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Semiconductor Manufacturing Automation References 925

lems, and report them to the quality engineers. R2R

control intelligently adapts process control parameters

based on in situ measurements from process sensors.

The response models between the measurement and

control parameters are dynamic, nonlinear, multiple-

input multiple-output (MIMO), and uncertain [52.30].

Therefore, advanced stochastic or statistical functional

models and algorithms, or neural networks are used.

An equipment engineering system (EES) is for tool

vendors to remotely monitor process control of tools

at fabs and tune process parameters. It is intended

to reduce the initial ramp-up period and cost. Tool

vendors cannot keep high-class engineers at customer

sites for long periods, for instance, even more than

6months. Another automation technology for qual-

ity is e-Diagnostics, which enables tool vendors in

remote locations to detect an anomaly in tools in

production at fabs quickly. It can prevent or reduce

production of defective wafers and reduce the lead

time to dispatch tool engineers to customer sites.

Tool vendors and SEMI have developed EES and e-

Diagnostics technologies and standards, including data

standards, security control, remote control or manipula-

tion, etc. [52.31].

52.5 Conclusion

Semiconductor manufacturing fabs have extensively

developed and implemented state-of-the-art industrial

automation technologies. We have brieﬂy reviewed

them in this Chapter. There remain many challenges

for the future, such as for 450 mm fabs. Future

fabs for manufacturing nanodevices may require quite

new concepts of equipment and material handling,

and hence new automation technologies. Concepts,

technologies, and practices of semiconductor manufac-

turing automation can give insights into automation

of other manufacturing industries or service sys-

tems.

References

52.1 C. Haris: Automated material handling system. In:

Semiconductor Manufacturing Handbook,ed.by

H. Geng (McGraw-Hill, New York 2005) pp. 32.1–

32.11

52.2 S. Venkatesh, R. Davenport, P. Foxhoven, J. Nul-

man: A steady-state throughput analysis of cluster

tools: Dual-blade versus single-blade robots,

IEEE Trans. Semicond. Manuf. 10(4), 418–424

(1997)

52.3 J.-H. Paek, T.-E. Lee: Operating strategies of cluster

tools with intermediate buffers, Proc. 7th Annu.

Int. Conf. Ind. Eng. (2002) pp. 1–5

52.4 C. Jung: Stedy State Scheduling and Modeling of

Multi-Slot Cluster Tools. M. Sc. Thesis (Department

of Industrial Engineering, KAIST 2006)

52.5 H.L. Oh: Conﬂict resolving algorithm to improve

productivity in single-wafer processing, Proc. Int.

Conf. Model. Anal. Semicond. Manuf. (MASM)

(2000) pp. 55–60

52.6 H.J. Yoon, D.Y. Lee: Real-time scheduling of wafer

fabrication with multiple product types, Proc. IEEE

Int. Conf. Syst. Man Cybern. (1999) pp. 835–840

52.7 T.-E. Lee, H.-Y. Lee, S.-J. Lee: Scheduling a wet

station for wafer cleaning with multiple job ﬂows

and multiple wafer-handling robots, Int. J. Prod.

Res. 45(3), 487–507 (2007)

52.8 T.-E. Lee, M.E. Posner: Performance measures and

schedules in periodic job shops, Oper. Res. 45(1),

72–91 (1998)

52.9 T.-E. Lee: Stable earliest starting schedules for pe-

riodic job shops: a linear system approach, Int. J.

Flex.Manuf.Syst.12(1), 59–80 (2000)

52.10 T.-E. Lee, R. Sreenivas, H.-Y. Lee: Workload bal-

ancing for timed event graphs with application to

cluster tool operation, Proc. IEEE Int. Conf. Autom.

Sci. Eng. (2006) pp. 1–6

52.11 J.-H. Kim, T.-E. Lee, H.-Y. Lee, D.-B. Park:

Scheduling of dual-armed cluster tools with time

constraints, IEEE Trans. Semicond. Manuf. 16(3),

521–534 (2003)

52.12 T. Murata: Petri nets: properties, analysis and ap-

plications, Proc. IEEE 77(4), 541–580 (1989)

52.13 Y.-H.Shin,T.-E.Lee,J.-H.Kim,H.-Y.Lee:Model-

ing and implementating a real-time scheduler for

dual-armed cluster tools, Comput. Ind. 45(1), 13–27

(2001)

52.14 T.-E. Lee, S.-H. Park: An extended event graph

with negative places and negative tokens for time

window constraints, IEEE Trans. Autom. Sci. Eng.

2(4), 319–332 (2005)

52.15 J.-H. Kim, T.-E. Lee: Schedule stabilization and

robust timing control for time-constrained clus-

Part F 52

926 Part F Industrial Automation

ter tools, Proc. IEEE Conf. Robot. Autom. (2003)

pp. 1039–1044

52.16 T.-E. Lee, H.-Y. Lee, Y.-H. Shin: Workload balanc-

ing and scheduling of a single-armed cluster tools,

Proc. Asian-Pac. Ind. Eng. Manag. Syst. Conf. (2004)

pp. 1–6

52.17 H.J. Kim: Scheduling and Control of Dual-Armed

Cluster Tools With Post Processes. M. Sc. The-

sis (Department of Industrial Engineering, KAIST

2006)

52.18 H.-Y. Lee, T.-E. Lee: Scheduling single-armed clus-

ter tools with reentrant wafer ﬂows, IEEE Trans.

Semicond. Manuf. 19(2), 224–240 (2006)

52.19 J.-S. Lee: Scheduling Rules for Dual-Armed Clus-

ter Tools With Cleaning Processes. M. Sc. Thesis

(Department of Industrial Engineering, KAIST 2008)

52.20 SEMI E38.1-95: Cluster tool module communica-

tion(CTMC), SEMI International Standards (2007)

52.21 J.-H. Lee, T.-E. Lee, J.-H. Park: Cluster tool mod-

ule communication based on a high-level ﬁeldbus,

Int. J. Comput. Integr. Manuf. 17(2), 151–170 (2004)

52.22 Y.-J. Joo, T.-E. Lee: A virtual cluster tool for testing

and verifying a cluster tool controller and a sched-

uler, IEEE Robot. Autom. Mag. 11(3), 33–49 (2004)

52.23 D.-Y. Liao, H.-S. Fu: A simulation-based, two-

phased approach for dynamic OHT allocation and

dispatching in large-scaled 300 mm AMHS man-

agement, Proc. IEEE Int. Conf. Robot. Autom. 4,

3630–3635 (2002)

52.24 D.-Y. Liao, H.-S. Fu: Speedy delivery-dynamic OHT

allocation and dispatching in large-scale, 300 mm

AMHS management, IEEE Robot. Autom. Mag. 11(3),

22–32 (2004)

52.25 J.S. Pettinato, D. Pillai: Technology decisions to

minimize 450-mm wafer size transition risk, IEEE

Tans. Semicond. Manuf. 18(4), 501–509 (2005)

52.26 D. Pillai: The future of semiconductor manufactur-

ing, IEEE Robot. Autom. Mag. 13(4), 16–24 (2006)

52.27 SEMI The international technology roadmap for

semiconductors (ITRS): an update, SEMI Eur. Stand.

Autumn Conf. (2006)

52.28 SEMI International Standards, SEMI (2007), CD-ROM

52.29 D. Krafzig, K. Banke, D. Slama: Enterprise SOA:

Service-Oriented Architecture Best Practices (Pren-

tice Hall, Upper Saddle River 2005)

52.30 J. Moyne, E. del Castillo, A.M. Hurwitz: Run-to-Run

Control in Semiconductor Manufacturing (CRC, New

York 2001)

52.31 H. Wohlwend: e-Diagnostics Guidebook: Revi-

sion 2.1 (Int. SEMATECH Manuf. Initiative, 2005),

http://www.sematech.org/docubase/abstracts/

4153deng.htm

Part F 52

927

Nanomanufac

53. Nanomanufacturing Automation

Ning Xi, King Wai Chiu Lai, Heping Chen

This chapter reports the key developments for

nanomanufacturing automation. Automated CAD

guided nanoassembly can be performed by an

improved atomic force microscopy (AFM). Al-

though CAD guided automated manufacturing

has been widely studied in the macro-world,

nanomanufacturing is challenging. In nano-

environments, the nanoobjects are usually

distributed on a substrate randomly, so the

nanoenvironment and the available nanoobjects

have to be modeled in order to design a feasible

nanostructure. Because of the positioning errors

due to the random drift, the actual position of

each nanoobject has to be identiﬁed by our lo-

cal scanning method. The advancement of AFM

increases the efﬁciency and accuracy to manip-

ulate and assemble nanoobjects. Besides, the

manufacturing process of carbon nanotube (CNT)

based nanodevices is discussed. A novel auto-

mated manufacturing system has been especially

designed for manufacturing nanodevices. The

system integrates a new dielectrophoretic (DEP)

microchamber into a robotic based deposition

workstation and increases the yield to form

semi-conducting CNTs for manufacturing nano-

devices. Therefore, by using the proposed CNT

separation and deposition system, CNT based

53.1 Overview.............................................. 927

53.2 AFM-Based Nanomanufacturing............. 930

53.2.1 Modeling of the Nanoenvironments 930

53.2.2 Methods

of Nanomanipulation Automation. 930

53.2.3 Automated Local Scanning Method

for Nanomanipulation Automation 935

53.2.4 CAD Guided Automated

Nanoassembly ............................ 937

53.3 Nanomanufacturing Processes ............... 937

53.3.1 Dielectrophoretic Force

on Nanoobjects........................... 938

53.3.2 Separating CNTs

by an Electronic Property

Using the Dielectrophoretic Effect.. 939

53.3.3 DEP Microchamber

for Separating CNTs...................... 939

53.3.4 Automated Robotic CNT Deposition

Workstation................................ 940

53.3.5 CNT-Based Infrared Detector ......... 944

53.4 Conclusions.......................................... 944

References .................................................. 944

nanodevices with speciﬁc and consistent

electronic properties can be manufactured

automatically and effectively.

53.1 Overview

Nanoscale materials with unique mechanical, elec-

tronic, optical, and chemical properties have a variety

of potential applications such as nanoelectromechanical

systems (NEMS) and nanosensors. The development

of nanoassembly technologies will potentially lead to

breakthroughs in manufacturing new revolutionary in-

dustrial products. The techniques for nanoassembly

can be generally classiﬁed into bottom-up and top-

down methods. Self-assembly in nanoscale is reported

as the most promising bottom-up technique, which is

applied to make regular, symmetric patterns of na-

noentities. However, many potential nanostructures and

nanodevices are asymmetric, which cannot be manu-

factured using self-assembly only. A top-down method

would be desirable to fabricate complex nanostruc-

tures.

Part F 53

928 Part F Industrial Automation

The semiconductor fabrication technique is a ma-

tured top-down method, which has been used in the fab-

rication of microelectromechanical systems (MEMS).

However, it is difﬁcult to build nanostructures using this

method due to limitations of the traditional lithogra-

phy. Although smaller features can be made by electron

beam nanolithography, it is practically very difﬁcult

to position the feature precisely using e-Beam nano-

lithography. The high cost of the scanning electron

microscopy (SEM), ultrahigh vacuum condition, and

space limitation inside the SEM vacuum capsule also

impede its wide application.

Atomic force microscopy (AFM) [53.1] has proven

to be a powerful technique to study sample surfaces

downto the nanoscale. It can work with both conductive

and insulating materials and in many conditions, such

as air and liquid. Not only can it characterize sample

surfaces, it can also modify them through nanolithog-

raphy [53.2, 3] and nanomanipulation [53.3, 4], which

is a promising nanofabrication technique that combines

top-down and bottom-up advantages. In recent years,

many kinds of AFM-based nanolithographies have been

implemented on a variety of surfaces such as semicon-

ductors, metals, andsoft materials [53.5–8].A variety of

AFM-based nanomanipulation schemes have been de-

veloped to position and manipulate nanoobjects [53.9–

13]. However, nanolithography itself can hardly be

considered as sufﬁcient for fabrication of a com-

plete device. Thus, manipulation of nanoobjects has

to be involved in order to manufacture nanostructures

and nanodevices. The AFM-based nanomanipulation is

much more complicated and difﬁcult than the AFM-

based nanolithography because nanoobjects have to be

manipulated from one place to another by the AFM tip,

and sometimes it is necessary to relocate the nanoob-

jects during nanomanipulation while nanolithography

can only draw patterns. Since the AFM tip as the ma-

nipulation end-effector can only apply a point force on

a nanoobject, the pushing point on the nanoobject has

to be precisely controlled in order to manipulate the

nanoobjects to their desired positions. In the most re-

cently available AFM-based manipulation methods, the

manipulation paths are obtained either manually using

haptic devices [53.9, 10] or in an interactive way be-

tween theusers and the atomic force microscope (AFM)

images [53.11,12]. The main problem of these schemes

is their lack of real-time visual feedback, so an aug-

mented reality interface has been developed [53.14,15].

But positioning errors due to deformation of the can-

tilever and random drift such as thermal drift cause

the nanoobjects to be easily lost or manipulated to

wrong places during manipulation; the result of each

operation has to be veriﬁed by a new image scan

before the next operation starts. This scan-design-

manipulation-scan cycle is usually time consuming and

inefﬁcient.

In order to increase the efﬁciency and accuracy

of AFM-based nanoassembly, automated CAD guided

nanoassembly is desirable [53.16]. In the macroworld,

CAD guided automated manufacturing has been widely

studied [53.17]. However, it is not a trivial extension

from the macroworld to the nanoworld. In the nanoenvi-

ronments, the nanoobjects,which includenanoparticles,

nanowires, nanotubes, etc., are usually distributed on

a substrate randomly. Therefore, the nanoenvironment

and the available nanoobjects have to be modeled

in order to design a feasible nanostructure. Because

manipulation of nanoparticles only requires transla-

tion, while manipulation of other nanoobjects such as

nanowires involve both translation and rotation, manip-

ulation of nanowires is more challenging than that of

nanoparticles. To generate a feasible path to manipulate

nanoobjects, obstacle avoidance must also be consid-

ered. Turns around obstacles should also be avoided

since they may cause the failure of the manipulation.

Because of the positioning errors due to the random

drift, the actual position of each nanoobject must be

identiﬁed before each operation.

Beside, the deformation of the cantilever caused by

manipulation force is one of the most major nonlineari-

ties and uncertainties. It causes difﬁculties in accurately

controlling the tip position, and results in missing the

position of the object. The softness of the conventional

cantilevers also causes the failure of manipulation of

sticky nanoobjects because the tip can easily slip over

the nanoobjects. An active atomic force microscopy

probe is used as an adaptable end effector to solve these

problems by actively controlling the cantilever’s ﬂex-

ibility or rigidity during nanomanipulation. Thus, the

adaptable end effector is controlled to maintain straight

shape during manipulation [53.18].

Apart from nanoassembly, manufacturing process

of nanodevices is important. Carbon nanotube (CNT

)

has been investigated as one of the most promising can-

didates to be used for making different nanodevices.

CNTs have been shown to exhibit remarkable electronic

properties, such as ballistic transport and semiconduct-

ing behavior, which depend on their diameters and

chiralities. Recently, it was demonstrated that CNTs

can be used to build various types of devices such as

nanotransistors [53.19], logic devices [53.20], infrared

detectors [53.21, 22], light emitting devices [53.23],

Part F 53.1

Nanomanufacturing Automation 53.1 Overview 929

chemical sensors [53.24, 25], etc. The general man-

ufacturing processes of CNT-based devices is shown

in Fig.53.1. The most challenging parts include CNT

selection, deposition, and assembly. Basically, CNT

assembly can be done by our AFM-based nanoma-

nipulation system [53.26]. With the advancement of

our automated local scanning method for AFM sys-

tems [53.27], automated assembly for CNT-based

devices can be done effectively. However, electronic

properties of CNTs vary and CNTs can beclassiﬁed into

two types: semiconducting CNTs and metallic CNTs.

Therefore, an automatic method for the selection and

deposition of a single CNT with a speciﬁc electronic

property should be established [53.28,29].

Selection of a CNT with the desired electronic

property is crucial to its application. Basically, sev-

eral approaches have been pursued to separate different

electronic types of CNTs. Arnold et al. demonstrated

that semiconducting CNTs and metallic CNTs were

separated by using some encapsulating agents or sur-

factants [53.30]. Besides, Avouris et al. demonstrated

turning a metallic CNT into a semiconducting CNT

after removal of metallic carbon shells by an electri-

cal breakdown process [53.31]. Krupke et al. reported

a technique to enrich metallic CNT thin ﬁlm. They

demonstrated that metallic CNTs were concentrated on

a substrate by using dielectrophoresis[53.32,33]. Based

on the review of these CNT separation techniques,

we develop a microchamber to ﬁlter different types of

CNTs effectively.

Various methods have been proposed to move and

deposit a CNT to the metal microelectrodes; this ad-

vances the manufacturing process of the CNT-based

nanodevices. A nanorobotic technique uses nanomanip-

ulators inside a scanning electron microscopy (SEM)to

perform the nanomanipulation. Since a sample cham-

ber of an SEM

is spacious, it is possible to put some

custom-design nanomanipulators inside the chamber.

Yu et al. put a custom piezoelectric vacuum manipula-

torinsidethechamberofanSEM, and they visually

observed the manipulation process of CNTs [53.34].

Dong et al. also developed a 16-degree-of-freedom

nanorobotic manipulator to characterize CNTs inside

an SEM system [53.35]. The idea of nanoassembly

inside SEM is promising, but it needs a vacuum en-

vironment for proper operation. Alternatively, electric

ﬁeld assisted methods have been proposed to manipu-

late and deposit CNTs directly. Green et al. introduced

AC electrokinetics forcesto manipulatesub-micrometer

particles on microelectrode structures [53.36]. Bundled

CNTs have also been manipulated by dielectrophoretic

CNT assembly

CNT deposition

Reliable

nanomanufactoring

process for

CNT-based devices

Semiconducting

CNT selection

Nanolithography

Substrate fabrication

Chip packaging

Band gap tuning

Chip design

Fig. 53.1 Flow chart of nanomanufacturing of CNT-based devices

(DEP) force [53.37, 38]. Moreover, Dong and Nel-

son reported the batch fabrication of CNT bearings

and transistors by assembling CNTs on a silicon chip

using DEP force [53.39, 40]. A fabricated chip was

immersed in a reservoir that contained CNT suspen-

sion, and CNTs were deposited on the microchip by

applying a composite AC/DC electric ﬁeld. This elec-

tric ﬁeld manipulation technique is an effective and

feasible method to batch manipulate CNTs manually.

However, an automated robotic system for mass pro-

duction of consistent CNT-based devices has not been

archived.

An automated nanomanipulation system is dis-

cussed in Sect.53.2. The collision-free paths are

generated based on the CAD model, the environment

model, and the model of the nanoobjects. A local

scanning method is developed to obtain the actual po-

sition of each nanoobject to compensate for the random

drift. Moveover, automatic nanoassembly of nanostruc-

tures using the designed CAD models is presented.

The nanomanufacturing process of CNT-based device

is discussed in Sect.53.3. The process includes the de-

velopment of a novel CNT separation system and an

automated deposition processes for both single-walled

carbon nanotubes (SWCNTs) and multi-walled carbon

nanotubes (MWCNTs).

Part F 53.1

930 Part F Industrial Automation

53.2 AFM-Based Nanomanufacturing

In recent years, many kinds of nanomanipulation

schemes have been developed to manipulate nanoob-

jects. A nanorobotic technique uses nanomanipulators

inside an SEM to perform the nanomanipulation [53.34,

35]. The idea of nanoassembly inside SEM is promis-

ing, but it needs a vacuum environment for proper

operation. AFM is a promising tool for nanomanu-

facturing [53.12, 41]. Nanoobjects were manipulated

by an AFM tip to build nanostructures and devices

effectively because of its high resolution. Besides, it

does not need to work in a vacuum environment,

which allows more freedom in the nanomanufacturing

process. In order to use AFM for nanomanufactur-

ing, further studies and improvements have been done.

Since nanoobjects are usually distributed on a sub-

strate randomly in the nanoworld, the nanoenvironment

and the nanoobjects must be modeled in order to de-

sign a feasible nanostructure. In order to manipulate

nanoobjects automatically, obstacle avoidance must be

considered to generate a feasible path to manipulate

nanoobjects. Because of positioning errors due to the

random drift, the actual position of each nanoobject

must be identiﬁed before each operation; this correc-

tion can be done by our local scanning method. In order

to increase the efﬁciency and accuracy of AFM-based

nanoassembly, automatedCAD guidednanoassembly is

desirable.

53.2.1 Modeling of the Nanoenvironments

Because the nanoobjects are randomly distributed on

a surface, the positionof each nanoobject must be deter-

mined inorder to perform automatic manipulation. Also

the nanoobjects have different shapes, such as nanopar-

ticles and nanowires, as shown in Fig. 53.2. They must

be categorized before manipulation because the manip-

ulation algorithms for these nanoobjects are different.

After an AFM image is obtained, the nanoobjects

can be identiﬁed and categorized. The X, Y coordinates

and the height information of each pixel can be obtained

from the AFMscanning data. Becausethe height,shape,

and size of nanoobjects are known, they are used as

criteria to identify nanoobjects and obstacles based on

a fuzzy method as follows. Firstly, all pixels higher than

a threshold height are identiﬁed. The shapes of clus-

tered pixels are categorized and compared withthe ideal

shapes of nanoobjects. If the shape of clustered pixels is

close to the ideal shape, the pixels are assigned a higher

probability (p

). Secondly, if the height of a pixel is

close to the ideal height of nanoobjects, a higher prob-

ability (p

) is assigned to it. Thirdly, the neighboring

pixels with higher probability (p

) are counted and

the area of the pixels is identiﬁed. If the area is close to

the size of nanoobjects, the pixels are assigned a higher

probability (p

). If theprobability (p

) of apixel is

higher than a threshold, it is in a nanoobject. Using the

neighboring relationship of pixels, objects can then be

identiﬁed. The length of a nanoobject can be calculated

by ﬁnding the long and short axes using a least squares

ﬁtting algorithm. If the length/width ratio is larger than

a set value, it is considered as a nanowire, otherwise, as

a nanoparticle.

53.2.2 Methods

of Nanomanipulation Automation

Since the AFM tip can only apply force to a point

on a nanoobject in AFM-based nanomanipulation, it is

very challenging to generate manipulation paths to ma-

nipulate nanoobjectsto a desired location, especially for

nanowires, because manipulation of nanoparticles only

requires translation, while that of nanowires involves

translation as well as rotation. Turns around obstacles

should be avoided since they may cause manipulation

failure. In the following sections, automated manipula-

tion of nanoparticles and nanowires, respectively, will

be discussed.

02468

2 µm

Nanoparticle

Nanowire

Fig. 53.2 Nanoobjects obtained from AFM scanning. The

scanning area is 8μm×8μm

Part F 53.2

Nanomanufacturing Automation 53.2 AFM-Based Nanomanufacturing 931

Fig. 53.3 The straight line connection between an object

and a destination. O1 and O2 are objects, D1 and D2 are

destinations, S1 is an obstacle

Automated Manipulation of Nanoparticles

Once the destinations, objects, and obstacles are deter-

mined, a collision-free path can be generated by the tip

path planner.

A direct path (straight path) is a connection from

an object to a destination using a straight line without

any obstacles or potential obstacles in between. Fig-

ure 53.3 shows the connections between objects and

destinations. The paths from O2 to D2 and from O1 to

D2 are direct paths, and the path between O1 and D1 is

not a direct path due to collision.

Due to the van der Waals force between an object

and an obstacle, the object may beattracted to the obsta-

cle if the distance between them is too small. Therefore,

the minimum distance has to be determined ﬁrst to

avoid the attraction. Figure 53.4ashowsa particleobject

and a particle obstacle, and Fig.53.4b a particle object

and a nanowire obstacle, respectively.

In the ﬁrst case, all objects and obstacles are as-

sumed to be spheres; the van der Waals force can be

expressed as [53.42]

−A

, (53.1)

where F

is the van der Waals force, A is the Hamaker

constant, D is the distancebetween the two spheres, and

and R

are the radii of the two spheres. For the sec-

ond case that the obstacle is a nanowire, the nanowire

can be considered as separated nanoparticles, so the

van der Waals force between a nanoparticle and each

separated nanoparticles can be calculated using (53.1).

Different materials have different Hamaker con-

stants. Nevertheless, the Hamaker constants are found

to lie in the range (0.4−4)×10

−19

J [53.42]. If an ob-

ject is not attracted to an obstacle, the van der Waals

force between an object and a destination has to be bal-

anced by the friction force between the object and the

surface. The friction force between the object and the

surface can be formulated as [53.43]

=μ

+νF

, (53.2)

Object Obstacle

Object

Nanowire

Fig. 53.4a,b The van der Waals force between objects and

obstacles. The objects are nanoparticles.

(a) The obstacle is

a nanoparticle. R

and R

are the radius of the two spheres

respectively, D isthe distance between the two spheres, F

is the van der Waals force,and F

the friction force.(b) The

obstacle is a nanowire. The nanowire can be considered as

a line of nanoparticles. R is the radius of the sphere

where F

is the friction force, μ

is the sliding friction

coefﬁcient between an object and the substrate surface,

ν is the shear coefﬁcient, F

is the repulsive force,

and F

is the adhesive force. When pushing an object,

the minimum repulsive force equals the adhesive force.

Then (53.2) becomes

=(μ

+ν)F

. (53.3)

The adhesive force F

can be estimated by [53.43]

, (53.4)

where A

is thenominal contact area between anobject

and a substrate surface, A

is the nominal contact area

between the AFM tip and the substrate surface, and F

is the measured adhesive force between the AFM tip

and the surface.

Since the van der Waals force must be balanced by

the friction force during manipulation, the minimum

distance D

min

can be calculated using (53.1), (53.3)and

(53.4)

min

(μ

+ν)A

. (53.5)

The distance between an object and a nanowire must

be larger than D

min

during manipulation. If there is an

Part F 53.2

932 Part F Industrial Automation

Fig. 53.5 (a) A path with turns. An object may be lost

during turns.

(b) A virtual object and destination (VOD)

connects an object and a destination. O1 is an object, D1 is

a destination, S1 is an obstacle, and V1 is a VOD

obstacle that is close or on the straight line, the path

formed by the straight line is not considered as a di-

rect path. For example, the path between O2 and D1

in Fig.53.3 is not a direct path due to the attraction.

After the direct paths are generated, objects are as-

signed to the destinations one to one. There are some

destinations that may not have any objects assigned to

them. This is because there are no direct paths to some

destinations. Therefore, indirect paths (curved paths) to

avoid the obstacles must be generated. In general, it is

possible to lose particles during nanomanipulation in

both direct paths or curved paths, but a curved path as

shown in Fig.53.5 has a much higher risk of losing ob-

jects than a direct path. The AFM-based manipulation

system can use force feedback to detect the lost particle

during the manipulation. A surface must be scanned

again if an object is lost during manipulation. Because

the scanning time is much longer than the manipulation

time, turns should be avoided during nanomanipula-

tion. To solve the problem, a virtual-object-destination

algorithm has been developed. Figure 53.6 shows

a virtual-object-destination (VOD).

An object and a destination are connected using

direct paths through a VOD. Since there are many pos-

sible VODs to connect an object and a destination,

a minimum distance criterion is applied to ﬁnd a VOD.

The total distance to connect an object and a destination

through a VOD is

d =

−x

)

+(y

−y

)

−x

)

+(y

−y

)

, (53.6)

Fig. 53.6 Two VODs connect an object with a destination.

O1 is an object, D1 is the destination, and S1 and S2 are

obstacles

where x

, y

are the coordinates of the center of a VOD,

, y

are the coordinates of the center of an object, and

, y

are the coordinates of the center of a destination.

The connections between the VOD, object and des-

tination have to avoid the obstacles, i.e.,

(x −x

)

+(y−y

)

≥ D

min



, (53.7)

where x, y are the coordinates of the object center along

the path and x

, y

are the coordinates of the center of

the obstacle. R



is deﬁned as



= R

. (53.8)

Then a constrained optimization problem is formu-

lated

min

d =

−x

)

+(y

−y

)

−x

)

+(y

−y

)

subject to:

(x −x

)

+(y−y

)

≥ D

min



(53.9)

This isa single objectiveconstrained optimization prob-

lem. A quadratic loss penalty function method [53.44]

is adopted to deal with the constrained optimization

problem by formulating a new function G(x)

min

G(x) = min

d +β(min[0, g])

, (53.10)

where β is a big scalar and g is formulated using the

given constraint, i.e.

g =

(x −x

)

+(y−y

)

−(D

min



) . (53.11)

Then the constrained optimization problem is trans-

ferred into an unconstrained one using the quadratic

loss penalty function method. The pattern search

method [53.45] is adopted here to optimize the uncon-

strained optimization problem to obtain the VOD.

Part F 53.2

Nanomanufacturing Automation 53.2 AFM-Based Nanomanufacturing 933

If one virtual object and destination cannot reach

an unassigned destination, two or more VODsmust

be found to connect an object and a destination. Fig-

ure 53.6 illustrates the process. Similarly, the total

distance to connect the object and destination can be

calculated. The constraint is the same as (53.9). Then,

a single objective constrained optimization problem can

be formulated to obtain the VODs.

Automated Manipulation of Nanowires

The manipulation of a nanowire is much more compli-

cated than that of a nanoparticle because there is only

translation during manipulation of a nanoparticle, while

there are both translation and rotation during manipula-

tion of a nanowire. A nanowire can only be manipulated

to a desired position by applying force alternatively

close to its ends. From an AFM image, nanowires can

be identiﬁed andrepresented bytheir radius andtwo end

points. Each end point on a nanowire must be assigned

to the corresponding point on the destination. The start-

ing pushing point is important since it determines the

direction along which the object moves. By choosing

a suitable step size, an AFM tip path can be gener-

ated. Therefore, the steps of automated manipulation

of nanowire are: ﬁnd the initial position and destination

of a nanowire, ﬁnd the corresponding points, ﬁnd start-

ing pushing point, and calculate the pushing step and

plan the tip trajectory. The details of the steps are given

below.

To automatically manipulate a nanowire, its behav-

ior under a pushing force has to be modeled. When

a pushing force is applied to a nanowire, the nanowire

starts to rotate around a pivot if the pushing force is

larger than the friction force. Figure 53.7 shows the

applied pushing force and the pivot. The nanowire ro-

tates around point D when it is pushed at point C by

the AFM tip. The nanowire under pushing may have

different kinds of behavior, which depend on its own

geometry property. If the aspect ratio of a nanowire is

deﬁned as

σ =d/L .

(53.12)

A nanowire with the aspect ratio of σ>25 usually

behaves like a wire, which will deform or bend un-

der pressure. The rotation behavior was observed for

nanowires with aspect ratio of σ<15. In this case,

the pushing force F from the tip causes the friction

and shear force F



= μ

F+νF

along the rod axis

direction when the pushing direction is not perpendic-

ular to the rod axis, where μ

and ν are the friction

and shear coefﬁcients between the tip and the nanowire,

Static point

Nanowire

a) b)

Fig. 53.7a,b The behavior of a nanowire under a pushing force:

(a) F is the applied external force, L is the length of the nanowire

(b) the detailed force model. D is the pivot where the nanowire

rotates, C is the pushing point

which depend on the material properties and the envi-

ronment, F

is the adhesion force between the tip and

the nanowire.

Fortunately, it is easy to prove that the force F



hardly causes the rod to move along the rod axis direc-

tion. Assuming that the shear forces between rod and

surface are equal along all directions during moving,

fL = f



max

d . (53.13)

Because the shear force is usually proportional to the

contact area, and the contact area between a nanowire

and surface is much greater than that between the tip

and the nanowire,

νF

 f



d . (53.14)

Also note that

F ≤ fL= f



max

d , (53.15)

and because μ is usually very small, ﬁnally it is reason-

able to assume that



d = F



μF+νF

< f



max

d . (53.16)

This means that the rod will have no motion along the

axis direction and, therefore, the static point D must

be on the axis of the nanowire. Considering the above

analysis, the nanowire can be simpliﬁed as a rigid line

segment. The external forces applied on the nanowire in

surface plane can be modeled as shown inFig.53.7. The

pivot D can be either inside the nanowire or outside the

nanowire. First assume that D is inside the nanowire.

In this case, all the torques around D are self-balanced

during smooth motion.

F(l−s) =

f(L −s)

, (53.17)

Part F 53.2

934 Part F Industrial Automation

Nanowire

(initial position)

Nanowire

(destination)

Fig. 53.8 The initial position of the nanowire and the destination

where it is manipulated

where F is the applied external force, f is the evenly

distributed friction and shear force density on the

nanowire, L is the length of the nanowire, s is the

distance from one end of the nanowire (point A

in Fig.53.7) to the pivot D, and l is the distance from

A to C, where the external force is applied. Equa-

tion (53.17) can be written as

F =

f(L −s)

+ fs

2(l−s)

(53.18)

The pivot can be found by minimizing F with respect to

s,i.e.

=0 ⇒ s

−2ls+lL−L

/2 =0 . (53.19)

Sincewehaveassumedthat0< s < L, a unique solu-

tion of the pivot for any 0 < l < L except l = L/2 can

be determined by

s =

⎧

⎨

⎩

−lL+L

/2 l < L/2

l−

−lL+L

/2 l > L/2

(53.20)

When l = L/2, there is no unique solution. A detailed

analysis will show that s can be any value when the

F, pushing point

Nanowire (destination)

Nanowire (initial position)

Starting position

End position

Fig. 53.9 The manipulation of a nanowire from an initial position to its destination

force F is applied in the exact middle of the rod, the

point T becomes a bifurcation point. Now, assume the

static point D is outside of rod and on the left side. Not-

ing that s < 0 now, the self-balanced torque equation

becomes

f(l−s) = fL(L/2−s) ,

(53.21)

namely

F =

fL(L/2−s)

2(l−s)

(53.22)

It can be seen that F can only be minimized at l = L/2

=0, for l = L/2 .

(53.23)

Similarly, ifstatic pointD ison theright side (s > 0), the

analysis results shouldbe the same. Practically, it is hard

to keep T at this bifurcation point (l = L/2). Therefore,

during manipulation, it is better to avoid pushing the

exact middle of the rod because it is hard to predict the

behavior of the rod in this case.

The corresponding points between a nanowire and

its destination have to be matched in order to plan a ma-

nipulation path. Figure 53.8 shows the initial position

and the destination of a nanowire. P

and P

are the

initial positions, and P

and P

are the destinations.

The nanowire rotates anti-clockwise and moves

downward if the starting pushing point is close to P

Similarly, the nanowire rotates clockwise and moves

upward if the starting pushing point is close to P

The starting pushing point can be determined by the

angle β as shown in Fig. 53.8.Ifβ>90

◦

, the starting

pushing point should be close to P

. Otherwise, P

Figure 53.9 shows the process to manipulate a nanowire

from its initial position to its destination. The manipu-

lation scheme of a nanowire has to go through a zigzag

strategy in order to position the nanowire with speciﬁed

orientation.

Part F 53.2