Simultaneous Patterning of Nanoparticles and Polymers Using an

Article pubs.acs.org/Langmuir

Simultaneous Patterning of Nanoparticles and Polymers Using an Evaporation Driven Flow in a Vapor Permeable Template Michael T. Demko,*,†,‡ Timothy P. Brackbill,†,‡ and Albert P. Pisano†,‡,§ †

Berkeley Sensor & Actuator Center (BSAC), ‡Department of Mechanical Engineering, and §Department of Electrical Engineering & Computer Sciences, University of California at Berkeley, Berkeley, California 94720, United States ABSTRACT: Nanoparticles and polymers have great potential for lowering cost and increasing functionality of printed sensors and electronics. However, creation of practical devices requires that many of these materials be patterned on a single substrate, and many current patterning processes can only handle a single material at a time, necessitating alignment of serial processing steps. Higher throughput and lower cost can be achieved by patterning multiple materials simultaneously. To this end, the microfluidic molding process is adapted to pattern various nanoparticle and polymer inks simultaneously, in a completely additive manner, with three-dimensional control and high relative positional accuracy between the different materials. A differential template distortion observed in channels containing different inks is analyzed and found to result from pressure force in the template due to flow of a highly viscous and highly concentrated ink in small channels. The resulting optimization between patterning speed and dimensional fidelity is discussed.

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INTRODUCTION Nanoparticles and polymers are important materials for printed sensors and electronics due to their interesting material properties combined with the ease of patterning these materials from solutions onto a variety of different substrates.1−4 Since these materials are not always compatible with standard lithography processes used in commercial electronics manufacturing, there has been significant research efforts toward creation of alternative manufacturing processes that can create micro- and nanoscale patterns from these materials. However, these alternative patterning methods are often designed to pattern only a single material at a time.5−9 While many interesting applications have been realized from individual materials, practical sensing and electronics applications need multiple different materials to be incorporated into a single device, requiring that patterns of different materials be formed with a high level of relative positional accuracy. Such patterns of different materials are often formed using serial processing steps, as is typical in manufacturing of electronics and microsystems,10 although significant cost savings can be realized by patterning these multiple materials simultaneously in a single process. Several processes have been developed which are capable of patterning simultaneously, including inkjet printing,6 electrohydrodynamic jet printing,9 electrospinning,11 hot embossing,12 micromolding in capillaries,8 and microfluidic molding,13 although use of these processes for simultaneous patterning has been limited as of yet. Of these processes, microfluidic molding is particularly interesting as it enables patterning of materials rapidly, over large areas, in three dimensions and in a completely additive manner. This process uses a vapor permeable template to guide an evaporation driven flow of ink, enabling complete filling of the template features with solute and solidification of the ink while the template is in © 2012 American Chemical Society

place on the substrate. As a result, the geometry of the patterned features is maintained even after the template is removed.13 This work describes the conversion of this process to enable patterning of multiple materials simultaneously and discusses important considerations related to local dimensional distortion due to elastic deformation of the template. Such local deformation is a result of viscous pressure losses due to flow of concentrated nanoparticle and polymer inks in the template channels and differs from the macroscopic template deformations encountered by applying pressure to the template to force contact with the substrate. While templates reinforced with a rigid material have been successfully used to manage macroscopic deformations,14 such approaches are ineffective at combating local deformations. However, as shown here, such local deformations can be managed by controlling the initial concentration of the ink. As a result, there exists a trade-off between high patterning speeds and low dimensional distortion, and an optimization of initial ink concentration is necessary.

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ALIGNED PATTERNING OF MULTIPLE MATERIALS The process for patterning multiple materials simultaneously is shown in Figure 1. A template is created from a vapor permeable polymer containing the negative image of the features to be patterned. These features are connected to larger ink reservoirs which exist in the back of the template. Here, the template is created from poly(dimethylsiloxane) (PDMS) by casting on a master consisting of a silicon wafer with patterned SU-8 photoresist. The ink reservoirs are created by including Received: April 18, 2012 Revised: May 29, 2012 Published: May 30, 2012 9857

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Figure 2. The press used for patterning the multiple inks consists of a moving platform with a heated spring stage. The template, which contains ink reservoirs that are attached to the features, is attached to a removable faceplate containing ink loading holes which allow access to the ink reservoirs.

Figure 1. The process for patterning multiple different inks simultaneously on a substrate. A vapor permeable template with reservoirs molded into the back is pressed into clean solvent on a substrate. The various inks are loaded into the different reservoirs, and evaporation of solvent through the template drives the flow of ink into the features. When the solvent is depleted and only the solid solutes remain, the template is removed.

first solvent is removed by evaporation, followed by the ink to be patterned. Additionally, each reservoir can be loaded with a different ink, containing different solutes and solvents. The system is heated to evaporate the solvent, which draws the ink from the reservoirs into the features. The solvent in the ink itself also begins to evaporate, causing the solutes to concentrate inside the template. Eventually, the solute dries completely, at which time the template can be removed. The complete drying of solvent prevents the reflow of the ink on the substrate, enabling the shapes of the features to be preserved. As a demonstration of such a patterning process, gold nanoparticles and cellulose acetate polymer were patterned on a polyimide substrate. The gold nanoparticles were suspended to a concentration of 1% in terpineol, while the cellulose acetate was dissolved in N-methylpyrrolidone (NMP) to a concentration of 0.5%. The clean solvent used for prefilling the template was NMP. These materials were chosen as they are very different, and the inks formed from these materials have very distinct properties. As such, the versatility of the patterning process can be truly demonstrated. These two materials were patterned in channels with 1 cm length, 15 μm width, and 10 μm height. Lines of different materials were patterned such that they were interdigitated for a length of 500 μm with a spacing of 15 μm between lines. The patterning was done at 90 °C for 30 min. The results of the patterning are shown in Figure 3. The two different materials are indeed patterned together, showing a very high degree of relative positional accuracy. The features are patterned over large areas and with a three-dimensional profile. However, the dimensions of the patterned features from the two different materials are remarkably different, even though

metal taper pins on the template, positioned in such a way as to contact the silicon master at the locations where the ink reservoirs are to join with the features. Once the polymer is cured, the metal taper pins and silicon master are removed and saved for reuse. The PDMS templates are attached to a custom-built patterning press, as shown in Figure 2, consisting of a moving platform with a heated spring stage opposite a fixed acrylic plate containing holes matching the location of the ink reservoirs on the template. The spring stage allows gradual pressure to be applied between the template and the substrate as the moving platform is actuated and enables automatic correction of any errors in the parallelism of the template and the substrate, while the heater allows control over the evaporation rate of solvent through the template. The substrate is placed on the spring stage, and the PDMS template is attached to the acrylic plate by van der Waals forces. The ink reservoirs in the template are filled with clean solvent, and the substrate is coated in the same solvent. At this point, the template and substrate are brought into contact by actuating the moving platform. Since there are no solutes in the clean solvent, any residual layer trapped under the template in regions where it should be excluded will simply evaporate through the template, leaving nothing behind. Excess solvent is then removed from the reservoirs using a syringe and replaced with the ink, taking care to avoid introducing air bubbles into the system. The solvents used in the inks can be the same or different from that used in the previous step. If the solutes in the ink are not compatible with the previous solvent, another clean solvent can be added to the reservoir while the 9858

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Figure 3. Gold nanoparticles and cellulose acetate polymer are patterned simultaneously on a polyimide substrate. SEM micrographs taken (a, b) from above and (c) from a 45° tilt to show the height of features. (d) A fluorescence micrograph of the lines showing clear distinction between the two materials.

the channel dimensions on the template were identical. As will be discussed later, this dimensional distortion is due to differences in pressures between channels containing different materials. Since the two inks have dissimilar physical properties which can lead to differences in viscous losses in channels containing these inks, a differential pressure between adjacent channels will cause elastic deformation of the template, leading to the observed dimensional distortion in the patterned features. Managing the pressure losses in the channels is therefore critical to successful patterning of multiple materials. The magnitudes of these pressures are related to the channel dimensions, evaporation rate, initial ink concentration, and physical properties of the ink. Since many of these same parameters are also related to patterning speed, an optimization between high patterning speed and high dimensional accuracy is necessary.

Figure 4. A schematic of the setup used for determining the viscosity of differing concentrations of solutions. Air pressure is used to force fluid through a capillary of known dimensions, which is collected on a balance. The known air pressure and measured flow rate are used to determine the viscosity of the fluid.

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pressure drop due to fluid flow in the capillary is much higher than elsewhere in the system, and the body forces on the fluid due to gravity are negligible compared to the force on the fluid from the applied pressure. Solving for viscosity and substituting in mass flow rate ṁ for volumetric flow rate by dividing by solvent density ρ results in

VISCOSITY OF INK AS A FUNCTION OF SOLUTE CONCENTRATION During patterning, solvent evaporation causes an increase in the concentration of the ink as it flows through the channel. This increase in solute density can cause a nearly exponential rise in the viscosity for both nanoparticle and polymer inks.15−17 An understanding of the relationship between viscosity and concentration is therefore important to accurate prediction of pressure differences in channels containing different inks. To measure the viscosity of the concentrations of cellulose acetate in NMP, a capillary flow viscometer was constructed, as illustrated schematically in Figure 4. A silica capillary of known length and diameter was attached to a fluid reservoir and positioned above a fluid collection vessel on a balance. A known pressure was applied to the top of the fluid in the reservoir using a precision 0−100 kPa regulator and confirmed with a Honeywell 0−100 kPa pressure sensor. The resulting mass flow rate of fluid was determined by monitoring the weight of fluid exiting the capillary as a function of time using the balance. The viscosity was determined from the applied pressure and the measured flow rate using the Hagen−Poiseuille equation dV πR4 ⎛⎜ ΔP ⎞⎟ =− dt 8η ⎝ L ⎠

πR4ρ |ΔP| (2) 8ṁ L The mass flow rate is obtained from the slope of the weight as a function of time as collected from the balance. Since, in the current setup, discrete droplets fall on the scale, the measurement is run for 5 min to ensure an accurate determination of the flow rate. Since the radius of the capillary is critical to the accurate determination of the viscosity, DI water is measured in order to calibrate this parameter. In order to match 0.932 cP viscosity of water at a temperature of 23.4 °C, the diameter of the capillary was determined to be 147.2 μm, which is within the allowed tolerance on the 150 μm nominal diameter as specified by the manufacturer. After calibration, the viscosity of the pure solvent, NMP, was then measured. The obtained viscosity was 1.76 cP, which is different from the 1.70 cP viscosity reported on the manufacturers specifications by 3.85%, which is an acceptable margin of error. Various inks consisting of different concentrations of cellulose acetate in NMP were then measured. The results shown in Figure 5a confirm that viscosity increases very rapidly with solute concentration. η=

(1)

where V is the fluid volume, t is the time, R is the radius of the capillary, P is the pressure, L is the total length of the capillary, and η is the viscosity. Use of this equation is valid because the 9859

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Figure 5. (a) Viscosity of ink increases rapidly with increasing concentration. (b) Dimensionless concentration increases as a function of dimensionless position, and the extent of the solute penetration is a function of time. (c) Dimensionless pressure loss in the channel is shown as a function of initial concentration, illustrating the trade-off that exists between patterning time and dimensional distortion. (d) Channel width difference as a function of pressure difference from the solid model.

cross-sectional area A, and a permeable perimeter length of Pp which exhibits a loss of solvent due to evaporation expressed by a volume flow rate per unit of permeable surface area q″, the velocity is

An empirical model for the viscosity as a function of solute concentration was developed to aid the subsequent analysis of the pressure gradients in the channel and corresponding template distortion. A least-squares regression was performed on a third-order polynomial, resulting in η(C) = 0.38C 3 − 0.19C 2 + 3.36C + 1.77

v (x ) =

(3)

where the viscosity η has units of cP and the concentration C has units of g/dL. This relation is plotted along with the experimental date in Figure 5a.

q″Pp A

(L − x )

(4)

where x is the position along the length of the channel. For convenience, a dimensionless position may be defined as x̅ = x/ L and a dimensionless time as t ̅ = t/ts, where ts = A/(q″Pp). The velocity can therefore be written as

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PRESSURE LOSSES DUE TO FLUID FLOW IN TEMPLATE FEATURES Evaporation of solvent through the vapor permeable template drives the flow of ink. The magnitude of the pressure loss that accompanies this flow of fluid is dependent on the viscosity of the ink, which was shown in the previous section to be a strong function of the concentration of solutes in the ink, which is itself a function of position in the channel. Here, the pressure losses in the channels are determined, which are then used in the next section as inputs to the solid model for determining template distortion. An analytical model of the system is developed by considering an evaporation driven flow of ink inside of a vapor permeable template. First, the average velocity of fluid in the channel is determined, from which the concentration of solute in the channel is found as a function of position and time. Using the empirical model for the viscosity of the ink as a function of concentration developed in the previous section, the pressure losses in the channel are then determined. The average velocity of fluid in the channel as a function of position can be determined by considering a simple mass balance on the system. Considering a channel with length L,

v (x ̅ ) =

L (1 − x ̅ ) ts

(5)

The concentration of solute in the channel is, in general, a function of both position and time. As a first-order approximation, the channel can be modeled as a onedimensional entity, having only a dimension of length. Such a model neglects both diffusion of the solute and velocity gradients across the width of the channel by assuming all particles travel at the average velocity since, as shown in a previous work, the influence of convection of solute is much stronger than diffusion throughout the channel for all practical patterning situations.13 This approximation enables a simple analytical solution, and errors induced in doing so are within an acceptable range for this simple model. Such a model of the evolution of concentration as a function of distance in the channel is derived by performing a control volume mass balance on the solute in the channel considering only the effects of convection. The detailed derivation of such an equation is given in a previous publication13 and results in 9860

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Langmuir C̅(x ̅ , t ̅ ) =

1 u[1 − exp( − t ̅ ) − x ̅ ] 1 − x̅

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ELASTIC DEFORMATION OF THE TEMPLATE DUE TO PRESSURE FORCES Pressure differences in the channels will cause some elastic deformation of the template, resulting in nonrectangular cross sections or discrepancies between designed and actual dimensions of patterned features. While such template distortions are often unwanted, reproducible distortions could be useful in certain devices or processes, such as decreasing line widths or increasing undercutting on the sides of patterned features for use in lift-off processes.19 To provide a better understanding of this phenomenon, a finite element model of the template is used together with the previously created pressure model to determine the magnitude and shape of this template distortion, which is then verified by comparing the model to SEM images of actual patterned features. In the finite element model, the template is approximated using alternating channels containing two different inks which are separated by a spacing equal to the width of the patterned features, as shown in Figure 6, which approximately matches

(6)

where C̅ = C/C0 is the dimensionless concentration normalized to the initial concentration of ink in the reservoir C0 and u(ζ) is the unit step function. This result is plotted in Figure 5b. The elapsed time determines how far solute penetrates into the channel, while concentration sharply increases as it approaches the end of the channel as a result of the velocity linearly approaching zero at this location. The pressure losses in the channel are determined by considering the flow of fluid through the template features. For this, the square channels are approximated as having a circular cross section using a hydraulic radius Rh given by18 Rh =

bh b+h

(7)

where b and h are the width and height of the channel, respectively. Such an approximation leads to only small additional errors, provided the aspect ratio of the channels is sufficiently close to 1:1, and enables a simple analytical solution. The axial pressure gradient in a cylindrical channel is related to the average velocity in the channel by18 v (x ) =

R h 2 dP 8η(x) dx

Article

(8)

Substituting the expression for the velocity as a function of position and converting to dimensionless variables results in dP 8L2 = η(x ̅ )(1 − x ̅ ) dx ̅ tsR h 2

Figure 6. A schematic illustration of the finite element model. Alternating channels contain a similar ink with different initial concentrations, which leads to different pressures in the channels. This pressure difference can cause deformations in the channels due to bending of the wall separating the channels.

(9)

It is convenient at this point to define a dimensionless pressure as P̅ = P/P0 where P0 = (8L2η0)/(Rh2ts). Physically, the scaling factor P0 represents the pressure loss in the channel that would exist if only clean solvent moved at the maximum flow rate throughout the entire channel. This results in η(x ̅ ) dP ̅ = (1 − x ̅ ) dx ̅ η0

the geometry of the templates used in the subsequent experiments. The inks used are presumed to be of the same materials but with a different initial concentration of solutes, resulting in two negative pressures of different magnitude inside these alternating channels. This differential negative pressure can cause bending of the template wall separating adjacent channels, resulting in dimensional distortion of the final patterned features. The model is set up as a 2D plane strain problem in COMSOL Multiphysics. The template is 1 mm thick, and the width of the modeled section is 0.7 mm. Ten channels of 15 μm width and 10 μm height are spaced 15 μm apart at the center of this template. Alternating channels are set at the two different pressures calculated from the previous model for the given inks. Contact pairs are set up with the top of each channel and the two sidewalls to ensure that under severe deformations the channel walls cannot pass through one another. From earlier testing, the elastic modulus of the PDMS is shown to be 950 ± 70 kPa with a Poisson’s ratio of 0.49. The top surface of the template was given an evenly distributed pressure load of 6.9 kPa to mimic the force applied by the press. The bottom surfaces of the mold that are in contact with the substrate are prevented from moving in the vertical dimension but are allowed friction-free motion in the plane of the substrate. This friction-free assumption is justified since there exists some lubrication between the surfaces from the solvent and a large amount of time over which the template can move on the substrate to reduce stresses in the system. The sides of the template are free to move, but one midpoint on the left side of

(10)

The pressure in the channel may be determined by integrating the above pressure gradient using the expression for the viscosity as a function of concentration from eq 3 and concentration as a function of position from eq 6. The physical origin of the viscous losses suggests a potential method for reduction of the resulting pressures losses in the channels. Given that the pressure gradients are linearly dependent on viscosity and that viscosity is a strong function of concentration, the onset of the high-viscosity region of fluid can be moved closer to the end of the channel by reducing the initial concentration of the ink. The variation in the maximum pressure drop across the channel is plotted as a function of initial ink concentration in Figure 5c. At higher concentrations, the maximum pressure drop increases rapidly with increasing concentration, suggesting that high levels of template distortion could result in this region. At low concentrations, the pressure drop becomes independent of initial concentration, suggesting that reduction of initial concentration in this region will increase patterning time without any corresponding reduction in template distortion. An optimum range of initial concentrations exists between these two extremes, where an appropriate balance between patterning time and dimensional fidelity can be achieved. 9861

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the template is fixed to eliminate translation of the template which can prevent convergence of the finite element model. The pressures inside the template were calculated using eq 10 with eqs 3 and 6 for the viscosity as a function of position and with an initial concentration of 0.5% and 0.05% in alternating channels, which matches the conditions of subsequent experiments. Experimentally, two different inks consisting of cellulose acetate dissolved in acetone to the same concentration as used in the finite element model were loaded into two different reservoirs. Patterns with dimensions matching those used in the finite element model were created by evaporating the acetone through the template at room temperature for 30 min, allowing both inks to fill their respective 1 cm long channels. A qualitative comparison of the finite element model and the experimental results, given in Figure 7a,b, shows excellent

properties or by using inks with a sufficiently low initial concentration. The validity of the pressure as a function of initial concentration was demonstrated experimentally by patterning two different concentrations of cellulose acetate ink in close proximity to a gold nanoparticle ink, which was kept at a constant initial concentration, on a polyimide substrate. The results, shown in Figure 8, demonstrate that a lower initial

Figure 8. SEM micrographs of gold nanoparticle and cellulose acetate polymer lines, with (a) low concentration (0.2%) and (b) high concentration (1.0%) cellulose acetate ink. Higher pressure losses due to more rapid increases in viscosity of the drying polymer ink cause a larger distortion of features patterned with the higher concentration ink.

concentration of the cellulose acetate ink results in more similar dimensions between the gold and polymer lines, while use of higher concentration ink leads to a greater difference in dimensions between channels containing the two materials, which is as predicted by the above model.

Figure 7. (a) Finite element results for template deformation. The deformed surface is 1:1 scale, and the black lines are the undeformed shape. The surface is colored by x-displacement in μm. (b) SEM image of the experimental results using the same conditions as given in the finite element model, showing good qualitative agreement.

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CONCLUSIONS In this work, a very useful method for patterning multiple solute materials was developed. In a single step, multiple different polymers or nanoparticles can be patterned with a high degree of relative positional accuracy. However, the use of materials having physical properties that vary differently with solute concentration creates a situation in which template distortion can become an important design consideration. An analytical model of the fluid flow during patterning was used together with a finite element model of the solid template to gain understanding of the system, from which it was determined that such deformation can be avoided through the use of low concentrations of solutes in the ink. The models were compared to experiments using cellulose acetate polymer dissolved in NMP to various concentrations, resulting in reasonable correlation. The understanding of the template distortion as developed here is critical to eliminating such distortion or harnessing it for use in some manufacturing processes. While use of less concentrated inks is one proven method of eliminating this distortion, use of more rigid yet vapor permeable polymers

agreement. The physical dimensions of the patterned features from the channels containing the more concentrated ink are smaller than those on the template due to the bending of the walls between adjacent channels caused by the differential negative pressure. Conversely, the dimensions of features from channels containing the lower concentration ink are larger than those on the template due to bending of the walls away from the channel with the higher pressure. To quantify the magnitude of the deformation due to the flow of viscous ink in the template, the finite element model was used to find the dimensional distortion of features as a function of the pressure difference between adjacent channels. The result, given in Figure 5d, shows that the dimensional distortion increases proportionally with the pressure difference between the two sets of channels. If the intent of the template is to have the patterned features be the size of the template, care must be taken to ensure that the magnitude of the pressure difference between adjacent channels remains sufficiently low, which can be done by either using ink with matched physical 9862

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could also assist in improving patterning fidelity while allowing use of inks with higher initial solute concentration, increasing patterning speed. If some distortion of template features is desired for a given process, such as undercutting for use in liftoff processes, specific inks can be chosen which give an appropriate feature profile. For patterning materials with high affinity for the template, such deformation could be used in a controlled manner to pattern features with a smaller size than those on the template, after which the template is returned to its original shape or even reversed in its distortion by patterning a secondary material, thus reducing friction on patterned features and promoting release. The process developed here could be highly useful for creating multiplexed sensors or printed electronics. By patterning the materials simultaneously in a single template, several material deposition, etching, and alignment steps can be eliminated, resulting in substantial cost reductions. Furthermore, the versatility of the process with respect to specific materials eliminates many constraints previously imposed by use of serial deposition and etching processes with a large number of materials.

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(14) Luo, C.; Meng, F.; Francis, A. Fabrication and application of silicon-reinforced PDMS masters. Microelectron. J. 2006, 37, 1036− 1046. (15) Mooney, M. The Viscosity of a Concentrated Suspension of Spherical Particles. J. Colloid Sci. 1951, 6, 162−170. (16) Chen, C.-N.; Huang, C.-T.; Tseng, W. J.; Wei, M.-H. Dispersion and rheology of surfactantmediated silver nanoparticle suspensions. Appl. Surf. Sci. 2010, 257, 650−655. (17) Thomas, D. K.; Thomas, T. A. J. Viscosity-Concentration Relationships in Solutions of High Polymers. J. Appl. Polym. Sci. 1960, 3, 129−131. (18) White, F. M. Viscous Fluid Flow; McGraw-Hill: New York, 2006; pp 109−117. (19) Liang, J.; Kohsaka, F.; Matsuo, T.; Li, X.; Ueda, T. Improved bilayer lift-off process for MEMS applications. Microelectron. Eng. 2008, 85, 1000−1003.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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