Reinforcement of a PDMS master using an oxide-coated silicon plate

Microelectronics Journal 37 (2006) 5–11 www.elsevier.com/locate/mejo

Reinforcement of a PDMS master using an oxide-coated silicon plate Cheng Luoa,*, Fang Menga, Xinchuan Liua, Yiyun Guob a

Biomedical Engineering Program and Institute for Micromanufacturing, Louisiana Tech University, 911 Hergot Avenue, Ruston, LA 71272, USA Electrical Engineering Program and Institute for Micromanufacturing, Louisiana Tech University, 911 Hergot Avenue, Ruston, LA 71272, USA

b

Received 28 April 2005; received in revised form 9 June 2005; accepted 13 June 2005 Available online 8 August 2005

Abstract In this work, a new method was developed to increase the stiffness of Polydimethylsiloxane (PDMS) masters using oxide-coated silicon plates, aimed at reducing the residual and deflecting deformations of the PDMS masters for proper pattern transfer. Using this method, these two types of deformations in the reinforced PDMS master have been reduced. q 2005 Elsevier Ltd. All rights reserved. Keywords: PDMS master; Pattern transfer; Residual and deflecting deformations; Reinforcement

1. Introduction PDMS is a biocompatible [1], ultra-violet transparent [2], and gas permeable elastomer [3] that can withstand a wide temperature range (K100 to 1008C). It is not photodefinable (i.e. not a photoresist), and is usually patterned by a molding process [4–6]. PDMS is easy to process and has been widely applied in the micromachining field [1–8]. In particular, it has been used as the master material in soft lithography for pattern transfer [7,8]. PDMS is soft and flexible, enabling it to have intimate contact with substrates and consequently make good pattern transfer to those substrates. On the other hand, due to its large expansion coefficient, PDMS may have large residual deformation after it is patterned via a molding process. The residual deformations of PDMS masters may cause misalignment problems along horizontal directions when they are employed to transfer patterns on pre-defined features on the substrates. Furthermore, due to its low stiffness, PDMS may have pairing and deflecting deformations when it is used to transfer patterns [7,8]. Paring deformations mean that the long structures in PDMS masters tend to stick together under their own weight, leading to the failure of pattern transfer. Meanwhile, in order to have a good pattern * Corresponding author. Tel.: C1 318 257 5136; fax: C1 318 257 5104. E-mail address: [email protected] (C. Luo).

0026-2692/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.06.012

transfer from a PDMS master to a substrate, a pressure is applied on the PDMS master to make it have intimate contact with the substrate. Under this pressure, the surfaces at the bottom of the convex PDMS features may have large deflections, making those surfaces come into contact with the substrate (which are so-called sagging deformations) and causing undesirable printing. Even small deflections of those surfaces may cause problems. For example, crosssection changes in concave PDMS patterns may lead to generation of improper patterns in a microcapillary molding method of soft lithography [9]. Therefore, it is necessary to reduce these three types of deformations (i.e. residual, pairing, and deflecting deformations) in a PDMS master for transferring patterns to substrates in a reliable manner. In the three types of deformations, the pairing problem appears relatively easy to solve. When the ratio between the feature height and the feature separation in the PDMS master is smaller than 0.5, the two neighboring structures should not have contact with each other. PDMS structures are the replica of the corresponding structures in the mold. Therefore, if the concave features in the mold are designed to have a low aspect ratio, then the pairing deformations of the PDMS structures can be avoided. However, the aspect ratios of voids cannot be too low. For example, voids of low aspect ratio (!0.2) are susceptible to sagging deformations [10]. Thus, it seems that, to avoid the pairing deformations, a good aspect ratio of recessed PDMS patterns is between 0.2 and 0.5. In this work, we focus on reducing residual and deflecting deformations of a PDMS master by reducing its

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thermal expansion coefficient and increasing its stiffness, respectively. The stiffness of a material can be increased by adding, for example, stiffer particles or fibers inside [11]. The average stiffness of the resulting composite material increases due to the contribution of the reinforcements. Likewise, if those particles or fibers have smaller thermal expansion coefficients than this material, then the average thermal expansion coefficient of the resulting composite material is reduced. Accordingly, the residual and deflecting deformations of the composite material should be smaller than those of a pure material. Using a similar idea, we added SU-8 particles in a PDMS master [12]. SU-8 is a negative photoresist. It has a higher stiffness and a lower thermal expansion coefficient than PDMS. With the addition of SU-8 particles, average residual strain of the reinforced PDMS was reduced from 5 to 1%. Nevertheless, there exist two problems associated with the particle and fiber reinforcement approaches. First, the local stiffness and thermal expansion coefficient of the material between two neighboring particles or fibers still remain the same such that large local residual and deflecting deformations may still exist. Second, particles or fibers may not uniformly distribute in the composite material. The composite material is usually made by first adding particles or fibers in a liquid solution of the material, then stirring the solution to make particles or fibers uniformly suspended inside the solution, and finally solidifying the solution. Particles or fibers may sink down inside the solution after the stirring process, causing the non-uniform distribution problem [12,13]. To avoid these two obstacles in the particle and fiber reinforcement approaches, we chose a plate, instead of particles and fibers, to reinforce PDMS. The plate was embedded throughout the PDMS, allowing for a better control of both global and local deformations of the PDMS. The outline of this work is as follows. In Section 2, the design of a reinforced master is presented and reduction of its deformations is discussed. In Section 3, the fabrication of the reinforced master is introduced. In Sections 4 and 5, residual and deflecting deformations in the pure and reinforced PDMS masters are compared based on experimental and numerical results, respectively. Finally, in Section 6, this work is summarized.

2. Design of the reinforced PDMS masters and reduction of deformations 2.1. Design of the reinforced PDMS masters Schematic of a reinforced PDMS master is shown in Fig. 1. The master consists of a microstructure-formed PDMS layer and a SiO2-coated silicon plate. Due to the contribution of the silicon plate, both residual and deflecting deformations of the PDMS master are expected to be reduced. On the other hand, the PDMS surface in the

PDMS master

}

Mold

Silicon plate Patterned PDMS

SU-8 features Silicon substrate

Fig. 1. Schematic of the reinforced PDMS master and its mold.

reinforced master still maintains its high flexibility along the vertical direction and thus has intimate contact with a substrate during pattern transfer. The thin SiO2 coating on the silicon plate functions as an intermediate layer to increase the adhesion between the PDMS and the silicon plate. We used three criteria to choose a reinforcing material: (1) it should be much stiffer than PDMS, (2) should have a much lower thermal expansion coefficient than PDMS, and (3) should be easily obtained with desired shape and thickness. Silicon was adopted in this work since it meets these requirements. Silicon is much stiffer than PDMS. Its Young’s modulus is 150 GPa [14], which is about 200,000 times of that of PDMS. Meanwhile, silicon has a much smaller thermal expansion coefficient than PDMS. Their thermal expansion coefficients are about 2.6!10K6/K [15] and 3.1!10K4 K [16], respectively. Therefore, the thermal expansion coefficient of PDMS is about 119 times of that of silicon. In addition, silicon is the most widely used material in the integrated circuit and microfabrication processes [17]. Its wafers are commercially available, and the plates with desired thicknesses and shapes can be easily fabricated from the silicon wafers using the existing microfabrication techniques [17]. As such, the silicon plate was chosen in this work as the reinforcing structure. 2.2. Reduction of the residual deformations The residual strains in both pure and reinforced PDMS masters are qualitatively estimated using a one-dimensional model as follows. Let us first consider the residual strain of a pure PDMS master and then that of a reinforced PDMS master. In this work, the PDMS patterns were formed on a mold at the temperature of 70 8C and subsequently cooled down to the room temperature of 20 8C. The mold consists of two parts: a layer of about 100-mm-thick SU-8 features lying on a 500-mm-thick silicon substrate (Fig. 1). SU-8 is a high contrast, epoxy-based thick-film photoresist that employs standard ultra-violet exposure tools for pattern delineation. The exposed, and subsequently cross-linked portions of the film are rendered insoluble to liquid developers making SU-8 a negative-tone photoresist. SU-8 has been widely applied in the microelectromechanical systems (MEMS) area for various high-aspect-ratio patterning purposes [18–21]. When a material of a thermal expansion coefficient, C, cools down from a high

C. Luo et al. / Microelectronics Journal 37 (2006) 5–11

temperature, T1, to a low temperature, T2, its shrinkage is C(T1KT2) [22]. The thermal expansion coefficient of SU-8 is 5.2!10K5 K [23]. Therefore, during the cooling process, the PDMS, SU-8, and silicon intend to shrink by 1.550, 0.247, and 0.013%, respectively. Due to their different shrinking degrees, when they cool down together, the PDMS intends to stretch the SU-8 and the SU-8 intends to stretch the silicon. Conversely, the silicon intends to compress the SU-8 and the SU-8 intends to compress the PDMS. The Young’s moduli of SU-8 and PDMS are 4.4 GPa [23] and 750 kPa [24], respectively, indicating that the silicon is 200,000 times stiffer than the PDMS and 34 times stiffer than the SU-8. Consequently, the attachment of the PDMS and the SU-8 on the silicon substrate should only produce negligibly small stretch in the silicon, i.e. the silicon substrate still shrinks by about 0.013%. Furthermore, both the PDMS master and the mold also shrink by about 0.013% due to the constraint of the silicon substrate, implying that compressive residual strain in the PDMS is 1.537%, which is the difference between 1.550 and 0.013%. After the PDMS is peeled off from the SU-8 mold and is free of the constraint of the silicon, the PDMS intends to release this compressive residual strain of 1.537%, leading to the same ratio of difference between the designed (or say, desired) PDMS patterns and the generated patterns and causing the potential misalignment problem. In case a silicon plate is embedded in a PDMS master, the silicon plate has almost full freedom to shrink during the cooling process, since the PDMS has negligibly small effects on its deformation and this silicon plate has the same shrinking ratio as the silicon substrate. Thus, the residual deformation induced in the silicon plate during the cooling process is zero. Meanwhile, the PDMS in this reinforced PDMS master after the cooling process still has the compressive residual strains of 1.537%. Unlike the pure PDMS master, the reinforced PDMS master does not fully relax the compressive residual strain of 1.537% in PDMS after it is peeled off from the mold. Instead, the reinforced PDMS just relaxes the compressive residual strain of the silicon plate because the silicon plate is much stiffer than PDMS and dominates the residual deformations of the reinforced PDMS master after release from the mold. Since the silicon plate has no residual strains, the reinforced PDMS master has no residual deformations accordingly after it is peeled off from the mold, which avoids the potential misalignment problem. 2.3. Reduction of deflection Reduction of deflection in the reinforced PDMS master is qualitatively explained based on a linear pressure-deflection equation as follows. Let us consider a plate. The load acting on a plate is normal to its surface, and deflections are small in comparison with the plate thickness. Then the differential equation of the deflection surface is (see Eqs. (3) and (103) in [25]).

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v4 wðx; yÞ v4 wðx; yÞ v4 wðx; yÞ C 2 C vx4 vx2 vy2 vy4 Z

12qðx; yÞð1Kn2 Þ ; Eh3

(1)

where x and y are coordinates of a typical point on the plate, w(x,y) stands for deflection at the point, q(x,y) represents applied pressure at the point, h denotes the plate thickness, and E and n represent Young’s modulus and Poisson’s ratio, respectively. It can be seen from this equation that the deflection is inversely proportional to the Young’s modulus. When a reinforcement plate is added to PDMS, the average Young’s modulus of the reinforced PDMS across its  is cross-section, E, E d C E2 d2 E Z 1 1 Z d1 C d2

E1 C E2 dd21 1 C dd21

[11], where E1 and E2 are Young’s moduli of PDMS and silicon, respectively, and d1 and d2 are thicknesses of PDMS and reinforcement plate, separately. It can be directly seen from the above equation that E is a function of d2/d1. Since the first derivative of E with respect to d2/d1 is positive, E increases with d2/d1. This implies that, in order to have large  the PDMS layer should be much thinner than the silicon E, plate. In this work, the thickness of the Si plate was chosen to be 500 mm, which is the thickness of commonly used silicon wafers. That is, d2Z500 mm. According to the above equation, even when d1Zd2Z500–mm, E still has a value of 75 GPa, which is comparable to the Young’s moduli of aluminum and gold, which are 78.5 and 69.6 GPa, respectively. Accordingly, the average Young’s modulus of a reinforced PDMS master is much higher than that of a pure PDMS. Therefore, when suffering the same pressure distribution, the average deflection in a reinforced PDMS master should be much smaller than that in the pure PDMS master. Consequently, the surfaces at the bottom of the convex PDMS features in the reinforced PDMS master should have a smaller deflection than that in a pure PDMS master as well.

3. Fabrication of reinforced PDMS masters and residual deformations The three-step molding procedure of making the reinforced PDMS masters is as follows (Fig. 2): (1) Spincoat a thin layer of PDMS (ratio between PDMS and its curing agent is 10:1) on a mold (Fig. 2a), (2) place a SiO2coated, 500-mm-thick silicon plate on the PDMS layer (Fig. 2b), and (3) bake the sample at 70 8C, cool it down to the room temperature (i.e. 20 8C), and peel off the reinforced PDMS master from the mold with care (Fig. 2c). The thickness of the PDMS layer on the silicon plate can be controlled by spin rate, spin time, the concentration of

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SU-8 features Silicon plate

PDMS Step 1

Step 2

Silicon substrate Step 3 Reinforced master Fig. 2. Illustration of the three-step molding procedure: (1) spin-coat a PDMS layer on a mold, (2) place a silicon plate on top of the PDMS layer, and (3) peel off PDMS together with the silicon plate from the mold.

the curing agent in PDMS, and the quantity of PDMS used for spin-coating. The peeling-off problem is the critical obstacle that we faced in this molding procedure. As shown in Fig. 3, the peeling-off force is applied at the edge of a PDMS master to avoid the damage on the PDMS patterns and is perpendicular to the PDMS master. A bending moment is generated at the debonding location O for separating the PDMS master and the mold. In the meantime, this force yields a stress on the cross-section of the structure at O. This stress increases with the peeled-off area since the bending moment increases with the distance. When the peeled-off area reaches a critical value, the stress is larger than the fracture stress of silicon and the silicon plate in the master breaks. The reinforcing silicon plates used in this work have thicknesses of 500G25 mm and are coated with 2-mm-thick oxide layers. As indicated in Section 2.3, the PDMS layer in the reinforced master needs to be thin such that the reinforced master has a large stiffness for better reducing deflections. The pattern area of interest in this work is 3 cm long and 3 cm wide. After the addition of a silicon plate of the same lateral dimensions, the thinnest PDMS layer that could be peeled off from the substrate together with such a silicon plate is about 246 mm. Fig. 4 shows a top view of the corresponding reinforced PDMS master, and Fig. 5 shows part of its cross-section. When the PDMS layer is thick, it is relatively easy to peel-off the reinforced PDMS master because the bending moment at the peeling off location is shared by a large cross-section. For example, when the PDMS layer is about 1 mm thick, according to our tests, the largest silicon plate that can be embedded in the PDMS master without any damages during the peeling-off process is 5 cm wide and 5 cm long, about one quarter of a 4 in silicon wafer in size. Obviously, with a thicker PDMS layer,

O Si plate

PDMS

a larger silicon plate can be peeled-off. However, it is believed that the effect of this silicon plate on the deflection of the surfaces at the bottom of the convex PDMS features will be reduced accordingly due to large distance between those surfaces and the silicon plate. The residual strains in the type of reinforced PDMS masters shown in Figs. 4 and 5 were compared with those in a  pure PDMS master. The residual strain is defined as jðlKlÞ=lj, where l is the characteristic dimension of a pattern in the silicon mold, l is the corresponding dimension of this pattern in the released PDMS master, j$j and stands for absolute value. Six types of patterns of different dimensions (range from 12.08 to 386.02 mm) and various shapes, including channels, square dots and square holes, were considered. These features were fabricated on the same wafer. An AMRAY 1830 Scanning Electron Microscope (SEM) of a resolution of 10 nm was used to take the pictures of those patterns and measure their characteristic dimensions. The patterns in the PDMS samples were coated with 10-nm-thick aluminum for taking SEM pictures of these samples. The average residual strains of each type of patterns in the reinforced and pure PDMS masters are given in Table 1. Three points can be directly observed from this table: (1) The residual strains in the pure PDMS masters vary with patterns. Since the patterns are located at different

Peeling off force

SU-8 Mold

Fig. 3. Illustration of the peeling-off process.

Fig. 4. A top view (digital camera picture) of a reinforced PDMS master.

C. Luo et al. / Microelectronics Journal 37 (2006) 5–11

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Fig. 5. SEM picture of the cross-section of part of a reinforced PDMS.

locations, this indicates that the deformations in the pure PDMS masters are not uniform. (2) Residual strains in the reinforced PDMS masters are much lower than their counterparts in pure PDMS masters. For example, after the PDMS masters are reinforced with silicon plates, the average residual strains in the replicas of 332.05 mm channels, 386.02 mm square holes, and 12.08 mm square dots have been reduced from 1.5 to 0.19%, from 5.3 to 0.64%, and from 3.4 to 0.19%, respectively. This indicates that the local deformations of the reinforced PDMS masters are smaller than those of the pure PDMS masters. Furthermore, the global deformations can be considered as the average deformations of those patterns. Therefore, the global residual deformations in the reinforced PDMS master are smaller than those in the pure PDMS master as well. (3) We estimated in Section 2.2 based on thermal expansion coefficients and Young’s moduli of PDMS and Si that, after integration of a silicon plate, the residual strains of the PDMS master could be reduced from 1.537 to 0%. This estimation partially interprets why residual deformations of a PDMS master after the embedment of a silicon plate were reduced to 0.42% on average. The average strains in the pure and reinforced PDMS master are about 3 and 0.42%, respectively. The two values are about 1.5 and 0.4%, respectively, higher than the corresponding values estimated in Section 2.2. This may be due to that the one-dimensional model used to estimate the deformation is not sophisticated enough to predict the exact global and local deformations of a PDMS master. The following factors may also affect the deformations: the curing time, the thicknesses of PDMS layers, the thickness and planar dimensions of the silicon plate, and the individual PDMS patterns. In the near future, we would like to establish a more sophisticated model, which also considers those factors for better prediction of residual deformations in a PDMS master.

4. Reduction of deflection The cross-section deformations of both pure and reinforced PDMS masters are not easy to observe since the cross-sections have direct contact with the substrates. Therefore, the deflections of the surfaces at the bottom of the convex features in both pure and reinforced PDMS masters were compared using a simulation model established in the finite-element software ANSYS 8.0. PDMS is a rubber-elastic material, which shows non-linear stress– strain behavior. Thus, in this simulation model the PDMS deformations were characterized using a non-linear Moony– Rivlin stress–strain relationship, instead of a traditional linearly elastic stress–strain function, since the Moony– Rivlin relationship is uniquely suited for rubber-elastic deformations [26,27]. This relationship has been used, for example, to find the deformation of polymethyl methacrylate (PMMA) during a hot-embossing process [28]. According to the Moony–Rivlin stress–strain relationship, the stress is expressed as

si Z l i

vW ; vli

(2)

Table 1 Deformation and strain data for PDMS with and without a reinforcing silicon plate Features and their dimension in the SU-8 mold

Average residual strains in a pure PDMS master (%)

Average residual strains in a reinforced PDMS master (%)

332.05 mm channels 386.02 mm square holes 113.22 mm square dots 31.05 mm square dots 22.02 mm square dots 12.08 mm square dots

1.5 5.3

0.19 0.64

3.2

0.33

2.4 2.2 3.4

0.42 0.74 0.19

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Fig. 6. Simulation results: simulation models of (a1) pure and (b1) reinforced PDMS masters, cross-section deformations of (a2) pure and (b2) reinforced PDMS masters, and close-up view of the cross-section deformations of (a3) pure and (b3) reinforced PDMS masters under pressure 24 kPa. The maximum deflections of both structures happened at the middle lines of the trenches; the maximum deflection in the pure PDMS master is 23.7 mm while that in the reinforced PDMS master is 5.42 mm.

W Z C10 ðI1 K3Þ C C01 ðI2 K3Þ; I1 Z l21 C l22 C l23 ; I2 Z l21 l22 C l22 l23 C l23 l21 ;

(3)

where the C01 and C10 are Moony constants. They are derived from the following approximated relations [26]: C01 Z 0:25C10 ; 6ðC10 C C01 Þ zE:

(4)

In Eq. (4), E is the Young’s modulus of PDMS. By Eq. (4), we have C01 Z 0:034E; C10 Z 0:134E:

(5)

Due to non-linear nature in Eq. (2), it is difficult to find an analytical solution. Therefore, numerical simulation is needed to find the residual deformation. Since the software ANSYS 8.0 allows the simulation of a material using the Moony–Rivlin stress–strain relationship, it was chosen in this work to establish the simulation model. The simulated pure and reinforced masters are given in Fig. 6(a1) and (b1), respectively. The simulated pure PDMS master is 6.9 mm long and 5 mm wide. It has a thickness and structures similar to the PDMS layer shown in Fig. 5. This master includes an array of trenches, each trench of a width of 350 mm and a depth of 97 mm. The sidewall between every two neighboring trenches is 295 mm, and the total thickness of this PDMS master is 250 mm. Compared with the simulated pure PDMS master, the reinforced PDMS master in the numerical model has an additional 500-mm-thick silicon plate. The deflections of the surfaces at the bottom of the PDMS trenches in both masters were found and

compared. Pressure was applied on the top surface of each master, and varied from 10 to 24 kPa, which is in the lower portion of the pressure range (0–40 kPa) used in pattern transfer [29]. In simulation, the bottom surface of each master was fixed. Maximum deflections occurred at the middle lines of the bottom trench surfaces in both masters. When applied pressure was 24 kPa, the maximum deflection in the pure PDMS master was 23.7 mm (Fig. 6(a2) and (a3)) while the maximum deflection of the counterpart in the reinforced PDMS master was only 5.42 mm (Fig. 6(b2) and (b3)), indicating that the cross-section changes of the trenches in the reinforced PDMS master were much smaller than that in the pure PDMS master. Fig. 7 gives the simulated relationship between the maximum deflections and the applied pressures in the two masters. The maximum deflections in both masters increased with applied pressures in a linear manner. The maximum deflection in the pure Pure PDMS master

25 Maximum deflection (µm)

where l is the expansion rate and W is a strain density function. W is expressed as

20 15 10 Reinforced PDMS master 5 0 10

12

14

16

18

20

22

24

Applied pressure (KPa) Fig. 7. The simulated relationship between the maximum deflection and the applied pressure.

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PDMS master increased from 9.9 to 23.7 mm when the applied pressure varied from 10 to 24 kPa. In contrast, the maximum deflection in the reinforced PDMS master increased from 2.39 to 5.42 mm. The pure PDMS master had larger deflections than the reinforced PDMS master. The maximum deflection in the pure PDMS master was about four times as large as that in the reinforced PDMS for each applied pressure, indicating that the introduction of a reinforcing silicon plate to a PDMS master led to large reduction in cross-section changes of PDMS features during the potential pattern transfer.

5. Summary In this work, a new method was developed to reduce the residual and deflecting deformations of a PDMS master using a stiffer oxide-coated silicon plate. The details of this method were presented, including design and fabrication of the reinforced PDMS masters, and experimental and numerical results on reduction of residual and deflecting deformations. With the addition of the reinforcing silicon plate, the average residual strains in the masters have been reduced from 3 to 0.42% and the maximum deflections have been reduced by around four times. Based on the presented results, this method can be potentially used to fabricate silicon reinforced PDMS masters for transferring patterns to substrates in a reliable fashion. In the near future, we would like to focus on establishing a sophisticated theoretical model for the developed method to have a deeper understanding of the reinforcing mechanisms.

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