effects of channeling.

Micro-machining and mask repair 277