Microelectronic Engineering 87 (2010) 1–9

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Microelectronic Engineering

journal homepage: www.elsevier .com/locate /mee

Prediction of nanopattern topography using two-dimensional focusedion beam milling with beam irradiation intervals

Jin Han, Hiwon Lee, Byung-Kwon Min *, Sang Jo LeeSchool of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 October 2008Received in revised form 11 April 2009Accepted 8 May 2009Available online 19 May 2009

Keywords:MicrofabricationSputtering simulationIon beam machiningPatterning

0167-9317/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.mee.2009.05.010

* Corresponding author. Tel.: +82 2 2123 5813; faxE-mail address: bkmin@yonsei.ac.kr (B.-K. Min).

Beam irradiation intervals are a critical parameter in the fabrication of nanopatterns via focused ion beam(FIB) milling. The beam irradiation intervals are defined in terms of the overlap. In this paper, the nano-pattern height on a silicon surface is predicted using a mathematical FIB milling model that varies theoverlap. The proposed model takes into account the angle dependence of the sputtering yield and rede-position effect, together with the superposition of a bi-Gaussian beam. The model was verified by com-paring the results of a nanopattern machining experiment to those of a simulation based on the model.The simulation calculated the final two-dimensional geometry from ion milling parameters. The resultsof the simulation indicate that the proposed model is more precise than one that only considers thesuperposition of a Gaussian beam.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

The fabrication of nanostructure devices is the key to nanoscaleengineering and nanotechnology. In recent years, focused ion beam(FIB) systems have frequently been used in nanofabricationbecause of their direct writing capability and high resolution [1].FIB techniques were originally developed to analyze cross-sectionsof nanoscale material and repair masks in semiconductor processes[2]. However, FIB systems are currently used in a variety ofmachining applications. Instead of using a beam mask, FIB systemsutilize digital scanning of a single ion beam with a variable irradi-ation interval in order to generate arbitrary beam-irradiatedshapes. Recently, an FIB process utilizing this feature, known asFIB milling, has been applied to nanofabrication. For example, FIBmilling is used to make micro-molds and nano-imprint templates[3], transmission electron microscopy specimens [4], and three-dimensional structures such as micromachining tools [5], micro-lenses [6], and masters for microcontact printing [7]. In addition,FIB milling has been applied to produce precise nanopatterns.

For accurate fabrication of nanostructures, proper process plan-ning for FIB milling is crucial. Because FIB milling utilizes a high-energy charged particle beam for machining, ion beam propertiesand ion beam sputtering must be considered in the process plan-ning. For example, the ion beam intensity has a Gaussian distribu-tion, and thus the ion-machined shape (such as whether thebottom surface is flat or rippled) is determined by the superposi-tion of the beam path. The sputtering behavior of three-dimen-

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sional machining is also complex since the sputter yield dependson the incident angle on the substrate, and the redeposition ofsputtered material decreases the accuracy of the machining. On ac-count of these issues, much research has been performed to devel-op a model for FIB milling processes that will predict the finalgeometry of the product.

Nassar et al. [8] and Vasile et al. [9] developed mathematicalmodels for computer simulations to predict the final geometriesof ion-machined structures. In these models, a pixel addressscheme was applied to simulate a three-dimensional cavity, takinginto account the dwell time and sputter yield variations withrespect to the ion energy and incidence angle. Ishitani and Ohnishi[10] developed an improved FIB milling simulation model by con-sidering redeposition effects. They proposed a mathematical modelto calculate the net redeposition atom flux on the trench sidewallwith respect to the scan speed and ion incident angle. Assayag et al.[11] proposed a bi-Gaussian model to describe the beam intensityprofile with greater accuracy.

FIB milling processes are applicable to nanopattern fabrication.By adjusting the beam path and irradiation interval, nanoscale rip-ple structures with a repeating spatial pattern [12] can be gener-ated. The repeating nanopatterns have a variety of applications,such as in high capacity data storage media [13] and base struc-tures for optical devices [14]. To predict and design the geometryof the fabricated nanopatterns, including the pattern height andshape, with nanoscopic accuracy, a more accurate FIB milling pro-cess model is desired. In this manuscript, an improved FIB millingmodel is proposed that integrates the various aspects of ion beamsputtering and considers the nanoscopic characteristics of the pro-cesses. This model is experimentally verified and implemented in a

2 J. Han et al. / Microelectronic Engineering 87 (2010) 1–9

nanopattern fabrication process. Although the model developmentis focused on pattern fabrication, the simulation model can be ap-plied to general FIB milling without modification.

Section 2 introduces the parameters of an FIB milling processand describes the process characteristics, such as the Gaussianbeam distribution model, sputtering yield with respect to incidentangle, and redeposition effects. In Section 3, pattern fabricationsimulation results based on the proposed FIB milling model arediscussed and compared to the experimental results. Section 4summarizes the findings of the study.

2. FIB milling process

2.1. FIB milling parameters

In an ion milling process, the beam scanning sequence, irradia-tion points, and interval are determined by the user. Fig. 1 illus-trates the raster scan FIB milling process parameters. Sputteringoccurs only when the beam is active on the target; the beam isblanked between the irradiation points, as depicted in Fig. 1(a).The ion beam intensity and beam diameter are depicted inFig. 1(b). The beam is irradiated with an interval of pitch p, asshown in Fig. 1(c).

The parameters of an FIB milling process are the beam diameter,beam current, ion dose, dwell time, and beam overlap. The beamdiameter is adjusted by the ion optics, and can be described bythe full-width half-maximum (FWHM) parameter. In this study, abeam diameter of 60 nm was used. The beam current is definedas the number of ions delivered to the target per unit time. Theion dose refers to the total number of ions irradiated in the targetarea. The dwell time is the beam irradiation time at each beamspot. The beam is blanked and moved to the next beam spot assoon as the dwell time has passed. The beam overlap refers tothe amount of superposition of adjacent beams. The overlap (seeFig. 1(c) and (d)) is defined as follows:

O ¼ 1� pd

ð1Þ

where O denotes the overlap, p (pitch) is the distance between thecenters of two adjacent beam spots (shown in Fig. 1(c)), and d is thebeam diameter (FWHM). For example, an overlap of �1 means that

Fig. 1. Schematics of focused ion beam milling parameters: (a) beam irradiation positiooverlap.

the distance between adjacent beam spots is twice the beam diam-eter. An overlap of 0.5 means half of the diameter is overlapped. Theoverlap value must be less than unity. Because the beam diameter istaken to be the FWHM value, even when the overlap is less thanzero, the beam-radiated areas on the target surface may overlapeach other (see Fig. 1(d)).

The workspace of raster scan FIB milling is described by a two-dimensional coordinate system. Since the intensity of an ion beamhas a Gaussian-like profile (Fig. 1(b)), the superposition of thebeam generates three-dimensional patterns as depicted in Fig. 2.The geometric properties of the patterns can be adjusted by vary-ing the FIB milling parameters.

2.2. FIB milling process characteristics

Because FIB milling processes are based on high-energy ionbombardment, knowledge of the beam shape characteristics is re-quired to construct an FIB milling model. Sputtering occurs whenatoms are ejected by energetic ions hitting the target surface. Theratio between the number of incident ions and the ejected atomsis called the sputtering yield. Some portion of the sputteredatoms becomes reattached to the target surface; this is calledredeposition. Therefore, the primary factors affecting the geome-try of an FIB milled surface are: (1) the ion beam intensity, (2) thesputtering yield, and (3) the redeposition. In real FIB milling pro-cesses, the prediction of an FIB-milled surface geometry is a chal-lenging task since the ion beam intensity has a Gaussian-likeprofile and the sputtering yield and redeposition depend on thetarget surface geometry. For example, the sputtering yield is afunction of the ion incidence angle, while the incidence angle isdetermined by the target surface geometry. The surface geometryis then affected by the beam intensity profile and the redeposi-tion of the sputtered materials. Therefore, to accurately predictthe geometrical characteristics of an FIB-milled surface (such asthe pattern height), the interaction between the factors must beconsidered. In this manuscript, the beam incident angle depen-dency of the sputtering yield is modeled after the results ofYamamura et al. [15], and the redeposition is based on a modelby Orloff [16]. In considering the ion beam energy level used inFIB milling, other effects (such as amorphorization and swelling[17,18]) are ignored in this study.

n, (b) beam intensity and diameter (FWHM), (c) beam diameter and pitch, and (d)

Fig. 2. Schematic prediction of a nanopattern: (a) two-dimensional prediction and (b) three-dimensional prediction.

0 L

x

i=1 i=2 i=N

p

i=N-1…. ….i=n

bi-Gaussian curve

Fig. 3. Schematics of the beam scanning sequence and irradiation points.

J. Han et al. / Microelectronic Engineering 87 (2010) 1–9 3

2.2.1. Ion beam intensity profileIn an FIB milling process, the pattern geometry is determined by

the superposition of individual beams. Since the beam intensityhas a profile, a model of the beam intensity profile is required toestimate the final pattern geometry. In previous FIB simulationstudies, many researchers have used a Gaussian distribution profileto model the beam profile [8–10].

However, precise measurements of the beam profile at the tar-get surface have demonstrated that the actual profile deviatesslightly from a Gaussian distribution [19]. To measure the beamprofile more accurately, Kubena and Ward evaluated the currentdensity of the dot exposure of a beam in a negative organic resis-tance structure [19]. They found that a Gaussian distribution is agood fit in the center region of the beam, but an exponential profileis a better fit at the tails of the beam where a lower current pre-vails. To obtain a more accurate description of the beam intensityprofile, Assayag et al. [11] proposed the use of a bi-Gaussian func-tion composed of two Gaussian functions: one for the core regionof the beam and the other for the tail region of the beam.

In this manuscript, the bi-Gaussian model proposed by Assayaget al. [11] is used to describe the beam intensity profile. A simpleGaussian profile has been successfully used in conventional ionsputtering simulation models [8–10]. However, in patterning pro-cesses, modeling error accumulation leads to substantial geometri-cal inaccuracies in the final results since the beam superpositionoccurs mostly in the tail regions. Using a bi-Gaussian representa-tion, the ion intensity profile at a distance d from the beam centeris

DðdÞ ¼ Df

g� we

� dr1ffiffi2p

h i2

þ ð1�wÞe� d

r2ffiffi2p

h i20@

1A ð2Þ

where g denotes the atomic density, Df is the ion dose in a singleframe, and r is the standard deviation of the beam diameter definedby d = 2.235r; r1 represents the core region while r2 represents thetail region. Df is calculated by dividing the ion dose Dt by the num-ber of scan frames, Ns. Here, w is a weight factor for the bi-Gaussiandistribution.

2.2.2. Angle-dependant sputtering yieldAs described in Section 2.1, the beam scanning sequence and

irradiation points are characterized by a, p, and L (see Fig. 3). L isthe total processing length in the x direction, and p is the distance

between the centers of two adjacent beam spots. When a beam hitsthe surface, the sputtering depth at distance x when i = n is

SnðxÞ ¼Df

g� yðxÞ � we

� ðx�ðn�1ÞpÞr1ffiffi2p

h i2

þ ð1�wÞe� ðx�ðn�1ÞpÞ

r2ffiffi2p

h i20@

1A

24

35 ð3Þ

where y(x) is the sputtering yield dependence on the incident angleand n is the number of beam spots in the x direction. In ion beamsputtering processes, the sputtering yield varies according to theion incident angle. Therefore, the sputtering yield must be modeledwith respect to the incident angle in order to calculate the patterngeometry, especially when the beam is irradiated on a non-flatsurface.

The sputtering yield can be expressed as a function of incidentangle. Yamamura et al. [15] proposed a mathematical model thatprovides a good fit to experimental data for all incident angles. Thismodel can be expressed as

yðxÞ ¼ Y cos h�f e�cðcos h�1�1Þ ð4Þ

where Y is the sputtering yield at a normal ion incidence, and c and fare constant that depend on the ion–solid combination. In the caseof 30 keV Ga ions irradiated to a silicon substrate f and c are calcu-lated as 2.04 and 0.37 according to Adams and Vasile [20]. Sputter-ing yield Y is calculated as 3.0 as a result of a sputtering experimentusing volume loss method.

To verify the sputtering yield function, a milling experimentwas conducted using a silicon sample by varying the stage-tiltingangle from 0� to 60�. The sputtering yield at each angle was calcu-lated by volume loss method. Fig. 4 compares the experimental re-sults and the sputtering yields calculated by Eq. (4). A simulationresult using SRIM simulation [21] was also plotted as a reference.

0 10 20 30 40 50 60 70 80 900

5

10

15

20

25

30

35

Sput

terin

g yi

eld

(ato

ms/

ion)

Incident angle (deg)

by experiment SRIM simulation Eq. (4)

Fig. 4. Sputtering yield with respect to beam incident angle.

4 J. Han et al. / Microelectronic Engineering 87 (2010) 1–9

A good agreement was observed for all three curves. The sputteringyield increased with the angle up to around 80� on account of theincreased probability of a collision cascade. After reaching a maxi-mum value at about 80�, the sputtering yield rapidly decreased tozero due to the ion reflection at the impinging surface.

2.2.3. Effect of redepositionIn FIB milling processes, redeposition occurs when sputtered

atoms stick to the sidewall or milled surfaces of the material.

Fig. 5. Schematic diagram of

Fig. 6. Results of the simulated redeposition. (a) Milling depth change

Fig. 5 depicts redeposition as modeled by Orloff [16]. The amountof redeposition during the sputtering process at i = 1 above the bot-tom surface is given (as in [16]) by:

RðxÞ ¼ KZ L

0SðxÞ cos u cos U

rdx ð5Þ

where S(x) is the result of Eq. (3), K is a sticking coefficient relatedfactor for the milled surface and sputtered atoms, 0 and L are thestarting and end points of the redeposition area, and r is the dis-tance between the sputtered and redeposited points. Note that /,U, and r must be calculated from the geometry of the substrate.The dashed line in Fig. 5 indicates that a sputtered atom cannotreach an obstructed surface. The reachability of a sputtered atommust be considered when R(x) is calculated.

Fig. 6 shows the redeposition effect for an ion beam millingsimulation when the beam is irradiated on a single spot. InFig. 6(a), the dashed line represents a surface milled by a Gauss-ian beam without redeposition, while the solid line includes theeffect of redeposition. Fig. 6(b) depicts the amount of redeposi-tion. Therefore, to accurately calculate the geometry, FIB millingmodels must incorporate the effect of redeposition. Furthermore,the amount of redeposition is location dependent, as shown inFig. 6(b).

2.3. Geometry evolution model via consecutive ion irradiation

The amount of sputtering and redeposition is linked in FIB mill-ing processes since both processes are affected by the surfacegeometry and vice versa. Therefore, a model that describes the

the redeposition model.

with and without redeposition effect, (b) amount of redeposition.

Table 1Simulation parameters.

Parameter Value

Ion species Ga+

Acceleration voltage (keV) 30Beam current (pA) 700Beam diameter (nm, FWHM) 60Beam overlap AdjustableTotal ion dose (ions/cm2) 1.0 � 1018

Dwell time (ls) AdjustableMachined area (lm) 5 � 5Substrate material Si

1 2 3 4 5 6 7

x 10-6

0

1

2

3

4

5

6

x 10-6

Dep

th [m

]

Width [m]

Considering bi-Gaussian, angle and redeposition effectsConsidering bi-Gaussian effects and angle effectsConsidering bi-Gaussian effects

Fig. 8. Comparison of simulation result considering beam incident angle andredeposition effects.

J. Han et al. / Microelectronic Engineering 87 (2010) 1–9 5

milling process mechanism must incorporate the interaction ofthese linked processes. To implement this requires a numericalprocedure that calculates the geometric modifications at eachbeam irradiation point on the raster.

After the beam hits the first point of the raster, the surface pro-file due to sputtering and the amount of redeposition on the rasterline (S1(x) and R1(x)) are given by Eqs. (3) and (5), respectively.Hence,

S1ðxÞ ¼Df

g� yðxÞ � we

� ðx�pþaÞr1ffiffi2p

h i2

þ ð1�wÞe� ðx�pþaÞ

r2ffiffi2p

h i20@

1A ð6Þ

R1ðxÞ ¼ KZ L

0S1ðxÞ

cos u cos Ur

dx ð7Þ

Although sputtering and redeposition occur simultaneously, thetwo profiles are calculated sequentially for the sake of computa-tional convenience. The values of /, U, and r used in Eq. (7) are ob-tained from Eq. (6). The resultant surface profile height, P1(x),considering both sputtering and redeposition, is

P1ðxÞ ¼ S1ðxÞ þ R1ðxÞ ð8Þ

Similarly, the sputtering amount S2(x) resulting from the beamhitting the second position of the raster (i = 2) is

S2ðxÞ ¼Df

g� yðxÞ � we

� ðx�2pþaÞr1ffiffi2p

h i2

þ ð1�wÞe� ðx�2pþaÞ

r2ffiffi2p

h i20@

1A ð9Þ

Likewise, the redeposition R2(x) is

Sputtering yield parameter (Eq. 4)

Redeposition

Iteration (i,

Final geometry

Surf

ace

evol

utio

n

Basic input

Sputtering

Superposition of bi-GauIncident angle ef

Fig. 7. Flow chart of the s

R2ðxÞ ¼ KZ L

0S2ðxÞ

cos u cos Ur

dx ð10Þ

where the values of /, U, and r are determined by the surface profileheight P1(x) + S2(x). The resultant surface profile height at i = 2 is

P2ðxÞ ¼ P1ðxÞ þ S2ðxÞ þ R2ðxÞ ð11Þ

After a single pass is finished (i.e., i = n) the final surface profileheight for the entire raster scan line is

PnðxÞ ¼ Pn�1ðxÞ þ SnðxÞ þ RnðxÞ ð12Þ

Because the geometric evolution is highly dependent on the his-tory of the beam radiation, it is difficult to estimate the surfaceprofile by a single equation. Therefore, it is appropriate to use anumerical simulation to calculate the surface profile.

FIB milling parameter (Eq. 1)

(Eq. 7)

Ns)

(Eq. 12)

parameters

Surf

ace

prof

ile (

Eq.

8)

(Eq. 6)

ssian beam (Eq. 3)fect (Eq. 4)

imulation procedure.

6 J. Han et al. / Microelectronic Engineering 87 (2010) 1–9

The number of scan frames (Ns) determined by the dwell time,overlap, and ion dose must all be considered in the superpositionof the beam shape since the milling process repeatedly executesthe scanning procedure, moving one step at a time until reachingthe total ion dose at each target (except in the single passmethod).

Fig. 9. Surface evolution simulation. (a) Beam irradiation points, (b–e) surface

The number of scan frames is calculated by dividing the totalion dose by the ion dose at a single spot. By obtaining the numberof scan frames and applying the ion dose to each scan frame, theproposed model can precisely determine the effect of redepositionand the angle dependency of the sputtering yield, together withthe superposition of the bi-Gaussian beam.

evolution during two layer milling process with three irradiation points.

Fig. 10. Surface evolution simulation. (a) Beam irradiation points, (b–e) Surface evolution during two layer milling process with ten irradiation points.

J. Han et al. / Microelectronic Engineering 87 (2010) 1–9 7

3. Simulation and experimental verification

3.1. Simulation of pattern fabrication using an FIB milling process

A computer simulation program for predicting the geometry ofnanopatterns was designed on the basis of the FIB milling model

discussed in the previous section. The simulation parameters of areal FIB system (SMI3050, SII Nanotechnology) were implementedto provide an experimental verification of the computer program.Table 1 summarizes the simulation parameters and their values.

In the simulation model, the pattern area was considered to be amatrix domain divided into two-dimensional rectangular meshes,

-10 -8 -6 -4 -2 0

0

200

400

600

800

1000

1200

1400

Patte

rn h

eigh

t [nm

]

Overlap

Experimental results Simulation results

Fig. 12. Results of the experimental and simulated nanopattern fabrication: patternheight with respect to overlap values.

8 J. Han et al. / Microelectronic Engineering 87 (2010) 1–9

with cell sizes of 0.5 nm � 0.5 nm or smaller. The mesh size wasdetermined by considering the lattice parameter (about0.439 nm) and the sputtering yield (three or more when bom-barded by 30 keV Ga+ ions) of silicon. Using the matrix properties,each point could be computed by reading the matrix data stored intemporary variables. The surface evolution algorithm proceeded byupdating the front position of the nodes using a Z-map. The calcu-lation of the curvature angle for the surface evolution was deter-mined up to a discrete increment of a point. Some error may beintroduced, especially adjacent to a region of a singularity or aninflection point, due to the finite size effect [22,23]. Unrealistic cur-vature angles may also result in errors, such as loop, swallowtailand rarefaction; smoothing is necessary to obtain a more accuratesimulation. Numerical analyses designed to compensate for thisunrealistic angle typically apply the average angle to the adjacentregion of a point after each procedure, rather than using surfacesmoothing. In such analyses, this method is practical, and yieldsreliable and stable results.

Fig. 7 provides a flow chart of the simulation procedure. Theprocedure was divided into a basic input parameter step and a sur-face evolution step. Basic input parameters were divided into twogroups. The first group comprised input data for calculating thesputtering yield and the angular dependence of the sputteringyield, S(h), namely the acceleration voltage affecting the equationsrelated to the irradiated ions and the target material. The secondgroup consisted of data pertaining to the FIB milling parameters,such as the beam diameter, beam current, ion dose, dwell time,and overlap; these data affect the equations related to the numberof scan frames, ion dose per single frame, and beam pitch.

The quantity of irradiated ions, beam pitch, and sputtering yieldwere calculated from the basic input parameters. These valueswere used in the surface evolution step, in which the superpositionof the bi-Gaussian beam and the effects of the incident angle wereconsidered, followed by the effect of redeposition on the givengeometry. These procedures were repeated up to a set number ofscan frames.

Fig. 8 depicts the contribution of each modeling element to thewhole simulation procedure. The simulation conditions are as inTable 1, and an overlap value of (�7) was used. The thin solid linerepresents the machined surface profile that results when onlybeam superposition is considered in the model. As shown, the pat-tern height was 460 nm. Because the incident angle effect was notconsidered, the sputtering yield was underestimated. The dashedline represents the case in which the incident angle effect is con-sidered; here the estimated pattern height was 1950 nm. In thiscase, the estimated pattern height was higher than the actualmachining result because the pattern filling effect of the redeposi-tion was not accounted for. When all the model elements discussedin Section 2 were combined, the estimated pattern height was1040 nm (thick solid line in the figure), which is between the val-

(a) (b)

1 2 3 4 5 6 7x 10-6

0

1

2

34

5

6

x 10-6

Dep

th [m

]

Width [m]

Fig. 11. Comparison of the simulated and the experimental results (overlap: �7,

ues obtained for the other cases. The results of this simulation willbe verified in next subsection.

Fig. 9 illustrates the simulation process in detail. Fig. 9(a) showsthe ion beam intensity at each irradiation position. The exposedareas near each beam location were superposed. Fig. 9(b)–(e)shows the evolution of the surface when the beam was scannedas in Fig. 9(a). The first plot in Fig. 9(b) represents the generationof the first spot. Fig. 9(c) shows the generation of the second spot.The spot generated by the first beam position was modified by thebeam overlapping and redeposition. Fig. 9(e) shows that the firstspot was irradiated again when the second frame was machined.Repeating these simulation steps generates the final pattern shape.

Fig. 10 shows a case where the overlap value is small enough togenerate a flat surface. As can be seen in the figure, although thebeam scanning pitch had an interval (see Fig. 10(a)), the interactionbetween the overlap, the incident angle effects, and the redeposi-tion resulted in the generation of a flat surface (see Fig. 10(e)).

3.2. Experimental verification

The patterning simulation results were compared to experi-mental results to verify the mathematical model. Fig. 11(a) showsthe simulation results, while Fig. 11(b) shows a cross-sectional im-age of the pattern machined under the same conditions used forthe simulation. An overlap of (�7) and a beam current of 700 pAwere used. A 1.5 lm-thick carbon layer was deposited on the ma-chined pattern for better image contrast and protection. As shown

(c)

beam current: 700 pA). (a) Simulation result, (b and c) experimental result.

J. Han et al. / Microelectronic Engineering 87 (2010) 1–9 9

in Fig. 11(b), the machined pattern height was 1115 nm, while thesimulated depth was 1040 nm. The experimental pattern width(FWHM) was 300 nm, while the simulated width was 320 nm, asshown Fig. 11(c). The simulated pattern shape also agreed wellwith the experimental results.

By using the proposed simulation, the pattern height with re-spect to overlap value can be predicted. Fig. 12 compares the nano-pattern height predicted by proposed simulation and theexperimental results at various overlap values. As can be seen,the simulation result successfully predicts pattern heights. Thepattern height decreased as the beam irradiation points becomecloser. For a given beam condition, if the overlap value was greaterthan �2 the pattern height became almost zero which means thesurface turned out to be flat.

4. Conclusions

We conducted a comprehensive investigation of FIB milling. Themain factors influencing FIB milling are the superposition of the bi-Gaussian distribution, the angle dependence of the sputteringyield, and the redeposition effect. Nanopattern features in siliconwere simulated to verify a mathematical model incorporatingthese factors. With an overlap of (�7), a beam current of 700 pA,a beam diameter of 70 nm, and an ion dose of 1.0 � 1018 ions/cm2, the experimental pattern height was 1115 nm, whichmatched well to the simulation result of 1040 nm. The patternheight decreased as the overlap increased. For overlap valuesgreater than (�2), a pattern shape did not form due to the effectsof the incident angle and redeposition together with superpositionof the ion beam profile. The results of the simulations were consis-tent with the experimental results for various overlap values. Thepattern height was unaffected by the dwell time variations. Simu-lations based on this model are thus capable of modeling the fab-rication of various shapes. The modeling and simulations could bemade more precise and controllable by using a detailed form of theion beam profile. Future research will address three-dimensionalfabrication, which could be accomplished by employing the pro-

posed milling model to calculate and apply an inverse simulationof the amount of beam irradiation for each spot.

Acknowledgment

This research was supported by the Next Generation New Tech-nology Development Program funded by Ministry of KnowledgeEconomy (MKE), Republic of Korea.

References

[1] P. Kitslaar, M. Strassner, I. Sagnes, E. Bourhis, X. Lafosse, C. Ulysse, C. David, R.Jede, L. Bruchhaus, J. Gierak, Microelectron. Eng. 83 (2006) 811.

[2] K. Arshak, M. Mihov, S. Nakahara, A. Arshak, D. McDonagh, Jpn. Microelectron.Eng. 39 (2005) 78.

[3] W. Li, S. Dimov, G. Lalev, Microelectron. Eng. 84 (2007) 829.[4] L.A. Giannuzzia, F.A. Stevieb, Micron 30 (1999) 197.[5] S. Arscott, D. Troadec, Nanotechnology 16 (2005) 2295.[6] Y. Fu, Microelectron. Eng. 56 (2001) 333.[7] T. Morita, K. Watanabe, R. Kometani, K. Kanda, Y. Haruyama, T. Kaito, J.-I.

Fujita, M. Ishida, Y. Ochial, T. Tajima, S. Matsui, Jpn. J. Appl. Phys. 42 (2003)3874.

[8] R. Nassar, M. Vasile, W. Zhang, J. Vac. Sci. Technol. B 16 (1998) 109.[9] M.J. Vasile, J. Xie, R. Nassar, J. Vac. Sci. Technol. B 17 (1999) 2085.

[10] T. Ishitani, T. Ohnishi, J. Vac. Sci. Technol. A 9 (1991) 3084.[11] G. Ben Assayag, C. Vieu, J. Gierak, P. Sudraud, A. Corbin, J. Vac. Sci. Technol. B 11

(1993) 2420.[12] A.A. Tseng, J. Micromech. Microeng. 14 (2004) R15.[13] T. Tsvetkova, S. Takahashi, A. Zayats, P. Dawson, R. Turner, L. Bischoff, O.

Angelov, D. Dimova-Malinovska, Vacuum 79 (2005) 94.[14] S. Cabrini, A. Carpentiero, R. Kumar, L. Businaro, P. Candeloro, M. Prasciolu, A.

Gosparini, C. Andreani, M. De Vittorio, T. Stomeo, And E. Di Fabrizio,Microelectron. Eng. 78–79 (2005) 11.

[15] Y. Yamamura, Y. Itakawa, N. Itoh, Institute of Plasma Physics, IPPJ-AM-26,Nagoya University, Nagoya, Japan, 1983.

[16] J. Orloff, Handbook of Charged Particle Optics CRC Press, Boca Raton, FL, 1997.[17] L. Bischoff, J. Teichert, V. Heera, Appl. Surf. Sci. 184 (2001) 372.[18] C. Lehrer, L. Frey, S. Petersen, H. Ryssel, J. Vac. Sci. Technol. B 19 (2001) 2533.[19] R.L. Kubena, J.W. Ward, Appl. Phys. Lett. 51 (1987) 1960.[20] D.P. Adams, M.J. Vasile, J. Vac. Sci. Technol. B 24 (2006) 836.[21] <http://www.SRIM.org>.[22] E. Platzgummer, A. Biedermann, H. Langfischer, S. Eder-Kapl, M. Kuemmel, S.

Cernusca, H. Loeschner, C. Lehrer, L. Frey, A. Lugstein, E. Bertagnolli,Microelectron. Eng. 83 (2006) 936.

[23] H.-B. Kim, G. Hobler, A. Lugstein, E. Bertagnolli, J. Micromech. Microeng. 17(2007) 1178.