1 High-Resolution Direct Patterning of Gold Nanoparticles by the
2 Microfluidic Molding Process
3 Michael T. Demko,*,†,‡ Jim C. Cheng,†,§ and Albert P. Pisano†,‡,§
4†Berkeley Sensor & Actuator Center (BSAC), ‡Department of Mechanical Engineering, and
5§Department of Electrical Engineering & Computer Sciences, University of California at Berkeley, Berkeley,
6 California 94720, United States
7 Received June 3, 2010. Revised Manuscript Received August 6, 2010
8 A novel microfluidic molding process was used to formmicroscale features of gold nanoparticles on polyimide, glass, and9 silicon substrates. This technique uses permeation pumping to pattern and concentrate a nanoparticle ink inside microfluidic10 channels created in a porous polymer template in contact with a substrate. The nanoparticle ink is self-concentrated in the11 microchannels, resulting in dense, close-packed nanoparticle features. Themethod allows for better control over the structure12 of printed features at a resolution that is comparable to inkjet printing, and is purely additivewith no residual layers or etching13 required. The process uses low temperatures and pressures and takes place in an ambient environment. After patterning, the14 gold nanoparticles were sintered into continuous and conductive gold traces.
15 Introduction
16 Precise patterning of nanoparticles is critical for a number of diffe-17 rent applications, including low temperature electrode deposition,1
18 optical coatings and photonics,2,3 biosensors,4 catalysts,5 and19 MEMS applications.6 Several methods are available for patterning20 nanoparticles, the most popular of which is inkjet printing.7,8 Inkjet21 printing is attractive due to its simplicity, high throughput, and low22 material loss. However, patterning with inkjet printing is limited to a23 resolution of around 20-50 μm with current printers,8 with higher24 resolution possible by adding complexity to the substrate prior to25 printing.9 Electrohydrodynamic printing has been proposed to26 increase the resolution beyond the limits of inkjet printing, achieving27 a line resolution as small as 700 nm.10 Both inkjet and electrohy-28 drodynamic printing, however, do not allow precise control over the29 structure of the printed lines, often resulting in lines with scalloped30 edges or nonuniform width, and offer only limited control over the31 height of the printed features.1,8,11,12 Recently, nanoimprint litho-32 graphyhasbeenproposedas ameansofdecreasing the feature size of33 patterned nanoparticles while allowingmore precise control over the
34structure of the printed lines.13-15 In this fabrication method, the35nanoparticle inks are patterned by pressing with an elastomer mold36and the particles dried into their final shape. While the resolution of37this method is improved over inkjet printing, there exists a residual38layer on the substrate thatmust be etched away after patterning, and39control over the height of features can be frustrated by capillary40interactions between the mold and the drying ink, especially along41the length of longer features. As an alternative to nanoimprint litho-42graphy, nanoparticle self-assemblymethods basedon capillary filling43of photoresist templates have been proposed.16While these can pro-44duce high aspect ratio features with smooth edges, the photoresist45must be etched away in subsequent processing steps without remov-46ing the particles themselves, which can be technically challenging or47nonfeasible in some instances. Here, we demonstrate a nanoparticle48patterning method based on permeation pumping17-19 that concen-49trates nanoparticles in selective regions inside a vapor-permeable50polymer mold. This method is completely additive (no etching51required) and allows for control over the structure of the patterned52lines, including smooth edges and control over the height of the53patterned features. The resolution obtained is comparable to that54obtained with inkjet printing. Long, continuous lines of gold nano-55particles were patterned over large areas. After patterning, the gold56nanoparticles were sintered into conductive traces. This method is57compatible with the idea of ambient environment roll-to-roll proces-58sing and works on a wide variety of substrates with a wide variety of59nanoparticle inks.
60Experimental Method
61Gold nanoparticles encapsulated in a hexanethiol monolayer62were synthesized using a two-phase reduction method follow-63ing the method of Brust et al. and subsequently encapsulated in64a hexanethiol self-assembled monolayer and dispersed in an
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65 alpha-terpineol solvent.20 The specific nanoparticle synthesis66 method used here has been documented in previous publications.14
67 The ink was diluted to 3.5 wt% in alpha-terpineol. Amaster temp-68 late was made using standard photolithography using SU8-200769 resist on a silicon wafer. The master template consisted of lines that70 are 15 μm in width, 9.5 μm in height, and 1 cm in length. PDMS71 (Sylgard 184 - Dow) prepolymer and cross-linker were mixed in a72 10:1 ratio, poured over the siliconwafer and cured. After curing, the73 PDMS elastomer template was removed and cleaned by sonication74 in ethanol for 10min and then dried. The resulting PDMS template75 wasporous to solvent vapors.Thenanoparticleswerepatternedona76 substrate using the microfluidic molding self-assembly method,77 which is illustrated schematically in Figure 1F1 . A polyimide, glass,78 or silicon substrate was placed in a custom-built press, coated with79 fresh solvent free of nanoparticles and positioned below the pat-80 ternedPDMSelastomer template.Thepolymer templatewasplaced81 on the top side of the press and the fresh solvent patterned by82 pressing. The pressure used was just enough to completely conform83 the elastomermold to the substrate, and did not exceed 14 kPa. This84 filled the template channels completely with fluid, and excluded the85 fluid from all other areas. Any residual fluid trapped between the86 mold and substrate in areas without patterned features was simply87 evaporated through the porous polymer template in subsequent88 steps and, since this fluid containednonanoparticles, left no residual89 layer. Next, the nanoparticle ink was added to designated filling90 ports at the ends of the channels. The temperature of the systemwas91 raised to 75 �C to evaporate the solvent through the porous polymer92 mold. The evaporating fluid drew the nanoparticle ink into the93 microfluidic channels, which replaced the fluid lost through eva-94 poration.As the inkwas brought into the channel, the solvent of the
95nanoparticle ink began to evaporate, self-concentrating the nano-96particles in the fluid. Eventually, the nanoparticle ink became so97concentrated that the ink could no longer flow in the microchannel.98At this point, the remaining solvent evaporated and the nanopar-99ticles in the slurry began to close-pack. Some volume reduction of100the nanoparticle features occurred at this point, as will be discussed101later, but cohesion of the liquid in the solvent ensured that the102nanoparticles remained in continuous traces, and the volume103reduction occurred uniformly only in directions perpendicular to104free surfaces. When the ink was completely dried in the microchan-105nel, the system was cooled and the polymer template removed.106Following the nanoparticle patterning, the nanoparticles were107sintered by heating in an oven. The nanoparticles were placed in an108oven and the temperature increased to 220 �C for 8 h. The elevated109temperature allows for oxidation of the hexanethiol monolayer and110sinteringof thegoldnanoparticles.The longbake timewasnecessary111to ensure the maximum conductivity of the gold, allowing the112diffusion of the oxidized thiols from the interior of the gold traces.
113Theoretical Calculations
114Thepatterningof the nanoparticles in themicrofluidic channels115can be separated into two distinct stages: filling and drying. In the116filling stage, the nanoparticle ink is drawn into the channel and117self-concentrated by the evaporating solvent. This continues until118the nanoparticle ink saturates at some point in the channel. After119this point, part of the channel is saturated with nanoparticles and120sustains no additional fluid flow, and part continues to allow fluid121flow and self-concentration of the nanoparticle ink. The channel122continues to fill with nanoparticles until the entire length of the123channel is saturated with particles, at which time the nanoparticle124patterning is complete.125Each of the two stages was modeled by considering a one-126dimensional channel. This model is appropriate as long as the127length of the channel is much longer than the width and height of128the channel to ensure that lateral diffusion across the channel is129much stronger than diffusion along the length of the channel,130causing a nearly uniform concentration at any given cross section.131The velocity in the channel is approximated as a slug flow, and an132effective diffusivity used to account for the Taylor dispersion due133to the shear-enhanced diffusion of nanoparticles across stream-134lines in the parabolic velocity distribution. This one-dimensional135channel is open to a reservoir of nanoparticle ink at a constant136concentration at one end, and closed at the other.137For the filling stage, the velocity of the fluid in the channel is138found by assuming a constant rate of evaporation of the solvent139through the porous walls of the polymer template. This mass flux140due to evaporation is representedby a volume flow rate per unit of141surface area of the porous polymer template, q0 0. To a first142approximation, q00 is assumed constant. This approximation143ignores the dependence of the evaporation rate on the nanopar-144ticle concentration, which is valid for a sufficiently low concen-145tration nanoparticle ink and not valid for areas with highly146concentrated ink toward the end of the channel. Given that the147velocity of the fluid at the closed end of the channel must be zero,148the velocity as a function of length along the channel is
vðxÞ ¼ q00Pp
AðL0 - xÞ ð1Þ
149where Pp is the part of the perimeter of the microchannel150consisting of the porous polymer, A is the cross sectional area151of the one-dimensional channel, and L0 is the total length of the152channel. The equation for the velocity shows a characteristic153length scale equal to the length of the channel, and a characteristic154time scale given by ts = A/(q0 0Pp). The dimensional variables are
Figure 1. Microfluidic molding process.
(20) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. J. Chem.Soc.-Chem. Commun. 1994, 801–802.
B DOI: 10.1021/la1022533 Langmuir XXXX, XXX(XX), XXX–XXX
Article Demko et al.
155 nondimensionalied based on these characteristic scales, resulting156 in an equation for the velocity given by
vðxÞ ¼ L0
tsð1- xÞ ð2Þ
157 where the quantities with bars above are nondimensional equiva-158 lents of the corresponding dimensional variable without the bar159 above. An equation for the nanoparticle concentration φ(x,t) can160 be found by considering the flux of nanoparticles by both161 advection and diffusion. In one dimension, the advective diffusion162 equation is
δφ
δtþ δ
δxðvφÞ ¼ δ
δxD
δφ
δx
� �ð3Þ
163 where D(x) is the effective diffusivity of the nanoparticles in the164 one-dimensional system, and will be discussed in detail later.165 Equation 3 is nondimensionalized based on the constant con-166 centration of the ink in the reservoir φ0 and the length and time167 scales given above, and eq 2 is inserted. This results in
δφ
δt¼ φþðx- 1Þ δφ
δxþDts
L20
δ2φ
δx2þ ts
L20
dD
dx
δφ
δxð4Þ
168169 At x = 0, the nanoparticle ink concentration is equal to the170 concentration of the ink in the reservoir (φh=1), which is taken to171 be a constant. The nanoparticle flux is zero at the end of the172 microcapillary, at x = 1. At t = 0, there are no nanoparticles in173 the channel, so φh = 0.174 Themagnitude of the diffusivity of nanoparticles in solvent can175 be estimated using the Einstein-Stokes equation for diffusion of176 spherical particles through a liquid with low Reynolds number.177 This equation is given by
D0 ¼ kBT
6πηrð5Þ
178 where η is the fluid viscosity, r is the particle radius, kB is the179 Boltzmann constant, and T is the temperature. However, the180 value of the diffusivity must be modified to include shear-181 enhanced diffusion caused by velocity gradients perpendicular182 to the direction of the flow. These velocity gradients enhance the183 diffusion of nanoparticles as compared to the slug flow assumed184 here. A correction factor is therefore used to account for this185 enhanced diffusion21
DðxÞ ¼ 1
48
½vðxÞrh�2D0 ð6Þ
186 where rh is the hydraulic radius of the microchannel.187 The partial differential equation for the nanoparticle concen-188 tration was solved numerically using an explicit Euler method.189 Additionally, in the case where diffusion is negligible throughout190 the channel, the last two terms in eq 4 are negligible and an191 analytical solution to the above partial differential equation192 exists. This solution is given by
φðx, tÞ ¼ 1
1- xuð1- expð- tÞ- xÞ ð7Þ
193where u(ζ) is the unit step function. The numerical solution for194concentration as a function of position for various times is plotted195together with the analytical solution for concentration versus196position in the limit of very long times (see Figure 2 F2). The effect of197diffusion is seen to cause a smearingof the concentration profile at198the end of the channel, and is observed to be stronger near the199entrance of the channel due to the stronger velocity gradients and200corresponding shear-enhanced diffusion, allowing the concentra-201tion gradient to be much steeper at the end of the microchannel.202The filling stage continues until the maximum concentration of203nanoparticles is reached at somepoint in the channel, stopping the204flow of fluid and nanoparticles in that region. At this point, the205drying stage begins and the effective length of the channel with206respect to nanoparticle self-concentration and fluid flow,L(t), can207no longer be considered a constant, but is rather a function of208time. The dimensionless velocity can be modeled as
vðx, tÞ ¼ L0
ts
LðtÞL0
- x
!ð8Þ
209210The effective diffusivity is the same as in eq 6, except it is now a211function of time as well as position. The nondimensionalized212equation for the concentration of nanoparticles can be modified213to
δφ
δt¼ φþ x-
LðtÞL0
!δφ
δxþDts
L20
δ2φ
δx2þ ts
L20
δD
δx
δφ
δxð9Þ
214215Again, the nanoparticle ink concentration is taken as constant216at the ink reservoir, and the nanoparticle flux at the effective217length of the channel is zero. The initial condition is chosen to218match the concentration profile from the filling stage when the219channel first clogs with nanoparticles. This equation was solved220numerically using an explicit Euler method, and the length of the221wet channel was recorded as a function of time. Additionally, for222the case in which diffusion is negligible everywhere, an analytical223solution exists for the length as a function of time. In dimension-224less form, this is given by
LðtÞL0
¼ exp -φ0
φf
t
� �ð10Þ
225where φf is the saturation concentration of nanoparticles. The226numerical solution to eq 9 for the length of the channel as a
Figure 2. Nanoparticle ink concentrations versus length and timein the filling stage for ts = 31 s. The dotted black line shows theanalytical solution for the case inwhichD=0 in the limit as tf¥.
(21) Probstein, R. F. Physiochemical Hydrodynamics; Wiley: New York, 1994;p 90.
227 function of time was found to closely follow the analytical228 solution without diffusion given in eq 10. Note that, after a long229 time, the effective length of the channel approaches zero, and the230 entire channel fills uniformly with nanoparticles.
231 Results
232 To characterize the filling process, optical images were taken233 using a Canon 5DMark II camera with a Canon EF 100 mm f/2.8234 macro lens with a working distance of 8 cm. Continuous video was235 taken of the filling process, and the video was subsequently split up236 into individual frames for analysis. Images were analyzed using237 Matlab (MathWorks) to convert the images to grayscale and238 subtract the background from the images. ImageJ was used to239 analyze the average intensity of the light in the images along the240 microchannels. The light intensity in the images is proportional to241 the nanoparticle concentration, with darker areas containing more242 nanoparticles. Since the location of the maximum light intensity is243 easily tracked and corresponds identically to the location of the244 maximum nanoparticle concentration, the location of the max-245 imum light intensity was tracked and plotted as a function of time246 and compared to the analytical model (see Figure 3F3 ). The time scale247 of the filling process was found by minimizing the least squared248 error between the theory and data. For the experimental data here,249 the time scale was found to be approximately ts = 31 s.250 Once the unsintered gold nanoparticles were successfully251 patterned, images of the resulting patterns were obtained. An252 optical microscope (Olympus BH-2) was used to confirm that the253 pattern was transferred over the entire area of the die. The optical254 image of the result for the glass and polyimide substrates are255 shown in Figure 4F4 .256 A scanning electron microscope (LEO 1550, Zeiss) was used to257 show the fine details of the resulting pattern andmeasure the final258 dimensions of the resulting printed features (see Figure 5F5 ). The259 width of the printed lines, measured using an SEM, were 11 μm.260 The height of the printed lines were measured by imaging with a261 90� tilt, which showed a uniform height of approximately 6.5 μm262 over the entire area (see Figure 6F6 a). Additionally, the features did263 show some sag in the center, known in the literature as the rabbit-264 ear effect (see Figure 6b). The volume reduction and resulting265 rabbit-ear height profile was to be expected. At the end of the266 filling stage, the nanoparticle ink becomes so concentrated that it267 canno longer flow in the channel, yet additional volume reduction268 results from further solvent evaporation and possibly some269 oxidation and removal of thiol groups on the gold nanoparticles.270 The nanoparticles pack densely together, leaving a gap between271 the particles and the top of the mold. The presence of this gap272 causes capillary adhesion between the remaining liquid solvent
273and the solid mold to form the rabbit-ear profile in the final dry274structure. However, this effect is small, as the height of the sag in275the center of the features was limited to approximately 15%of the276total height of the feature.
Figure 3. Position of the maximum concentration in the channelas a function of time.
Figure 4. Optical micrograph of a nanoparticle pattern on (a)glass and (b) polyimide.
Figure 5. SEM image of the top of a line of patterned goldnanoparticles on a polyimide substrate.
Figure 6. SEM image of (a) the side of a patterned line of nano-particles and (b) a cut cross-section of the patterned particle lineshowing a slight rabbit-ear effect.
D DOI: 10.1021/la1022533 Langmuir XXXX, XXX(XX), XXX–XXX
Article Demko et al.
277 The gold nanoparticles were then sintered, and the resulting278 gold traces imaged (see Figure 7F7 ). The average height of the279 sintered gold particles was approximately 2.5 μm. The feature280 heights exhibited a small amount ofwaviness over short distances,281 but the average height of the traces was constant over the entire282 area. The profile of the sintered gold traces was significantly283 different from that of the unsintered particles. The reflow of the284 gold during sintering changed the shape profile from having285 rabbit-ears to having a dome shape. After the reflow, the average286 line width was around 16 μm.287 The sintered gold lines were electrically characterized. The288 resistance of the lines as a function of distance was measured (see289 Figure 8F8 ). The resulting measurements were linear over large
290distances, showing that the conductivity and the cross-sectional291area of the sintered gold are constant over the entire printed area.292This result further proves that the initial nanoparticle patterns293were uniformover large areas. The cross-sectional areaof the gold294wires was approximated using a circular segment with the average295height and width of the patterned lines. Using the measured296resistance per unit length and the calculated cross-sectional area297of the gold traces, the average resistivity of the lines wasmeasured298to be 6.7 � 10-7 Ω m. The gold lines are approximately 4% of299the conductivity of bulk gold. This value is slightly lower than300other values reported in the literature for thermally annealed301gold nanoparticles, which may be caused by the larger height302of the printed features and the corresponding difficulty for the303oxidized hexanethiol monolayer to migrate out of the sintered304gold.1,13,15,22-24
305Conclusions
306The proposed method for patterning nanoparticles allows for307excellent control over the structure of the printed features,308including both line widths and heights. In contrast to other309nanoimprint-based patterning methods, this process is designed310to form uniform nanoparticle patterns over large areas and leave311no residual layer thatmust be etched away later. Additionally, the312nanoparticles can be patterned at low temperatures and pressures313in an ambient environment. The process can be done very quickly314and the method is compatible with a roll-to-roll processing315methodology. Finally, the proposed technology has the potential316to be scaled down to achieve higher resolution, while retaining317control over the structure of the printed features.
318Acknowledgment.The authors thankHeng Pan andCostas P.319Grigoropoulos for providing the gold nanoparticles, and320Timothy P. Brackbill for his assistance with the imaging of the321nanoparticle filling process. This work was supported by NSF322Grant No. CMMI-0825189.
Figure 7. SEM image of the side of a sintered gold line, showing adifferent height and profile from the unsintered nanoparticles.
Figure 8. Average line resistance as a function of distance. Eachpoint is the average of three measurements on different lines, andthe error bars represent the standard deviation of the three mea-surements.
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