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Journal of Mechanical Science and Technology 25 (4) (2011) 977~985 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-011-0217-2 Design of a nano-printer based on AFPN (Active Fountain Pen Nano-lithography) using switch control Kyoil Hwang 1 , ChunYup Shin 1 , Rui Mingwu 1 , Suk-Han Lee 2 and Hun-mo Kim 1,* 1 School of Mechanical Engineering, SungKyunKwan University of Suwon, Gyounggi, Korea 2 School of Electrical Engineering, SungKyunKwan University of Suwon, Gyounggi, Korea (Manuscript Received May 11, 2010; Revised February 16, 2011; Accepted February 18, 2011) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract In this paper, the design and the construction analysis of an innovative nano-printer system are presented. A nano-printer system is comprised of automatic transmission parts and modified Active Fountain Pen Nano-lithography (AFPN) device. The patterning is made by a switch control method. For accurate control and fabrication of this device, the fluidic system is simplified by embedding a PZT (Lead Zirconate Titanate) plate in the nano-printer. And, without the cantilevers connecting the reservoir and tip, less energy loss is in- duced and the whole device becomes more sophisticated. In this paper, the critical channel size is decided for the whole simulation, and then the mechanical and piezoelectric properties of PZT are analyzed by the commercial software, ANSYS. The deformation of the PZT can be controlled precisely. Based on the analysis of the fluidic dynamics of this system, the line width of the pattern was found to de- pend on the mass of the meniscus formed at the tip. As long as the initial mass of the meniscus is set, the maximum patterning speed can be determined as well. Consequently the printing velocity of this system can be increased considerably beyond that of DPN (Dip- Pen Nano-lithography) or FPN (Fountain Pen Nano-lithography) because the mass of meniscus can be controlled by the applied voltage. Keywords: AFPN (Active Fountain Pen Nano-lithography); Nano-printer; PZT; Printing velocity ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Due to the rapid progress in information technology during the past few decades, micro- and nanotechnology has been used for various applications in realms such as semiconduc- tors, military, biology, electronics and information and com- munications. Among these applications, the design and manu- facture of three dimensional microstructures have received much attention. The LIGA (Lithographie, Galvanoformung, Abformung) manufacturing process, which uses wet etching, dry etching, plasma etching and the X-ray produced by the radioactive ray accelerator, has been developed and used. The technologies for the manufacture of micrometer sized three dimensional structures are known as NEMS (Nano Electronic Mechanical Systems), which can even produce nanometer sized manufactured goods [1]. Present studies have stated that DPN (Dip-Pen Nano-lithography) [2], acknowledged to be the best nano-scale patterning method, has a limit in the amount of ink formed on the tip surface and has to frequently re-ink and re-position its probe when the ink is exhausted during patterning. To compensate for this disadvantage, FPN (Foun- tain Pen Nano-lithography) was developed. With channels embedded along the cantilevers and the appended reservoir, the FPN approach can realize continuous patterning. But it still can not control the initial mass of the meniscus. The me- niscus of the ink formed at the tip has an important effect on the patterning speed [3, 4]. In order to improve the patterning performance, AFPN using an active pumping method was developed [5, 6]. There is a flexible membrane part inside the AFPN system that controls the initial mass of the meniscus by only using mechanical force to efficiently control the length between the lines and to increase the patterning speed. How- ever, the actual commercialization of this method has been limited due to the localization of parts designs. Moreover, the AFPN device is very difficult to manufacture because of its complex structures. Therefore, it is imperative to develop a device with improved patterning speed that can be easily fab- ricated for commercialization. Accordingly, a novel design of a nano printer based on the AFPN is presented. In this paper, the design and the construc- tion of this nano printer are discussed in detail. The nano printer system is comprised of a reservoir, a PZT plate and transmission parts. The PZT plate works as a switch to control the outlet flow because of its deformability by the supply volt- This paper was recommended for publication in revised form by Associate Editor In-Ha Sung * Corresponding author. Tel.: +82 31 290 7500, Fax.: +82 31 290 7666 E-mail address: [email protected] © KSME & Springer 2011

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Page 1: Design of a nano-printer based on AFPN (Active Fountain ... · PDF fileDesign of a nano-printer based on AFPN (Active Fountain Pen Nano-lithography) ... a novel design of a nano printer

Journal of Mechanical Science and Technology 25 (4) (2011) 977~985

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-011-0217-2

Design of a nano-printer based on AFPN

(Active Fountain Pen Nano-lithography) using switch control† Kyoil Hwang1, ChunYup Shin1, Rui Mingwu1, Suk-Han Lee2 and Hun-mo Kim1,*

1School of Mechanical Engineering, SungKyunKwan University of Suwon, Gyounggi, Korea 2School of Electrical Engineering, SungKyunKwan University of Suwon, Gyounggi, Korea

(Manuscript Received May 11, 2010; Revised February 16, 2011; Accepted February 18, 2011)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract In this paper, the design and the construction analysis of an innovative nano-printer system are presented. A nano-printer system is

comprised of automatic transmission parts and modified Active Fountain Pen Nano-lithography (AFPN) device. The patterning is made by a switch control method. For accurate control and fabrication of this device, the fluidic system is simplified by embedding a PZT (Lead Zirconate Titanate) plate in the nano-printer. And, without the cantilevers connecting the reservoir and tip, less energy loss is in-duced and the whole device becomes more sophisticated. In this paper, the critical channel size is decided for the whole simulation, and then the mechanical and piezoelectric properties of PZT are analyzed by the commercial software, ANSYS. The deformation of the PZT can be controlled precisely. Based on the analysis of the fluidic dynamics of this system, the line width of the pattern was found to de-pend on the mass of the meniscus formed at the tip. As long as the initial mass of the meniscus is set, the maximum patterning speed can be determined as well. Consequently the printing velocity of this system can be increased considerably beyond that of DPN (Dip- Pen Nano-lithography) or FPN (Fountain Pen Nano-lithography) because the mass of meniscus can be controlled by the applied voltage.

Keywords: AFPN (Active Fountain Pen Nano-lithography); Nano-printer; PZT; Printing velocity ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

Due to the rapid progress in information technology during the past few decades, micro- and nanotechnology has been used for various applications in realms such as semiconduc-tors, military, biology, electronics and information and com-munications. Among these applications, the design and manu-facture of three dimensional microstructures have received much attention. The LIGA (Lithographie, Galvanoformung, Abformung) manufacturing process, which uses wet etching, dry etching, plasma etching and the X-ray produced by the radioactive ray accelerator, has been developed and used. The technologies for the manufacture of micrometer sized three dimensional structures are known as NEMS (Nano Electronic Mechanical Systems), which can even produce nanometer sized manufactured goods [1]. Present studies have stated that DPN (Dip-Pen Nano-lithography) [2], acknowledged to be the best nano-scale patterning method, has a limit in the amount of ink formed on the tip surface and has to frequently re-ink and re-position its probe when the ink is exhausted during

patterning. To compensate for this disadvantage, FPN (Foun-tain Pen Nano-lithography) was developed. With channels embedded along the cantilevers and the appended reservoir, the FPN approach can realize continuous patterning. But it still can not control the initial mass of the meniscus. The me-niscus of the ink formed at the tip has an important effect on the patterning speed [3, 4]. In order to improve the patterning performance, AFPN using an active pumping method was developed [5, 6]. There is a flexible membrane part inside the AFPN system that controls the initial mass of the meniscus by only using mechanical force to efficiently control the length between the lines and to increase the patterning speed. How-ever, the actual commercialization of this method has been limited due to the localization of parts designs. Moreover, the AFPN device is very difficult to manufacture because of its complex structures. Therefore, it is imperative to develop a device with improved patterning speed that can be easily fab-ricated for commercialization.

Accordingly, a novel design of a nano printer based on the AFPN is presented. In this paper, the design and the construc-tion of this nano printer are discussed in detail. The nano printer system is comprised of a reservoir, a PZT plate and transmission parts. The PZT plate works as a switch to control the outlet flow because of its deformability by the supply volt-

† This paper was recommended for publication in revised form by Associate Editor In-Ha Sung

*Corresponding author. Tel.: +82 31 290 7500, Fax.: +82 31 290 7666 E-mail address: [email protected]

© KSME & Springer 2011

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978 K. Hwang et al. / Journal of Mechanical Science and Technology 25 (4) (2011) 977~985

age, and the reservoir provides sufficient ink for continuous patterning. The size of the channel is important due to the working principle of our system, and the critical dimensions are decided for the simulation in the paper. Because the flow in the microchannel is laminar and steady, the flow velocity is affected by the size of the opened channels and the pressure difference between the inlets and outlets. The mechanical and piezoelectric properties of the PZT are also simulated to show that switch control is achievable by using the supply voltage. To realize continuous patterning and prepare for the design of the control system, we need to obtain the maximum patterning speed. Although the patterning speed, which is greatly de-pendent on the mass of the initial meniscus, was analyzed [7], subsequent analysis related to the maximum possible pattern-ing velocity is proposed. A remarkably higher patterning ve-locity is achieved the nano printer based on the AFPN method using switch control than the nano printer based on the DNP method.

2. Working principle

The ultimate purpose of this paper is to develop a printer that possesses the advantages of both AFPN and piezoelectric inkjet printers to actualize nano-sized patterning. Fig. 1 is the cross section of the entire structure of the printer. The reser-voir is directly on the tip portion and the PZT element, the actuator, is attached to the slap of the channel. The polariza-tion direction of the piezoelectric element is set in the same direction as the z-axis. Both ends along the x-axis of the slag are constrained to maximize the size of the piezoelectric mate-rial element, and no voltage is applied at the initial state.

As shown in Fig. 1(a), at the initial state, the slab is drooped by the flux pressure inside the AFPN’s reservoir, and the tip is in contact with the substrate, so that the channel is enclosed and the flow is stopped. In Fig. 1(b), displacement occurs when a voltage by the direct current is supplied to the piezo-electric element (PZT-4) on top of the channel slab. Since the polarization direction of the piezoelectric element is set in the same direction as the z-axis, the deformation of the PZT plate

will act against the droops caused by the weight of water in-side the reservoir. When this deformation is big enough, as shown in Fig. 1(c), a flux will appear. Due to the small dimen-sion of the channel, the flow is considered laminar. In a sense, the magnitude of the outflow flux is dependent on the size of the opened channel.

Fig. 2 shows the construction of the nano-printer. Assuming a steady supply of ink, a constant input flux pressure can be maintained, and the outflow flux can be controlled by the PZT actuator via the supplied voltage. Fig. 3 is an outline of the connection between the reservoir and the PZT in the nano-printer, and (a) is the side-view and (b) is the bird’s eye view. The ink is stored in the reservoir, and the capacity of the res-ervoir is designed so that sufficient initial pressure can be supplied to enclose the channel. Fig. 4 is a detailed drawing of the reservoir, the PZT, the channel and the tip, where (a) is the sectional view, and (b) is a magnification of Fig. 3(b).

3. Analysis and result

In our design, the slab upon the channel should be deflected at the rest time to prevent the ink from flowing out. In the view of the mechanics, the deflection of the slab is dependent on its thickness. Accordingly, the thickness of the slab should

Fig. 1. Working principle.

Fig. 2. The whole shape of the nano-printer.

(a)

(b)

Unit: µm Fig. 3. (a) Shape and Size of the Reservoir and the Tip from the Side;(b) Shape and Size of the Reservoir and the PZT Actuator from theTop.

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K. Hwang et al. / Journal of Mechanical Science and Technology 25 (4) (2011) 977~985 979

be designed so that the deflection of the slab caused by the weight of the ink in the reservoir is the same as the thickness of the channel. Furthermore, the simulation of the piezoelec-tric performance with respect to flow control by voltage is carried out. The efficiency of a nano printer device is very important in the commercialization of the device. In our pre-vious work [7], the patterning speed was found to be related to the initial mass of the meniscus formed at the tip, but the pat-terning speed should be below a critical value to make a uni-form pattern, because the surface tension of the ink is limited. In this paper, all analyses were done under the assumption that the ink is water. 3.1 The channel construction design

A structural analysis and a simulation of the nano printer were carried out because the construction of the channel is of great importance in the performance of patterning. In this pa-per, the channel was constructed using Inventor 10, and the analysis was done using ANSYS workbench10.

Since the basic design proposed in this paper was based on the AFPN device, SixNy was assumed as the construction ma-terial, for the moment, and the PZT was deposited onto the slab, as shown in Fig. 1. In order to cause a sufficient deflec-tion of the slab to enclose the channel, the reservoir should be made of Pyrex, which has an excellent property for a thick structure. In this analysis, the size of reservoir is assumed to be 2000µm×3000µm×500µm (W×L×H), as shown in Fig. 3.

When the reservoir is full of water, the mass of water and the corresponding pressure are calculated as [8],

63 10m V WLH Kgρ ρ −= = = ×

24.905 /P gH N mρ= = (1)

where ρ is the density of water, H, W, and L are the height,

width and length of the reservoir, respectively. And the pres-sure at the bottom of reservoir, denoted as P in the equation, is considered the inlet pressure shown in Fig. 4(b).

With respect to mechanics, the deflection of the slab is gov-erned by the Navier solution [9]:

2 21 1

2 2

42

1( , )

(

sin sin)m n

mnPx y

D m n

b

mx mya a

a

ωπ

π π∞ ∞

= =

=

+∑∑ (2)

where ω is the deflection of slab, a and b represent the di-mensions of the cross section of the reservoir, (a=2000 µm, b=3000 µm), and mnP is the coefficient that can be repre-sented by P, the pressure of the ink calculated by Eq. (1). The ‘m’ and ‘n’ are mode shapes, and D is the flexural rigidity expressed as follows [9]:

3

212(1 )EtD

V=

− (3)

where E is the Young’s modulus, v is the Poisson’s ratio, and the thickness of SiN is expressed as t. The material property values of SixNy are given in Table 1.

The maximum deflection of the slab is at the center, where x=a/2, y=b/2. As when m, n are greater than 1, the magnitude of ω is so small that we can neglect it without losing accu-racy. So the maximum deflection should be approximated (units of t and ω are µm),

2 2 3

2 2

max 42

1 20.555

(

.1 1 )

P

D t

ba

ωπ

=

+

× = (4)

In order to find the adequate size of the channels, a 2D

simulation in ANSYS was carried out. During ANSYS simu-

Unit: µm

Fig. 4. (a) Cross Section of the Inside of the Inlet; (b) Top View of theInlet.

Table 1. Values of the Material Properties of SixNy.

Young's modulus (E) 212 GPa

Poisson's ratio (υ) 0.25

Density (ρ) 3100kg/m3

Fig. 5. Droop displacement with respect to the thickness of SiN.

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lation, the two ends of the channels were fixed, and the pres-sure, caused by the ink in the reservoir, was changed into an equivalent concentrated force exerted on the center of the slab.

Fig. 5 is a contrast graph derived from the simulation and the numerical analysis of MATLAB. The numerical analysis is based on Eq. (4). Because a 2D model was used in the ANSYS simulation, some details of the constructions were not perfectly performed. As shown in the figure, although the graphs show the same trend, there is still a little discrepancy between them. Because the channel needs to be enclosed by the flux, the thickness of the channel and the amount of the droop must be equivalent to each other. Besides, with respect to manufacturing efficiency, both the thickness of the SiN layer and that of the channels were chosen 2.2 µm. We con-sider this result to be acceptable for a realistic system. There-fore, the following analysis was carried out for channels of 2.2 µm thickness. 3.2 Deflection of slab due to reaction force

The reaction force at the tip refers to the forces that clear the blockage of the channel caused by the primary flux pressure and, at the same time, allows the outflow of the flux. At the initial stage, the tip and the substrate are in contact with no external forces exerted. When the supply voltage is applied on the piezoelectric actuator, the difference between the pressure caused by the piezoelectric actuator and the pressure of water exerted on the tip at the same time causes a reaction force. Eq. (4) solves for the droop of the upper part of the channel while the concentrated load (the reaction force) on the tip is kept constant and exerted in the positive direction of the z-axis [6].

max 3 3 21

1 2(tanh )22 cosh

2m

mFab m

mD m

ππω ππ

=

= × −∑

6

5 2

6 101.2443 10

2(tanh )2 cosh

2

ππ

−× ×

= ××

− (5)

max3.12F ω= (6) where F refers to the reaction force when the PZT deforms, as shown in Fig. 1. From the solution of the above equation, the reaction force required to lift the slab by 2.2 µm was deter-mined to be 6.83 µN. When the reaction force exerted on the tip manifests as a concentrated load, the consequent effect is identical to the effect of the concentrated load on the channel’s upper side.

The relationship between the size of the opened channel and concentrated load is shown in Fig. 6. The numerical simu-lation is derived from Eq. (6). Because the simulation is de-rived from 2D modeling, the relation of the concentrated load and drooping shows discrepancies from the simulation result of the entire structure. Therefore, in this paper, 6.83 µN from the numerical analysis is adopted for further discussion. Be-cause voltage effects on the PZT is considered as a concen-

trated force, we can predict the voltage effects on the deforma-tion of the PZT by the results in Fig. 6 3.3 The amount of the droop caused by the piezo-electric

actuator

The displacement of the tip is caused by the deforming force of the PZT due to the supplied voltage. In order to gen-erate the desired displacement, the supplied voltage should be changed into the equivalent force that makes the same dis-placement as that caused by the supplied voltage. This is the same drive principle of the head of a piezoelectric inkjet printer that allows the creation of three dimensional micro structures. In order to analyze the displacement of a piezoelec-tric element, the material property values, behavior properties and physical properties of the element must be understood and analyzed. First, the behavior properties are analyzed by the reverse piezoelectric effect. The compaction and the mechani-cal behaviors are expressed as polarization. In this paper, compaction is generated by making the directions of both polarization and the electric field identical. As both ends of the x-axis are confined, the compaction of the PZT will impel the tip to move up. The amount of droop due to the pressure was simulated using ANSYS multi physics analysis tools based on the governing equation [10]. In this analysis, PZT-4 was used with the corresponding property values listed in Table. 2 [11].

The direction of polarization was in the same direction as that of the z-axis, and the analyzed result of the droop at 450

Table 2. Material Properties of PZT-4.

Elastic Stiffness [N/m2]

c11=1.39×1011 c12=7.78×1010 c13=7.43×1010 c33=1.15×1011 c44=3.06×1010 c66=2.56×1010

Piezoelectric Constants [C/m2] e31=-5.2 e33=15.1 e15=12.7

Permittivity Constants [F/m] ε11=6.74×10-9 ε33=5.87×10-9

Density [kg/m3] 7500

Fig. 6. Deflection caused by the concentrated load.

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K. Hwang et al. / Journal of Mechanical Science and Technology 25 (4) (2011) 977~985 981

volts is expressed by ANSYS multi physics in Fig. 7. Fig. 7(a) is the top view of the result, and red zone is the lo-

cation of the maximum displacement. Fig. 7(b) is the actual shape of the deformation of the PZT. In order to eliminate the influence from the fluid, layers of SixNy and PZT-4 were made to contact with each other during the modeling. For the ANSYS multi physics analysis, the amount of the droop was simulated by applying elements of solid 5 and solid 45 for the piezoelectric material and SixNy sheet, respectively.

Based on Fig. 7, the displacement amount corresponding to

each supply voltage is shown in Fig. 8. The fan-shaped ex-pression of the amount of displacement of the PZT actuator caused by voltage is confirmed. Therefore, the relationship between the drive voltage and the displacement of the PZT can be estimated, and the corresponding reaction force can be determined based on Fig. 8. And the flux can be controlled by the reaction force. The relationship between the voltage and reaction force is examined based on this result.

3.4 The relationship between the piezo-electric element and

the reaction force

In order to analyze the relationship between the supply volt-age and the reaction force, the deformation force caused by voltage is treated as a constant pressure exerting on the chan-nel slab.

Fig. 9 shows the dependence of the deflection of the slab on the concentrated load and supply voltage.

By our previous analysis, a reaction force of 6.83µN is re-quired to lift the slab up by 2.2µm. Moreover, for the same magnitude of movement of the slab, the corresponding voltage is approximately 450 volt. And the required supply voltage for the minimum unit of the opened channel, 0.1 µm, is approxi-mate 20.37 volts. Then, the desired flux can be selected.

The discrepancy between the compared graphs is due to the fact that the supplementary structure was not taken into ac-count as it was in the discrepancy of the earlier results.

(a)

(b)

Fig. 7. (a) Top view of the slab corresponding to supply voltage usingANSYS; (b) Actual shape of PZT deformation corresponding to supplyvoltage using ANSYS.

Fig. 8. Analysis of the PZT actuator corresponding to supply voltageusing ANSYS.

Fig. 9. Analysis of the displacement of droop due to supply voltage and concentrated load.

Fig. 10. Result of flow rate analysis and the size of the opened channel.

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3.5 Outflow analysis

The outflow generated by opening the channels is consid-ered laminar flow. A flow simulation is done using FLUENT, and the model is made by Inventor 10 and meshed in the Gambit.

All the wall surfaces are characterized by the no- slip condi-tion, and a constant pressure of 4.905 Pa (from Eq. (1)) is applied at the inlets, as shown in Fig. 4. Fig. 10 shows the results of the flux analysis under the assumption that the size of the channel is opened to its maximum level. Figs. 11 and 10 show the cross sections of the channel.

The speed of the outflow depending on the location in the cross sectional direction of the outlet is shown in Fig. 12, where the maximum velocity is 45 µm/s, and the maximum speed is observed in the center of the outlet. Then the mass flow rate at the outlets was determined as,

122.475 10 /outM vA kg sρ −= = × (7) where outA is the cross sectional area of the outlet.

The height of the outlet can be adjusted with the activation of the PZT actuator. The outflow may vary depending on the height of channel. This idea is analyzed, and the results are shown in Figs. 13 and 14. Fig. 13 shows the outflow speed at various outlet heights. The x-axis stands for the height of the outlet. The size of outlet can be controlled by PZT-4, and the y-axis stands for the corresponding outflow speed. The analy-sis is done by increasing the outlet height from 0.2µm up to 2.2µm. Fig. 14 shows flow rate according to the velocity shown in Fig. 13. The x-axis represents the outlet height, and the y-axis is the mass flow rate. Although a typical fluid analysis of a three dimensional L-tube requires a speedy cal-culation for variables x, y, and z, it is excluded in this paper since the outflow needs to be analyzed foremost than that of the distribution of the velocity inside the channel [12]. 3.6 The analysis of maximum patterning speed

To form a uniform pattern, the meniscus at the tip must be unbroken, and the line width must be fixed. For this reason, the external force applied on the tip can not be infinitely large, but rather be under a critical value. If any external forces ex-

ceeding the tension force are applied, the meniscus will break. In the paper, the meniscus is modeled under the assumption that the shape of the tip is spherical and that the fluid is water.

3.6.1 The dynamic model of the meniscus with respect to the

movement of the tip Fig. 15 suggests a meniscus model accounting for tip

movement. When the tip moves the meniscus, two reaction forces are at work. The first is the viscous friction, or the ki-netic friction, generated between the surface and the meniscus. This friction is determined by Eq. (8), [13]

21

8bF fLPUρ= (8)

Fig. 11. Flow analysis result.

Fig. 12. Flow speed at various locations along the cross sectional direc-tion of the outlet.

Fig. 13. Flow speed analysis according to outlet height.

Fig. 14. Mass flow rates analysis according to outlet height.

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K. Hwang et al. / Journal of Mechanical Science and Technology 25 (4) (2011) 977~985 983

where ρ is the density of the ink, f the friction constant, L the length between lines, P the height of the meniscus and U is the patterning speed. The second force is the capillary friction or the static friction due to the surface tension force of the ink. Eq. (9) is the equation of the static force [7]. Here, since the friction constant f is an essential element of the design, it was obtained by simulation to acquire approximately 100nm of length between the lines.

(2 )rF k Rdrγπ= (9)

where k is a constant, R the radius of the tip, d the distance between the tip and the surface, r the radius of the rotation of the meniscus shape, and γ the surface tension force. The k is a constant concerning the shape of the tip, and it is assumed as 1 in this paper because it is assumed that the part just in the mid-dle of the spherical shape of the tip comes in touch with the ink. By combining Eqs. (8) and (9), dynamic modeling was completed and was expressed by Eq. (10).

2(2 )FPLxF ma k Rd

rρ γπ

ε= + + (10)

where F refers to the external force applied on the meniscus, m the original mass of the meniscus and a the acceleration of tip.

Eq. (10) is a nonlinear function for speed. However, since the meniscus moves according to the movement of the tip, the acceleration of the tip and that of the meniscus are the same. Therefore, the acceleration is assumed as 210 /secmµ . It is the design acceleration that should be considered in development of an actual system in the future because this happens to be the primary external force existing in AFM. The amount of me-niscus depends on the time of contact between the tip and the surface, and, in the early stage, the length of the pattern and the length between the lines can also vary the amount of the meniscus, so the length between lines and the length of the pattern should be maintained at 100 nm and 100 µm, respec-tively, which would give the maximum meniscus amount (m) of 2.475×10-12 kg.

3.6.2 The maximum external force

The maximum external force applied on the tip is the same with that converted from the surface tension force of the ink.

The surface tension force of water is 87.29 10 /N mµ−× . Therefore, assuming that the shape of the meniscus is a hemi-sphere, as shown in Fig. 16, the surface tension force is given by Eq. (11).

87.29 102LF π−= × × (11)

where L is the width of the pattern. The maximum external force in this case is 21.14 10 Nµ−× . Therefore, the external force applied by the tip to the meniscus has to be less than or equal to 21.14 10 Nµ−× .

3.6.3 Result

Fig. 17 shows the result of the maximum velocity with re-spect to the initial mass of the meniscus for a uniform pattern. The x-axis of the graph represents the initial mass, and y-axis represents the pattern speed. As the mass of the initial menis-cus increases, the length of the pattern increases by the square root. But, as suggested in section 3.6.1, 2.475×10-12 kg is re-quired when the length between the lines and pattern length are 100 nm and 100µm, respectively. Then, the speed is 95µm/sec, while the friction coefficient f is designed to be 2.53 in this condition. If the friction coefficient is increased, the speed will increase, but this coefficient is determined by the relationship between the ink and the substrate.

4. Conclusion

Due to the basic development of nano-scale patterning by application of the piezoelectric method, a structural analysis of the nano printer system was carried out according to the flux

Fig. 15. Dynamic of meniscus model.

Fig. 16. Shape of the meniscus in static state.

Fig. 17. Maximum speed with respect to the mass of the initial menis-cus for 100nm pattern.

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pressure and the deformation of the piezoelectric element by supply voltage. According to our simulation, the required voltage is high, about 450 volts, for generation of a deflection of 2.2µm. It is reasonable but awkward for operation. How-ever, when the thickness of SiN is decreased to 1µm, the cor-responding voltage is 235 volts, so a low operation voltage is achievable when a thinner SiN layer is made in the future. By the way, the numerical analysis and simulation results showed discrepancies, although a better result may be attained if a more detailed structural design or lattice formation is analyzed.

The outflow fluid analysis showed that the desired outflow flux can be controlled by the value of the supply voltage, which induces changes in the size of the opened outlet when a uniform flux pressure is applied at the inlet and the outlet. Finally, according to the simulation, the pattern speed of this system was approximately 100µm/sec while that of the DPN was a few µm/sec and that of the FPN was a few tens of µm/sec. This means faster manufacturing by about tens to hundreds of times than that of the existing manufacturing method. It is necessary to develop actual manufacturing equipment in the future. However, further analysis is expected. The accurate assessment of the ink property, for example, whether it is hydrophilic or hydrophobic, needs to be consid-ered in an accurate flow analysis and pattern speed analysis. Especially, the pattern analysis should be carried out by changing the shape of the tip to an inverse triangular structure, not a spherical structure. Moreover, the modeling results will have to be confirmed by experiments in the future.

Acknowledgement

This work is carried out for the Direct Nano Patterning Pro-ject supported by the Ministry of Knowledge and Economy under the National Strategic Technology Program.

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Kyoil Hwang received his B.S. degree in Mechanical Engineering from Sung kyunkwan University, Korea, in 2000. He then received his M.S. degree from Sungkyunkwan University in 2002. He is a doctor candidate in the Automatic Control Laboratoryat Sungkyunkwan University.

Rui Mingwu received his B.S. degree in Mechanical Engneering from Shandong University, China, in 2008. He is a M.S. degree candidate in the Automatic Control Laboratoryat Sung kyun kwan University.

Chun yup Shin received his B.S. degree in aero-space engineering from Kyung sang National University. He then received his M.S. degree from Sungkyunkwan University in 2008.

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Suk Han Lee recived his B.S. degree from Seoul National University in 1972. He then received his M.S. degree from Seoul National University in 1974. He recived his Ph.D degree from Purdue University, U.S.A, 1982. He is a pro-fessor in the Department of Electronics at Sungkyun kwan University.

Hun Mo Kim received his B.S. degree in Mechnical Engineering from Sung kyunkwan University, Korea, in 1984. He then received his M.S degree of Aerospace Engineering from University of Michigan, U.S.A. 1990. He then received Ph.D degree in Mechanical Engineering fromUniversity of

Alabama , U.S.A. 1993. He is a professor in the Department of Mechanical Engineering atSungkyunkwan University.